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Geometry and Curve Definition NAPA

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Napa Oy 6 © Napa Ltd 2006
Curve Example
CUR EXAMPLE ’Example curve’ Z 0 XY (0 0) (4 1) (8 4)
y
x
Napa Oy 7 © Napa Ltd 2006
Location Surface
• A location surface can be:
Napa Oy 10 © Napa Ltd 2006
Curve Points Example
CUR EXAMPLE ‘Comment text’ X 0 YZ (1 2) CUR1 (4 6) CUR2 CUR3 P1 Z Point object P1
cur3 cur2
cur1
Y
X
Napa Oy 11 © Napa Ltd 2006
• A principal plane Example: X 15 A general plane Example: THR (0 0 6) (0 8 12) (-2 0 12) A curved surface Example: XZ (8 0) (9 4.8) (11 8)
•
•
Napa Oy 8 © Napa Ltd 2006
Sorting of Curve Points
• Default: The points are sorted according to the ascending values of the coordinate given by the first symbol in the shape definition e.g. XY or YX and secondly by the given order • Exception: Option * cancels the default sorting - points are set in the given order
Example 1
CUR EXA1 Z 0 XY (15 55) (55 15)
Napa Oy 20 © Napa Ltd 2006
Example 2
CUR EXA2 Z 0 XY (15 55) (30 25) (55 15)
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Example 3
A /- -/ B
• The syntax <> or >< before the curve coordinates specifies that ALL angles are free angles
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Free Angle: Example
C
C
C
CUR EXA5 Z 0 XY (15 55) (30 25) /- (55 15)
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Example 6
CUR EXA6 Z 0 XY (15 55) -/ (30 25) /- (55 15)
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Example 7
Napa Oy 29 © Napa Ltd 2006
This is NOT a circle!
Example 11
CUR EXA11 Z 0 XY (15 55) (30 20) /- (55 15)
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Example 12
CUR EXA12 Z 0 YX (15 55) (30 20) /- (55 15)
NOTE! Coordinates are always input in the order (x y) (y z) (x z) or (x y z)
Napa Oy 12 © Napa Ltd 2006
Sorting of Curve Points: Example
CUR EXAMPLE1 Z 0 XY (2 2) (3 4) (4.5 3) (3.5 1) (2 2) (3 4) (3.5 1) (4.5 3) as sorted by NAPA CUR EXAMPLE2 Z 0 XY * (2 2) (3 4) (4.5 3) (3.5 1) CUR EXAMPLE3 Z 0 YX (2 2) (3 4) (4.5 3) (3.5 1) (3.5 1) (2 2) (4.5 3) (3 4) as sorted by NAPA
C
A B C D
A B -/ C D
A B C /- D
A B -/ C /- D
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Curve Examples
• • • Definition syntax Sorting of points Effect of angles
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Geometry and Curve Definition
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Contents
• NAPA Geometry hierarchy • Curve definition
• • • • points and angles using intersecting curves multiple intersection points side conditions
Z
C B A
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Without the 60 degree ‘out’ angle Y
Free Angle
• A free angle at a point means that the curve behaves as at endpoint • The symbol of the free angle is the minus sign “-”
STEM/Z=5 STEM/Z>5 STEM/Z<5 STEM/Z=#5 intersection intersection intersection intersection where where where where z z z z = 5m > 5m < 5m is closest to 5m
CUR EXA3 Z 0 XY (15 55) 0/ (30 25) (55 15)
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Example 4
CUR EXA4 Z 0 XY (15 55) /-45 (30 25) (55 15)
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Example 5
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Multiple Intersection Points
• If the intersection between the location surface and a referenced curve gives more than one intersection point, the following syntaxes can be used to choose the point:
TASK GM DEFSM NhomakorabeaDR
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Curve Definition
• The curve shape is defined in a main coordinate plane (xy, yz, xz) and projected onto a given location surface
CUR EXA7 Z 0 XY (15 55) -/ (20 30) (30 20) /- (55 15)
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Example 8
CUR EXA8 Z 0 XY <> (15 55) (20 30) (30 20) (55 15)
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• Useful commands • Curve examples and definition exercises
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NAPA Geometry Hierarchy
Points, angles Curves Surfaces Rooms Arrangements
X
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Curve Definition: Points
• A curve shape is defined by points • The points can be given
• Directly with coordinates (X, Y) or (X, Z) or (Y, Z) • By referring to other curves • By using point objects
Napa Oy 16 © Napa Ltd 2006
Free Angle
• The most simple way to create a knuckle is to add a free angle on both sides of a point:
-/ A /-
• The most simple way to create a straight line between two points is to add free angles between them:
Location Surface Example
Z
CUR C1 ‘Plane location surface’ X -2 YZ (2 4) (5 5) (6.6 4) (8 5)

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Geometric sensing of known planar shapes

Geometric sensing of known planar shapes

International Journal of Robotics Research, 154:365-392, 1996.

Geometric Sensing of Known Planar Shapes
Yan-Bin Jia Michael Erdmann The Robotics Institute and School of Computer Science Carnegie Mellon University Pittsburgh, Pennsylvania 15213-3891 March 12, 1995
1 Introduction
Sensing a part involves determining both its shape and pose. By pose we mean the position as well as the orientation of the part. Prior to selecting a sensing method, we often will make some assumptions about the shape of the part to be sensed. The resulting sensing method is a ected greatly by what is known about the shape. For instance, without making any assumptions, we might not even be able to start segmentation of the part image, whereas knowing that the shape is convex polygonal, we can employ some simple non-vision technique such as nger probing. An e ective sensing method should make use of its knowledge about the part shape as much as possible to attain simplicity, e ciency, and robustness. Parts in many assembly applications are manufactured to high precisions, so we can make the assumption that their shapes are known reasonably well in advance. Accordingly, the design of sensing strategies should be based on the geometry of parts. The task of sensing reduces to obtaining enough geometric constraints that, when combined with the part geometry, su ce to derive the part poses. Consequently, minimizing the necessary geometric constraints becomes very important for reducing the sensing complexity. In this article, we propose two approaches for sensing polygonal parts in known shapes, one applicable to a continuum of possible poses and the other applicable to nite possible poses. Perhaps the simplest geometric constraint on a polygon is incidence|when some edge touches a xed point or some vertex is on a xed line. For instance, Figure 1a shows an 8-gon constrained by two points p1; p2 and two lines l1; l2. The question we want to ask is: Generally, how many such constraints are necessary to x the polygon in its real position? Note that any two such incidence constraints will con ne all possible positions to a locus curve which consists of a nite number of algebraic curves parameterized by the part's orientation. Three constraints, as long as not de ned by collinear points or concurrent lines, will allow only a nite number of valid poses. These poses occur when di erent locus curves, each given by a pair of constraints, intersect at the same orientations. An upper 3
最小圆覆盖

最小圆覆盖


Adding a point
Question: Suppose we remembered not only Ci−1 , but also the two or three points defining it. It looks like if pi is outside Ci−1 , the new circle Ci is defined by pi and some points that defined Ci−1 . Why is this false?
Computational Geometry
Lecture 6: Smallest enclosing circles and more
Introduction Smallest enclosing circle algorithm Randomized incremental construction
Computational Geometry
Lecture 6: Smallest enclosing circles and more
Introduction Smallest enclosing circle algorithm Randomized incremental construction
Randomized incremental construction A more restricted problem A yet more restricted problem Efficiency analysis
Adding a point
Ci−1
Ci−1
pi pi
Computational Geometry

Facility location Properties of the smallest enclosing circle
napa使用技巧

napa使用技巧


3.
如何把报告的起始页设为第 8 页
修改起始页可以有以下办法。 在 List Window 中选择菜单 File/New List... 注意是 New List...，不是 New List 这样会有一个窗口，在里面可以设置起始页。 如果用命令的格式（一般在宏里较常用） NL PN=8 （意思是 New list page number=8） （大部分 NAPA 命令都是一些简写，大家只要记住它的英文说法，就不会忘记命令了） NL 还有其它很多用法 注意： NL 在大部分子任务目录下都可以使用，但在 Task?>主目录和某些子任务目录下不能使用。
5.如何输出进水角曲线？
!end stab 进入 STAB 子任务目录 plot oi cal1 cal2 绘制 Opening Immersion 曲线，cal1 cal2 是两个需要输出的进水点。 建议在执行上面的命令前，先打开 Plot Window 或 Geometry Window。 这样在看到图形后就可以把它存为 DXF 文件。在 AutoCAD 中进行润色加工。 （NAPA 的图形功能还是比较弱的）
1. 如何输出报告
一般我们使用 LIST 命令时，结果会显示在主窗口上； 但我们只要在菜单中选择 TOOLS/List Window... 然后再使用 LIST 命令，结果就会出现在 List Window 上； 然后我们可以使用预览和打印命令查看和输出报告。
2. 怎样生成电子版报告
根据上面的方法，将把报告直接打印到打印机上； 为了解决这个问题； 建议安装 Acrobat5.0 以上的完全版， 这样会有 Acrobat Distiller 打印机可以使用。 只要我们在 List Window 上选择该打印机， 我们就可以输出报告成 Acrobat 文件了。 缺点是 Acrobat 只支持行编辑，而且编辑能力较差。 如果在 Window2000 中将 Acrobat Distiller 打印机设为默认打印机， 以后就不用再每次进入 NAPA 都重新选择该打印机了。 另一个办法是将 List Window 中的内容全部选中，Paste 到 Notepad，Word 等其它编辑程序中， 缺点是在 List Window 中的格式将不复存在。 但我们可以通过 Excel 引入 TXT 文件的方法解决它。
3_curve

3_curve

Geometry and Curve DefinitionContents•NAPA Geometry hierarchy •Curve definition•Location surface•Definition points and angle conditions•Multiple intersection points•Side conditions•Curve/curve definition•Point objects•Useful commands•Curve definition exercisesNAPA Geometry HierarchyPoints, anglesCurvesSurfacesRooms Arrangementso αCoordinate systemZ •Default: righthanded•Can be changed in REFY•Curves are defined in DEF task which can be entered directly from TASK levelDRDEFSM GM TASK•The curve shape is defined in a main coordinate plane (xy, yz, xz) and projected onto a given location surfaceCurve ExampleCUR EXAMPLE ’Example curve’Z 0XY (0 0) (4 1) (8 4)yxLocation Surface• A location surface can be:• A principal planeExample:X 15• A general planeExample:THR (0 0 6) (0 8 12) (-2 0 12)• A curved surfaceExample:XZ (8 0) (9 4.8) (11 8)Location Surface ExampleCUR C1 ‘Plane location surface’X -2YZ (2 4) (5 5) (6.6 4) (8 5)CUR C2 ‘Curved location surface’XY (3 2) (5 5) (9 8)YZ (2 4) (5 5) (6.6 4) (8 5)XYZ-XPRO XPRO YPRO ZC1,C2C1C1C2C2ZYXYZXCurve Definition:Points•A curve shape is defined by points •The points can be given•Directly with coordinates(X, Y)or(X, Z)or(Y, Z)•By referring to other curves•By using point objectsCurve Points ExampleCUR EXAMPLE ‘Comment text’X 0YZ (1 2) CUR1 (4 6) CUR2 CUR3 P1Point object P1cur1cur2cur3X YZSorting of Curve Points•Default: The points are sorted accordingto the ascending values of the coordinate given by the first symbol in the shapedefinition e.g. XY or YX and secondly by the given order•Exception: Option * cancels the defaultsorting -points are set in the given orderNOTE!Coordinates are always input inthe order (x y) (y z) (x z) or (x y z)Sorting of Curve Points: Example CUR EXAMPLE2Z 0XY * (2 2) (3 4) (4.5 3) (3.5 1)CUR EXAMPLE1Z 0XY (2 2) (3 4) (4.5 3) (3.5 1)(2 2) (3 4) (3.5 1) (4.5 3) as sorted by NAPACUR EXAMPLE3Z 0YX (2 2) (3 4) (4.5 3) (3.5 1)(3.5 1) (2 2) (4.5 3) (3 4) as sorted by NAPACurve Angles•Angle conditions can be used to give the curve the correct shape•An angle condition is marked by a slash “/”between the definition point and the angle •Mathematical direction:+counter-clockwise-clockwise0along x-axis or y-axis+xy+yz +x zCurve Angles SyntaxYZ A /60 0/ B /60 CFrom point A with angle 60 degreesTo point B with angle of 0 degreesFrom point B with angle 60 degreesA BCWithout the 60 degree ‘out’angleZY•A free angle at a point means that the curve behaves as at endpoint•The symbol o f the free angle is the minus sign “-”•The most simple way to create a knuckle is to add a free angle on both sides of a point: -/ A /-•The most simple way to create a straight line between two points is to add free angles between them:A /--/ B•The syntax <> or >< before the curve coordinates specifies that ALL angles are free anglesFree Angle:ExampleA B -/ C D A B C /-D A B -/ C /-D A B C D C C C CCurve Examples •Definition s yntax •Sorting of points •Effect of a nglesExample 1 CUR EXA1Z 0XY (15 55) (55 15)CUR EXA2Z 0XY (15 55) (30 25) (55 15)CUR EXA3Z 0XY (15 55) 0/ (30 25) (55 15)CUR EXA4Z 0XY (15 55) /-45 (30 25) (55 15)CUR EXA5Z 0XY (15 55) (30 25) /-(55 15)CUR EXA6Z 0XY (15 55) -/ (30 25) /-(55 15)CUR EXA7Z 0XY (15 55) -/ (20 30) (30 20) /-(55 15)CUR EXA8Z 0XY <> (15 55) (20 30) (30 20) (55 15)CUR EXA9Z 0XY * (10 35) (35 60) (60 35) (35 10) (10 35)CUR EXA10Z 0XY * (10 35) /90 (35 60) /0 (60 35) /-90,(35 10) /180 90/ (10 35)This is NOT a circle!CUR EXA11Z 0XY (15 55) (30 20) /-(55 15)Example 12CUR EXA11Z 0YX (15 55) (30 20) /-(55 15)Multiple Intersection Points•If the intersection between the location surface and a referenced curve givesmore than one intersection point,thefollowing syntaxes can be used tochoose the point:STEM/Z=5intersection where z = 5mSTEM/Z>5intersection where z > 5mSTEM/Z<5intersection where z < 5mSTEM/Z=#5intersection where z is closest to 5mMultiple Intersection Points: Example CUR TF4XY (81.9 0) (86 5)ZY STEM/Z=5/75 KNF DECKFCUR FRF5; X 82.5ZY STEM/Z<2/25,(1.08 2.2) 152/ STEM/Z=#4•Side conditions (SC) on a curve affect the behavior of the surface near the curve, e.g. they are angle conditions for the surface along the curve•Example side conditions:SC P limit curve for a flat area (plane) SC M main frame (all other curvesmust be“inside”i.e. defines themaximum of Y )SC -//-knuckle (free angle in and out)Side Condition:ExamplesCUR KNF ‘Knuckle Curve Fwd’XZ (68 7.1) (85 8.5)XY FSF -30/ (81 3.1) -90/ STEM SC -//-CUR FSF ‘Flat of Side’Y 6.5XZ (62 2.2) /0 (65 2.2) 65/ (72 11.5) SC PCUR FBF ‘Flat of Bottom’Z 0XY FRF/PFRF1 /0 PFBF (80 0) SC P CUR FRF ‘Main Frame Fwd’X 62YZ (0 0) -/ PFRF1 PFRF2, /-(6.5 11.5)SC MCurve/curve• A curve/curve definition is used to:1. Refer to an intersection point2. Specify the tangent of a surfaceCurve/curve:Example1CUR WLF2Z TF4/STEMXY FSF (75.5 4.2) TF4/STEMTF4Z location~TF4/STEM STEMWLF2Curve/curve:Example 1 (cont’d)STEMTF4WLF2The tangent of the surface at the intersection point isdefined by curves STEM and TF4. This affects the entrance angle of WLF2. WLF2 has no effect on the tangent plane.WLF2TF4STEMCurve/curve:ExamplesCUR TA2XY TRANS/Y=1.3 /0 FRA5/WLA2XZ TRANS FRA1 FRA2 FRA5/WLA2CUR TA1XZ FRA3/Z=1.7 FRA5/WLA2XY FRA3 FRA4 FRA5/WLA2CUR TF5ZX FRF3/WLF2(81 4.9) STEM/TF4ZY FRF3/WLF2FRF4 STEMCUR TF1ZY STEM/WLF1 WLF2/FRF3XZ WLF2/FRF3FRF4 FRF5 FRF6,STEM/WLF1Point Object Definition•There are five main ways to definepoint objects:•Directly as coordinates POI P1 (3 1 1)•Reflection POI P2 –P1•Translation POI P3 P1(Y+1 Z-2)•Along a curve POI P4 CUR1/X=18•Intersection point POI P5 CUR1/CUR2The XYZ curve•A curve without a location surfacedefined as a group of coordinates•Point objects can be used•References to other curves needadditional informationCURVE XYZ_EXXYZ (0 1 2) P1 FRA1/TA1 FRA/Z=5DES The command DES gives a description of objects in the form accepted for inputExample: DES FRF5CUR FRF5X 82.5ZY STEM/Z<2, /25, (1.08,2.2), 152/,STEM/Z=#4LIS The command LIS producessupplementary data about a curveExample: LIS FRF5LIST OF CURVE: FRF5**************************************X Y Z T SC REF.CURVE 82.500 0.000 0.352 25.00 25/ STEM/Z<21.0802.200 92.540.000 3.925 152.00 152/ STEM/Z=*4Tangent angle infoCommand PRO defines the projection that will be used when drawing an objectExamples:YZX YXZYZXX ZY PRO XPRO FPRO A PRO ZPRO YNote that these have a fixed convention !PLOT curveDraws the specified curve !Z WZoom (fit) to window!EClear the drawing area COL colourChange the colourCOM RNDUse random colourCurve Definition ExercisesBoundary curves of the fore body HULLF:•Limits of the surface•Border curves of the plane areas•Knuckle lineExercise 1: Main frameCurve FRFX = 62(0 0)(4.7 0)(6.5 1.8) (6.5 11.5)Exercise 2: StemCurve STEM Y = 0(84 2.2)FRF(80 0)(82.2 4)(81.7 4.4)(81.9 5)(85.5 11.5)Exercise 3: Deck lineFRFCurve DECKF Z = 11.5With rounded noseSTEM(84 2.5)(75 6.3)(72 6.5)。