缺项样条插值(Ⅰ)(英文)

数控专业英语数控专业英语大全数控的学习肯定少不了专业英语的了解，以下是小编整理的数控专业英语大全，欢迎参考阅读!increment n.增量incremental adj.增量的index 分度，索引initial adj.原始的initialization n.C523初始化initialize v.初始化input n.v.输入INS（） v.插入v.插入instruction n.说明interface n.接口internal adj.内部的interpolate v.插补interpolation n.插补interrupt v.中断interruption n.中断intervent n.间隔，间歇involute n.渐开线ISO n.国际标准化组织jog n.点动jump v.跳转key n.键keyboard n.键盘label n.标记，标号ladder diagram 梯形图language n.语言lathe n.车床LCD n.液晶显示least adj.最小的length n.长度LIB（library） n.库library n.库life n.寿命light n.灯limit n.极限limit switch n.限位开关line n.直线linear adj.线性的linear scale n.直线式传感器link n,v.连接list n,v.列表load n.负荷，v.装载local adj.本地的locate v.定位，插销location n.定位，插销lock v.锁定logic n.逻辑look ahead v.预，超前loop n.回路，环路LS n.限位开关LSI n.大规模集成电路machine n.机床，v.加工macro n.宏macro program n.宏程序magazine n.刀库magnet n.磁体，磁magnetic a.磁的main program n.主程序maintain v.维护maintenance n.维护MAN（manual） n.手动management n.管理manual n.手动master adj.主要的max adj.最大的，n.最大值maximum adj.最大的，n.最大值MDI n.手动数据输入meaning n.意义measurement n.测量memory n.存储器menu n.菜单message n.信息meter n.米metric adj.米制的mill n.铣床，v.铣削min adj.最小的，n.最小值minimum adj.最小的'，n.最小值minus v.减，adj.负的minute n.分钟mirror image n.镜像miscellaneous function n.辅助功能MMC n.人机通讯单元modal adj.模态的modal G code n.模态G代码mode n.方式model n.型号modify v.修改module n.模块MON（monitor） v.监控monitor v.监控month n.月份motion n.运动motor n.电机mouse n.鼠标MOV（移动） v.移动move v.移动movement n.移动multiply v.乘N number n.程序段号N.M n.牛顿。

[转载]插值算法（⼀）：各种插值⽅法⽐较原⽂地址：插值算法（⼀）：各种插值⽅法⽐较作者：稻草⼈确定性随机性确定性随机性趋势⾯（⾮精确）回归（⾮精确）泰森（精确）克⾥⾦（精确）密度估算（⾮精确）反距离权重（精确）薄板样条（精确）整体拟合利⽤现有的所有已知点来估算未知点的值。

局部插值使⽤已知点的样本来估算位置点的值。

确定性插值⽅法不提供预测值的误差检验。

随机性插值⽅法则⽤估计变异提供预测误差的评价。

对于某个数据已知的点，精确插值法在该点位置的估算值与该点已知值相同。

也就是，精确插值所⽣成的⾯通过所有控制点，⽽⾮精确插值或叫做近似插值，估算的点值与该点已知值不同。

1、反距离加权法（Inverse Distance Weighted）反距离加权法是⼀种常⽤⽽简单的空间插值⽅法，IDW是基于“地理第⼀定律”的基本假设:即两个物体相似性随他们见的距离增⼤⽽减少。

它以插值点与样本点间的距离为权重进⾏加权平均，离插值点越近的样本赋予的权重越⼤，此种⽅法简单易⾏，直观并且效率⾼，在已知点分布均匀的情况下插值效果好，插值结果在⽤于插值数据的最⼤值和最⼩值之间，但缺点是易受极值的影响。

2、样条插值法（Spline）样条插值是使⽤⼀种数学函数，对⼀些限定的点值，通过控制估计⽅差，利⽤⼀些特征节点，⽤多项式拟合的⽅法来产⽣平滑的插值曲线。

这种⽅法适⽤于逐渐变化的曲⾯，如温度、⾼程、地下⽔位⾼度或污染浓度等。

该⽅法优点是易操作，计算量不⼤，缺点是难以对误差进⾏估计，采样点稀少时效果不好。

样条插值法⼜分为张⼒样条插值法（Spline with Tension）规则样条插值法（Regularized Spline）薄板样条插值法 (Thin-Plate Splin)3、克⾥⾦法（Kriging）克⾥⾦⽅法最早是由法国地理学家Matheron和南⾮矿⼭⼯程师Krige提出的，⽤于矿⼭勘探。

这种⽅法认为在空间连续变化的属性是⾮常不规则的，⽤简单的平滑函数进⾏模拟将出现误差，⽤随机表⾯函数给予描述会⽐较恰当。

3DMAX命令中英文3D MAX命令中英文BOMB爆炸MODIFIER-BASED基于修改器BEND弯曲NOISE噪波SKEW倾斜TAPER锥化TWIST扭曲STRETCH拉伸SYSTEMS系统BONES骨骼SUNLIGHT太阳光DAYLIGHT日光BIPED两足动物修改面板SELECTION MODIFIERS选择修改器MESH SELECT网格选择POLY SELECT多边形选择PATCH SELECT面片选择SPLINE SELECT样条线选择FFD SELECT FFD选择SELECT BY CHANNEL按通道选择SURFACE SELECT（NSURF SEL）NURBS曲面选择PATCH/SPLINE EDITING面片/样条线编辑EDIT PATCH编辑面片EDIT SPLINE编辑样条线CROSS SECTION横截面SURFACE曲面DELETE PATCH删除面片DELETE SPLINE删除样条线LATHE车削NORMALIZE SPLINE规格化样条线FILLET/CHAMFER圆角/切角TRIM/EXTEND修剪/延伸RENDERABLE SPLINE可渲染样条线SWEEP扫描MESH EDITING网格编辑DELETE MESH删除网格EDIT MESH编辑网格EDIT POLY编辑多边形EXTRUDE挤出FACE EXTRUDE面挤出NORMAL法线SMOOTH平滑BEVEL倒角BEVEL PROFILE倒角剖面TESSELLATE细化STL CHECK STL检查CAP HOLES补洞VERTEXPAINT顶点绘制OPTIMIZE优化MULTIRES多分辨率VERTEX WELD顶点焊接SYMMETRY对称EDIT NORMALS编辑法线EDITABLE POLY可编辑多边形EDIT GEOMETRY编辑几何体SUBDIVISION SURFACE细分曲面SUBDIVISION DISPLACEMENT细分置换PAINT DEFORMATION绘制变形CONVERSION转化TURN TO POLY转换为多边形TURN TO PATCH转换为面片TURN TO MESH转换为网格ANIMATION MODIFIERS动画EDIT ENVELOPE编辑封套WEIGHT PROPERTIES权重属性MIRROR PARAMETERS镜像参数DISPLAY显示ADVANCED PARAMETERS高级参数GIZMO变形器MORPHER变形器CHANNEL COLOR LEGEND通道颜色图例GLOBAL PARAMETERS全局参数GLOBAL PARAMETERS全局参数CHANNEL LIST通道列表CHANNEL PARAMETERS通道参数ADVANCED PARAMETERS 高级参数FLEX柔体PARAMETERS参数SIMPLE SOFT BODIES简章软体WEIGHTS AND PAINTING权重和绘制FORCES AND DEFLECTORS力和导向器ADVANCED PARAMETERS高级参数ADVANCED SPRINGS高级弹力线MELT融化LINKED XFORM链接变换PATCH DEFORM面片变形PATH DEFORM路径变形SURF DEFORM曲面变形PATCH DEFORM（WSM）面片变形（WSM）PATH DEFORM （WSM）路径变形（WSM）SURF DEFORM（WSM）曲面变形（WSM）SKIN MORPH蒙皮变形SKIN WRAP蒙皮包裹SKIN WRAP PATCH蒙皮包裹面片SPLINE IK CONTROL样条线IK控制ATTRIBUTE HOLDER属性承载器UV COORDINATES MODIFIERS UV坐标修改器UVW MAP UVW贴图UNWRAP UVW展开UVWUVW XFORM UVW变换MAPSCALER（WSM）贴图缩放器（WSM）MAPSCALER贴图缩放器（OSM）CAMERA MAP摄影机贴图CAMERA MAP（WSM）摄影机贴图（WSM）SURFACE MAPPER（WSM）曲面贴图（WSM）PROJECTION投影UVW MAPPING ADD UVW贴图添加UVW MAPPING CLEAR UVW贴图清除CACHE TOOLS缓存工具CACHE TOOLS缓存工具POINT CACHE点缓存POINT CACHE（WSM）点缓存（WSM）SUBDIVISION SURFACES细分曲面TURBOSMOOTH涡轮平滑MESHSMOOTH网格平滑HSDS MODIFIER HSDS修改器FREE FORM DEFORMATIONS自由形式变形FFD MODIFIERS FFD修改FFD BOX/CYLINDER FFD长方形/圆柱体PARAMETRIC MODIFIERS参数化修改器BEND弯曲TAPER锥化TWIST扭曲NOISE噪波STRETCH拉伸SQUEEZE挤压PUSH推力RELAX松弛RIPPLE涟漪WA VE波浪SKEW倾斜ALICE切片SPHERIFY球形化AFFECT REGION影响区域LATTICE晶格MIRROR镜像DISPLACE置换XFORM变换SUBSTITUTE替换PRESERVE保留SHELL壳SURFACE曲面MATERIAL材质MATERIAL BY ELEMENT按元素分配材质DISP APPROX置换近似DISPLACE MESH（WSM）置换网格（WSM）RADIOSITY MODIFIERS沟通传递修改器SUBDIVIDE（WSM）细分（WSM）SUBDIVIDE细分CAMERAS摄影机CAMERA CORRECTION摄影机校正CLOTH MODIFIERS布料修改器CLOTH布料GARMENT MAKER衣服生成器DEFORMATIONS变形REACTOR CLOTH REACTOR布料REACTOR ROPE REACTOR绳索REACTOR SOFTBODY REACTOR软体层次命令面板PIVOT轴ADJUST PIVOT调节轴ADJUST TRANSFORM调整变换SKIN POSE蒙皮姿势IK反向运动INVERSE KINEMATICS反向运动学OBJECT PARAMETERS对象参数AUTO TERMINATION自动终结SLIDING/ROTATIONAL JOINTS滑动/转动关节LINK INFO链接信息运动命令面板PARAMETERS参数ASSIGN CONTROLLER指定控制器PRS PARAMETERS变换参数KEY INFO（BASIC）关键信息（基本）KEY INFO（ADVANCED）关键信息（高级）TRAJECTORIES轨迹显示命令面板DISPLAY COLOR显示颜色HIDE BY CATEGORY按类别隐藏HIDE隐藏FREEZE冻结DISPLAY PROPERTIES显示属性LINK DISPLAY链接显示STANDARD PRIMITIVES标准几何体BOX长方体CONE圆锥体SPHERE球体GEO SPHERE几何球体CYLINDER圆柱体TUBE管状体TORUS圆环PYRAMID四棱锥TEAPOT茶壶PLANE平面EXTENDED PRIMITIVES扩展基本体HEDRA异面体TORUS KNOT环形结CHAMFERBOX切角长方体CHAMFERCYL切角圆柱体OIL TANK油罐CAPSULE胶囊SPINDLE纺缍L-EXT L形墙C-EXT C形墙RING EAVE环形波HOSE软管PRISM棱柱COMPOUND OBJECTS复合对象MORPH变形SCATTER散布CONFORM一致CONNECT连接MESHER网格化LOFT放样TERRAIN地形SHAPE MERGE图形合并BOOLEAN布尔BLOB MESH水滴网格PARTICLE SYSTEMS粒子系统SPRAY喷射SHOW雪BLIZZARD暴风雪PARRAY粒子陈列PCLOUD粒子云SUPER SPRAY超级喷射PATCH GRIDS面片栅格QUAD PATCH四边形面片TRI PATCH三角形面片EDITABLE PATCH可编辑面片DOORS门WINDOWS窗AEC EXTENDED AEC扩展FOLIAGE植物RAILING栏杆WALL墙DYNAMICS OBJECTS动力学对象DAMPER阻尼哭SPRING弹簧STAIRS楼梯L-TYPE STAIR L型楼梯SPIRAL STAIR螺旋楼梯STRAIGHT STAIR 直线楼梯U-TYPE STAIR U型楼梯SHAPES图形SPLINES样条线LINE线RECTANGLE矩形CIRCLE圆ELLIPSE椭圆ARC弧DOUNUT圆环NGON多边形STAR星形TEXT文本HELIX螺旋线SECTION截面NURBS CURVES NURBS曲线EXTENDED SPLINES扩展样条线WRECTANGLE W矩形CHANNEL通道ANGLE角度TEE三通WIDE FLANGE宽法兰LIGHTS灯光STANDARD标准灯光TARGET SPOT目标聚光灯FREE SPOT自由聚光灯TARGET DIRECT目标平行光FREE DIRECT自由平行光OMNI泛光灯SKYLIGHT天光MR AREA OMNI MR区域泛光灯MR AREA SPOT MR区域聚光灯PHOTOMETRIC光度学灯光TARGET POINT LIGHT目标点光源FREE POINT LIGHT自由点光源TARGET LINEAR LIGHT目标线光源FREE LINEAR LIGHT自由线光源TARGET AREA LIGHT目标面光源FREE AREA LIGHT自由面光源IES SUN LIGHT IES太阳光IES SKY LIGHT IES天光ISOTROPIC/DIFFUSE LIGHT DISTRIBUTION等向/漫反射灯光分布SPOTLIGHT DISTRIBUTION聚光灯分布WEB DISTRIBUTION光域网分布PHOTOMETRIC WEBS光域网灯光共同参数GENERAL PARAMETERS常规参数SHADOW PARAMETERS阴影参数SPOTLIGHT PARAMETERS聚光灯参数ADVANCED EFFECTS高级效果MENTAL RAY INDIRECT ILLUMINATION MENTAL RAY间接照明MENTAL RAY LIGHT SHADER MENTAL RAY灯光明暗器标准灯光附加参数INTENSITY/COLOR/ATTENUATIONINTENSITY/COLOR/ATTENUATION强度/颜色/衰减DIRECTIONAL PARAMETERS平行光参数ATMOSPHERES&EFFECTS大气和效果HAIR LIGHT ATTRIBUTE头发灯光属性光度学灯光附加参数INTENSITY/COLOR/DISTRIBUTION强度/颜色/分布LINEAR LIGHT PARAMETERS线光源参数AREA LIGHT PARAMETERS区域光源参数AREA LIGHT SAMPLING区域灯光采样WEB PARAMETERS光域网参数特定阴影类型ADVANCED RAY-TACED PARAMETERS高级光线跟踪参数AREA SHADOWS区域阴影RAY-TRACED SHADOW PARAMETERS光线跟踪阴影参数SHADOW MAP PARAMETERS阴影贴图参数OPTIMIZATIONS优化MENTAL RAY SHADOW MAP MENTAL RAY阴影贴图CAMERAS摄影机FREE CAMERA自由摄影机TARGET CAMERA目标摄影机摄影机共同参数MULTI-PASS DEPTH OF FIELD多过程景深MULTI-PASS MOTION BLUR多过程运动模糊DEPTH OF FIELD（MENTAL RAY）景深（MENTAL RAY）HELPERS辅助对象STANDARD标准辅助工具DUMMY虚拟对象GRID栅格POINT点TAPE卷尺PROTRACTOR量角器COMPASS指南针ATMOSPHERIC APPARATUS大气装置BOXGIZMO长方形框SPHEREGIZMO球形框CYLGIZMO圆柱体框CAMERAMATCH摄影机匹配。

absolute error绝对误差,relative error and significant digits 相对误差和有效数字(n-digit)accurate to 5 decimal places精确到5位小数degree accuracy准确度Newton-Raphson formula牛顿-拉夫森公式Root根sum of和Newton-cotes牛顿—柯特斯Coefficients系数Convergence集合sufficient and necessary condition充分必要条件iterative formula迭代公式fixed point bisection method固定点的二分法fixed point iteration固定点迭代法integration积分法linear system线性方程组triangular factorization三角分解Gauss-Seidel iteration高斯-赛德尔迭代Gaussian elimination高斯消去法，高斯消元;Jacobi method雅可比法the clamped cubic spline夹紧的三次样条the first derivative一阶导数curve fitting曲线拟合the least-squares line coefficient最小二乘线系数function函数Polynomial多项式node结点of degree n度degree of precision精密度interpolation插值approximate逼近，近似error term误差项tend to倾向于cubic spline Taylor interpolation三次样条函数的泰勒插值Hermite interpolation埃尔米特插值high-degree polynomials高阶多项式quadrature formula求积分公式constant Simpson’s rule常数辛普森规则Trapezoidal’s rule composite Simpson rule 组合梯形公式和辛普森公式Integral积分the initial value problem初始值问题Euler’s method欧拉方法spectral radius谱半径norm interval规范区间Chebyshev polynomial切比雪夫多项式strengths and weaknesses长处和短处definite integral定积分quadratic Lagrange interpolation二次拉格朗日插值divided-difference table 差分表compute计算三角分解插值切比雪夫三次样条代数精度Gauss_Seidel, Jocabi, Euler，插值型求积公式。

数值分析中常用数学词汇英中文对照abbreviation 简写符号;简写absolute error 绝对误差absolute value 绝对值accelerate 加速accumulation 累积accuracy 准确度act on 施于action 作用; 作用力add 加addition 加法addition formula 加法公式addition law 加法定律additive property 可加性adjoint matrix 伴随矩阵algebra 代数algebraic 代数的algebraic equation 代数方程algebraic expression 代数式algebraic fraction 代数分式;代数分数式algebraic inequality 代数不等式algebraic number 代数数algebraic operation 代数运算algorithm 算法系统; 规则系统alternating series 交错级数alternative hypothesis 择一假设; 备择假设; 另一假设analysis 分析;解析angle 角anti-clockwise direction 逆时针方向;返时针方向anti-derivative 反导数; 反微商anti-logarithm 逆对数;反对数anti-symmetric 反对称approach 接近;趋近approximate value 近似值approximation 近似;略计;逼近Arabic system 阿刺伯数字系统arbitrary 任意arbitrary constant 任意常数arc 弧arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积argument (1论证; (2辐角argument of a function 函数的自变量arithmetic 算术array 数组; 数组ascending order 递升序ascending powers of X X 的升幂assumption 假定;假设asymmetrical 非对称asymptote 渐近augmented matrix 增广矩阵average 平均;平均数;平均值axiom 公理back substitution 回代base (1底;(2基;基数basis 基belong to 属于bias 偏差;偏倚billion 十亿binary number 二进数binary operation 二元运算binary system 二进制binomial 二项式bisection method 分半法;分半方法boundary condition 边界条件boundary line 界(线;边界bounded 有界的bounded above 有上界的;上有界的bounded below 有下界的;下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号bracket 括号breadth 阔度calculation 计算calculator 计算器;计算器calculus (1 微积分学; (2 演算cancel 消法;相消Cartesian coordinates 笛卡儿坐标category 类型;范畴centre 中心;心chain rule 链式法则chance 机会change of base 基的变换change of variable 换元;变量的换characteristic equation 特征(征方程characteristic function 特征(征函数characteristic root 特征(征根chart 图;图表check digit 检验数位checking 验算circle 圆classification 分类clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coefficient 系数cofactor 余因子; 余因式coincide 迭合;重合collection of terms 并项collinear 共线collinear planes 共线面column (1列;纵行;(2 柱column matrix 列矩阵column vector 列向量combination 组合common denominator 同分母;公分母common difference 公差common divisor 公约数;公约common factor 公因子;公因子common multiple 公位数;公倍comparable 可比较的complement 余;补余completing the square 配方complex number 复数complex number plane 复数平面complex root 复数根component 分量composite function 复合函数; 合成函数computation 计算computer 计算机;电子计算器concept 概念conclusion 结论condition 条件conditional 条件句;条件式conjugate 共轭constant 常数constant of integration 积分常数constraint 约束;约束条件continuity 连续性continuous function 连续函数contradiction 矛盾converge 收敛convergence 收敛性convergent 收敛的convergent iteration 收敛的迭代convergent sequence 收敛序列convergent series 收敛级数convex 凸convexity 凸性coordinate 坐标corollary 系定理; 系; 推论correspondence 对应counter clockwise direction 逆时针方向;返时针方向counter example 反例counting 数数;计数criterion 准则critical point 临界点critical region 临界域cirtical value 临界值cube 正方体;立方;立方体cubic 三次方;立方;三次(的 cubic equation 三次方程cubic roots of unity 单位的立方根cumulative 累积的curve 曲线decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制definite integral 定积分definition 定义degree (1 度; (2 次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of ODE 常微分方程次数delete 删除; 删去denary number 十进数denominator 分母dependence (1相关; (2应变derivable 可导derivative 导数determinant 行列式diagonal 对角线diagonal matrix 对角矩阵difference 差difference equation 差分方程differentiable 可微differential 微分differential coefficient 微商; 微分系数differential equation 微分方程differential mean value theorem 微分中值定理differentiate 求...的导数differentiation 微分法digit 数字dimension 量; 量网; 维(数direction 方向; 方位discontinuity 不连续性discontinuous 间断(的;连续(的; 不连续(的discontinuous point 不连续点discrete 分立; 离散distance 距离diverge 发散divergence 发散(性divergent 发散的divergent iteration 发散性迭代divergent sequence 发散序列divide 除dividend (1被除数;divisible 可整除division 除法division algorithm 除法算式divisor 除数;除式;因子dot 点dot product 点积echelon form 梯阵式echelon matrix 梯矩阵eigenvalue 本征值eigenvector 本征向量element 元素elementary row operation 基本行运算elimination 消法elimination method 消去法;消元法empty set 空集equivalent 等价(的error 误差error estimate 误差估计error term 误差项estimate 估计;估计量evaluate 计值exact 真确exact solution 准确解;精确解;真确解exact value 法确解;精确解;真确解example 例expand 展开experiment 实验;试验experimental 试验的exponent 指数exponential function 指数函数express…in terms of… 以………表达extreme point 极值点extreme value 极值extremum 极值factor 因子;因式;商factor method 因式分解法factorial 阶乘factorization 因子分解;因式分解fallacy 谬误FALSE 假(的falsehood 假值finite 有限finite sequence 有限序列first derivative 一阶导数first order differential equation 一阶微分方程fixed point 不动点fixed point iteration method 不动点迭代法for all X 对所有X for each /every X 对每一Xform 形式;型format 格式;规格formula(formulae 公式fraction 分数;分式function 函数fundamental theorem of calculus 微积分基本定理Gaussian elimination 高斯消去法general form 一般式;通式general solution 通解;一般解general term 通项given 给定;已知global 全局; 整体global maximum 全局极大值; 整体极大值global minimum 全局极小值; 整体极小值gradient (1斜率;倾斜率;(2梯度graph 图像;图形;图表graphical method 图解法graphical representation 图示;以图样表达graphical solution 图解growth 增长higher order derivative 高阶导数horizontal 水平的;水平hypothesis 假设identity 等(式identity matrix 恒等矩阵if and only if/iff 当且仅当;若且仅若if…, then 若….则;如果…..则illustration 例证;说明image 像点;像imaginary number 虚数implicit function 隐函数imply 蕴涵;蕴含improper integral 广义积分; 非正常积分increase 递增;增加indefinite integral 不定积分independence 独立;自变inequality 不等式;不等inequality sign 不等号infinite 无限;无穷infinite sequence 无限序列;无穷序列infinite series 无限级数;无穷级数infinitesimal 无限小;无穷小infinity 无限(大;无穷(大initial approximation 初始近似值initial condition 原始条件;初值条件initial value 初值;始值initial-value problem 初值问题inner product 内积input 输入integer 整数integral 积分integrate 积;积分;......的积分integration 积分法integration by parts 分部积分法integration by substitution 代换积分法;换元积分法interchange 互换intermediate value theorem 介值定理interpolating polynomial 插值多项式interpolation 插值interval 区间intuition 直观invalid 失效;无效invariance 不变性invariant (1不变的;(2不变量;不变式inverse 反的;逆的inverse function 反函数;逆函数inverse matrix 逆矩阵inverse problem 逆算问题invertible 可逆的invertible matrix 可逆矩阵iterate (1迭代值; (2迭代iteration 迭代iterative method 迭代法known 己知Lagrange interpolating polynomial 拉格朗日插值多项代leading coefficient 首项系数leading diagonal 主对角线lemma 引理limit 极限limit of sequence 序列的极限line of best-fit 最佳拟合line segment 线段linear 线性;一次linear convergence 线性收敛性linear differeantial equation 线性微分方程linear equation 线性方程;一次方程linear equation in two unknowns 二元一次方程;二元线性方程linearly dependent 线性相关的linearly independent 线性无关的local maximum 局部极大(值local minimum 局部极小(值logic 逻辑long division method 长除法loop 回路lower bound 下界lower triangular matrix 下三角形矩阵Maclaurin expansion 麦克劳林展开式magnitude 量;数量;长度;大小mantissa 尾数matrix 阵; 矩阵matrix addition 矩阵加法matrix equation 矩阵方程matrix multiplication 矩阵乘法matrix operation 矩阵运算maximize 极大maximum absolute error 最大绝对误差mean value theorem 中值定理method of completing square 配方法method of interpolation 插值法; 内插法method of least squares 最小二乘法; 最小平方法method of substitution 代换法;换元法method of successive substitution 逐次代换法; 逐次调替法minimize 极小minus 减modulus of a complex number 复数的模monomial 单项式multiple 倍数multiple root 多重根multiplication 乘法multiplicity 重数multiplier 乘数;乘式multiply 乘mutually independent 独立; 互相独立mutually perpendicular lines 互相垂直n factorial n阶乘n th derivative n阶导数n th root n次根;n次方根n the root of unity 单位的n次根natural logarithm 自然对数necessary and sufficient condition 充要条件necessary condition 必要条件negative 负neighborhood 邻域Newton-Cote's rule 牛顿- 高斯法则Newton-Raphson's method 牛顿- 纳逊方法Newton's formula 牛顿公式Newton's method 牛顿方法non-linear 非线性non-linear equation 非线性方程non-negative 非负的non-singular (1满秩的; (2非奇异的non-singular matrix 满秩矩阵non-trivial 非平凡的non-zero 非零norm 模方; 范数normal (1垂直的;正交的;法线的(2正态的(3正常的;正规的normalize 正规化normalized form 标准型notation 记法;记号null 零; 空null set 空集null vector 零向量number 数numerator 分子numerical method 计算方法;数值法objective function 目标函数octant 卦限odd function 奇函数one-to-one 一个对一个one-one correspondence 一一对应operation 运算order of a matrix 矩阵的阶ordinary differential equation 常微分方程origin 原点orthogonal 正交orthogonality 正交性 outcome 结果 output 输出 parameter 参数；参变量parametric equation 参数方程 partition 分割; 划分 periodic function 周期函数permutation 排列 perpendicular 垂线；垂直(于 phase 相; 位相 pivot 支点 plot 绘图plus 加 point 点 polynomial 多项式 polynomial equation 多项式方程 positive 正 post-multiply 后乘; 自右乘 premultiply 前乘; 自左乘 prime 素 product 乘积；积 proper integral 正常积分 property 性质 quadratic convergence 二阶收敛性 quadratic formula 二次公式 quadratic function 二次函数 quadratic inequality 二次不等式 quadrature 求积法 quadrilateral 四边形 quotient 商；商式 quotient rule 商法则 R.H.S 右 rank 秩 rate of convergence 收敛率 ratio 比 ; 比率 rational function 有理函数 real number 实数 real part 实部 real root 实根 reciprocal 倒数 rectangle 长方形；矩形 recurrence formula 递推公式 recurrent 循环的 recurring decimal 循环小数 reduce 简化 region 区域 region of convergency 收敛区域 regular 正；规则 relative error 相对误差 remainder term 余项root 根 rotation 旋转 rounded number 舍数 rounding(off 舍入；四舍五入 row 行；棋行 row vector 行向量; 行矢量 rule 规则；法(则 satisfy 满足；适合 scalar 纯量; 无向量, 标量 scalar matrix 纯量矩阵 scale 比例尺；标度；图尺 scientific notation 科学记数法 secant (1正割; (2割线 secant method 正割法 second derivative 二阶导数 second order ordinary differential equation 二阶常微分方程 sentence 句；语句 sequence 序列series 级数 set 集 shaded portion 有阴影部分 shape 形状 shear 位移 side 边；侧 sign 符号；记号 signed number 有符号数 significant figure 有效数字 signum 正负号函数similar 相似 simplify 简化 Simpson's integral 森逊积分 Simpson's rule 森逊法则singular 奇的 singular matrix 奇异矩阵; 不可逆矩阵 span 生成 square (1平方；(2正方形 square bracket 方括号square matrix 方(矩阵 stability 稳度 stationary 平稳 stationary point 平稳点; 逗留点; 驻点 straight line 直线 subset 子集 substitute 代入 substitution 代入; 代入法subtract 减 subtraction 减法 successive approximation 逐次逼近法 successive derivative 逐次导数 successive differentiation 逐次微分法 sufficiency 充份性 sufficient and necessary condition 充要条件 sufficient condition 充份条件 sufficiently close 充份接近suffix 下标 sum 和 summation 求和法; 总和 symbol 符号; 记号 symmetry 对称; 对称性Taylor’s expansion 泰勒展开式 term 项 transpose 移项；转置 transpose of matrix 倒置矩阵；转置矩阵 trapezium 梯形 trapezoidal integral 梯形积分 trapezoidal rule 梯形法则 trial 试；试验 triangle 三角形 triangular matrix 三角矩阵 trigonometric equation 三角方程 trigonometric function 三角函数 triple 三倍 trivial solution 平凡解truncation error 截断误差 undefined 未下定义(的 undetermined coefficient 待定系数unequal 不等 unique solution 唯一解 uniqueness 唯一性 unit 单位 unit area 单位面积unit circle 单位圆 unknown 未知数；未知量 upper bound 上界 upper limit 上限 upper triangular matrix 上三角形矩阵 validity 真确性; 有效性 variable 变项；变量；元；变元；变数 vector 向量; 矢量 vector function 向量函数; 矢量函数 vector product 矢量积; 矢量积 vector space 向量空间 verify 证明；验证 weight (1重量；(2权 weighted average, weighted mean 加权平均数 without loss of generality 不失一般性 x-axis x 轴x-coordinate x 坐标 x-intercept x 轴截距 y-axis y 轴 y-coordinate y 坐标 y-intercept y轴截距 zero 零 zero factor 零因子 zero matrix 零矩阵 zero vector 零向量 zeros of a function 函数零值。

样条函数插值样条函数插值，是在有限的几何点中求出一组平滑函数，可以精确的贴近原来的数据的过程。

样条函数插值最早是在19世纪末由V. Schoenberg提出的，用于在复合空间中进行自由流体动力学和扩散模拟的数值方法，随着被提出的时间的推移，样条函数插值得到了不断的发展，现如今被广泛的用于数据拟合、函数拟合、仿射变换、几何曲线建模、机器学习等应用上。

样条函数插值法，通常指用于数据拟合的办法。

它是将原先的数据点（插值点）集合连接，形成一系列的平滑曲线，然后在这些曲线上根据每一条曲线规律生成具有明确调整参数的单个函数，即样条曲线函数，该函数可用来表示插值点集合中每一处点，从而可以实现数据拟合。

使用样条函数插值拟合数据的不同之处，就在于样条函数插值拟合完成初始数据可以尽可能的扩展，边界地带可以沿着给定点扩展，此外，它也有良好的几何特性，可以连续变化，具有一定的多参数优化能力，确定多参数的优化问题的逼近度，确定拟合的参数等强大的能力，使其能更有效的完成拟合。

此外，样条函数拟合的原理可以用简单的几何形式来描述，即将整个空间中的点分为三种不同的情况。

将首尾的点假定为特定参考点，而中间的点连接成一个平滑曲线，内部每一条曲线段以某种最小二乘拟合方式来生成具体的样条曲线，每条曲线段有两个参数，斜率和曲线弧度。

并且根据参数调整，可以使得这条曲线会拟合出原始数据点集中最佳的接近度，同时这条曲线也可以优化在给定参数范围内的定义域内的曲线，以使得样条函数拟合所得结果最接近数据集的原始值。

样条函数拟合的技术广泛应用于数据拟合、函数拟合、图像处理等领域，比如计算机视觉领域中可以应用于精细分割，几何形状拟合，曲线和曲面建模等等。

样条函数拟合一般应用在缺少精确计算的情况下，比如波形拟合和几何图形拟合等情形，它具有在定义域内的精度可控性和多参数优化也很有用，这在曲面建模和机器学习上也有大的应用价值，证明其对普遍的函数估计有着不可忽略的作用。

附录Ⅱ工具箱数学词汇英汉对照表Ⅱ.1 概率论与数理统计词汇英汉对照表Aabsolute value 绝对值accept 接受acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算case 个案category 类别center of gravity 重心central tendency 中心趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对照components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述附录II 工具箱数学词汇英汉对照表·535·design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估计estimation of parameters 参数估计estimations 估计量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值Ffactor 因素，因子factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线fitted value 拟合值fixed model 固定模型fixed variable 固定变量fractional factorial design 部分析因设计frequency 频数F-test F检验full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度MATLAB 6.1与工程数学应用指南（下册）·536·Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-square estimation 最小二乘估计least-square method 最小二乘法level 水平level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数likelihood ratio test 似然比检验linear 线性的linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数logistic 逻辑的lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差mean sum of square 均方和measure 衡量media 中位数M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程multiple response 多响应multivariate analysis 多元分析Nnegative relationship 负相关nonadditively 不可加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验normal distribution 正态分布null hypothesis 零假设number of cases 个案数Oone-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classification 单向分类optimal 优化的optimum allocation 最优配制order 排序order statistics 次序统计量origin 原点orthogonal 正交的outliers 异常值Ppaired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimation 参数估计附录II 工具箱数学词汇英汉对照表·537·partial correlation 偏相关partial correlation coefficient 偏相关系数partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估计poisson distribution 泊松分布polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关power 幂P-P plot P-P概率图predict 预测predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率probability density function 概率密度函数probit analysis 概率分析proportion 比例Qqadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项quality control 质量控制quantitative 数量的，度量的quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank 秩rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数regression line 回归线reject 拒绝rejection region 拒绝域relationship 关系reliability 可靠性repeated 重复的report 报告，报表residual 残差residual sum of squares 剩余平方和response 响应risk function 风险函数robustness 稳健性root mean square 标准差row 行run 游程run test 游程检验Ssample 样本sample size 样本容量sample space 样本空间sampling 取样sampling inspection 抽样检验scatter chart 散点图S-curve S形曲线separately 单独地sets 集合sign test 符号检验significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布skewness 偏度MATLAB 6.1与工程数学应用指南（下册）·538·small sample problem 小样本问题smooth 平滑sort 排序soruces of variation 方差来源space 空间spread 扩展square 平方standard deviation 标准离差standard error of mean 均值的标准误差standardization 标准化standardize 标准化statistic 统计量statistical quality control 统计质量控制std. residual 标准残差stepwise regression analysis 逐步回归stimulus 刺激strong assumption 强假设stud. deleted residual 学生化剔除残差stud. residual 学生化残差subsamples 次级样本sufficient statistic 充分统计量sum 和sum of squares 平方和summary 概括，综述Ttable 表t-distribution t分布test 检验test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验test of independence 独立性检验test rules 检验法则test statistics 检验统计量testing function 检验函数time series 时间序列tolerance limits 容许限total 总共，和transformation 转换treatment 处理trimmed mean 截尾均值true value 真值t-test t检验two-tailed test 双侧检验Uunbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布Vvalue of estimator 估计值variable 变量variance 方差variance components 方差分量variance ratio 方差比various 不同的vector 向量Wweight 加权，权重weighted average 加权平均值within groups 组内的ZZ score Z分数附录II 工具箱数学词汇英汉对照表·539·Ⅱ.2 最优化方法词汇英汉对照表Aactive constraint 活动约束active set method 活动集法analytic gradient 解析梯度approximate 近似arbitrary 强制性的argument 变量attainment factor 达到因子Bbandwidth 带宽be equivalent to 等价于best-fit 最佳拟合bound 边界Ccoefficient 系数complex-value 复数值component 分量constant 常数constrained 有约束的constraint 约束constraint function 约束函数continuous 连续的converge 收敛cubic polynomial interpolation method三次多项式插值法curve-fitting 曲线拟合Ddata-fitting 数据拟合default 默认的，默认的define 定义diagonal 对角的direct search method 直接搜索法direction of search 搜索方向discontinuous 不连续Eeigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的Ffeasible 可行的feasible solution 可行解finite-difference 有限差分first-order 一阶GGauss-Newton method 高斯-牛顿法goal attainment problem 目标达到问题gradient 梯度gradient method 梯度法Hhandle 句柄Hessian matrix 海色矩阵Iindependent variables 独立变量inequality 不等式infeasibility 不可行性infeasible 不可行的initial feasible solution 初始可行解initialize 初始化inverse 逆invoke 激活iteration 迭代iteration 迭代MATLAB 6.1与工程数学应用指南（下册）·540·JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子large-scale 大型的least square 最小二乘least squares sense 最小二乘意义上的Levenberg-Marquardt method列文伯格-马夸尔特法line search 一维搜索linear 线性的linear equality constraints 线性等式约束linear programming problem 线性规划问题local solution 局部解Mmedium-scale 中型的minimize 最小化mixed quadratic and cubic polynomial interpolation and extrapolation method混合二次、三次多项式内插、外插法multiobjective 多目标的Nnonlinear 非线性的norm 范数Oobjective function 目标函数observed data 测量数据optimization routine 优化过程optimize 优化optimizer 求解器over-determined system 超定系统Pparameter 参数partial derivatives 偏导数polynomial interpolation method多项式插值法Qquadratic 二次的quadratic interpolation method 二次内插法quadratic programming 二次规划Rreal-value 实数值residuals 残差robust 稳健的robustness 稳健性，鲁棒性Sscalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method序列二次规划法simplex search method 单纯形法solution 解sparse matrix 稀疏矩阵sparsity pattern 稀疏模式sparsity structure 稀疏结构starting point 初始点step length 步长subspace trust region method 子空间置信域法sum-of-squares 平方和symmetric matrix 对称矩阵Ttermination message 终止信息termination tolerance 终止容限the exit condition 退出条件the method of steepest descent 最速下降法transpose 转置Uunconstrained 无约束的under-determined system 负定系统附录II 工具箱数学词汇英汉对照表·541·Vvariable 变量vector 矢量Wweighting matrix 加权矩阵Ⅱ.3 样条词汇英汉对照表Aapproximation 逼近array 数组a spline in b-form/b-spline b样条a spline of polynomial piece /ppform spline分段多项式样条Bbivariate spline function 二元样条函数break/breaks 断点Ccoefficient/coefficients 系数cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式cubic smoothing spline 三次平滑样条cubic spline 三次样条cubic spline interpolation三次样条插值/三次样条内插curve 曲线Ddegree of freedom 自由度dimension 维数Eend conditions 约束条件Iinput argument 输入参数interpolation 插值/内插interval 取值区间Kknot/knots 节点Lleast-squares approximation 最小二乘拟合Mmultiplicity 重次multivariate function 多元函数Ooptional argument 可选参数order 阶次output argument 输出参数Ppoint/points 数据点Rrational spline 有理样条rounding error 舍入误差（相对误差）Sscalar 标量sequence 数列（数组）spline 样条spline approximation 样条逼近/样条拟合spline function 样条函数spline curve 样条曲线spline interpolation 样条插值/样条内插spline surface 样条曲面smoothing spline 平滑样条MATLAB 6.1与工程数学应用指南（下册）·542·T tolerance 允许精度U univariate function 一元函数V vector 向量W weight/weights 权重Ⅱ.4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图converge 收敛coordinate 坐标系Ddecomposed 分解的decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditionsDirichlet边界条件Eeigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解Ggeneralized Neumann boundary condition推广的Neumann边界条件geometry 几何形状geometry description matrix 几何描述矩阵geometry matrix 几何矩阵graphical user interface（GUI）图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值loop 循环Mmachine precision 机器精度mixed boundary condition 混合边界条件NNeuman boundary condition Neuman边界条件node point 节点nonlinear solver 非线性求解器normal vector 法向量附录II 工具箱数学词汇英汉对照表·543·PParabolic 抛物线型的partial differential equation 偏微分方程plane strain 平面应变plane stress 平面应力Poisson's equation 泊松方程polygon 多边形positive definite 正定Qquality 质量Rrefined triangular mesh 加密的三角形网格relative tolerance 相对容限relative tolerance 相对容限residual 残差residual norm 残差范数Ssingular 奇异的sparce matrix 稀疏矩阵stiffness matrix 刚度矩阵subregion 子域Ttriangular mesh 三角形网格Uundetermined 未定的uniform refinement 均匀加密uniform triangle net 均匀三角形网络Wwave equation 波动方程。

数学专业英语词汇（L）l distribution l分布l function l函数l integral 勒贝格积分l measurable function 勒贝格可测函数l null set l零集l'hospital rule 洛必达规则labeled graph 标号图labile 不稳定的laboratory system of coordinates 实验室坐标系labyrinth 迷宫lacation principle 介值定理lacunarity 缺项性lacunary series 间隙级数lacunary space 缺项空间lag 延迟lag correlation 滞后相关lag correlation coefficient 滞后相关系数lag covariance 落后协方差lag of phase 相位滞后lag regression 落后回归lagrange bracket 拉格朗日括号lagrange equation of motion 拉格朗日运动方程lagrange interpolation formula 拉格朗日插置公式lagrange interpolation polynomial 拉格郎日插值多项式lagrange multiplier 拉格朗日乘子lagrange problem 拉格朗日问题lagrange remainder term 拉格朗日剩余项lagrange residual term 拉格朗日剩余项lagrange theorem 拉格朗日定理lagrangian 拉格朗日算子thermocouple pyrometer 热电偶高温计lagrangian function 拉格朗日算子lagrangian operator 拉格朗日算符laguerre differential equation 拉盖尔微分方程laguerre function 拉盖尔函数laguerre polynomial 拉盖尔多项式lambert series 兰伯特级数lame equation 拉梅方程lame function 拉梅函数laminar 薄层的laminar flow 层流片流landau symbol 兰道记号landen transformation 兰登变换language of formula 公式语言laplace beltrami operator 拉普拉斯贝尔特拉米算子laplace distribution 拉普拉斯分布laplace equation 拉普拉斯方程laplace expansion 拉普拉斯展开laplace expansion theorem 拉普拉斯展开定理laplace integral 拉普拉斯积分laplace linear equation 拉普拉斯线性方程laplace transform 拉普拉斯变换laplacian 拉普拉斯算子laplacian equation 拉普拉斯方程large sample analysis 大样本分析large sample test 大样本检验last multiplier 最后乘子last term 末项latency 潜在latent 潜在的lateral 横的lateral area 侧面积lateral surface 侧面latin cube 拉丁立方latin rectangle 拉丁矩形latin square 拉丁方latitude 纬度lattice 格子;格lattice constant 点阵常数lattice design 格子设计lattice distribution 格分布lattice function 点阵函数lattice isomorphism 格同构lattice matrix 点阵矩阵lattice of sets 集格lattice operation 格运算lattice ordered group 格序群lattice point at the boundary 边界格点lattice theoretic 格论的lattice theory 格论latticehomomorphism 格同态latus rectum 通径laue's equations 劳卮方程laurent series 罗郎级数law 法则law of commutation 交换律law of composition 合成律law of cosines 余弦定律law of deduction 演绎定律law of double negation 双重否定律law of errors 误差律law of excluded middle 排中律law of exponentiation 指数定律law of inertia 惯性律law of iterated logarithm 迭对数定律law of large numbers 大数定律law of similarity transformation 相似变换律law of sines 正弦定律law of small numbers 小数定律law of tangents 正切定律laws of integral exponents 整指数定律leading coefficient 首项系数leading diagonal 衷角线leading ideal 猪想leading term 知项leaf 叶least common denominator 最小公分母least common left multiple 左最小公倍数least common multiple 最小公倍数least common right multiple 右最小公倍数least significant digit 最小有效数字least squares approximation 最小二乘逼近least squares estimator 最小二乘估计量least upper bound 最小上界lebesgue area 勒贝格面积lebesgue decomposition 勒贝格分解lebesgue integrable 勒贝格可积的lebesgue integral 勒贝格积分lebesgue measurable 勒贝格可测的lebesgue measure 勒贝格测度lebesgue number 勒贝格数lebesgue space 勒贝格空间lebesgue stieltjes integral 勒贝格斯蒂尔吉斯积分left adjoint 左伴随的left adjoint homomorphism 左伴随同态left almost periodic function 左殆周期函数left alternative division ring 左交错可除环left alternative law 左交错律left alternative ring 左交错环left annihilator 左零化子left artinian ring 左阿廷环left associated element 左相伴元素left balanced functor 左平衡函子left closed object 在闭对象left completion 左完备化left continuous 左方连续的left continuous function 左连续函数left coset 左陪集left coset space 左傍系空间left derivative 左导数left derived functor 左导函子left differential 左微分left direct product 左直积left directed quasiorder 逆有向拟序left distributive 左分配的left distributive law 左分配律left divisor 左因子left end point 左端点left exact functor 左正合函子left exactness 左正合性left faithful functor 左一一的函子left hand differentiable function 左可微函数left hand lower dini derivative 左下狄尼导数left hand side 左边left hand symmetrizable kernel 左方可对称化核left hand upper dini derivative 左上狄尼导数left handed co ordinate system 左手坐标系left handed curve 左旋曲线left handed system 左手坐标系left hereditary ring 左遗传环left homotopy inverse 左同伦逆元left ideal 左理想left identity element 左幺元left injective dimension 左内射维数left inner product 左内积left invariant mean 左不变平均值left invariant measure 左不变测度left inverse 左逆的left inverse element 左逆元left inverse matrix 左逆阵left inverse operator 左逆算子left invertible element 左可逆元left invertible mapping 左可逆映射left isolated point 左孤立点left kernel 左核left length 左长left limit value 左极限值left linear topology 左线性拓扑left localization 左局部化left mean 左平均left module 左模left monotonicity 左单翟left multiplication ring 左乘环left noetherian semigroup 左诺特半群left non zerodivisor 左非零因子left operator 左算子left order 左整环left periodic group 左周期群left primitive ideal 左本原理想left primitive ring 左本原环left projective space 左射影空间left quasi inverse 左拟逆元left quasi regularity 左拟正则性left quasi simple ring 左拟单环left quasigroup 左拟群left quotient 左商left quotient field 左商域left quotient ring 左商环left radical 左根基left regular element 左正则元素left regular representation 左正则表示left regularity 左正则性left remainder 左剩余left representation 左表示left resolution 左分解left satellite 左卫星函子left semihereditary ring 左半遗传环left semilinear mapping 左半线性映射left side contiuous function 左连续函数left side derivative 左导数left side half open interval 左半开区间left side limit value 左极限值left sided decomposition 左分解left simple groupoid 左单广群left simple semigroup 左单半群left tensor product 左张量乘积left topology 左拓扑left translation 左平移left zero divisor 左零因子leg of a right triangle 直角三角形的侧边legendre function 勒让德函数legendre polynomial 勒让德多项式legendre relation 勒让德关系legendre symbol 勒让德记号legendre transform 勒让德变换leibniz series 莱布尼兹级数leibniz theorem 莱布尼兹定理lemma 引理lemniscate 双纽线lemniscate function 双纽线函数lemniscate of bernoulli 伯努利双纽线length 长度length of arc 弧长length of curve 曲线的长length of normal 法线的长length of queue 队列长度length of tangent 切线的长length of vector 向量的长length unit 长度单位lens 透镜lens space 透镜空间leptokurtic distribution 尖峰态分布less than or equal 小于或等于letter 文字level 水准level curve 阶层曲线level line 等高线level plane 水准面level surface 等位面lever 杠杆levi decomposition 列维分解levi problem 列维问题lexicographic 词典的lexicographic order 字典顺序liapunov function 李雅普诺夫函数library 厍library subroutine 库存子程序lie algebra 李代数lie continuous group 李连续群lie derivative 李导数lie group 李群lie homomorphism 李同态lie ring 李环lie series 李级数lie subring 李子环life insurance 寿命保险life table 死亡率表life time 生存时间lifting 提升lifting map 提升映射lifting theorem 提升定理like term 同类项likelihood 似然likelihood function 似然函数likelihood ratio 似然比likelihood ratio test 似然比值检验limacon of pascal 帕斯卡蚶线limes inferior 下极限limes superior 上极限limit 极限limit case 极限情况limit circle 极限圆limit circle type 极限圆型limit cycle 极限环limit distribution 极限分布limit element 极限元limit function 极限函数limit in the sense of pointwise convergence 点态收敛极限limit of efficiency 有效极限limit of error 误差限度limit of integration 积分极限limit of proportionality 比例极限limit on the left 左极限limit on the right 右极限limit ordinal number 极限序数limit point 极限点limit point type 极限点型limit relation 极限关系limit theorem 极限定理limit theorem in probability theory 概率论极限定理limit value 极限值limitation 限制limited 有界的limited function 有界函数limiting cone 极限锥limiting distribution 极限分布limiting point 极限点limiting position 极限位置limitless 无界的limits of integration 积分限line 线line at infinity 无穷远线line bundle 线丛line coordinates 线坐标line critical graph 线临界图line element 线素line graph 线图line integral 线积分line of curvature 曲率线line of discontinuity 不连续线line of horizon 水平线line of intersection 交线line of nodes 交点线line of steepest descent 最速下降线line of vector 向量线line segment 线段linear 线的linear acceleration 线性加速度linear algebra 线性代数linear approximation 线性近似linear approximation problem 线性逼近问题linear associative algebra 线性结合代数linear closure 线性闭包linear combination 线性组合linear convergence 线性收敛linear density 线密度linear dependence 线性关系linear difference equation 线性差分方程linear differential equation 线性微分方程linear differential equation with constant coefficients 常系数线性微分方程linear dimension 线性维数linear eigenvalue problem 线性特盏问题linear equation 线性方程linear extrapolation 线性外插linear form 线性形式linear fractional function 单应函数linear fractional transformation 线性分式变换linear function 线性函数linear functional 线性泛函linear genus 线性狂linear group 线性群linear homogeneous equation 线性齐次方程linear hull 线性闭包linear independence 线性无关linear integral equation 线性积分方程linear integral equation of the third kind 第三种线性积分方程linear interpolation 线性插值linear isomorphism 线性同构linear manifold 线性廖linear map 线性映射linear measure 线性测度linear operator 线性算子linear optimization 线性最优化linear optimization problem 线性最优化问题linear order 线性有序类linear orderedness 线性次序linear ordinary differential equation 线性常微分方程linear pencil 线性束linear programming 线性规划linear quotient optimization 线性商最优化linear regression 线性回归linear relationship 线性关系linear space 线性空间linear subspace 线性子空间linear subsystem 线性子系linear system 线性系linear system of curves 线性曲线系linear system of differential equations 线性微分方程系linear transformation 线性变换linear vector function 线性向量函数linear velocity 线速度linearity 线性linearization 线性化linearly dependent set 线性相关集linearly dependent system 线性相关集linearly independent set 线性无关系linearly independent system 线性无关系linearly ordered class 线性有序类linearly ordered set 线性有序集link group 连接群liouville number 刘维尔数liouville theorem 刘维尔定理lipschitz condition 李普希茨条件lipschitz constant 李普希茨常数lipschitz continuity 李普希茨连续性lipschitz continuous function 李普希茨连续函数lipschitz space 李普希茨空间listing knot 8字纽结liter 升literal constant 文字常数literal expression 文字式litre 升lituus 连锁螺线load 载荷load curve 载荷曲线lobachevski space 双曲空间lobachevskian geometry 双曲几何学local arcwise connectedness 局部弧连通性local base 局部基local betti group 局部贝蒂群local borel set 局部波莱尔集local class field theory 局部类域论local compactness 局部紧性local condition 局部条件local continuity 局部连续性local convergence 局部收敛local coordinate system 局部坐标系local degree 局部次数local degree of map 局部映射度local extremum 局部极值local group 局部群local isomorphism 局部同构local lie group 局部李群local limit theorem 局部极限定理local lipschitz condition 局部李普希茨条件local maximum 局部极大local minimum 局部极小local parameter 局部参数local property 局部性质local ring 局部环local ringed space 局部环式空间local uniformization 局部单值化local uniformizing 局部单值化localization 局部化localization principle 局部化原理localizing subcategory 局部化子范畴locally analytic function 局部解析函数locally arcwise connected space 局部弧连通空间locally bounded function 局部有界函数locally closed set 局部闭集locally compact mapping 局部紧映射locally compact space 局部紧空间locally connected continuum 局部连通连续统locally connected set 局部连通集locally connected space 局部连通空间locally constant function 局部常值函数locally constant sheaf 局部常数层locally contractible space 局部可缩空间locally convex algebra 局部凸代数locally convex space 局部凸空间locally convex topology 局部凸拓扑locally euclidean connection 局部欧几里得联通locally euclidean group 局部欧几里得群locally euclidean manifold 局部欧几里得廖locally euclidean space 局部欧几里得空间locally finite category 局部有限范畴locally finite complex 局部有限复形locally finite family of sets 局部有限集族locally finite graph 局部有限图locally finite sum 局部有限和locally flat 局部平坦的locally free sheaf 局部自由层locally homomorphic function 局部同态函数locally pathconnected space 局部道路连通空间locally regular confidence region 局部正则置信区域locally separable space 局部可分空间locally soluble group 局部可解群locally trivial embedding 局部平凡嵌入locally unbiased test 局部无偏检验locally uniformizing parameter 局部单值化参数locally uniformly convergent sequence 局部一致收敛序列locally zero function 局部零函数location 存储单元location parameter 位置参数location principle 介值locus 轨迹log curve 对数曲线log log paper 重对数坐标纸logarithm 对数logarithm table 对数表logarithm to the base 10 常用对数logarithm to the basese 讷代对数logarithmic 对数的logarithmic branchpoint 对数分歧点logarithmic convexity 对数凸性logarithmic coordinates 对数座标logarithmic curve 对数曲线logarithmic decrement 对数衰减logarithmic derivative 对数导数logarithmic distribution 对数分布logarithmic equation 对数方程logarithmic function 对数函数logarithmic integral 对数积分logarithmic normal distribution 对数正态分布logarithmic paper 对数坐标纸logarithmic potential 对数位势logarithmic residue 对数残数logarithmic scale 对数尺度logarithmic series 对数级数logarithmic singularity 对数奇点logarithmic slide rule 对数计算尺logarithmic spiral 对数螺线logarithmic table 对数表logic 逻辑logic calculus 逻辑学logic of pocket calculator 袖珍计算机的逻辑logic of relations 关系逻辑logic product 合取logic sum 析取logical 逻辑的logical circuit 逻辑电路logical comparison 逻辑比较logical diagram 逻辑图logical element 逻辑元件logical operation 逻辑运算logical paradox 逻辑悖论logical shift 逻辑移位logical symbol 逻辑符号logical variable 逻辑变量logically true proposition 逻辑地真命题logicism 逻辑皱logico mathematical model 逻辑数学模型logistic 暹辑斯谛logistic curve 逻辑斯谛曲线logistic system 形式系统lognormal distribution 对数正态分布longitude 经度longitudinal 经度的longitudinal axis 纵向轴loop 闭路loop of a curve 曲线的闭路loop space 圈空间lopology of the uniformity 一致拓扑lorentz group 洛伦茨群thermocouple pyrometer 热电偶高温计lorentz transformation 洛伦茨变换loss 损失loss function 损失函数loss system 损失系统lot 一批lot tolerance fraction defective 批容许废品率low of cosines 余弦定律lower approximate limit 下近似极限lower bound 下界lower central series 降中心列lower class 下类lower control limit 下控制界限lower darboux integral 达布下积分lower darboux sum 达布下和lower density 下密度lower dini derivative 狄尼下导数lower envelope 下包络lower half plane 下半平面lower integral 下积分lower limit 下限lower limit of integration 积分的下极限lower measure 内测度lower order 低位lower pure value 下方值lower quartile 第一四分位数lower semi modular lattice 下半模格lower semicontinuity 下半连续性lower semicontinuous decomposition 下半连续分解lower semicontinuous function 下半连续函数lower semilattice 下半格lower sum 下和lower triangular matrix 下三角形矩阵lower value 下方值lower variation 负变差lowest common denominator 最小公分母lowest common multiple 最低公倍数lowest term 最低项loxodrome 斜驶曲线loxodromic matrix 斜驶矩阵loxodromic spiral 斜驶曲线loxodromic transformation 斜驶变换lozenge diagram 菱形图形lune 弓形。

3DMAX中英文对照大全[一、File〈文件〉]New〈新建〉Reset〈重置〉Open〈打开〉Save〈保存〉Save As〈保存为〉Save copy As<保存副本为>Save selected〈保存选择〉XRef Objects〈外部参照物体〉XRef Scenes〈外部参照场景〉File link Mananger <文件连接管理器>Merge〈合并〉Merge Animation〈合并动画动作〉Replace〈替换〉Load Animation<下载动画>Save Animation<保存动画>Import〈输入〉Export〈输出〉Export Selected〈导出选择对象〉Asset Tracking<资源追踪>Archive〈存档〉Summary Info〈摘要信息〉File Properties〈文件属性〉View Image File〈查看图像文件〉Exit〈退出〉[二、Edit〈菜单〉]Undo Select<撤销选择>Redo〈重做〉Hold <暂存>Fetch〈取回〉Delete〈删除〉Clone〈克隆〉Select All〈全部选择〉Select None〈不选择〉Select Invert〈反向选择〉Select By〈参考选择〉：Color〈颜色选择〉Name〈名字选择〉Rectangular Region〈矩形选区〉Circular Region〈圆形选区〉Fabce Region〈围栏选区〉Lasso Region〈套索选区〉Region:〈区域选择〉：Window〈窗口〉Crossing〈交叉〉Edit Named Selection Sets〈编辑命名选择集〉Object Properties〈对象属性〉[三、Tools〈工具〉]Transform Type-In〈键盘输入变换〉Selection Floater〈选择浮动对话框〉Display Floater〈视窗浮动对话框〉Layer manager<图层管理>Light Lister〈灯光列表〉Manage scene states<管理场景状态>Mirror〈镜像〉Array〈阵列〉Align〈对齐〉Quick Align<快速对齐>Snapshot〈快照〉Spacing Tool〈间距工具〉Clone and Align<克隆并对齐>Normal Align〈法线对齐〉Align Camera〈对齐摄影机〉Align to View〈对齐视窗〉Place Highlight〈放置高光〉Isolate Selection〈孤立当前选择〉Rename Objects〈物体更名〉Assign vertex colors<指定顶点颜色>Color clipboard<颜色剪贴板>Camera Match <摄影机匹配>Grab viewport<抓取视口>Measure Distance<测量距离>Channel info<通道信息>[四、Group〈群组〉]Group〈群组〉Ungroup〈撤消群组〉Open〈打开组〉Close〈关闭组〉Attach〈附加〉Detach〈分离〉Explode〈分散组〉Assembly <集合>：Assemble<集合>Disassemble<分解>Open<打开组>Close<关闭组>Attach<附加>Detach<分离>Explode<分散组>[五、Views〈查看〉]Undo View Change<取消视窗变化>Redo View change〈重做视窗变化〉Save Active left View<保存当前左视窗>Restore Active left View〈还原当前左视窗〉Grids〈栅格〉：Show Home Grid〈显示栅格〉Activate Home Grid〈激活主栅格命令〉Activate Grid Object〈激活栅格对象〉Activate Grid to View〈栅格及视窗对齐命令〉Viewport Background〈视窗背景〉Update Background Image〈更新背景图像〉Reset Background Transform〈重置背景变换〉Show Transform Gizmo〈显示变换坐标系〉Show Ghosting〈显示重像〉Show Key Times〈显示关键点时间〉Shade Selected〈着色选择对象〉Show Dependencies〈显示从属关系〉Create Camera from View〈从视窗创建摄影机〉Add Default Lights To Scene〈添加默认灯光到场景〉Redraw All Views〈重画所有视窗〉Activate All Maps〈显示所有贴图〉Deactivate All Maps〈关闭显示所有贴图〉Update During Spinner Drag〈微调器实时显示〉：Adaptive Degradation〈自适应降级〉Object display culling<对象显示消隐>Expert Mode〈专家模式〉[六、Create〈创建〉]Standard Primitives〈标准图元〉：Box〈立方体〉Cone〈圆锥体〉Sphere〈球体〉GeoSphere〈三角面片球体〉Cylinder〈圆柱体〉Tube〈管状体〉Torus〈圆环体〉Pyramid〈角锥体〉Plane〈平面〉Teapot〈茶壶〉Extended Primitives〈扩展图元〉：Hedra〈多面体〉Torus Knot〈环面纽结体〉Chamfer Box〈斜切立方体〉Chamfer Cylinder〈斜切圆柱体〉Oil Tank〈桶状体〉Capsule〈角囊体〉Spindle〈纺锤体〉L-Extrusion〈L形体按钮〉Gengon〈导角棱柱〉C-Extrusion〈C形体按钮〉RingWave〈环状波〉Hose〈软管体〉Prism〈三棱柱>}AEC objects<>：Foliage<植物>Railing<栏杆>Wall<墙>Pivot door<枢轴门>Sliding door<推拉门>Biford door<折叠门>Straight stair<直线楼梯>L-type stair<L型楼梯>U-type stair<U型楼梯>Spiral stair<螺旋形楼梯>Awning window<遮蓬式窗>Casement window<平开窗>Fixed window<固定窗>Pivoted window<旋开窗>Sliding window<推拉窗>Projected window<伸出式窗>Compound<>：Morph<变形>Scatter<散布>Conform<一致>Connect<连接>Blobmesh<水滴网格>Shapemerge<图形合并>Boolean<布尔>Terrain<地形>Loft<放样>Mesher<网格化>Particles〈粒子系统〉：Particle Flow Source<粒子流源>Spary〈喷溅系统〉Snow〈雪花系统〉Blizzard<暴风雪系统>Parray<粒子阵列系统>Pcloud<粒子云系统>Super spray<超级喷射系统> Patch Grids<>：Quad patch<四边形面片>Tri patch<三角形面片> NURBS <nurbs曲线>：Cv surface <CV曲面>Point surface <点曲面>Cv curve <CV曲线>Point curve <点曲线> Dynamics<>：Damper <阻尼器>Spring <弹簧>Extended shapes<扩展图形>：Wrectangle <W矩形>Channel <通道>Angle <角度>Tee <三通>Wind Flange<宽法兰> Shapes〈形状〉：Line〈线条〉Rectangle〈矩形〉Circle〈圆〉Ellipse〈椭圆〉Arc〈弧〉Donut〈圆环〉NGon〈多边形〉Star〈星型〉Text〈文字〉Helix〈螺旋线〉Section〈截面〉Lights〈灯光〉：Standard lights<标准灯光>:【Target Spotlight〈目标聚光灯〉Free Spotlight〈自由聚光灯〉Target Directional〈目标平行光〉Directional〈平行光〉Omni〈泛光灯〉Skylight〈天光〉mr Area spot <mr区域聚光灯>mr Area omni <mr区域泛光灯>】Photometric lights <>：【Target Point〈目标指向点光源〉Free Point〈自由点光源〉Target linear〈指向面光源〉Free linear <自由线光源>Free area〈自有面光源〉Target area〈目标面光源〉Presets <预设>：（）】Daylight system<日光系统>Camera〈相机〉：Free Camera〈自由相机〉Target Camera〈目标相机〉Creat camera from view <从视窗创建相机>[七、Modifiers〈修改器〉]Selection Modifiers〈选择修改器〉：FFD Select〈自由变形选择修改器〉Mesh Select〈网格选择修改器〉Poly Select〈多边形选择修改器〉Patch Select〈面片选择修改器〉Select by channel<>Spline Select〈样条选择修改器〉V olume Select〈体积选择修改器〉NURBS Surface Select〈NURBS表面选择修改器〉Patch/Spline Editing〈面片/样条线修改器〉：Cross Section〈截面相交修改器〉Delete Patch〈删除面片修改器〉Delete Spline〈删除样条线修改器〉Edit Patch〈面片修改器〉Edit Spline〈样条线修改器〉Fillet/Chamfer〈圆切及斜切修改器〉Lathe〈车床修改器〉Normalize Spline〈规格化样条线修改器〉Rnderable spline modifier<>Surface〈表面生成修改器〉Sweep <>Trim/Extend〈修剪及延伸修改器〉Mesh Editing〈表面编辑〉:Cap Holes〈顶端洞口编辑器〉Delete Mesh〈编辑网格物体编辑器〉Edit Mesh <编辑网格物体编辑器>Edit Normals〈编辑法线编辑器〉Edit ploy <>Extrude〈挤压编辑器〉Face Extrude〈面拉伸编辑器〉Multires <>Normal modifider〈法线编辑器〉Optimize〈优化编辑器〉Smooth〈平滑编辑器〉STL Check〈STL检查编辑器〉Symmetry〈对称编辑器〉Tessellate〈镶嵌编辑器〉Vertex Paint〈顶点着色编辑器〉Vertex Weld〈顶点焊接编辑器〉Conversion <>:turn to mesh <>turn to patch <>turn to ploy <>Animation Modifiers〈动画编辑器〉:attribute holder<>Flex〈伸缩编辑器〉Morpher〈变体编辑器〉Melt〈熔化编辑器〉Linked XForm〈连结参考变换编辑器〉Patch Deform〈面片变形编辑器〉Patch Deform (wsm) <>Path Deform〈路径变形编辑器〉Path Deform (wsm)<>Skin〈皮肤编辑器〉Skin morph〈〉Skin warp〈〉Skin warp path〈〉splineIK control <>Surf Deform〈表面变形编辑器〉Surf Deform (wsm)〈空间变形编辑器〉Cloth <蒙皮>：Cloth<>Garment maker <>Hair and fur<>: Hair and fur(wsm)<>UV Coordinates〈贴图轴坐标系〉:Camera Map〈相机贴图编辑器〉Camera Map (wsm)〈环境相机贴图编辑器〉Mapscaler(wsm)<>Projection <>Unwrap UVW〈展开贴图编辑器〉UVW Map〈UVW贴图编辑器〉UVW Maping add <>UVW Maping clear <>UVW Xform〈UVW贴图参考变换编辑器〉Cache Tools〈捕捉工具〉：Point Cache〈点捕捉编辑器〉Point Cache （wsm）〈点捕捉编辑器〉Subdivision Surfaces〈表面细分〉:HSDS Modifier〈分级细分编辑器〉MeshSmooth〈表面平滑编辑器〉TurboSmooth <>Free Form Deformers〈自由变形工具〉:FFD 2×2×2〈自由变形工具2×2×2〉FFD 3×3×3〈自由变形工具3×3×3〉FFD 4×4×4〈自由变形工具4×4×4〉FFD Box〈盒体自由变形工具〉FFD Cylinder〈圆柱体自由变形工具〉Parametric Deformers〈参数变形工具〉:Affect Region〈面域影响〉Bend〈弯曲〉Displace〈置换〉Lattice〈栅格〉Mirror〈镜像〉Noise〈噪声〉physique<>Push〈推挤〉Preserve〈保持〉Relax〈松弛〉Ripple〈波纹〉Shell<>Slice〈切片〉Skew〈倾斜〉Stretch〈缩放〉Spherify〈球形扭曲〉Squeeze〈压榨〉Twist〈扭曲〉Taper〈锥形化〉Substitute <>XForm〈参考变换〉Wave〈波浪〉Surface〈表面编辑〉:Disp Approx〈近似表面替换〉Disp Mesh (wsm)〈〉Material〈材质变换〉Material By Element〈元素材质变换〉NURBS Editing〈NURBS面编辑〉:Disp Approx〈近似表面替换〉Surf Deform〈表面变形编辑器〉Surface Select〈NURBS表面选择〉Radiosity〈光能传递修改器〉:Subdivide〈细分〉Subdivide (wsm)〈超级细分〉Cameras 〈〉: Cameras correction〈〉[八、Character〈角色人物〉]Create Character〈创建角色〉Destroy Character〈删除角色〉Lock〈锁住〉Unlock〈解锁〉Insert Character〈插入角色〉Save Character〈保存角色〉Bone Tools〈骨骼工具〉Set Skin Pose〈调整皮肤姿势〉Assume Skin Pose〈还原姿势〉Skin Pose Mode〈表面姿势模式〉[九、Reactor 〈反应器〉]Create object <>:Rigid body collection<>Cloth collection<>Soft body collection<>Rope collection<>Deforming mesh collection<>Spring〈弹力控制器〉Plane<>linear Dashpot<>Angular Dashpot<>Motor<>Wnd<>Toy car<>Fracture<>Water<>Constraint solver<>Rag doll constraint <>Hinge constraint <>Point-point constraint <>Prismatic constraint <>Car-wheel constraint <>Point-path constraint <>Apply modifier<>:Cloth modifier <>Soft body modifier <>Rope modifier <>Open property Editor<>Utilities<>:Analyze world<>Converxity test<>View stored collisions<>Reduce keys(selection)<>Reduce keys(all)<>Delete keys(selection)<>Delete keys(all)<>Preview animation<>Creat animation<>About reactor<>[十、Animation〈动画〉]IK Solvers〈反向动力学〉：HI Solver〈非历史性控制器〉HD Solver〈历史性控制器〉IK Limb Solver〈反向动力学肢体控制器〉SplineIK Solver〈样条反向动力控制器〉Constraints〈约束〉：Attachment Constraint〈附件约束〉Surface Constraint〈表面约束〉Path Constraint〈路径约束〉Position Constraint〈位置约束〉Link Constraint〈连结约束〉LookAt Constraint〈视觉跟随约束〉Orientation Constraint〈方位约束〉Transform Constraint〈变换控制〉：Link Constraint〈连接约束〉Position/Rotation/Scale〈PRS控制器〉Transform Script〈变换控制脚本〉Position Controllers〈位置控制器〉：Audio〈音频控制器〉Bezier〈贝塞尔曲线控制器〉Expression〈表达式控制器〉Linear〈线性控制器〉Motion Capture〈动作捕捉〉Noise〈燥波控制器〉Quatermion(TCB)〈TCB控制器〉Reaction〈反应器〉Spring〈弹力控制器〉Script〈脚本控制器〉XYZ〈XYZ位置控制器〉Attachment Constraint〈附件约束〉Path Constraint〈路径约束〉Position Constraint〈位置约束〉Surface Constraint〈表面约束〉Rotation Controllers〈旋转控制器〉：Audio〈音频控制器〉EulerXYZ〈XYZ位置控制器〉Linear〈线性控制器〉Motion Capture〈动作捕捉〉Noise〈燥波控制器〉Quatermion(TCB)〈TCB控制器〉Reaction〈反应器〉Spring〈弹力控制器〉Script〈脚本控制器〉smooth <>lookArt Constraint〈〉Orientation Constraint〈〉Scale Controllers〈比例缩放控制器〉：Audio〈音频控制器〉Bezier〈贝塞尔曲线控制器〉Expression〈表达式控制器〉Linear〈线性控制器〉Motion Capture〈动作捕捉〉Noise〈燥波控制器〉Quatermion(TCB)〈TCB控制器〉Reaction〈反应器〉Script〈脚本控制器〉XYZ〈XYZ位置控制器〉Parameter Editor <>Parameter collector <>Wire Parameters〈参数绑定〉:Wire Parameters〈参数绑定〉Parameter Wiring Dialog〈参数绑定对话框〉Reaction Manager<>Make Preview〈创建预视〉View Preview〈观看预视〉Rename Preview〈重命名预视〉Toggle Limits<>Delete selected Animation<>[十一、Graph Editors〈图表编辑器〉]Track View-Curve Editor〈轨迹窗曲线编辑器〉Track View-Dope Sheet〈轨迹窗拟定图表编辑器〉NEW Track View〈新建轨迹窗〉Delete Track View〈删除轨迹窗〉Saved Track View〈已存轨迹窗〉New Schematic View〈新建示意观察窗〉Delete Schematic View〈删除示意观察窗〉Saved Schematic View〈显示示意观察窗〉Particle View <>Motion mixer <>[十二、Rendering〈渲染〉]Render〈渲染〉Environment〈环境〉Effects〈效果〉Advanced Lighting〈高级光照〉:Lights Tracer<>Radiosity<>Exposure Control<>Lighting Analysis<>Render To Texture〈贴图渲染〉Batch render<>Raytracer Settings〈光线追踪设置〉Raytrace Global Include/Exclude〈光线追踪选择〉Mental ray message window <>Activeshade Floater〈活动渲染窗口〉Activeshade Viewport〈活动渲染视窗〉Material Editor〈材质编辑器〉Material/Map Browser〈材质/贴图浏览器〉Video Post〈视频后期制作〉Show Last Rendering〈显示最后渲染图片〉Panorama Exporter<>Print Size wizardRAM Player〈RAM播放器〉[十三、Customize〈用户自定义〉]Customize User Interface〈定制用户界面〉Load Custom UI Scheme〈加载自定义用户界面配置〉Save Custom UI Scheme〈保存自定义用户界面配置〉Revert to Startup Layout〈恢复初始界面〉Custom UI and Default Switcher <>Show UI〈显示用户界面〉:Show command Panel〈命令面板〉Floating Toolbars Panel〈浮动工具条〉Show Main Toolbar〈主工具条〉Show Track Bar〈轨迹条〉Lock UI Layout〈锁定用户界面〉Configure User Paths〈设置用户路径〉Configure system Paths〈设置系统路径〉Units Setup〈单位设置〉Grid and Snap Settings〈栅格和捕捉设置〉Viewport Configuration〈视窗配置〉Plug-in Manager〈插件管理〉Preferences〈参数选择〉[十四、MAXScript〈MAX脚本〉]New Script〈新建脚本〉Open Script〈打开脚本〉Run Script〈运行脚本〉MAXScript Listener〈MAX脚本注释器〉Macro Recorder〈宏记录器〉Visual MAXScript Editer〈可视化MAX脚本编辑器〉Debugger dialog <>[十五、Help〈帮助〉]New Features Guide <>User Referebce〈用户参考〉MAXScript Referebce〈MAX脚本参考〉Tutorials〈教程〉Hotkey Map〈热键图〉Additional Help〈附加帮助〉3ds max on the Web〈3ds max网页〉:Online sport <>Updates <>Resources <>Parteners <>traning<>Autivate 3ds max〈授权〉License Borrowing<> :Borrow license<>Return license<>About 3ds max〈关于3ds max〉第六课：多边形建模一、定义：在原始简单的模型上，通过增减点、线、面数或调整点、线、面的位置来产生所需要的模型，这种建模方式称为多边形建模。

Algebraic operation 代数运算一种图像处理运算，包括两幅图像对应像素的和、差、积、商。

Aliasing 走样（混叠）当图像象素间距和图像细节相比太大时产生的一种人工痕迹。

Arc 弧（l）图的一部分（2）表示一段相连曲线的像素集合。

Binary image 二值图像只有两级灰度的数字图像（通常为0和1，黑和白）。

Blur 模糊由于散焦、低通滤波、摄像机运动等引起的图像清晰度的下降。

Border 边框一幅图像的首、未行或列。

Boundary chain code 边界链码定义一个物体边界的方向序列。

Boundary pixel 边界像素至少和一个背景象素相邻接的内部像素（比较：外部像素、内部像素）。

Boundary tracking边界跟踪一种图像分割技术，通过沿弧从一个像素顺序探索到下一个像素的方法将弧检测出来。

Brightness 亮度和图像一个点相关的值，表示从该点的物体发射或反射的光的量。

Change detection 变化检测通过相减等操作将两幅匹准图像的像素加以比较从而检测出其中物体差别的技术。

Class 类见模或类。

Closed curve 封闭曲线一条首尾接于一点的曲线。

Cluster 聚类，集群在空间（如在特征空间）中位置接近的点的集合。

Cluster analysis 聚类分析在空间中对聚类的检测、度量和描述。

Concave 凹的如果说某个物体是“凹的”是指至少存在两个物体内部的点，其连线不能完全包含在物体内部（反义词为凸的）。

Connected 连通的。

Contour encoding 轮廓编码对具有均匀灰度的区域，只将其边界进行编码的一种图像压缩技术。

Contrast 对比度物体平均亮度（或灰度）与其周围背景的差别程度。

Contrast stretch 对比度扩展一种线性的灰度变换。

Convex 凸的指连接物体内部任意两点的直线均落在物体内部。

Convolution 卷积一种将两个函数组合生成第三个函数的运算，卷积刻画了线性移不变系统的运算。

missing values encountered in interpolated fields
"missing values encountered in interpolated fields" 是一个英文短语，直译为中文是“在插值字段中遇到缺失值”。

这句话通常出现在处理数据或进行数值计算时。

当某个字段或数据集中存在缺失值，而该值需要进行插值（interpolation）处理时，可能会遇到这样的问题。

简单来说，插值是一种数学方法，用于估算在给定数据点之间的未知值。

当存在缺失值时，插值算法可能无法准确地估算这些缺失值，从而导致问题。

为了解决这个问题，通常需要对数据进行预处理，例如填充缺失值或采用其他技术处理缺失数据，以便在执行插值操作时获得更准确的结果。

插值法计算方法举例插值法是一种用来通过已知数据点的近似值来推测未知数据点的方法。

它通常用于数据的平滑和预测，尤其在缺少数据或数据不完整的情况下。

以下是一些插值法的具体计算方法举例：1. 线性插值法（Linear Interpolation）：线性插值法是最简单的插值方法之一、假设我们有两个已知数据点(x1, y1)和(x2, y2)，要推测处于两个数据点之间的未知点(x, y)。

线性插值法通过使用已知点之间的线性关系来计算未知点的值。

具体公式为：y=y1+(x-x1)*((y2-y1)/(x2-x1))2. 多项式插值法（Polynomial Interpolation）：多项式插值法通过使用一个低次数的多项式函数来逼近已知数据点，并预测未知数据点。

常见的多项式插值方法包括拉格朗日插值和牛顿插值。

其中，拉格朗日插值使用一个n次多项式来逼近n个已知点，而牛顿插值使用差商（divided differences）和差商表来逼近已知点。

具体公式为：P(x) = a0 + a1 * (x - x1) + a2 * (x - x1) * (x - x2) + ... + an * (x - x1) * (x - x2) * ... * (x - xn-1)3. 样条插值法（Spline Interpolation）：样条插值法是一种更复杂的插值方法，它通过拟合已知数据点之间的线段和曲线，来推测未知数据点。

常见的样条插值方法包括线性样条插值、二次样条插值和三次样条插值。

样条插值法具有良好的平滑性和曲线性质，通常在连续数据的插值和平滑方面效果更好。

具体公式为：S(x) = Si(x)，其中x属于[xi, xi+1]，Si(x)是第i段（i = 1, 2, ..., n-1）中的插值函数。

4. 逆距离加权插值法（Inverse Distance Weighting, IDW）：逆距离加权插值法是一种基于距离的插值方法，通过使用已知数据点的权重来推测未知数据点。

t distribution 学生t分布t number t数t statistic t统计量t test t检验t1topological space t1拓扑空间t2topological space t2拓扑空间t3topological space 分离空间t4topological space 正则拓扑空间t5 topological space 正规空间t6topological space 遗传正规空间table 表table of random numbers 随机数表table of sines 正弦表table of square roots 平方根表table of values 值表tabular 表的tabular value 表值tabulate 制表tabulation 造表tabulator 制表机tacnode 互切点tag 标签tame 驯顺嵌入tame distribution 缓增广义函数tamely imbedded 驯顺嵌入tangency 接触tangent 正切tangent bundle 切丛tangent cone 切线锥面tangent curve 正切曲线tangent function 正切tangent line 切线tangent of an angle 角的正切tangent plane 切平面tangent plane method 切面法tangent surface 切曲面tangent vector 切向量tangent vector field 切向量场tangent vector space 切向量空间tangential approximation 切线逼近tangential component 切线分量tangential curve 正切曲线tangential equation 切线方程tangential stress 切向应力tangents method 切线法tape 纸带tape inscription 纸带记录tariff 税tautology 重言taylor circle 泰勒圆taylor expansion 泰勒展开taylor formula 泰勒公式taylor series 泰勒级数technics 技术technique 技术telegraph equation 电报方程teleparallelism 绝对平行性temperature 温度tempered distribution 缓增广义函数tend 倾向tendency 瞧tension 张力tensor 张量tensor algebra 张量代数tensor analysis 张量分析tensor bundle 张量丛tensor calculus 张量演算法tensor density 张量密度tensor differential equation 张量微分方程tensor field 张量场tensor form 张量形式tensor form of the first kind 第一张量形式tensor function 张量函数tensor of torsion 挠率张量tensor product 张量乘积tensor product functor 张量乘积函子tensor representation 张量表示tensor space 张量空间tensor subspace 张量子空间tensor surface 张量曲面tensorial multiplication 张量乘法term 项term of higher degree 高次项term of higher order 高次项term of series 级数的项terminability 有限性terminable 有限的terminal decision 最后判决terminal edge 终结边terminal point 终点terminal unit 级端设备terminal vertex 悬挂点terminate 终止terminating chain 可终止的链terminating continued fraction 有尽连分数terminating decimal 有尽小数termination 终止terminology 专门名词termwise 逐项的termwise addition 逐项加法termwise differentiation 逐项微分termwise integration 逐项积分ternary 三元的ternary connective 三元联结ternary form 三元形式ternary notation 三进制记数法ternary number system 三进制数系ternary operation 三项运算ternary relation 三项关系ternary representation og numbers 三进制记数法tertiary obstruction 第三障碍tesseral harmonic 田形函数tesseral legendre function 田形函数test 检验test for additivity 加性检验test for uniform convergence 一致收敛检验test function 测试函数test of dispersion 色散检验test of goodness of fit 拟合优度检验test of hypothesis 假设检验test of independence 独立性检验test of linearity 线性检验test of normality 正规性检验test point 测试点test routine 检验程序test statistic 检验统计量tetracyclic coordinates 四圆坐标tetrad 四元组tetragon 四角形tetragonal 正方的tetrahedral 四面角tetrahedral angle 四面角tetrahedral co ordinates 四面坐标tetrahedral group 四面体群tetrahedral surface 四面曲面tetrahedroid 四面体tetrahedron 四面形tetrahedron equation 四面体方程theorem 定理theorem for damping 阻尼定理theorem of alternative 择一定理theorem of identity for power series 幂级数的一致定理theorem of implicit functions 隐函数定理theorem of mean value 平均值定理theorem of principal axes 轴定理theorem of residues 残数定理theorem of riemann roch type 黎曼洛赫型定理theorem on embedding 嵌入定理theorems for limits 极限定理theoretical curve 理论曲线theoretical model 理论模型theory of automata 自动机理论theory of cardinals 基数论theory of complex multiplication 复数乘法论theory of complexity of computations 计算的复杂性理论theory of correlation 相关论theory of differential equations 微分方程论theory of dimensions 维数论theory of elementary divisors 初等因子理论theory of elementary particles 基本粒子论theory of equations 方程论theory of errors 误差论theory of estimation 估计论theory of functions 函数论theory of games 对策论theory of hyperbolic functions 双曲函数论theory of judgment 判断论theory of numbers 数论theory of ordinals 序数论theory of perturbations 摄动理论theory of probability 概率论theory of proportions 比例论theory of relativity 相对论theory of reliability 可靠性理论theory of representations 表示论theory of sets 集论theory of sheaves 层理论theory of singularities 奇点理论theory of testing 检验论theory of time series 时间序列论theory of transversals 横断线论theory of types 类型论thermal 热的thermodynamic 热力学的thermodynamics 热力学theta function 函数theta series 级数thick 厚的thickness 厚度thin 薄的thin set 薄集third boundary condition 第三边界条件third boundary value problem 第三边界值问题third fundamental form 第三基本形式third isomorphism theorem 第三同构定理third proportional 比例第三项third root 立方根thom class 汤姆类thom complex 汤姆复形three body problem 三体问题three dimensional 三维的three dimensional space 三维空间three dimensional torus 三维环面three eighths rule 八分之三法three faced 三面的three figur 三位的three place 三位的three point problem 三点问题three series theorem 三级数定理three sheeted 三叶的three sided 三面的three sigma rule 三规则three termed 三项的three valued 三值的three valued logic 三值逻辑three valued logic calculus 三值逻辑学threshold logic 阈逻辑time interval 时程time lag 时滞time series analysis 时序分析timesharing 分时toeplitz matrix 托普利兹矩阵tolerance 容许tolerance distribution 容许分布tolerance estimation 容许估计tolerance factor 容许因子tolerance level 耐受水平tolerance limit 容许界限tolerance region 容许区域top digit 最高位数字topological 拓扑的topological abelian group 拓扑阿贝耳群topological algebra 拓扑代数topological cell 拓扑胞腔topological circle 拓扑圆topological completeness 拓扑完备性topological complex 拓扑复形topological convergence 拓扑收敛topological dimension 拓扑维topological direct sum 拓扑直和topological dynamics 拓扑动力学topological embedding 拓扑嵌入topological field 拓扑域topological group 拓扑群topological homeomorphism 拓扑同胚topological index 拓扑指数topological invariant 拓扑不变量topological limit 拓扑极限topological linear space 拓扑线性空间topological manifold 拓扑廖topological mapping 拓扑同胚topological pair 拓扑偶topological polyhedron 曲多面体topological product 拓扑积topological residue class ring 拓扑剩余类环topological ring 拓扑环topological simplex 拓扑单形topological skew field 拓扑非交换域topological space 拓扑空间topological sphere 拓扑球面topological structure 拓扑结构topological sum 拓扑和topological type 拓扑型topologically complete set 拓扑完备集topologically complete space 拓扑完备空间topologically equivalent space 拓扑等价空间topologically nilpotent element 拓扑幂零元topologically ringed space 拓扑环式空间topologically solvable group 拓扑可解群topologico differential invariant 拓扑微分不变式topologize 拓扑化topology 拓扑topology of bounded convergence 有界收敛拓扑topology of compact convergence 紧收敛拓扑topology of uniform convergence 一致收敛拓扑toroid 超环面toroidal coordinates 圆环坐标toroidal function 圆环函数torque 转矩torsion 挠率torsion coefficient 挠系数torsion form 挠率形式torsion free group 非挠群torsion group 挠群torsion module 挠模torsion of a curve 曲线的挠率torsion product 挠积torsion subgroup 挠子群torsion tensor 挠率张量torsion vector 挠向量torsionfree connection 非挠联络torsionfree module 无挠模torsionfree ring 无挠环torus 环面torus function 圆环函数torus group 环面群torusknot 环面纽结total 总和total correlation 全相关total curvature 全曲率total degree 全次数total differential 全微分total differential equation 全微分方程total error 全误差total graph 全图total image 全象total inspection 全检查total instability 全不稳定性total inverse image 全逆象total matrix algebra 全阵环total matrix ring 全阵环total order 全序total predicate 全谓词total probability 总概率total probability formula 总概率公式total regression 总回归total relation 通用关系total space 全空间total stability 全稳定性total step iteration 整步迭代法total step method 整步迭代法total stiefel whitney class 全斯蒂费尔惠特尼类total subset 全子集total sum 总和total variation 全变差totally bounded set 准紧集totally bounded space 准紧空间totally differentiable 完全可微分的totally differentiable function 完全可微函数totally disconnected 完全不连通的totally disconnected graph 完全不连通图totally disconnected groupoid 完全不连通广群totally disconnected set 完全不连通集totally disconnected space 完全不连通空间totally geodesic 全测地的totally nonnegative matrix 全非负矩阵totally ordered group 全有序群totally ordered set 线性有序集totally positive 全正的totally positive matrix 全正矩阵totally quasi ordered set 完全拟有序集totally real field 全实域totally reflexive relation 完全自反关系totally regular matrix method 完全正则矩阵法totally singular subspace 全奇异子空间totally symmetric loop 完全对称圈totally symmetric quasigroup 完全对称拟群touch 相切tournament 竞赛图trace 迹trace form 迹型trace function 迹函数trace of dyadic 并向量的迹trace of matrix 矩阵的迹trace of tensor 张量的迹tracing point 追迹点track 轨迹tractrix 曳物线trajectory 轨道transcendence 超越性transcendence basis 超越基transcendence degree 超越次数transcendency 超越性transcendental element 超越元素transcendental equation 超越方程transcendental function 超越函数transcendental integral function 超越整函数transcendental number 超越数transcendental singularity 超越奇点transcendental surface 超越曲面transfer 转移transfer function 转移函数transfinite 超限的transfinite diameter 超限直径transfinite induction 超限归纳法transfinite number 超限序数transfinite ordinal 超限序数transform 变换transformation 变换transformation equation 变换方程transformation factor 变换因子transformation formulas of the coordinates 坐标的变换公式transformation function 变换函数transformation group 变换群transformation of air mass 气团变性transformation of coordinates 坐标的变换transformation of parameter 参数变换transformation of state 状态变换transformation of the variable 变量的更换transformation rules 变换规则transformation theory 变换论transformation to principal axes 轴变换transgression 超渡transient response 瞬态响应transient stability 瞬态稳定性transient state 瞬态transient time 过渡时间transition function 转移函数transition graph 转换图transition matrix 转移矩阵transition probability 转移函数transitive closure 传递闭包transitive graph 传递图transitive group of motions 可迁运动群transitive law 可迁律transitive permutation group 可迁置换群transitive relation 传递关系transitive set 可递集transitivity 可递性transitivity laws 可迁律translatable design 可旋转试验设计translate 转移translation 平移translation curve 平移曲线translation group 平移群translation invariant 平移不变的translation invariant metric 平移不变度量translation number 殆周期translation of axes 坐标轴的平移translation operator 平移算子translation surface 平移曲面translation symmetry 平移对称translation theorem 平移定理transmission channel 传输通道transmission ratio 传输比transport problem 运输问题transportation algorithm 运输算法transportation matrix 运输矩阵transportation network 运输网络transportation problem 运输问题transpose 转置transposed inverse matrix 转置逆矩阵transposed kernel 转置核transposed map 转置映射transposed matrix 转置阵transposition 对换transversal 横截矩阵胚transversal curve 横截曲线transversal field 模截场transversal lines 截线transversality 横截性transversality condition 横截条件transverse axis 横截轴transverse surface 横截曲面trapezium 不规则四边形trapezoid 不规则四边形trapezoid formula 梯形公式trapezoid method 梯形公式traveling salesman problem 转播塞尔斯曼问题tree 树trefoil 三叶形trefoil knot 三叶形纽结trend 瞧trend line 瞧直线triad 三元组trial 试验triangle 三角形triangle axiom 三角形公理triangle condition 三角形公理triangle inequality 三角形公理triangulable 可三角剖分的triangular decomposition 三角分解triangular form 三角型triangular matrix 三角形矩阵triangular number 三角数triangular prism 三棱柱triangular pyramid 四面形triangular surface 三角曲面triangulate 分成三角形triangulation 三角剖分triaxial 三轴的triaxial ellipsoid 三维椭面trichotomy 三分法trident of newton 牛顿三叉线tridiagonal matrix 三对角线矩阵tridimensional 三维的trigammafunction 三函数trigonometric 三角的trigonometric approximation polynomial 三角近似多项式trigonometric equation 三角方程trigonometric function 三角函数trigonometric moment problem 三角矩问题trigonometric polynomial 三角多项式trigonometric series 三角级数trigonometrical interpolation 三角内插法trigonometry 三角学trihedral 三面形的trihedral angle 三面角trihedron 三面体trilateral 三边的trilinear 三线的trilinear coordinates 三线坐标trilinear form 三线性形式trinomial 三项式;三项式的trinomial equation 三项方程triplanar point 三切面重点 ?triple 三元组triple curve 三重曲线triple integral 三重积分triple point 三重点triple product 纯量三重积triple product of vectors 向量三重积triple root 三重根triple series 三重级数triple tangent 三重切线triply orthogonal system 三重正交系triply tangent 三重切线的trirectangular spherical triangle 三直角球面三角形trisecant 三度割线trisect 把...三等分trisection 三等分trisection of an angle 角的三等分trisectrix 三等分角线trivalent map 三价地图trivector 三向量trivial 平凡的trivial character 单位特贞trivial cohomology functor 平凡上同弹子trivial extension 平凡扩张trivial fibre bundle 平凡纤维丛trivial graph 平凡图trivial homogeneous ideal 平凡齐次理想trivial knot 平凡纽结trivial solution 平凡解trivial subset 平凡子集trivial topology 密着拓扑trivial valuation 平凡赋值triviality 平凡性trivialization 平凡化trochoid 摆线trochoidal 余摆线的trochoidal curve 摆线true error 真误差true formula 真公式true proposition 真命题true sign 直符号true value 真值truncated cone 截锥truncated cylinder 截柱truncated distribution 截尾分布truncated pyramid 截棱锥truncated sample 截样本truncated sequence 截序列truncation 舍位truncation error 舍位误差truncation point 舍位点truth 真值truth function 真值函项truth matrix 真值表truth set 真值集合truth symbol 真符号truth table 真值表truthvalue 真值tube 管tubular knot 管状纽结tubular neighborhood 管状邻域tubular surface 管状曲面turbulence 湍流turbulent 湍聊turing computability 图灵机可计算性turing computable 图灵机可计算的turing machine 图录机turn 转向turning point 转向点twice 再次twice differentiable function 二次可微函数twin primes 素数对twisted curve 空间曲线twisted torus 挠环面two address 二地址的two address code 二地址代码two address instruction 二地址指令two body problem 二体问题two decision problem 二判定问题two digit 二位的two dimensional 二维的two dimensional laplace transformation 二重拉普拉斯变换two dimensional normal distribution 二元正态分布two dimensional quadric 二维二次曲面two dimensional vector space 二维向量空间two fold transitive group 双重可迁群two person game 两人对策two person zero sum game 二人零和对策two phase sampling 二相抽样法two place 二位的two point distribution 二点分布two point form 两点式two sample method 二样本法two sample problem 二样本问题two sample test 双样本检验two sheet 双叶的two sided condition 双边条件two sided decomposition 双边分解two sided divisor 双边因子two sided ideal 双边理想two sided inverse 双边逆元two sided module 双边模two sided neighborhood 双侧邻域two sided surface 双侧曲面two sided test 双侧检定two stage sampling 两阶段抽样法two termed expression 二项式two valued logic 二值逻辑two valued measure 二值测度two variable matrix 双变量矩阵two way array 二向分类two way classification 二向分类twopoint boundary value problem 两点边值问题type 型type problem 类型问题typenumber 型数typical mean 典型平均。

AutoCAD中所有英语词汇的翻译,⽅便类起名英⽂词汇⼤陆词汇台湾词汇2D Solid ⼆维实体 2D 实⾯2D Wireframe ⼆维线框3D Array 三维阵列 3D 阵列3D Dynamic View 三维动态观察 3D 动态检视3d objects 三维物体 3D 物件3D Orbit 三维轨道 3D 动态3D Orbit 三维动态观察 3D 动态3D Studio 3D Studio 3D Studio3D Viewpoint 三维视点 3D 检视点3dpoly 三维多段线 3D 聚合线3dsin 3DS 输⼊ 3D 实体汇⼊3DSolid 三维实体 3D 实体3dsout 3DS 输出 3D 实体汇出abort 放弃中断abort 中断中断absolute coordinates 绝对坐标绝对座标abut 邻接相邻accelerator key 加速键快速键access 获取存取acisin ACIS 输⼊ ACIS 汇⼊acisout ACIS 输出 ACIS 汇出action 操作动作active 活动（的）作⽤中adaptive sampling ⾃适应采样最适取样add 添加加⼊Add a Printer 添加打印机新增印表机Add mode 添加模式Add Plot Style Table 添加打印样式表Add Plot Style Table 添加打印样式表Add Plotter 添加打印机Add Plotter 添加打印机Add to Favorites 添加到收藏夹加⼊我的最爱ADI ADI(Autodesk 设备接⼝) ADI (Autodesk 设备介⾯)adjacent 相邻相邻Adjust 调整调整Adjust Area fill 调整区域填充调整区域填满AdLM (Autodesk License Manager) AdLM（Autodesk 许可管理器）Administration dialog box 管理对话框管理对话⽅块Advanced Setup Wizard ⾼级设置向导进阶安装精灵Aerial View 鸟瞰视图鸟瞰视景affine calibration 仿射校准关系校正alert 警告警⽰alias 别名别名aliasing ⾛样锯齿化align 对齐对齐aligned dimension 对齐标注对齐式标注alignment 对齐(⽅式) 对齐allocate 分配配置Altitude 标⾼⾼度ambient color 环境⾊环境颜⾊ambient light 环境光环境光源angular dimension ⾓度标注⾓度标注angular unit ⾓度单位⾓度单位annotation 注释注解anonymous block ⽆名块匿名图块anti-aliasing 反⾛样消除锯齿aperture 靶框锁点框apparent intersections 外观交点外观交点append 附加附加Application key 授权申请号应⽤程式码appload 加载应⽤程序载⼊应⽤程式Apply 应⽤/申请套⽤approximation points 近似点近似点arc 圆弧弧Architectual Ticks 建筑标记建筑斜线area 区域,⾯积区域 ,⾯积Argument 参数引数Arrange icons 排列图标排列图⽰array 阵列阵列arrowhead 箭头箭头ASCII ASCII （美国标准信息交换码） ASCIIaseadmin ASE 管理 ASE 管理aseexport ASE 输出 ASE 汇出aselinks ASE 链接 ASE 连结aserows ASE ⾏ ASE 列aseselect ASE 选择 ASE 选取asesqled SQL 编辑 ASE SQL 编辑器Aspect 纵横向间距纵横向间距aspect ratio 宽⾼⽐纵横⽐assign 指定指定Assist 助理辅助associative dimension 关联标注关联式标注associative hatches 关联填充关联式剖⾯线attach v.附着贴附attdef 属性定义属性定义attdisp 属性显⽰属性显⽰attedit 属性编辑属性编辑attenuation 衰减衰减attenuation of light 灯光衰减光源衰减attext 属性提取属性萃取attredef 属性重定义属性重新定义attribute definition 属性定义属性定义Attribute Display 属性显⽰属性显⽰attribute extraction file 属性提取⽂件属性萃取档attribute extraction template file 属性提取样板⽂件属性萃取样板档attribute prompt 属性提⽰属性提⽰attribute tag 属性标签属性标签attribute value 属性值属性值audit 核查检核authorization code 授权码授权码AutoCAD library search path AutoCAD 库搜索路径 AutoCAD 资源库搜寻路径autocommit ⾃动提交⾃动确定AutoTrack ⾃动追踪⾃动追踪axis tripod 三轴架三向轴azimuth ⽅位⾓⽅位Back Clipping On 后向剪裁打开back view 后视图後视景background color 背景⾊背景颜⾊backup 备份备份Backward 反向左右反向bad 不正确的不正确base 基点基准,底端,底部base dimension 基准标注基线式标注base grips 基夹点基准掣点base point 基点基准点baseline 基线基准线基线式baseline dimension 基线标注基线式标注Basic color 基本⾊基本颜⾊batch plotting 批处理打印批次出图beam angles of spotlights 聚光灯光束⾓度点光源光线⾓度Beep on Error 出错报警错误时发出哔声bevel 倒⾓斜切bevel 倒⾓斜切beveling objects 斜⾓对象斜切物件Bezier curve Bezier 曲线 Bezier 曲线Big Font ⼤字体⼤字体bind 绑定并⼊bitmap 位图点阵图blend 合成混成blipmode 点标记模式点记模式block 块图块block definition 块定义图块定义block reference 块参照图块参考block table 块表图块表格bmpout BMP 输出 BMP 汇出body 体主体Boolean operation 布尔运算布林运算borders 边框图框bottom view 仰视图下视景boundary 边界边界boundary sets 边界集边界集bounding 边（框）边界框break (v.) 打断切断Bring Above Object 置于对象之上置於物件上⽅Bring to Top 顶置置於最上⽅brower 浏览器浏览器built-in 内置的内建bulge 凸度凸度bump map 凹凸贴图凸纹贴图button menu 按钮菜单按钮功能表BYBLOCK 随块 BYBLOCKBYLAYER 随层 BYLAYERbyte 字节位元组cabling 电缆布线配线cal 计算器校正calibrate 校准校正call 调⽤呼叫callback 回调(for LISP) 回覆callback 回叫回覆camera 相机照相机camera angle 相机⾓度相机⾓度Cancel 取消取消cap 封⼝封⼝cascade 层叠（的）重叠排列case （⼤⼩）写⼤⼩写cast 投射投射catalog ⽬录⽬录cell 单元储存格Center 圆⼼中⼼center mark 圆⼼标记中⼼点标记centerline 中⼼线中⼼线centroid 形⼼,质⼼矩⼼chamfer 倒⾓倒⾓change 修改变更character 字符字元Check 检查检查Check Box 复选框勾选框Check Spelling 拼写检查拼字检查child dimension style 下级标注样式⼦标注型式chord 弦翼弦chprop 修改特性变更性质circle 圆圆circular external reference 循环外部参照循环外部参考Circumference 圆周圆周class 类等级, 类别clause ⼦句⼦句Clean 清除清理Clean 清除清理clear 清除清除client 客户机⽤户端clip 剪裁截取Clipboard 剪贴板剪贴簿clipping boundaries 剪裁边界截取边界clipping planes 剪裁平⾯截取平⾯Close 闭合关闭(⽤於档案),闭合(⽤於边界,线,⾯域) cluster 组丛集code pages 代码页字码页color 颜⾊著⾊color depth 颜⾊深度颜⾊深度color map ⾊表颜⾊对映Color Wheel 颜⾊轮盘⾊轮color-dependent 颜⾊相关Color-Dependent Plot Style Table 颜⾊相关打印样式表column 列栏 (for database)combine 结合结合comma 逗号逗号command history 命令历史指令历程command line 命令⾏指令⾏command window 命令窗⼝指令视窗comment 注释注解commit 提交确定Compatibility 兼容性相容性compile 编译编译complex solids 复杂实体复杂实体component 分量元件Component 部件元件composite regions 组合⾯域复合⾯域composite tolerances 混合公差复合公差compound documents 合成⽂档复合⽂件cone 圆锥⾯圆锥体config 配置规划configuration 配置规划conic 圆锥曲线圆锥形的Constant 常量常数Construction Line 构造线建构线containers 容器容器Content Explorer 内容管理器内容浏览器Content Explorer 内容管理器内容浏览器contents 内容内容,⽬录context 环境上下⽂continuation 顺序连续性Continue 继续继续,延续Continue 继续继续,延续continue dimension 连续标注连续式标注contour lines 轮廓线等⾼线contrast 对⽐度对⽐contrast 对⽐度对⽐control (n.)控件控制coordinate filters 坐标过滤器座标过滤器coordinate system 坐标系座标系统coplanar 同⼀平⾯的共平⾯copy 副本复制,复本Copy Hyperlink 复制超级链接复制超级连结copyclip 复制剪贴复制截取copyhist 复制历史复制历程copylink 复制链接复制连结Corner ⾓点⾓点corner joint ⾓点转⾓接点correct v. 更正正确corrupt 毁损损坏create 创建建⽴Create Layout 创建布局criteria 条件准则criteria 条件准则Crop 修剪切齐crosshair ⼗字光标⼗字游标crossing 窗交框选crossing polygon 交叉多边形多边形框选crossing window 交叉窗⼝窗选cube ⽴⽅体⽴⽅体Cubic 三次三次,⽴⽅Current UCS 当前 UCS ⽬前的 UCSCurrent UCS 当前 UCS ⽬前的 UCScursor 游标游标cursor menu 光标菜单游标功能表curve 曲线曲线custom ⾃定义⾃订Custom installation ⾃定义安装⾃订安装Customize Menus ⾃定义菜单⾃订功能表Customize Menus ⾃定义菜单⾃订功能表Cut 剪切剪下cutclip 剪切剪下截取cylinder 圆柱体圆柱体cylindrical coordinate 柱坐标圆柱体座标dangle 不固定的悬挂Dark Color 暗⾊暗⾊dash 虚线虚线data integrity 数据完整性资料完整性database 数据库资料库datum 基准基准⾯datum axis 基准轴基准轴datum dimension 基准标注基准标注datum identifier 基准标识基准识别字datum reference frames 基准参考框架基准参考框datum reference letters 基准参考字母基准参考⽂字dbConnect 数据库连接资料库连结dbConnect Manager 数据库连接管理器dblist 数据库列表资料库列⽰DBMS drivers DBMS 驱动资料库管理系统 (DBMS)ddattdef 属性定义对话框动态属性定义ddatte 属性编辑对话框动态属性编辑ddattext 属性提取对话框动态属性萃取ddcolor 颜⾊对话框动态颜⾊设定ddedit ⽂字编辑对话框编辑⽂字与属性定义ddgrips 夹点对话框动态掣点设定ddim 标注设置对话框标注设定ddinsert 插⼊对话框图块插⼊ddmodify 图元编辑对话框动态修改ddptype 点类型对话框点型式ddrename 重命名对话框动态更名ddrmodes 绘图模式对话框绘图设定ddselect 对象选择对话框动态选取设定dducs UCS 对话框动态 UCS 设定dducsp UCS ⽅向对话框动态 UCS 预设ddunits 单位对话框动态单位设定ddview 视图对话框动态视景ddvpoint 视点对话框动态检视点deactivate 释放停⽤dealer 经销商经销商decal effect 修剪效果除去杂质效果decimal dimensions ⼗进制标注⼗进位标注decurve ⾮曲线化直线化default 缺省预设值,预设default drawing 缺省图形预设图⾯default drawing 缺省图形预设图⾯definition point 定义点定义点Degenerate 退化退化delay 延迟延迟delete 删除删除DELta 增量差值demand loading 按需加载应要求载⼊dependent symbols 依赖符号deployment 展开布署Depth Map 深度贴图深度贴图derive 导出导出description 说明描述Design Center 设计中⼼设计中⼼detach 拆离分离Detection 检测侦测deviation 极限偏差偏差deviation tolerances 极限公差偏差公差device 设备设备device 设备设备Device and Default Selection 设备和默认选择设备和预设值选取Dia 直径直径diameter 直径（标注）直径dictionary 词典字典diffuse color 漫射⾊漫射颜⾊digitizer 数字化仪数位板digitizing puck 数字化仪游标数位化指向器digitizing puck 数字化仪游标数位化指向器dim 标注标注dimaligned 对齐标注对齐式标注dimangular ⾓度标注⾓度标注dimbaseline 标注基线基线式标注dimcenter 圆⼼标注中⼼点标注dimcontinue 连续标注连续式标注dimdiameter 直径标注直径标注dimedit 标注编辑标注编辑dimension 标注标注dimension definition points 标注定义点标注定义点dimension format 标注格式标注格式dimension geometry 构成要素标注⼏何dimension line arc 尺⼨线圆弧标注线弧dimension properties 标注特性标注性质dimension scale 标注⽐例标注⽐例dimension style 标注样式标注型式dimension style families 标注样式族标注型式家族dimension style name 标注样式名标注型式名称dimension style overrides 标注样式替代标注型式取代dimension text 标注⽂字标注⽂字dimension units 标注单位标注单位dimension variables 标注变量标注变数dimlinear 线性标注线性标注dimordinate 坐标标注座标式标注dimoverride 标注替代标注取代dimradius 半径标注半径标注dimstyle 标注样式标注型式dimtedit 标注⽂字编辑标注⽂字编辑Direct Hatch 直接填充直接剖⾯Direction Control ⽅向控制⽅向控制Directory ⽬录⽬录Disable 禁⽤取消,停⽤discard 放弃舍弃Discontinued 停⽌使⽤的取消,停⽤dish 下半球⾯圆碟disk space 磁盘空间磁碟空间displacement point 位移点位移点display 显⽰显⽰器, 显⽰, 显⽰画⾯Display Order 显⽰次序显⽰顺序dist 距离距离distant light 平⾏光远光源distributing 分布分散式dithering 抖动递⾊diverge 分散的分散的Divide 等分等分divide 等分等分Division 等分分割,除法dock(undock) 固定（浮动）固定document ⽂档⽂件dome 上半球⾯圆顶donut 园环环Draft 草图草图drafting standards 绘图标准制图标准drafting techniques 绘图技术制图技巧drag and drop 拖放拖放draw 绘制/绘图 (如果后⾯未接宾语) 绘图drawing 图形图⾯,图档Drawing Aids 绘图辅助⼯具绘图辅助drawing area 绘图区域绘图区drawing boundaries 图形边界图⾯边界drawing browser 图形浏览器图⾯浏览器drawing database 图形数据库图形资料库drawing environment 图形环境绘图环境drawing extents 图形范围图⾯实际范围drawing file 图形⽂件图档drawing limits 图形界限图⾯范围drawing order 图形次序绘图顺序drawing project 图形项⽬绘图专案drawing scale 图形⽐例图⾯⽐例drawing standard 图形标准图⾯标准drawing status 图形状态图⾯状态drawing time 绘图时间绘图时间drawing units 图形单位图⾯单位driver 驱动程序驱动程式Dropdown List 下拉列表下拉式列⽰dsviewer 鸟瞰视图鸟瞰视景dtext 动态⽂本动态⽂字dump 转储倾出duplicate 重复重复的duplicating 复制复制dview 动态观察动态检视dxbin DXB输⼊ DXB 汇⼊dxfin DXF输⼊ DXF 汇⼊dxfout DXF输出 DXF 汇出Dynamic 动态动态Dynamic Dragging 动态拖动动态拖曳Dynamic Update 动态更新动态更新dynamic viewing 动态观察动态检视dynamic zooming 动态缩放动态缩放edge 边边缘Edge Surface 边界曲⾯边缘曲⾯edgesurf 边界曲⾯边缘曲⾯editor 编辑器编辑器EDUCATION VERSION 教学版教育版effect 效果效果Element 元素元素elev 标⾼⾼程elevation 标⾼⾼程ellipse 椭圆椭圆embed 内嵌，嵌⼊嵌⼊Encapsulated 封装 See also "EPS" 压缩end 端点结束,终点end angle 端点⾓度结束⾓度end tangent 端点切向结束切点end width 端点宽度结束宽度Ending 终⽌端点English units 英制单位英制ENTER ENTER（输⼊）输⼊entity 图元元件 . 图元entry 条⽬资料项environment 环境环境environment variable 环境变量环境变数equation ⽅程式⽅程式erase 删除删除existing 现有的既有的Exit 退出结束export 输出汇出expression 表达式表⽰式extend 扩展延伸extend 延伸，超出量（⽤于标注）延伸extension line 尺⼨界线延伸线Extent(s) 范围实际范围external data 外部数据外部资料external database 外部数据库外部资料库External Reference 外部参照外部参考Extract 选集萃取extrude 拉伸挤出face ⾯⾯facet 镶嵌⾯产⽣刻⾯factor 因⼦(see Scale Factor) 系数fade 褪⾊度渐层falloff angle 收缩⾓衰退⾓度Fast Zoom mode 快速缩放模式快速缩放模式fatal 致命错误致命错误Favorites 收藏夹我的最爱Favorites 收藏夹我的最爱feature 功能/（⼏何）特征特徵fence 栏选 (See also Selection fence) 篱选field 字段栏位file ⽂件档案fill 填充填实Filled Text 填充⽂字⽂字填实(⽤於填实线条、实体或实⾯) Filmroll Filmroll 胶卷filter 过滤器过滤器find 查找寻找⼯具finish 完成修饰finish 修饰（for render only) 修饰fit ⾃适应设置布满（⽤於预览时，布满视窗或图纸）fit points 拟合点拟合点flag 标志旗标Flat Shaded, Edges on 带边框平淡着⾊flat-shaded （平淡）着⾊floating viewports 浮动视⼝浮动视埠flood 布满⼤量Flyout Properties 弹出特性对话框图⽰列性质fog 雾雾fold 折叠摺痕Follow 跟随⾃动平⾯视景font 字体字体font map file 字体映射⽂件字体对映档form tolerance 形状公差成型公差formatting text 设置⽂字格式格式化⽂字frame 框架画格frame 帧画格frame 边框画格free-form ⾃由形式（的）⾃由形式freehand line 徒⼿画线⼿绘线Freeplotting ⾃由绘图⾃由出图freeze 冻结冻结freezing layers 冻结图层冻结图层From ⾃⾃Front Clipping On 前向剪裁打开front view 主视图前视景Full Preview 全视⼝预览完整预览General 基本⼀般generate ⽣成产⽣geometric characteristic symbols ⼏何特性⼏何特性符号Geometric Tolerance 形位公差⼏何公差geometry ⼏何图形⼏何图形global 全局（的）整体Gouraud renderings Gouraud Gouraud 着⾊ Gouraud 彩现Gradient 百分度渐层Grads 百分度分度graphic area 图形区图形区graphics cursor 图形光标图形游标graphics screen 图形屏图形萤幕graphics window 图形窗⼝图形视窗graphscr 图形屏图形萤幕gray 灰度灰阶grid ⽹格格点grid ⽹格,栅格格点grid mode 栅格模式格点模式grip 夹点掣点group 编组群组group code 组码群组码Haltftoning 半⾊调半⾊调handle 句柄处理码 (⽤於性质对话⽅块)handshaking 握⼿信号交握Hardcopy 硬拷贝硬体复制,硬本hardware linetype 硬件线型硬体线型hardware lock 保密锁硬体锁hardware requirement 硬件需求硬体需求hatch 图案填充剖⾯线hatch areas 填充区域剖⾯区域hatch boundaries 填充边界剖⾯边界hatch pattern 填充图案剖⾯线样式hatch styles 填充样式剖⾯样式hatchedit 填充编辑剖⾯线编辑Heads-up Design 轻松设计抬头设计Height ⾼度⾼度help 帮助说明Hidden Line 隐藏线隐藏线hidden-line image 消隐图像隐藏线影像hide 隐藏(adj.) 隐藏hide 消隐(v.) 隐藏hideplot 消隐出图隐藏出图highlight 突出显⽰亮显highlight 亮光 (for the color of 3D object) 亮显HIGHLIGHT 亮显亮显home page 主页⾸页home position 起始位置归位点hook line 钩线钩线hotspot 聚光⾓聚光点Hyperlink 超级链接超连结Icon 图标图⽰Identifier 标识符识别字IGES (International Graphics Exchange Specification) 初始图形交换标准基本图形交换规格Ignore 忽略忽略image 图像影像implement 实现实施import 输⼊汇⼊Imprint 压印盖印Imprint 压印盖印included angle 包含⾓夹⾓infinite lines ⽆限长线⽆限长直线information 信息资讯Inherit Properties 继承特性继承性质initial environment 初始环境初始环境Initialize 初始化起始设定in-place 在位现地inquiry 查询查询inscribed polygons 内接正多边形内接多边形insert 插⼊插⼊Insertion 插⼊点插⼊点insertobj 插⼊对象插⼊物件instance 引⽤实例Instruction 指⽰指⽰integer 整数整数IntelliMouse 智能⿏标智慧型滑⿏IntelliMouse 智能⿏标智慧型滑⿏Intensity 强度强度interactive 交互的互动式Interchange 互换交替interface 介⾯介⾯interfere ⼲涉⼲涉Interference ⼲涉⼲涉Interference ⼲涉⼲涉interlace 隔⾏交错internal 内部的内部Internet Utilities Internet应⽤程序⽹际⽹路公⽤程式interpolation points 插值点内插点intersect 交集交集interval 间距/间隔间隔时间Invalid ⽆效（的）⽆效inverse linear attenuation of light 线性衰减光线的线性反⽐衰减inverse square attenuation of light 平⽅衰减光线的平⽅反⽐衰减Invisible 不可见不可见invoke 调⽤呼叫island 孤岛孤⽴物件Island detection 孤岛检测侦测孤⽴物件ISO (International Standards Organization) ISO(国际标准化组织) ISO Isolation levels 隔离级别隔离层次isoline 素线等⾓线isometric 等轴测等⾓isometric snap style 等轴测捕捉样式等⾓锁点型式isometric view 等轴测视图等⾓视景isoplane 等轴测平⾯等⾓平⾯ISOPLANE 等轴测平⾯等⾓平⾯Italic 斜体斜体iterator 枚举器重述⼦join 合并结合joint 连接接合线Justification 对正对正⽅式justify 对正对正key 主键主键key n.名称主键knot vector 节点⽮量要点向量label 标签标签landscape 横向横式Landscape 配景，风景,if used for "landscape object" etc. 横式Landscape Edit 编辑配景Landscape Library 配景库景物图库lateral tolerance symbol 尺⼨公差符号侧向公差符号layer index 图层索引图层索引Layout 布局配置Layout from Template 来⾃样板的布局Layout from Template 来⾃样板的布局Layout Wizard 布局向导leader 引线引线Leading 前导前导Learning Assistance 学习助⼿学习助理Left View 左视图左视景legacy 传统旧式length 长度长度lengthen 拉长调整长度Lens Length 镜头长度镜头长度License Agreement 许可协议授权合约license key 许可证号授权码License Manager 许可管理器授权管理员License Server 许可服务器授权伺服器licenses 授权授权light 光源光源light color 浅⾊ (for RAMT-wood ) 亮⾊Light Color 暖⾊亮⾊lighting 照明效果照明Lightness 亮度亮度limits 图形界限范围,图⾯范围line ⾏线line 直线线line font 线型线字体line object 线性对象线物件line segment 线段线段line width 线宽线宽Linear Dimension 线性标注线性标注linetype 线型线型Lineweight 线宽线宽link 链接连结list 表串列list 列表串列list box 列表框列⽰框List Files ⽂件列表load 加载载⼊locale 局部本地location ⽹址(for Internet) 位置location 位置(for file and directory) 位置locked 锁定锁护locked layer 锁定图层锁护图层logfileoff 关闭⽇志⽂件关闭记录档logfileon 打开⽇志⽂件开启记录档logical 逻辑逻辑的long file name 长⽂件名长档名loop 环回路ltscale 线型⽐例线型⽐例LTSCALE 线型⽐例线型⽐例Ltype 线型线型lump 块⼩块magnet 磁吸磁铁magnification （缩放）⽐例倍率magnifying glass 放⼤镜放⼤境main window 主窗⼝主视窗major axis 长轴长轴Make 新建制作Make 建⽴制作malformed 有缺陷畸形的Manipulate 操作管理Manipulate 操作管理Manufacture 制造商制造商mapper 贴图贴图mapping 贴图贴图,对映marble ⼤理⽯⼤理⽯mark 标记标记massprop 质量特性质量性质match 匹配相符material condition 包容条件材质条件material condition symbols 包容条件符号材质条件符号Materials 材质对话框材质Materials Library 材质库材质库matlib 材质库材质库measure 测量测量measure 等距等分（菜单内容）测量Measurement 测量单位测量结果MEASUREMENT 在图形中设置测量值测量结果member 成员成员memory 内存记忆体menu 菜单功能表menu bar 菜单栏功能表列menuload 加载菜单⾃订功能表Merge 合并合并message 信息讯息metafile 图元⽂件中继档Method ⽅法⽅法 (⽤於物件导向程式观念)Middle 中央点中央Middle Center 正中点正中Midpoint 中点中点minsert 多重插⼊插⼊图块阵列mirror 镜像镜射mirror line 镜像射线镜射线mirror3d 三维镜像 3 D 镜射Miscellaneous File Names 其他⽂件名其它档名Miter 斜接斜接mledit 多线编辑复线编辑mline 多线复线mlstyle 多线样式复线型式mode 模式模式model 型号模型model 型号模型model (v)建模，(n)模型模型model space 模型空间模型空间Modification 修改修改monitor resolution 显⽰器分辨率萤幕解析度monochrome 单⾊（的）单⾊mouse ⿏标滑⿏move 移动移动mslide 制作幻灯制作幻灯⽚mspace 模型空间模型空间mtext 多⾏⽂字多⾏⽂字Multiline 多线⽐例复线multiline scale 多线⽐例复线⽐例Multiline Style 多线样式复线型式mview ⽣成视⼝多重视埠mvsetup 设置图纸规格多重视埠设定named object 命名对象具名物件named plot style table 命名的打印样式表具名的出图型式表Named UCS 命名 UCS 具名 UCSnamed view 命名视图具名的视景NE Isometric 东北等轴测东北等⾓NE Isometric 东北等轴测东北等⾓Nearest 最近点最近点nested 嵌套巢状式nested blocks 嵌套块巢状式图块new 新建开新档案new 新的开新档案New Layout 新建布局New Layout 新建布局NURB surfaces NURBS（⾮⼀致有理 B 样条曲线） NURBS 曲⾯NW Isometric 西北等轴测西北等⾓NW Isometric 西北等轴测西北等⾓object 对象物件Object Properties 对象特性物件性质Object Properties Manager 对象特性管理器物件性质管理员Object Snap 对象捕捉物件锁点object snap override 对象捕捉覆盖物件锁点取代Object Snap Setting 对象捕捉设置objects 对象物件Oblique 斜尺⼨界线倾斜obsolete 废弃旧式ODBC database ODBC数据库 ODBC 资料库offset 偏移偏移OLE OLE（对象链接和嵌⼊）物件连接与嵌⼊ (OLE)olelinks OLE链接 OLE 连结online help 联机帮助线上说明online manuals 联机⼿册线上⼿册oops 恢复取消删除opacity map 不透明贴图不透明贴图open 打开开启 (⼤部分⽤於档案)open 打开(的) 开启 (⼤部分⽤於档案)OPM(Object Property Manager) 对象特性管理器Optimization 优化最佳化option 选项选项Orbit 轨道动态, 动态检视Ordinate 坐标标注座标式orientation ⽅向⽅位origin 原点（对于坐标系）原点origin 原始位置(used for external Datebase) 原点origin 起点（对于尺⼨界线和标注）原点ortho 正交正交Ortho mode 正交模式正交模式orthogonal 正交正交的orthographic 正交正投影osnap 对象捕捉物件锁点outside 外部的外侧 (⽤於⽂字位置)overall dimension scale 全局⽐例整体标注⽐例overflow 溢出⾼溢 (相对於 underflow),溢位overlay 覆盖覆叠overline 上划线顶线override 忽略 - For common sentences 取代override 替代 - For dimension 取代overwrite 覆盖取代Palette 控制板选盘Palette 调⾊板选盘pane 窗格窗格paper space 图纸空间图纸空间parameter 参数参数parent dimension style 上级标注样式⽗系标注型式parse 分析分析Partial 部分局部Partial Load 部分加载局部载⼊Partial Load 部分加载局部载⼊password ⼝令密码Paste Special 选择性粘贴选择性贴上pasteclip 粘贴贴上截取pastespec 选择性粘贴选择性贴上path 路径路径pattern ⽅式 for "file search pattern" 样式pattern 图案 for hatch pattern, line pattern, etc. 样式pedit 多段线编辑聚合线编辑pen plotters 笔式绘图仪笔式绘图机pen speed 笔速笔速pen width 笔宽笔宽Perfomance 性能效能perimeter 周长周长personalization 个⼈化个⼈化pface 复合⾯聚合⾯Phong shading Phong 着⾊描影Photo Raytrace renderer 照⽚级光线跟踪渲染光线追踪相⽚彩现Photo Real renderer 照⽚级真实感渲染真实相⽚彩现photo realistic rendering 照⽚级真实感渲染相⽚质感彩现pick button 拾取键点选钮pickbox 拾取框点选框PICKFIRST 选择优先先点选picture 图⽚图⽚pixel 像素像素placeholder 占位符定位器plan 平⾯图平⾯plan view 平⾯视图平⾯视景planar projection 平⾯投影平⾯投影pline 多段线聚合线plot 打印出图Plot Configuration 打印配置出图规划plot files 打印⽂件出图档plot rotation 打印旋转出图旋转plot spooling 打印假脱机出图伫列Plot Style Manager 打印样式管理器plot style table 打印样式表出图型式表plotter 绘图仪绘图机plotter linetype 绘图仪线型绘图机线型Plotter Manager 打印机管理器Point Filters 点过滤点过滤器point marker 点标记点标记Point Sample 点采样取样点Point Style 点样式点型式pointer 指针指标pointing device 定点设备指向设备polar array 环形阵列环形阵列polar coordinate 极坐标极座标polar tracking 极轴追踪极座标追踪polar tracking 极轴追踪极座标追踪polyface meshes 多⾯⽹格聚合⾯⽹⾯polygon 正多边形多边形polygon 多边形多边形polygon meshes 多边形⽹格多边形⽹⾯polygon window 多边形窗⼝多边形视窗polygonal clipping boundaries 多边形剪切边界多边形截取边界polyline 多段线聚合线polyline clipping boundaries 多段线裁剪边界聚合线截取边界polyline segments 多段线线段聚合线线段polymesh 多边形⽹格聚合⽹⾯Popup List 弹出列表弹出列⽰port 端⼝埠Portrait 肖像直式Portrait 纵向，if used for paper layout 直式positional tolerances 位置公差位置公差precision 精度精确度predefine 预定义事先定义的preferences 系统配置环境设定Preferences dialog box 系统配置对话框「环境设定」对话⽅块preview 打印预览预览primitive 原型基本原件Priority 优先级优先权priviledge 特权专⽤权Procedural material 过程化材质程序材质process 处理程序Profile 配置/剖⾯(图) 轮廓program (v.) 编程程式Projected tolerance zone 投影公差带投影公差区Projected tolerances 投影公差投影公差prompt 提⽰提⽰Properties 特性内容Property painter 特性刷性质复制器Protocal 协议通讯协定prototype 原型原型proxy 代理代理proxy fonts 代理字体代理字型pull down menu 下拉菜单下拉功能表purge 清理清除pyramid 棱锥⾯三⾓锥体QDIM 快速标注快速标注qsave 快存快速存档qtext 快速⽂字快速⽂字Quadratic ⼆次⼆次quality 质量品质Quick Tour 快速指南快速导览radian 弧度弪度Radio Button 单选钮圆钮radius 半径半径raster file format 光栅⽂件格式⽹格档案格式Raster Image 光栅图像⽹格式影像raster image boundaries 光栅图像边界⽹格式影像边界ray 射线射线, 光线Ray Casting 射线法raytraced renderer 光线跟踪渲染光线追踪彩现raytraced shadows 光线跟踪阴影光线追踪阴影read 读取读取Realtime 实时即时模式recover 恢复修复recover 修复修复rectang 矩形矩形recursion 递归递回Redefine 重定义重新定义redo 重做重做redraw 重画重绘redrawall 全重画全部重绘reference 引⽤参考reference 参照参考reference angles 参考⾓参考⾓度reference point 参考点参考点refine 精度控制精细化reflection color 反射⾊反射⾊reflection mapping 反射贴图反射贴图refractive index 折射指数折射系数refresh 刷新更新regen 重⽣成重⽣regenall 全重⽣成全部重⽣regenauto ⾃动重⽣成⾃动重⽣regenerate 重⽣成重⽣regeneration 重⽣成重⽣region ⾯域⾯域registry 注册表登录reinit 重初始化重新起始设定reinstall 重新安装重新安装relative angles 相对⾓相对⾓度relative coordinates 相对坐标相对座标release 版本版本Reload 重载重新载⼊remove 删除移除rename 重命名更名rename 重命名更名render 渲染彩现renderer 渲染程序彩现程式Replace 替换取代replay 重放重播Requirement 需求需求reset 重置重设resizing 改变⼤⼩重新调整尺⼨resolution 融⼊解析度resolution 分辨率解析度restore 恢复取回resume 恢复执⾏继续执⾏Retain 保留保留return button 回车键 Enter 键revert 复原恢复原状revolve 旋转回转revsurf 旋转曲⾯回转曲⾯ridge 棱脊线Right-Angle 直⾓直⾓rmat 材质彩现材质rollback 回卷溯回root point 原点根点rotate 旋转旋转rotate3d 三维旋转旋转 3ＤRotation 旋转旋转routine 例⾏程序常式Rows dialog box “⾏”对话框列对话⽅块rpref 渲染选项彩现环境设定rscript 重复执⾏重新执⾏脚本rubber-band line 拖引线伸缩线rulesurf 直纹曲⾯规则曲⾯Run Script 运⾏脚本执⾏脚本running object snap 执⾏对象捕捉常驻式「物件锁点」running override 整体替代整体取代runout 跳动偏转度sample 样例取样Saturation 饱和度饱和度save 保存储存Save back 存回回存saveas 另存为另存新档saveimg 保存图像储存影像scale ⽐例缩放，（缩放）⽐例 if used as noun 调整⽐例, ⽐例scale factor ⽐例因⼦⽐例系数Scaled to Fit 按图纸空间缩放调整⽐例到布满scan 扫描扫描Scatter 散布图散量scene 场景场景schema 模式纲要schema 模式纲要screen 屏幕萤幕script 脚本脚本script files 脚本⽂件脚本档scroll bar 滚动条卷动轴SDI(MDI) 单⽂档界⾯(多⽂档界⾯)SE Isometric 东南等轴测东南等⾓SE Isometric 东南等轴测东南等⾓Search for Help on 搜索帮助寻找辅助说明主题section 区域，部分，节（相对于章节）剖⾯section 切割剖⾯section 截⾯剖⾯see 参见参阅segment 段，线段区段, 线段select 选择选取select all 全部选择全选Select object 对象选择选取物件selectable 可选择的可选取selection 选择集，选择选取,选项 (作名词⽤) selection sets 选择集选集Separate 分割分隔,个别的Separate 分割分隔,个别的Serial number 序列号序号session 任务阶段作业set 设置(v)，集合(n) 设定setting 设置设定shade 着⾊，灰度(⽤于单⾊ Gray ) 描影shader 着⾊程序描影程式shadow map 阴影贴图阴影贴图shape 形造型Sharpness 尖锐度鲜明度sheet 表，板(for ACIS only) 图纸Shell 抽壳薄壳shell SHELL 薄壳Shell 抽壳薄壳shortcut 快捷键快显show 显⽰展⽰Silhouette 轮廓剪影Single Face 单⼀表⾯单⾯single-pen plotter 单笔式绘图仪单笔绘图机size 数⽬尺⼨sizing 调整⼤⼩调整尺⼨sketch 徒⼿画徒⼿描绘slice 剖切⾯(as n.) 切割⾯slice 剖切切割⾯slide 幻灯⽚幻灯⽚slide libraries 幻灯库幻灯⽚库smooth shading 平滑着⾊平滑描影smoothing angle 平滑⾓度平滑⾓度snap 捕捉锁点snap angle 捕捉⾓度锁点⾓度snap grid 捕捉栅格锁点格点Snap mode 捕捉模式锁点模式snap resolution 捕捉分辨率锁点解析度SnapTips 捕捉提⽰锁点提⽰solid 填充实体, 2D 实⾯solid (⼆维)填充/(三维)实体实体, 2D 实⾯Solid Fill 实体填充实⾯填实solid modeler 实体建模实体模型器solids 实体实体, 3D 实体sorting 排序排序source applications 源⽂件source point 源点来源点space 空间空间spacing 间距间距Special Edit 特定编辑特殊编辑specific 指定（的）特定的specific 特有的特定的specify 指定指定specular reflection 镜⾯反射（⾼光）镜⾯反射Spelling 拼写检查拼字sphere 球⾯圆球体spherical projection 球⾯投影球⾯投影spline 样条曲线云形线spline frame 样条曲线框架云形线架构splinedit 样条编辑云形线编辑。

三次样条插值cubicsplineinterpolation什么是三次样条插值 插值（interpolation）是在已知部分数据节点（knots）的情况下，求解经过这些已知点的曲线，然后根据得到的曲线进⾏未知位置点函数值预测的⽅法（未知点在上述已知点⾃变量范围内）。

样条(spline)是软尺(elastic ruler)的术语说法，在技术制图中，使⽤软尺连接两个相邻数据点，以达到连接曲线光滑的效果。

样条插值是⼀种分段多项式(piecewise polynomial)插值法。

数学上，曲线光滑需要在曲线上处处⼀阶导连续，因此，在节点处需要满⾜⼀阶导数相等。

另外，为了使得曲线的曲率最⼩，要求曲线⼆阶导连续【1】，在节点处需要⼆阶导相等。

三次及以上多项式可以满⾜节点处光滑和曲率最⼩要求，但是次数⾼的曲线容易震荡，因此，就选⽤三次多项式即可。

数学表述 假设有n个已知节点： 函数关系记为：。

在区间中插值多项式曲线：注意，这⾥头曲线为，尾曲线为。

插值在节点处满⾜条件： （1）曲线经过节点： （2）曲线⼀阶导连续（光滑）： （3）曲线⼆阶导连续（曲率最⼩）： 边界条件：对两端节点的约束。

（B1）⾃然(natural (or free))边界条件 （B2）固定(clamped)边界条件 固定⼀阶导数： , 固定⼆阶导数： , （B3）⾮节点边界(not-a-knot ) 要求在第⼆个节点和倒数第⼆个节点，曲线的三阶导也连续：三次多样式函数的计算 样条函数采⽤n-1个三次多项式，每个三次多项式有4个参数，⼀共是4n-4个参数，因此需要4n-4个⽅程。

条件（1）n-1个曲线每个两端经过节点，提供2（n-1）=2n-2个⽅程； 条件（2）n-1个曲线相邻⼀阶导连续，提供n-2个⽅程； 条件（3）n-1个曲线相邻⼆阶导连续，提供n-2个⽅程； 以上⼀共是4n-6个⽅程，还需要2个⽅程，这两个⽅程由边界条件提供，条件（B1）, （B2）, （B3）每个均提供2个⽅程，这样就凑够了4n-4个⽅程。

代数ALGEBRA1. 数论natural number 自然数positive number 正数negative number 负数odd integer, oddnumber 奇数even integer, even number 偶数integer, whole number 整数positivewhole number 正整数negative whole number 负整数consecutive number 连续整数real number, rational number 实数，有理数irrational (number) 无理数inverse 倒数composite number 合数e.g. 4,6,8,9,10,12,14,15 …prime number 质数 e.g. 2,3,5,7,11,13,15 … reciprocal 倒数common divisor 公约数multiple 倍数(minimum) common multiple ( 最小)公倍数(prime) factor (质)因子common factor 公因子ordinary scale, decimalscale 十进制nonnegative 非负的tens十位units个位mode众数mean 平均数median 中值common ratio公比2. 基本数学概念arithmetic mean 算术平均值weighted average 力口权平均值geometric mean 几何平均数exponent指数，幂base 乘幂的底数，底边cube 立方数，立方体square root 平方根cube root 立方根common logarithm常用对数digit 数字constant 常数variable 变量inverse function 反函数complementaryfunction 余函数linear 一次的，线性的factorization 因式分解absolute value绝对值，e.g. | -32 | =32 round off四舍五入数学3. 基本运算add , plus 力口subtract 减difference 差multiply, times 乘product 积divide除divisible可被整除的divided evenly被整除dividend被除数，红禾U divisor因子，除数，公约数quotient 商remainder 余数factorial 阶乘power 乘方radical sign, root sign 根号round to 四舍五入to the nearest 四舍五入4. 代数式，方程，不等式algebraic term 代数项like terms, similar terms 同类项numerical coefficient数字系数literal coefficient字母系数inequality不等式triangle inequality 三角不等式range值域original equation 原方程equivalent equation 同解方程，等价方程linear equation 线性方程(e.g.5x+6=22)5. 分数，小数proper fraction 真分数improper fraction 假分数mixed number 带分数vulgarfraction，common fraction 普通分数simple fraction 简分数complex fraction繁分数numerator 分子denominator 分母(least) common denominator (最小)公分母quarter四分之一decimal fraction 纯小数infinite decimal 无穷小数recurring decimal 循环小数tenths unit 十分位6. 集合union 并集proper subset 真子集solution set 解集7. 数列arithmetic progression(sequence) 等差数歹U geometric progression(sequence) 等比数歹U8. 其它approximate 近似（anti）clockwise （逆）顺时针方向cardinal 基数ordinal 序数directproportion 正比distinct 不同的estimation 估计，近似parentheses 括号proportion 比例permutation 排歹U combination 组合table 表格trigonometric function 三角函数unit 单位，位几何GEOMETRY1. 角alternate angle 内错角corresponding angle 同位角vertical angle 对顶角central angle圆心角interior angle 内角exterior angle 夕卜角supplementary angles 补角complementaryangle 余角adjacent angle 邻角acute angle 锐角obtuse angle 钝角right angle 直角round angle 周角straight angle 平角included angle 夹角2. 三角形equilateral triangle 等边三角形scalene triangle 不等边三角形isosceles triangle 等腰三角形right triangle 直角三角形oblique 斜三角形inscribed triangle 内接三角形3. 收敛的平面图形，除三角形外semicircle 半圆concentric circles 同心圆quadrilateral 四边形pentagon 五边形hexagon六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形polygon 多边形parallelogram 平行四边形equilateral 等边形plane 平面square 正方形，平方rectangle 长方形regular polygon 正多边形rhombus 菱形trapezoid 梯形4. 其它平面图形arc 弧line, straight line 直线line segment 线段parallel lines 平行线segment of acircle弧形5. 立体图形cube 立方体，立方数rectangular solid 长方体regular solid/regular polyhedron正多面体circular cylinder 圆柱体cone圆锥sphere 球体solid 立体的6. 图形的附属概念plane geometry 平面几何trigonometry 三角学bisect 平分circumscribe 夕卜切inscribe内切intersect 相交perpendicular 垂直Pythagorean theorem 勾股定理（毕达哥拉斯定理）congruent全等的multilateral 多边的altitude 高depth 深度side 边长circumference, perimeter周长radian 弧度surface area 表面积volume 体积arm 直角三角形的股cross section 横截面center of a circle 圆心chord 弦diameter 直径radius 半径angle bisector 角平分线diagonal 对角线化edge 棱face of a solid 立体的面hypotenuse 斜边included side 夹边leg三角形的直角边median （三角形的）中线base底边，底数（e.g. 2的5次方，2就是底数）opposite直角三角形中的对边midpoint 中点endpoint 端点vertex （复数形式vertices）顶点tangent 切线的transversal 截线intercept 截距7. 坐标coordinate system 坐标系rectangular coordinate 直角坐标系ordinate 纵坐标number line 数车由quadrant 象限slope 斜率origin 原点abscissa 横坐标complex plane 复平面。

interp1d 对应公式摘要：一、interp1d 函数简介- 导入interp1d 函数- 函数功能：一维插值- 函数形式：interp1d(x, y, kind="linear", fill_value=None,bounds_error=False, assume_sorted=False)二、函数参数详解1.x：插值点的横坐标，一维数组或列表2.y：插值点的纵坐标，一维数组或列表3.kind：插值函数的类型，可选值有"linear"（线性插值）、"nearest"（最近邻插值）、"next"（二次插值）和"spline"（三次样条插值）4.fill_value：插值中可能出现的缺失值，默认为None5.bounds_error：当插值点在定义域外时是否抛出异常，默认为False6.assume_sorted：假设输入的x 和y 值已经排序，默认为False三、interp1d 函数应用实例1.线性插值2.最近邻插值3.二次插值4.三次样条插值正文：在Python 的NumPy 库中，interp1d 函数可以用于一维插值。

它可以将给定的插值点（x, y）插值到新的横坐标上，得到新的纵坐标值。

下面我们来详细了解一下interp1d 函数的使用方法和参数。

首先，我们通过import numpy as np 来导入interp1d 函数。

然后，可以使用如下形式调用interp1d 函数：```pythoninterp_func = interp1d(x, y, kind="linear", fill_value=None, bounds_error=False, assume_sorted=False)```其中，x 和y 分别为插值点的横坐标和纵坐标，kind 表示插值函数的类型，默认值为"linear"（线性插值）。

插值（英文）InterpolationIn the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.In engineering and science one often has a number of data points, as obtained by sampling or experimentation, and tries to construct a function which closely fits those data points. This is called curve fitting or regression analysis.Interpolation is a specific case of curve fitting, in which the function must go exactly through the data points.A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function. Suppose we know the function but it is too complex to evaluate efficiently. Then we could pick a few known data points from the complicated function, creating a lookup table, and try to interpolate those data points to construct a simpler function. Of course, when using the simple function to calculate new data points we usually do not receive the same result as when using the original function, but depending on the problem domain and the interpolation method used the gain in simplicity might offset the error.It should be mentioned that there is another very different kind of interpolation in mathematics, namely the "interpolation of operators". The classical results about interpolation of operators are the Riesz –Thorin theorem and the Marcinkiewicz theorem. There are also many other subsequent results.An interpolation of a finite set of points on an epitrochoid. Points through whichcurve is splined are red; the blue curve connecting them is interpolation.ExampleFor example, suppose we have a table likethis, which gives some values of anunknown function f .Plot of the data points as given in the table.xf (x )0010.841520.909330.14114?0.75685?0.95896?0.2794Interpolation provides a means of estimating the function at intermediate points, such as x = 2.5.There are many different interpolation methods, some of which are described below. Some of the concerns to take into account when choosing an appropriate algorithm are: How accurate is the method? How expensive is it? How smooth is the interpolant? How many data points are needed?Piecewise constant interpolationPiecewise constant interpolation, ornearest-neighbor interpolation.The simplest interpolation method is to locate the nearest data value,and assign the same value. In one dimension, there are seldom goodreasons to choose this one over linear interpolation, which is almost ascheap, but in higher dimensional multivariate interpolation, this can bea favourable choice for its speed and simplicity.Linear interpolationPlot of the data with linear interpolation superimposedOne of the simplest methods is linear interpolation(sometimes known as lerp). Consider the above example of determining f (2.5). Since 2.5 is midway between 2 and 3, it is reasonable to take f (2.5) midway between f (2) = 0.9093 and f (3) = 0.1411, which yields 0.5252.Generally, linear interpolation takes two data points, say(x a ,y a ) and (x b ,y b ), and the interpolant is given by:at the point (x ,y )Linear interpolation is quick and easy, but it is not very precise. Another disadvantage is that the interpolant is not differentiable at the point x k .The following error estimate shows that linear interpolation is not very precise. Denote the function which we want to interpolate by g , and suppose that x lies between x a and x b and that g is twice continuously differentiable. Then the linear interpolation error isIn words, the error is proportional to the square of the distance between the data points. The error of some other methods, including polynomial interpolation and spline interpolation (described below), is proportional to higher powers of the distance between the data points. These methods also produce smoother interpolants.Polynomial interpolationPlot of the data with polynomial interpolation appliedPolynomial interpolation is a generalization of linearinterpolation. Note that the linear interpolant is a linearfunction. We now replace this interpolant by a polynomial of higher degree.Consider again the problem given above. The followingsixth degree polynomial goes through all the seven points: Substituting x = 2.5, we find that f (2.5) = 0.5965.Generally, if we have n data points, there is exactly onepolynomial of degree at most n ?1 going through all the data points. The interpolation error is proportional to the distancebetween the data points to the power n . Furthermore, the interpolant is a polynomial and thus infinitely differentiable.So, we see that polynomial interpolation solves all theproblems of linear interpolation.However, polynomial interpolation also has some disadvantages. Calculating the interpolating polynomial is computationally expensive (see computational complexity) compared to linear interpolation. Furthermore, polynomial interpolation may exhibit oscillatory artifacts, especially at the end points (see Runge's phenomenon).These disadvantages can be avoided by using spline interpolation or restricting attention Chebyshev polynomials.Spline interpolationPlot of the data with spline interpolation applied Remember that linear interpolation uses a linear functionfor each of intervals [x k ,x k+1]. Spline interpolation useslow-degree polynomials in each of the intervals, andchooses the polynomial pieces such that they fit smoothlytogether. The resulting function is called a spline.For instance, the natural cubic spline is piecewise cubic and twice continuously differentiable. Furthermore, its secondderivative is zero at the end points. The natural cubic spline interpolating the points in the table above is given byIn this case we get f (2.5) = 0.5972.Like polynomial interpolation, spline interpolation incurs a smaller error than linear interpolation and the interpolant is smoother. However, the interpolant is easier to evaluatethan the high-degree polynomials used in polynomial interpolation. It also does not suffer from Runge's phenomenon.Interpolation via Gaussian processesGaussian process is a powerful non-linear interpolation tool. Many popular interpolation tools are actually equivalent to particular Gaussian processes. Gaussian processes can be used not only for fitting an interpolant that passes exactly through the given data points but also for regression, i.e., for fitting a curve through noisy data. In the geostatistics community Gaussian process regression is also known as Kriging.Other forms of interpolationOther forms of interpolation can be constructed by picking a different class of interpolants. For instance, rational interpolation is interpolation by rational functions, and trigonometric interpolation is interpolation by trigonometric polynomials. Another possibility is to use wavelets.The Whittaker –Shannon interpolation formula can be used if the number of data points is infinite.Multivariate interpolation is the interpolation of functions of more than one variable. Methods include bilinear interpolation and bicubic interpolation in two dimensions, and trilinearinterpolation in three dimensions.Sometimes, we know not only the value of the function that we want to interpolate, at some points, but also its derivative. This leads to Hermite interpolation problems.Interpolation in Digital Signal ProcessingIn the domain of digital signal processing, the term interpolation refers to the process of converting a sampled digital signal (such as a sampled audio signal) to a higher sampling rate using various digital filtering techniques (e.g.,convolution with a frequency-limited impulse signal). In this application there is a specific requirement that the harmonic content of the original signal be preserved without creating aliased harmonic content of the original signal above the original Nyquist limit of the signal (i.e., above fs/2 of the original signal sample rate). An early and fairly elementary discussion on this subject can be found in Rabiner and Crochiere's book Multirate Digital Signal Processing .[1]Related conceptsThe term extrapolation is used if we want to find data points outside the range of known data points.In curve fitting problems, the constraint that the interpolant has to go exactly through the data points is relaxed. It is only required to approach the data points as closely as possible (within some other constraints). This requires parameterizing the potential interpolants and having some way of measuring the error. In the simplest case this leads to least squares approximation.Approximation theory studies how to find the best approximation to a given function by another function from some predetermined class, and how good this approximation is.This clearly yields a bound on how well the interpolant can approximate the unknown function.See alsoSimple rational approximationReferences[1]R.E. Crochiere and L.R. Rabiner. (1983). Multirate Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall. (http://www.amazon.com/Multirate-Digital-Signal-Processing-Crochiere/dp/0136051626)Article Sources and Contributors6 Article Sources and ContributorsInterpolation Source: /w/index.php?oldid=384878591 Contributors: A.melkumyan, AlbertSM, Alberto da Calvairate, Algebraist, Andonic, Auntof6, BenFrantzDale,Berland, Betacommand, Bobet, Bobo192, CanadianLinuxUser, Ccooke123, Cdc, Chadernook, ChangChienFu, Chaos, Charles Matthews, Coneslayer, Conversion script, Cronholm144, DavidCary, Dcljr, DerHexer, Dick Beldin, Dicklyon, Dino, DoctorW, Dudzcom, Dungodung, Edrowland, El C, El-Ahrairah, Elwikipedista, Eric119, Everyking, Fgnievinski, Friginator, Giftlite, Grajales, Grunt, HGB, Harp, Hattrem, Hede2000, HenkvD, Herbee, Heron, Hippopottoman, Hyacinth, Ironholds, JJL, JahJah, Jaimeastorga2000, Japo, Jeltz, Jezhotwells, Jitse Niesen, JohnBlackburne, Kieff, Lotje, Marcello Quintieri, Martin.Budden, Math Champion, MathFacts, MathMartin, Matt37, Michael Hardy, Mike Peel, MuzikJunky, Niffux, Oleg Alexandrov, Oli Filth, Omicronpersei8, PabloCastellano, Patrick, Pdcook, Persian Poet Gal, RMFan1, Rich Farmbrough, Roger pearse,SWAdair, Shreevatsa, Spooky, Supertouch, S?awomir Bia?y, UFu, Uberjivy,Vtstarin, Wi-king, Woodinville, XJamRastafire, Xiaojeng, Yas, 134 anonymous editsImage Sources, Licenses and ContributorsImage:Splined epitrochoid.png Source: /w/index.php?title=File:Splined_epitroch oid.png License: Public Domain Contributors: User:Dino Image:Interpolation Data.svg Source: /w/index.php?title=File:Interpolation_Dat a.svg License: Public Domain Contributors: User:BerlandImage:Piecewise constant.svg Source: /w/index.php?title=File:Piecewise_consta nt.svg License: Public Domain Contributors: User:Berland Image:Interpolation example linear.svg Source: /w/index.php?title=File:Interpolation_exa mple_linear.svg License: Public Domain Contributors: User:BerlandImage:Interpolation example polynomial.svg Source: /w/index.php?title=File:Interpolation_exa mple_polynomial.svg License: Public Domain Contributors: User:BerlandImage:Interpolation example spline.svg Source: /w/index.php?title=File:Interpolation_exa mple_spline.svg License: Public Domain Contributors: User:Berland LicenseCreative Commons Attribution-Share Alike 3.0 Unported/licenses/by-sa/3.0/。