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Arnold featuresMemory-efficient, scalable raytracer rendering software helps artists render complex scenes quickly and easily.◆ See what's new (video: 2:31 min.)◆ Get feature details in the Arnold for Maya, Houdini, Cinema 4D, 3ds Max, or Katana user guidesSubsurface scatterHigh-performance ray-traced subsurface scattering eliminates the need to tune point clouds. Hair and furMemory-efficient ray-traced curve primitives help you create complex fur and hair renders.Motion blur3D motion blur interacts with shadows, volumes, indirect lighting, reflection, or refraction. Deformation motion blur and rotational motion are also supported. VolumesThe volumetric rendering system in Arnold can render effects such as smoke, clouds, fog, pyroclastic flow, and fire.InstancesArnold can more efficiently ray trace instances of many scene objects with transformation and material overrides. Subdivision and displacementArnold supports Catmull-Clark subdivision surfaces.OSL supportArnold now features support for Open Shading Language (OSL), an advanced shading language for Global Illumination renderers. Light Path ExpressionsLPEs give you power and flexibility to create Arbitrary Output Variables to help meet the needs of production.NEW|Adaptive samplingAdaptive sampling gives users another means of tuning images, allowing them to reduce render times without jeopardizing final image quality. NEW|Toon shaderAn advanced Toon shader is part of a non-photorealistic solution provided in combination with the Contour Filter.NEW|DenoisingTwo denoising solutions in Arnold offer flexibility by allowing users to use much lower-quality sampling settings. NEW|Material assignments and overrides Operators make it possible to override any part of a scene at render time and enable support for open standard framework such as MaterialX.NEW|Alembic proceduralA native Alembic procedural allows users to render Alembic files directly without any translation.NEW|Profiling API and structured statistics An extensive set of tools allow users to more easily identify performance issues and optimize rendering processes.Standard Surface shaderThis energy-saving, physically based uber shader helps produce a wide range of materials and looks. Standard Hair shaderThis physically based shader is built to render hair and fur, based on the d'Eon and Zinke models for specular and diffuse shading.Flexible and extensible APIIntegrate Arnold in external applications and create custom shaders, cameras, light filters, and output drivers. Stand-alone command-line rendererArnold has a native scene description format stored in human-readable text files. Easily edit, read, and write these files via the C/Python API.◆ See Arnold 5.1 release notesIntegrate Arnold into your pipeline•Free plug-ins provide a bridge to the Arnold renderer from within many popular 3D applications.•Arnold has supported plug-ins available for Maya, Houdini, Cinema 4D, 3ds Max, and Katana.•Arnold is fully customizable, with a powerful API to create custom rendering solutions.◆ See Arnold plug-ins。

Progressive Simplicial Complexes Jovan Popovi´c Hugues HoppeCarnegie Mellon University Microsoft ResearchABSTRACTIn this paper,we introduce the progressive simplicial complex(PSC) representation,a new format for storing and transmitting triangu-lated geometric models.Like the earlier progressive mesh(PM) representation,it captures a given model as a coarse base model together with a sequence of refinement transformations that pro-gressively recover detail.The PSC representation makes use of a more general refinement transformation,allowing the given model to be an arbitrary triangulation(e.g.any dimension,non-orientable, non-manifold,non-regular),and the base model to always consist of a single vertex.Indeed,the sequence of refinement transforma-tions encodes both the geometry and the topology of the model in a unified multiresolution framework.The PSC representation retains the advantages of PM’s.It defines a continuous sequence of approx-imating models for runtime level-of-detail control,allows smooth transitions between any pair of models in the sequence,supports progressive transmission,and offers a space-efficient representa-tion.Moreover,by allowing changes to topology,the PSC sequence of approximations achieves betterfidelity than the corresponding PM sequence.We develop an optimization algorithm for constructing PSC representations for graphics surface models,and demonstrate the framework on models that are both geometrically and topologically complex.CR Categories:I.3.5[Computer Graphics]:Computational Geometry and Object Modeling-surfaces and object representations.Additional Keywords:model simplification,level-of-detail representa-tions,multiresolution,progressive transmission,geometry compression.1INTRODUCTIONModeling and3D scanning systems commonly give rise to triangle meshes of high complexity.Such meshes are notoriously difficult to render,store,and transmit.One approach to speed up rendering is to replace a complex mesh by a set of level-of-detail(LOD) approximations;a detailed mesh is used when the object is close to the viewer,and coarser approximations are substituted as the object recedes[6,8].These LOD approximations can be precomputed Work performed while at Microsoft Research.Email:jovan@,hhoppe@Web:/jovan/Web:/hoppe/automatically using mesh simplification methods(e.g.[2,10,14,20,21,22,24,27]).For efficient storage and transmission,meshcompression schemes[7,26]have also been developed.The recently introduced progressive mesh(PM)representa-tion[13]provides a unified solution to these problems.In PM form,an arbitrary mesh M is stored as a coarse base mesh M0together witha sequence of n detail records that indicate how to incrementally re-fine M0into M n=M(see Figure7).Each detail record encodes theinformation associated with a vertex split,an elementary transfor-mation that adds one vertex to the mesh.In addition to defininga continuous sequence of approximations M0M n,the PM rep-resentation supports smooth visual transitions(geomorphs),allowsprogressive transmission,and makes an effective mesh compressionscheme.The PM representation has two restrictions,however.First,it canonly represent meshes:triangulations that correspond to orientable12-dimensional manifolds.Triangulated2models that cannot be rep-resented include1-d manifolds(open and closed curves),higherdimensional polyhedra(e.g.triangulated volumes),non-orientablesurfaces(e.g.M¨o bius strips),non-manifolds(e.g.two cubes joinedalong an edge),and non-regular models(i.e.models of mixed di-mensionality).Second,the expressiveness of the PM vertex splittransformations constrains all meshes M0M n to have the same topological type.Therefore,when M is topologically complex,the simplified base mesh M0may still have numerous triangles(Fig-ure7).In contrast,a number of existing simplification methods allowtopological changes as the model is simplified(Section6).Ourwork is inspired by vertex unification schemes[21,22],whichmerge vertices of the model based on geometric proximity,therebyallowing genus modification and component merging.In this paper,we introduce the progressive simplicial complex(PSC)representation,a generalization of the PM representation thatpermits topological changes.The key element of our approach isthe introduction of a more general refinement transformation,thegeneralized vertex split,that encodes changes to both the geometryand topology of the model.The PSC representation expresses anarbitrary triangulated model M(e.g.any dimension,non-orientable,non-manifold,non-regular)as the result of successive refinementsapplied to a base model M1that always consists of a single vertex (Figure8).Thus both geometric and topological complexity are recovered progressively.Moreover,the PSC representation retains the advantages of PM’s,including continuous LOD,geomorphs, progressive transmission,and model compression.In addition,we develop an optimization algorithm for construct-ing a PSC representation from a given model,as described in Sec-tion4.1The particular parametrization of vertex splits in[13]assumes that mesh triangles are consistently oriented.2Throughout this paper,we use the words“triangulated”and“triangula-tion”in the general dimension-independent sense.Figure 1:Illustration of a simplicial complex K and some of its subsets.2BACKGROUND2.1Concepts from algebraic topologyTo precisely define both triangulated models and their PSC repre-sentations,we find it useful to introduce some elegant abstractions from algebraic topology (e.g.[15,25]).The geometry of a triangulated model is denoted as a tuple (K V )where the abstract simplicial complex K is a combinatorial structure specifying the adjacency of vertices,edges,triangles,etc.,and V is a set of vertex positions specifying the shape of the model in 3.More precisely,an abstract simplicial complex K consists of a set of vertices 1m together with a set of non-empty subsets of the vertices,called the simplices of K ,such that any set consisting of exactly one vertex is a simplex in K ,and every non-empty subset of a simplex in K is also a simplex in K .A simplex containing exactly d +1vertices has dimension d and is called a d -simplex.As illustrated pictorially in Figure 1,the faces of a simplex s ,denoted s ,is the set of non-empty subsets of s .The star of s ,denoted star(s ),is the set of simplices of which s is a face.The children of a d -simplex s are the (d 1)-simplices of s ,and its parents are the (d +1)-simplices of star(s ).A simplex with exactly one parent is said to be a boundary simplex ,and one with no parents a principal simplex .The dimension of K is the maximum dimension of its simplices;K is said to be regular if all its principal simplices have the same dimension.To form a triangulation from K ,identify its vertices 1m with the standard basis vectors 1m ofm.For each simplex s ,let the open simplex smdenote the interior of the convex hull of its vertices:s =m:jmj =1j=1jjsThe topological realization K is defined as K =K =s K s .The geometric realization of K is the image V (K )where V :m 3is the linear map that sends the j -th standard basis vector jm to j 3.Only a restricted set of vertex positions V =1m lead to an embedding of V (K )3,that is,prevent self-intersections.The geometric realization V (K )is often called a simplicial complex or polyhedron ;it is formed by an arbitrary union of points,segments,triangles,tetrahedra,etc.Note that there generally exist many triangulations (K V )for a given polyhedron.(Some of the vertices V may lie in the polyhedron’s interior.)Two sets are said to be homeomorphic (denoted =)if there ex-ists a continuous one-to-one mapping between them.Equivalently,they are said to have the same topological type .The topological realization K is a d-dimensional manifold without boundary if for each vertex j ,star(j )=d .It is a d-dimensional manifold if each star(v )is homeomorphic to either d or d +,where d +=d:10.Two simplices s 1and s 2are d-adjacent if they have a common d -dimensional face.Two d -adjacent (d +1)-simplices s 1and s 2are manifold-adjacent if star(s 1s 2)=d +1.Figure 2:Illustration of the edge collapse transformation and its inverse,the vertex split.Transitive closure of 0-adjacency partitions K into connected com-ponents .Similarly,transitive closure of manifold-adjacency parti-tions K into manifold components .2.2Review of progressive meshesIn the PM representation [13],a mesh with appearance attributes is represented as a tuple M =(K V D S ),where the abstract simpli-cial complex K is restricted to define an orientable 2-dimensional manifold,the vertex positions V =1m determine its ge-ometric realization V (K )in3,D is the set of discrete material attributes d f associated with 2-simplices f K ,and S is the set of scalar attributes s (v f )(e.g.normals,texture coordinates)associated with corners (vertex-face tuples)of K .An initial mesh M =M n is simplified into a coarser base mesh M 0by applying a sequence of n successive edge collapse transforma-tions:(M =M n )ecol n 1ecol 1M 1ecol 0M 0As shown in Figure 2,each ecol unifies the two vertices of an edgea b ,thereby removing one or two triangles.The position of the resulting unified vertex can be arbitrary.Because the edge collapse transformation has an inverse,called the vertex split transformation (Figure 2),the process can be reversed,so that an arbitrary mesh M may be represented as a simple mesh M 0together with a sequence of n vsplit records:M 0vsplit 0M 1vsplit 1vsplit n 1(M n =M )The tuple (M 0vsplit 0vsplit n 1)forms a progressive mesh (PM)representation of M .The PM representation thus captures a continuous sequence of approximations M 0M n that can be quickly traversed for interac-tive level-of-detail control.Moreover,there exists a correspondence between the vertices of any two meshes M c and M f (0c f n )within this sequence,allowing for the construction of smooth vi-sual transitions (geomorphs)between them.A sequence of such geomorphs can be precomputed for smooth runtime LOD.In addi-tion,PM’s support progressive transmission,since the base mesh M 0can be quickly transmitted first,followed the vsplit sequence.Finally,the vsplit records can be encoded concisely,making the PM representation an effective scheme for mesh compression.Topological constraints Because the definitions of ecol and vsplit are such that they preserve the topological type of the mesh (i.e.all K i are homeomorphic),there is a constraint on the min-imum complexity that K 0may achieve.For instance,it is known that the minimal number of vertices for a closed genus g mesh (ori-entable 2-manifold)is (7+(48g +1)12)2if g =2(10if g =2)[16].Also,the presence of boundary components may further constrain the complexity of K 0.Most importantly,K may consist of a number of components,and each is required to appear in the base mesh.For example,the meshes in Figure 7each have 117components.As evident from the figure,the geometry of PM meshes may deteriorate severely as they approach topological lower bound.M 1;100;(1)M 10;511;(7)M 50;4656;(12)M 200;1552277;(28)M 500;3968690;(58)M 2000;14253219;(108)M 5000;029010;(176)M n =34794;0068776;(207)Figure 3:Example of a PSC representation.The image captions indicate the number of principal 012-simplices respectively and the number of connected components (in parenthesis).3PSC REPRESENTATION 3.1Triangulated modelsThe first step towards generalizing PM’s is to let the PSC repre-sentation encode more general triangulated models,instead of just meshes.We denote a triangulated model as a tuple M =(K V D A ).The abstract simplicial complex K is not restricted to 2-manifolds,but may in fact be arbitrary.To represent K in memory,we encode the incidence graph of the simplices using the following linked structures (in C++notation):struct Simplex int dim;//0=vertex,1=edge,2=triangle,...int id;Simplex*children[MAXDIM+1];//[0..dim]List<Simplex*>parents;;To render the model,we draw only the principal simplices ofK ,denoted (K )(i.e.vertices not adjacent to edges,edges not adjacent to triangles,etc.).The discrete attributes D associate amaterial identifier d s with each simplex s(K ).For the sake of simplicity,we avoid explicitly storing surface normals at “corners”(using a set S )as done in [13].Instead we let the material identifier d s contain a smoothing group field [28],and let a normal discontinuity (crease )form between any pair of adjacent triangles with different smoothing groups.Previous vertex unification schemes [21,22]render principal simplices of dimension 0and 1(denoted 01(K ))as points and lines respectively with fixed,device-dependent screen widths.To better approximate the model,we instead define a set A that associates an area a s A with each simplex s 01(K ).We think of a 0-simplex s 00(K )as approximating a sphere with area a s 0,and a 1-simplex s 1=j k 1(K )as approximating a cylinder (with axis (j k ))of area a s 1.To render a simplex s 01(K ),we determine the radius r model of the corresponding sphere or cylinder in modeling space,and project the length r model to obtain the radius r screen in screen pixels.Depending on r screen ,we render the simplex as a polygonal sphere or cylinder with radius r model ,a 2D point or line with thickness 2r screen ,or do not render it at all.This choice based on r screen can be adjusted to mitigate the overhead of introducing polygonal representations of spheres and cylinders.As an example,Figure 3shows an initial model M of 68,776triangles.One of its approximations M 500is a triangulated model with 3968690principal 012-simplices respectively.3.2Level-of-detail sequenceAs in progressive meshes,from a given triangulated model M =M n ,we define a sequence of approximations M i :M 1op 1M 2op 2M n1op n 1M nHere each model M i has exactly i vertices.The simplification op-erator M ivunify iM i +1is the vertex unification transformation,whichmerges two vertices (Section 3.3),and its inverse M igvspl iM i +1is the generalized vertex split transformation (Section 3.4).Thetuple (M 1gvspl 1gvspl n 1)forms a progressive simplicial complex (PSC)representation of M .To construct a PSC representation,we first determine a sequence of vunify transformations simplifying M down to a single vertex,as described in Section 4.After reversing these transformations,we renumber the simplices in the order that they are created,so thateach gvspl i (a i)splits the vertex a i K i into two vertices a i i +1K i +1.As vertices may have different positions in the different models,we denote the position of j in M i as i j .To better approximate a surface model M at lower complexity levels,we initially associate with each (principal)2-simplex s an area a s equal to its triangle area in M .Then,as the model is simplified,wekeep constant the sum of areas a s associated with principal simplices within each manifold component.When2-simplices are eventually reduced to principal1-simplices and0-simplices,their associated areas will provide good estimates of the original component areas.3.3Vertex unification transformationThe transformation vunify(a i b i midp i):M i M i+1takes an arbitrary pair of vertices a i b i K i+1(simplex a i b i need not be present in K i+1)and merges them into a single vertex a i K i. Model M i is created from M i+1by updating each member of the tuple(K V D A)as follows:K:References to b i in all simplices of K are replaced by refer-ences to a i.More precisely,each simplex s in star(b i)K i+1is replaced by simplex(s b i)a i,which we call the ancestor simplex of s.If this ancestor simplex already exists,s is deleted.V:Vertex b is deleted.For simplicity,the position of the re-maining(unified)vertex is set to either the midpoint or is left unchanged.That is,i a=(i+1a+i+1b)2if the boolean parameter midp i is true,or i a=i+1a otherwise.D:Materials are carried through as expected.So,if after the vertex unification an ancestor simplex(s b i)a i K i is a new principal simplex,it receives its material from s K i+1if s is a principal simplex,or else from the single parent s a i K i+1 of s.A:To maintain the initial areas of manifold components,the areasa s of deleted principal simplices are redistributed to manifold-adjacent neighbors.More concretely,the area of each princi-pal d-simplex s deleted during the K update is distributed toa manifold-adjacent d-simplex not in star(a ib i).If no suchneighbor exists and the ancestor of s is a principal simplex,the area a s is distributed to that ancestor simplex.Otherwise,the manifold component(star(a i b i))of s is being squashed be-tween two other manifold components,and a s is discarded. 3.4Generalized vertex split transformation Constructing the PSC representation involves recording the infor-mation necessary to perform the inverse of each vunify i.This inverse is the generalized vertex split gvspl i,which splits a0-simplex a i to introduce an additional0-simplex b i.(As mentioned previously, renumbering of simplices implies b i i+1,so index b i need not be stored explicitly.)Each gvspl i record has the formgvspl i(a i C K i midp i()i C D i C A i)and constructs model M i+1from M i by updating the tuple (K V D A)as follows:K:As illustrated in Figure4,any simplex adjacent to a i in K i can be the vunify result of one of four configurations in K i+1.To construct K i+1,we therefore replace each ancestor simplex s star(a i)in K i by either(1)s,(2)(s a i)i+1,(3)s and(s a i)i+1,or(4)s,(s a i)i+1and s i+1.The choice is determined by a split code associated with s.Thesesplit codes are stored as a code string C Ki ,in which the simplicesstar(a i)are sortedfirst in order of increasing dimension,and then in order of increasing simplex id,as shown in Figure5. V:The new vertex is assigned position i+1i+1=i ai+()i.Theother vertex is given position i+1ai =i ai()i if the boolean pa-rameter midp i is true;otherwise its position remains unchanged.D:The string C Di is used to assign materials d s for each newprincipal simplex.Simplices in C Di ,as well as in C Aibelow,are sorted by simplex dimension and simplex id as in C Ki. A:During reconstruction,we are only interested in the areas a s fors01(K).The string C Ai tracks changes in these areas.Figure4:Effects of split codes on simplices of various dimensions.code string:41422312{}Figure5:Example of split code encoding.3.5PropertiesLevels of detail A graphics application can efficiently transitionbetween models M1M n at runtime by performing a sequence ofvunify or gvspl transformations.Our current research prototype wasnot designed for efficiency;it attains simplification rates of about6000vunify/sec and refinement rates of about5000gvspl/sec.Weexpect that a careful redesign using more efficient data structureswould significantly improve these rates.Geomorphs As in the PM representation,there exists a corre-spondence between the vertices of the models M1M n.Given acoarser model M c and afiner model M f,1c f n,each vertexj K f corresponds to a unique ancestor vertex f c(j)K cfound by recursively traversing the ancestor simplex relations:f c(j)=j j cf c(a j1)j cThis correspondence allows the creation of a smooth visual transi-tion(geomorph)M G()such that M G(1)equals M f and M G(0)looksidentical to M c.The geomorph is defined as the modelM G()=(K f V G()D f A G())in which each vertex position is interpolated between its originalposition in V f and the position of its ancestor in V c:Gj()=()fj+(1)c f c(j)However,we must account for the special rendering of principalsimplices of dimension0and1(Section3.1).For each simplexs01(K f),we interpolate its area usinga G s()=()a f s+(1)a c swhere a c s=0if s01(K c).In addition,we render each simplexs01(K c)01(K f)using area a G s()=(1)a c s.The resultinggeomorph is visually smooth even as principal simplices are intro-duced,removed,or change dimension.The accompanying video demonstrates a sequence of such geomorphs.Progressive transmission As with PM’s,the PSC representa-tion can be progressively transmitted by first sending M 1,followed by the gvspl records.Unlike the base mesh of the PM,M 1always consists of a single vertex,and can therefore be sent in a fixed-size record.The rendering of lower-dimensional simplices as spheres and cylinders helps to quickly convey the overall shape of the model in the early stages of transmission.Model compression Although PSC gvspl are more general than PM vsplit transformations,they offer a surprisingly concise representation of M .Table 1lists the average number of bits re-quired to encode each field of the gvspl records.Using arithmetic coding [30],the vertex id field a i requires log 2i bits,and the boolean parameter midp i requires 0.6–0.9bits for our models.The ()i delta vector is quantized to 16bitsper coordinate (48bits per),and stored as a variable-length field [7,13],requiring about 31bits on average.At first glance,each split code in the code string C K i seems to have 4possible outcomes (except for the split code for 0-simplex a i which has only 2possible outcomes).However,there exist constraints between these split codes.For example,in Figure 5,the code 1for 1-simplex id 1implies that 2-simplex id 1also has code 1.This in turn implies that 1-simplex id 2cannot have code 2.Similarly,code 2for 1-simplex id 3implies a code 2for 2-simplex id 2,which in turn implies that 1-simplex id 4cannot have code 1.These constraints,illustrated in the “scoreboard”of Figure 6,can be summarized using the following two rules:(1)If a simplex has split code c12,all of its parents havesplit code c .(2)If a simplex has split code 3,none of its parents have splitcode 4.As we encode split codes in C K i left to right,we apply these two rules (and their contrapositives)transitively to constrain the possible outcomes for split codes yet to be ing arithmetic coding with uniform outcome probabilities,these constraints reduce the code string length in Figure 6from 15bits to 102bits.In our models,the constraints reduce the code string from 30bits to 14bits on average.The code string is further reduced using a non-uniform probability model.We create an array T [0dim ][015]of encoding tables,indexed by simplex dimension (0..dim)and by the set of possible (constrained)split codes (a 4-bit mask).For each simplex s ,we encode its split code c using the probability distribution found in T [s dim ][s codes mask ].For 2-dimensional models,only 10of the 48tables are non-trivial,and each table contains at most 4probabilities,so the total size of the probability model is small.These encoding tables reduce the code strings to approximately 8bits as shown in Table 1.By comparison,the PM representation requires approximately 5bits for the same information,but of course it disallows topological changes.To provide more intuition for the efficiency of the PSC repre-sentation,we note that capturing the connectivity of an average 2-manifold simplicial complex (n vertices,3n edges,and 2n trian-gles)requires ni =1(log 2i +8)n (log 2n +7)bits with PSC encoding,versus n (12log 2n +95)bits with a traditional one-way incidence graph representation.For improved compression,it would be best to use a hybrid PM +PSC representation,in which the more concise PM vertex split encoding is used when the local neighborhood is an orientableFigure 6:Constraints on the split codes for the simplices in the example of Figure 5.Table 1:Compression results and construction times.Object#verts Space required (bits/n )Trad.Con.n K V D Arepr.time a i C K i midp i (v )i C D i C Ai bits/n hrs.drumset 34,79412.28.20.928.1 4.10.453.9146.1 4.3destroyer 83,79913.38.30.723.1 2.10.347.8154.114.1chandelier 36,62712.47.60.828.6 3.40.853.6143.6 3.6schooner 119,73413.48.60.727.2 2.5 1.353.7148.722.2sandal 4,6289.28.00.733.4 1.50.052.8123.20.4castle 15,08211.0 1.20.630.70.0-43.5-0.5cessna 6,7959.67.60.632.2 2.50.152.6132.10.5harley 28,84711.97.90.930.5 1.40.453.0135.7 3.52-dimensional manifold (this occurs on average 93%of the time in our examples).To compress C D i ,we predict the material for each new principalsimplex sstar(a i )star(b i )K i +1by constructing an ordered set D s of materials found in star(a i )K i .To improve the coding model,the first materials in D s are those of principal simplices in star(s )K i where s is the ancestor of s ;the remainingmaterials in star(a i )K i are appended to D s .The entry in C D i associated with s is the index of its material in D s ,encoded arithmetically.If the material of s is not present in D s ,it is specified explicitly as a global index in D .We encode C A i by specifying the area a s for each new principalsimplex s 01(star(a i )star(b i ))K i +1.To account for this redistribution of area,we identify the principal simplex from which s receives its area by specifying its index in 01(star(a i ))K i .The column labeled in Table 1sums the bits of each field of the gvspl records.Multiplying by the number n of vertices in M gives the total number of bits for the PSC representation of the model (e.g.500KB for the destroyer).By way of compari-son,the next column shows the number of bits per vertex required in a traditional “IndexedFaceSet”representation,with quantization of 16bits per coordinate and arithmetic coding of face materials (3n 16+2n 3log 2n +materials).4PSC CONSTRUCTIONIn this section,we describe a scheme for iteratively choosing pairs of vertices to unify,in order to construct a PSC representation.Our algorithm,a generalization of [13],is time-intensive,seeking high quality approximations.It should be emphasized that many quality metrics are possible.For instance,the quadric error metric recently introduced by Garland and Heckbert [9]provides a different trade-off of execution speed and visual quality.As in [13,20],we first compute a cost E for each candidate vunify transformation,and enter the candidates into a priority queueordered by ascending cost.Then,in each iteration i =n 11,we perform the vunify at the front of the queue and update the costs of affected candidates.4.1Forming set of candidate vertex pairs In principle,we could enter all possible pairs of vertices from M into the priority queue,but this would be prohibitively expensive since simplification would then require at least O(n2log n)time.Instead, we would like to consider only a smaller set of candidate vertex pairs.Naturally,should include the1-simplices of K.Additional pairs should also be included in to allow distinct connected com-ponents of M to merge and to facilitate topological changes.We considered several schemes for forming these additional pairs,in-cluding binning,octrees,and k-closest neighbor graphs,but opted for the Delaunay triangulation because of its adaptability on models containing components at different scales.We compute the Delaunay triangulation of the vertices of M, represented as a3-dimensional simplicial complex K DT.We define the initial set to contain both the1-simplices of K and the subset of1-simplices of K DT that connect vertices in different connected components of K.During the simplification process,we apply each vertex unification performed on M to as well in order to keep consistent the set of candidate pairs.For models in3,star(a i)has constant size in the average case,and the overall simplification algorithm requires O(n log n) time.(In the worst case,it could require O(n2log n)time.)4.2Selecting vertex unifications fromFor each candidate vertex pair(a b),the associated vunify(a b):M i M i+1is assigned the costE=E dist+E disc+E area+E foldAs in[13],thefirst term is E dist=E dist(M i)E dist(M i+1),where E dist(M)measures the geometric accuracy of the approximate model M.Conceptually,E dist(M)approximates the continuous integralMd2(M)where d(M)is the Euclidean distance of the point to the closest point on M.We discretize this integral by defining E dist(M)as the sum of squared distances to M from a dense set of points X sampled from the original model M.We sample X from the set of principal simplices in K—a strategy that generalizes to arbitrary triangulated models.In[13],E disc(M)measures the geometric accuracy of disconti-nuity curves formed by a set of sharp edges in the mesh.For the PSC representation,we generalize the concept of sharp edges to that of sharp simplices in K—a simplex is sharp either if it is a boundary simplex or if two of its parents are principal simplices with different material identifiers.The energy E disc is defined as the sum of squared distances from a set X disc of points sampled from sharp simplices to the discontinuity components from which they were sampled.Minimization of E disc therefore preserves the geom-etry of material boundaries,normal discontinuities(creases),and triangulation boundaries(including boundary curves of a surface and endpoints of a curve).We have found it useful to introduce a term E area that penalizes surface stretching(a more sophisticated version of the regularizing E spring term of[13]).Let A i+1N be the sum of triangle areas in the neighborhood star(a i)star(b i)K i+1,and A i N the sum of triangle areas in star(a i)K i.The mean squared displacement over the neighborhood N due to the change in area can be approx-imated as disp2=12(A i+1NA iN)2.We let E area=X N disp2,where X N is the number of points X projecting in the neighborhood. To prevent model self-intersections,the last term E fold penalizes surface folding.We compute the rotation of each oriented triangle in the neighborhood due to the vertex unification(as in[10,20]).If any rotation exceeds a threshold angle value,we set E fold to a large constant.Unlike[13],we do not optimize over the vertex position i a, but simply evaluate E for i a i+1a i+1b(i+1a+i+1b)2and choose the best one.This speeds up the optimization,improves model compression,and allows us to introduce non-quadratic energy terms like E area.5RESULTSTable1gives quantitative results for the examples in thefigures and in the video.Simplification times for our prototype are measured on an SGI Indigo2Extreme(150MHz R4400).Although these times may appear prohibitive,PSC construction is an off-line task that only needs to be performed once per model.Figure9highlights some of the benefits of the PSC representa-tion.The pearls in the chandelier model are initially disconnected tetrahedra;these tetrahedra merge and collapse into1-d curves in lower-complexity approximations.Similarly,the numerous polyg-onal ropes in the schooner model are simplified into curves which can be rendered as line segments.The straps of the sandal model initially have some thickness;the top and bottom sides of these straps merge in the simplification.Also note the disappearance of the holes on the sandal straps.The castle example demonstrates that the original model need not be a mesh;here M is a1-dimensional non-manifold obtained by extracting edges from an image.6RELATED WORKThere are numerous schemes for representing and simplifying tri-angulations in computer graphics.A common special case is that of subdivided2-manifolds(meshes).Garland and Heckbert[12] provide a recent survey of mesh simplification techniques.Several methods simplify a given model through a sequence of edge col-lapse transformations[10,13,14,20].With the exception of[20], these methods constrain edge collapses to preserve the topological type of the model(e.g.disallow the collapse of a tetrahedron into a triangle).Our work is closely related to several schemes that generalize the notion of edge collapse to that of vertex unification,whereby separate connected components of the model are allowed to merge and triangles may be collapsed into lower dimensional simplices. Rossignac and Borrel[21]overlay a uniform cubical lattice on the object,and merge together vertices that lie in the same cubes. Schaufler and St¨u rzlinger[22]develop a similar scheme in which vertices are merged using a hierarchical clustering algorithm.Lue-bke[18]introduces a scheme for locally adapting the complexity of a scene at runtime using a clustering octree.In these schemes, the approximating models correspond to simplicial complexes that would result from a set of vunify transformations(Section3.3).Our approach differs in that we order the vunify in a carefully optimized sequence.More importantly,we define not only a simplification process,but also a new representation for the model using an en-coding of gvspl=vunify1transformations.Recent,independent work by Schmalstieg and Schaufler[23]de-velops a similar strategy of encoding a model using a sequence of vertex split transformations.Their scheme differs in that it tracks only triangles,and therefore requires regular,2-dimensional trian-gulations.Hence,it does not allow lower-dimensional simplices in the model approximations,and does not generalize to higher dimensions.Some simplification schemes make use of an intermediate vol-umetric representation to allow topological changes to the model. He et al.[11]convert a mesh into a binary inside/outside function discretized on a three-dimensional grid,low-passfilter this function,。

德国螺丝标准ICS 21.060.10Zylinderschrauben mit Innensechskant –Niedriger Kopf, mit SchlüsselführungIn keeping with current practice in standards published by the International Organization for Standardization (ISO), a comma has been used throughout as the decimal marker.Ref.No.DIN 6912:2002-12English price group 07Sales No.010709.03DEUTSCHE NORM December 20026912{No part of this translation may be reproduced without the prior permission ofDIN Deutsches Institut für Normung e.V., Berlin. Beuth Verlag GmbH , 10772Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).Translation by DIN-Sprachendienst.In case of doubt, the German-language original should be consulted as the authoritative text.Hexagon socket thin head cap screws withpilot recessContinued on pages 2 to 8.ForewordThis standard has been prepared by Technical Committee Schrauben m it Innenantrieb of the Normen-ausschuss Mechanische Verbindungselemente (Fasteners Standards Committee).The DIN 4000-2-1.2 tabular layout of article characteristics shall apply to screws covered in this standard.Amendments This standard differs from the May 1985 edition as follows:a)Hexagon socket head cap screws may now also be made of grade A4 stainless steel.b)For stainless steel screws, the range of sizes assigned to property class 70 has been changed.c)Minimum ultimate tensile loads have been specified.d)References have been updated.Previous editionsDIN 6912:1954x-03, 1967-12, 1985-05.All dimensions are in millimetres.1ScopeThis standard specifies dimensions and technical delivery conditions for sizes M4 to M36 hexagon sockethead cap screws with pilot recess, of product grade A and made of steel, stainless steel or nonferrous metal.Where screws are to comply with specifications other than those given in this standard, these shall be selected in accordance with the relevant standards (e.g. DIN EN 28839, DIN EN ISO 898-1,DIN EN ISO 3506-1, DIN EN ISO 4759-1, DIN ISO 261, and DIN ISO 965-2).Screws specified in this standard should not be used in the form of screw assemblies with captive washers as they are always required to have a short unthreaded portion of shank to compensate for the pilot recess.SupersedesMay 1985 edition.Page2DIN6912:2002-122Normative referencesThis standard incorporates, by dated or undated reference, provisions from other publications. These norma-tive references are cited at the appropriate places in the text, and the titles of the publications are listed below. For dated references, subsequent amendments to or revisions of any of these publications apply to this standard only when incorporated in it by amendment or revision. For undated references, the latest edition of the publication referred to applies.DIN962Designation system for fastenersDIN4000-2Tabular layouts of article characteristics for bolts, screws and fit boltsDIN EN20225Bolts, screws, studs and nuts – Symbols and designations for dimensioning(ISO225:1983)DIN EN26157-3Fasteners – Surface discontinuities – Part3: Bolts, screws and studs for special require-ments (ISO6157-3:1988)DIN EN28839Mechanical properties of fasteners – Bolts, screws, studs and nuts made of non-ferrous metals (ISO8839:1986) DIN EN ISO898-1Mechanical properties of fasteners made of carbon steel and alloy steel – Part1: Bolts, screws and studs (ISO898-1:1999)DIN EN ISO3269Fasteners – Acceptance inspection (ISO3269:2000)DIN EN ISO3506-1Mechanical properties of corrosion-resistant stainless steel fasteners – Part1: Bolts, screws and studs (ISO3506-1:1997)DIN EN ISO4042Fasteners – Electroplated coatings (ISO4042:1999)DIN EN ISO4753Fasteners – Ends of parts with external ISO metric screw thread (ISO4753:1999)DIN EN ISO4759-1Tolerances for fasteners – Part1: Bolts, screws and nuts – Product grades A, B and C (ISO4759-1:2000) DIN EN ISO10683Fasteners – Non-electrolytically applied zinc flake coatings (ISO10683:2000)DIN ISO261ISO general purpose metric screw threads – General plan (ISO261:1998)DIN ISO965-2ISO general purpose metric screw threads – Tolerances – Part2: Limits of sizes for gen-eral purpose external and internal screw threads – Medium quality (ISO965-2:1998) ISO8992:1986Fasteners – General requirements for bolts, screws, studs and nutsPage 3DIN 6912:2002-123DimensionsScrew dimensions shall be as given in figure 1 and table 1.See DIN EN 20225 for symbols.Maximum underhead fillet l f max = 1,7 r maxd a,max –d s,max r max =2For r min , see table 1.Detail XKey to figure 1)End chamfered (cf. DIN EN ISO 4753).2)Length of incomplete thread, u : 2 P maximum.3)Slight rounding or countersinking at the mouth of the socket is permitted (no further than e ).4)Top edge of head rounded or chamfered (optional).5)Bottom edge of head may be rounded or chamfered to d w , but shall always be free from burr.6)Datum for d w .7)d s applies if values of l s min are specified.Figure 1:Screw dimensions (notation)1)2)7)3)6)5)4)XPage 4DIN 6912:2002-12Tabl e 1:Screw dimensionsThread size (d )Reference dimension2)3)4)Max. = nominal sizeMin. = nominal size Max. = nominal sizeMax. = nominal sizeNominal sizeNominal size1)5)6)Shank length, l s , and grip length, l gNominal sizeNOTE: Use of sizes in brackets should be avoided.1)Thread pitch.2)For lengths, l , of 125 mm or less.3)For lengths, l , above 125 mm up to 200 mm.4)For lengths, l , exceeding 200 mm.5)emin = 1,14 s min .6)Commercial sizes of screws are those for which lengths l s and l ghave been specified. Nominal lengths, l , exceeding200 mm shall be graded in 20 mm steps.For screws with lengths above the dashed line, the maximum distance between the last fully formed thread and the bearingface, l g , shall be equal to 5 P . For lengths below the line, l g and l s are to be calculated using the following equations:l g max = l nom – b ; l smin = l g max – 5 P .(continued)Page 5DIN 6912:2002-12Table 1(concluded)Thread size (d )Reference dimension2)3)4)Max. = nominal sizeMin. = nominal size Max. = nominal sizeMax. = nominal sizeNominal sizeNominal size1)5)6)Nominal sizeFor footnotes, see page 4.Shank length, l s , and grip length, l gPage 6DIN 6912:2002-12MaterialSteelStainless steel Nonferrous metalGeneral requirements As specified in ISO 8992.ThreadTolerance 6gAs specified in DIN ISO 261 and DIN ISO 965-2.For sizes up to Property class 1)8.8M24: A2-70 or CuZn 2)(material)A4-70; for larger sizes: A2-50.As specified inDIN EN ISO 898-1.DIN EN ISO 3506-1.DIN EN 28839.Product grade AAs specified inDIN EN ISO 4759-1.As processed.Plain PlainDIN EN ISO 4042DIN EN ISO 4042applies with regard applies with regard to electroplating.to electroplating.DIN EN ISO 10683applies with regard to zinc flake coatings.DIN EN 26157-3applies with regard to limits for surface discontinuities.Acceptance As specified in DIN EN ISO 3269.inspection1)See clause 5 for tensile strength requirements.2)CU2 or CU3 grade copper-zinc alloy, at the manufacturer’s discretion.4Technical delivery conditionsTable 2:Technical delivery conditionsMechanical propertiesLimit deviations and geometrical tolerancesSurface finishSurfacediscontinuities 5Reduced strength5.1Screws made of steel (other than stainless)When tested as specified in DIN EN ISO 898-1 (test programme B), steel screws covered by this standard may not fulfill the tensile strength requirements for property class 8.8. All other requirements shall be met.When testing full-size screws, the loads given in table 4 shall be applied. Any failure shall occur in the shank,along the free threaded length or at the head/shank transition.Page 7DIN6912:2002-12 Table3:Minimum ultimate tensile loads for steel screws of property class 8.8(equal to 80% of the loads required in DIN EN ISO898-1)Thread size (d)M4M5M6M8M10M12M14 Minimum ultimate tensile562090801290023400371005390073600 load, in N Thread size (d)M16M18M20M22M24M27M30 Minimum ultimatetensile100000127000162000202000234000309000373000 load, in NThread size (d)M33M36Minimum ultimate tensile461000542000load, in N5.2Stainless steel screwsIn the case of stainless steel screws, the tensile strength shall be equal to 80% of the values specified in DIN EN ISO3506-1.5.3Nonferrous metal screwsIn the case of nonferrous metal screws, the minimum breaking load shall be equal to 80% of the values specified in DINEN28839.6DesignationDesignation of an M12 hexagon socket thin head cap screw (M12) with pilot recess, with a nominal length, l, of 60 mm (60), of property class 8.8:Screw DIN6912 – M12 é 60 – 8.8See DIN962 for supplementary order designations for special screw types and finishes.Page 8DIN 6912:2002-12Annex AMass of steel screwsThread size (d )Nominal length, lApprox. mass, in kg, per 1 000 unitsM4M5M6M8M10M12M14M16M18M20M22M24M27M30M33M36Thread size (d )Nominal length, lApprox. mass, in kg, per 1 000 units 10121620253035405060708090100110120130140253035405060708090100110120130140150160170180190200 NOTE:The values of mass specified for the commercial sizes are for guidance only.。

CATIAV5介绍与应用•CATIAV5 Overview•Introduction to Basic Functionsof CATIAV5目录•CATIAV5 Advanced FunctionApplication•Integrating CATIAV5 with othersoftware applications•CATIAV5 operating skills and 目录improvement suggestions01CATIAV5OverviewCATIAV5, developed by Dassault Syst è mes, originating from the need for an advanced 3D CAD tool in the aerospace industry Over time, it evolved to become a comprehensive product development solution With the integration of newtechnologies like parametricdesign, knowledge basedengineering, and advancedsimulation capabilities, CATIAV5has become a leading platformfor product design anddevelopmentToday, CATIAV5 is widely usedacross various industries such asautomotive, aerospace,shipbuilding, and more It hassignificantly transformed the wayproducts are designed,developed, and manufacturedOrigin and Early Development TechnicalAdvancementsGlobal Adoptionand ImpactBackground and Development History of CATIAVAnalysis of Software Characteristics and Advantages•Comprehensive 3D Modeling Capabilities: CATIAV5 offers powerful 3D modeling tools that enable designers to create complex shapes and assemblies with precision•Seamless Integration with Other Software: The software integrations smoothly with other CAD, CAM, and CAE tools, facilitating a seamless workflow between different design and manufacturing processes•Advanced Simulation and Analysis: CATIAV5 provides advanced simulation and analysis capabilities that enable engineers to test and validate designs before manufacturing, saving time and costs •User Friendly Interface: The software boards a user friendly interface that simplifies the learning curve for new users and enhances productivity for experienced designersApplication field and market demand•Automotive Industry: CATIAV5 is widely used in the automotive industry for vehicle design, component design, and assembly validation It advanced surface capabilities make it ideal for styling and Class-A surface development•Aerospace Industry: In the aerospace sector, CATIAV5 is used for aircraft design, engine design, and systems integration It ability to handle large assemblies and complex kinematics make it suitable for aerospace applications•Shipbuilding Industry: The shipbuilding industry utilities CATIAV5 for hull design, outfitting, and piping design The software's ability to handle large data sets and complex geometry facilities effective ship design processes•Other Industries: In addition to automotive, aerospace, and shipbuilding, CATIAV5 finds applications in various other industries such as machinery, consumer goods, and electronics It versatility and02Introduction toBasicFunctions ofCATIAV5Modeling function3D solid modelingCreate complex 3D shapes using a variety of modelingtechniques such as extrusion, rotation, shifting, and moreSurface modelingDesign and modify free form surfaces using advanced surfacemodeling toolsParameter modelingDefine relationships between model features to automaticallyupdate designs when changes are madeSketch based modelingCreate 2D sketches as the basis for 3D models, with tools forconstraint based design and dimensioningComponent assembly: Arrange and combine individual parts into larger assemblies, with tools for positioning, matching, and constraining componentsAssembly analysis: Evaluate the performance of assemblies, including motion simulation and collection detection Bill of Materials (BOM) generation: Automatically create lists of components and assemblies for manufacturing and procurement purposesInteraction checking: Identify and resolve potential claims or overlaps between components in an assemblyAssembly design function2D drawingcreationGenerate professional quality 2D drawings from 3D models, with tools for adding dimensions, annotations, and symbolsDrawingtemplatesCustomize drawinglayouts and formatsusing pre definedtemplates or createyour own templatesfor consistentdrawing standardsDrawingviewsCreate multipleviews of a 3D model,includingorthographic,isometric, andauxiliary viewsDetailedannotationsAdd detailed notesand calls to drawingsto clarify designintent andmanufacturingrequirementsEngineering drawing functionDesign sheet metal components with tools for creating bends, flanges, and other sheet metal featuresSheet metal part modelingSimulate the unfolding and flattering of sheet metal parts to facilitate manufacturing processes such as last cutting orpunching Unfolding and flatteringEvaluate the feasibility and feasibility of sheet metal designs, including checks for potential defects such as teachersor writersSheet metal analysisGenerate detailed drawings and reports for sheet metal components, including bend tables and flat patternsSheet metal documentatio nSheet metal design function03CATIAV5AdvancedFunctionApplicationMastering the creation and editing of basic surfaces such as planes, cylinders, and cones Understanding the principles of surface continuity and quality evaluation Proficient in advanced surface modeling techniques including lofting, sweeping, and filling Demonstrating surface design skills through practical examples such as automotive body designSurface Design Skills and Example DemonstrationsEstablishing a kinematic model of the mechanism tobe analyzed Simulating the motion process and analyzing the resultsMethod and steps of motion simulation analysisDefining constraints and driving forces for eachcomponent Optimizing the design based on simulation results and feedback01Understanding the basic principles and methods of fine element analysis02Mastering the operation and settings of the fine element analysis module in CATIAV503Analyzing product stress, strain, and placement underdifferent load conditions 04Optimizing product designbased on fine elementanalysis resultsApplication of Fine Element Analysis in Product DesignUnderstanding the basic principles and processes of mold designSharing practical experience in mold design, including common problems and solutions Mastering the mold design module in CATIAV5 and its operation methodsDiscussing the trends and developments of mold design technologyMold design process and practical experience sharing04IntegratingCATIAV5 withother softwareapplicationsIntegration method with SolidWorks softwareUsing dedicated interfacesCATIAV5 provides dedicated interfaces to connect with SolidWorks, allowing for seamless dataexchange between the two software packagesImporting and exporting filesBoth CATIAV5 and SolidWorks support variant file formats, such as IGES, STEP, and Parasolid,which can be used to import and export data between the two systemsUsing third party toolsThere are several third party tools available that can facilitate the integration of CATIAV5 andSolidWorks, improving additional functionality and automation01 02 03Preparing data for exportBefore exporting data from CATIAV5 to AutoCAD, it is important to ensure that the data is properly prepared and cleaned up to avoid any issues during the export processUsing DXF/DWG file formatsAutoCAD supports the DXF and DWG file formats, which can be used to exchange 2D data between CATIAV5 and AutoCADManaging layer and block information When exporting data to AutoCAD, it is important to manage layer and block information properly to ensure that the data is organized and easy to work with in AutoCADTips for exchanging data with AutoCAD softwareImplementing Collaborative Work in PLM Systems•Understanding PLM systems: Product Lifecycle Management (PLM) systems are used to manage the entire lifecycle of a product, from concept to disposal CATIAV5 can be integrated with PLM systemsto enable collaborative work across different departments and disciplines•Setting up collaborative workspaces: In a PLM system, collaborative workspaces can be set up to allow multiple users to work on the same project collectively, sharing data and designs in real-time •Managing data and versions: PLM systems provide powerful data and version management capabilities, which can be used to track changes made to designs and ensure that the latest versions are always available to all users•Leveling PLM collaboration tools: PLM systems often come with collaboration tools such as instant messaging, video conferencing, and digital mock up review, which can be used to enhance communication and collaboration between team members working in CATIAV505CATIAV5operating skillsandimprovementsuggestionsSetting shortcut keysCATIAV5 allows users to set shortcut keys for frequently used commands, which can greatly improve work efficiencySaving custom settingsAfter customizing the interface and shortcut keys, users can save their settings as a template for future useCustomizing the toolbarUsers can add or delete toolbars and buttons according to their needs, and adjust the position and size of the toolbarInterface customization and shortcut key setting methodsSummary of common problem solutionsProblem 1Software crashes or freezes Solution: Restart thesoftware or computer, check for software updates, orreduce the complexity of the modelProblem 2Difficultly in importing or exporting data Solution:Check the file format and version compatibility, or usea dedicated data conversion toolProblem 3Slow rendering speed Solution: Optimize the model,reduce the number of surfaces and details, orupgrade the computer hardware01There are many excellent online tutorials available for learning CATIAV5, including video tutorials, text tutorials,and forums Online tutorials02Dassault Syst è mes,the developer of CATIAV5, offers official training courses for users of different levelsOfficial training courses 03Many universities and colleges offer courses on CATIAV5 or related fields, which provide systematic learning opportunities forstudentsAcademicinstitutions04Joining professional associations related to CATIAV5 can help users stayProfessional associationsRecommended learning resources and training opportunitiesTHANKS感谢观看。

1032023.19 / Urban and Rural Planning and Design 城乡规划·设计益主体涉及广、建设项目数量多、开发建设周期长，其前瞻谋划和规划实施工作在新时期高质量发展要求下面临更大的挑战，也更迫切需要对工作转型方向与制度创新路径进行探索。

近年来，各地城市结合自身实际开展了丰富的城市重点地区建设实践，在规划建设管理各个环节已积累了较为成熟的经验，但由于规划决策与行为的分散性，各阶段参与主体缺乏整体统筹意识，大多呈现碎片化多头推进状态，造成实际推进效果与城市高品质建设预期仍有差距。

在此背景下，基于我国现有的规划体系特征及广州在重点功能片区的规划探索实践，思考并总结有效适用于城市重点地区全流程规划建设管理的工作路径要点，对当前城市建设发展具有重要的现实意义。

2当前城市重点地区规划建设中的重难点研判城市重点地区，通常指城市战略规划、国民经济和社会发展规划等确定必须重点推进城市规划的建设开发区域，包括重要的城市商业商务区、产业功能集聚区及特色发展地区等。

城市重点地区在城市发展战略中一般被赋予了更高的发展定位、更高的空间品质、更高的建设效率的期许，其规划建设管理因高强度空间开发、高运转建设周期、多维度主体诉求及财务成本压力叠加面临严峻的挑战。

2.1空间维度：高效集约的空间资源利用土地是重要的生产资料，城市重点地区的土地更具有稀缺性。

有限的土地资源、高昂的再开发成本，驱使城市空间向高强度、高密度方向演进，间接导致人、地、产等客观要素及技术逻辑的矛盾高度集聚在有限的土地载体上。

由于单位面积更小的土地承载更多的空间发展需求，需在有限的空间里处理好自然资源、历史文脉与现代开发之间的矛盾，对跨专业设计协调及后期建设施工管理等方面带来新的更大的挑战。

如商务区内部小街区、密路网的摘要 研究探讨了在新时期城市建设由高增量转向高质量发展的背景下，城市重点地区规划建设环节中存在的难点和痛点，如高效集约的空间资源利用、精明紧凑的开发建设周期、多元复杂的利益主体诉求、理想空间范式与现实经济性的平衡取舍考量等，并基于广州市重点功能片区的规划实践，指出建立伴随式与成长型的地区规划、空间组织与开发建设机制的意义，进而从顶层设计、详细规划、城市设计、土地开发等环节，总结提出全生命周期管理视角下的规划建设工作要点，以期为超大、特大城市重点地区的高质量发展提供路径指引与模式借鉴。

3d MAX 菜单中英文对照表Absolute Mode Transform Type-in绝对坐标方式变换输入Absolute/Relative Snap Toggle Mode绝对/相对捕捉开关模式ACIS Options ACIS选项Activate活动;激活Activate All Maps激活所有贴图Activate Grid激活栅格；激活网格Activate Grid Object激活网格对象；激活网格物体Activate Home Grid激活主栅格;激活主网格ActiveShade实时渲染视图；着色；自动着色ActiveShade(Scanline）着色(扫描线）ActiveShade Floater自动着色面板;交互渲染浮动窗口ActiveShade Viewport自动着色视图Adaptive适配;自动适配；自适应Adaptive Cubic立方适配Adaptive Degradation自动降级Adaptive Degradation Toggle降级显示开关Adaptive Linear线性适配Adaptive Path自适应路径Adaptive Path Steps适配路径步幅；路径步幅自动适配Adaptive Perspective Grid Toggle适配透视网格开关Add as Proxy加为替身Add Cross Section增加交叉选择Adopt the File’s Unit Scale采用文件单位尺度Advanced Surface Approx高级表面近似；高级表面精度控制Advanced Surface Approximation高级表面近似；高级表面精度控制Adv。

Lighting高级照明Affect Diffuse Toggle影响漫反射开关Affect Neighbors影响相邻Affect Region影响区域Affect Region Modifier影响区域编辑器；影响区域修改器Affect Specular Toggle影响镜面反射开关AI Export输出Adobe Illustrator(＊.AI)文件AI Import输入Adobe Illustrator(＊.AI）文件Align对齐Align Camera对齐摄像机Align Grid to View对齐网格到视图Align Normals对齐法线Align Orientation对齐方向Align Position对齐位置(相对当前坐标系）Align Selection对齐选择Align to Cursor对齐到指针Allow Dual Plane Support允许双面支持All Class ID全部类别All Commands所有命令All Edge Midpoints全部边界中点;所有边界中心All Face Centers全部三角面中心;所有面中心All Faces所有面All Keys全部关键帧All Tangents全部切线All Transform Keys全部变换关键帧Along Edges沿边缘Along V ertex Normals沿顶点法线Along Visible Edges沿可见的边Alphabetical按字母顺序Always总是www_bitscn_com中国.网管联盟Ambient阴影色；环境反射光Ambient Only只是环境光；阴影区Ambient Only Toggle只是环境光标记American Elm美国榆树Amount数量Amplitude振幅;幅度Analyze World分析世界Anchor锚Angle角度;角度值Angle Snap Toggle角度捕捉开关Animate动画Animated动画Animated Camera/Light Settings摄像机/灯光动画设置Animated Mesh动画网格Animated Object动画物体Animated Objects运动物体;动画物体；动画对象Animated Tracks动画轨迹Animated Tracks Only仅动画轨迹Animation动画Animation Mode Toggle动画模式开关Animation Offset动画偏移Animation Offset Keying动画偏移关键帧Animation Tools动画工具Appearance Preferences外观选项Apply Atmospherics指定大气Apply—Ease Curve指定减缓曲线Apply Inverse Kinematics指定反向运动Apply Mapping指定贴图坐标Apply—Multiplier Curve指定增强曲线Apply To指定到；应用到Apply to All Duplicates指定到全部复本Arc弧；圆弧Arc Rotate弧形旋转;旋转视图；圆形旋转Arc Rotate Selected弧形旋转于所有物体;圆形旋转选择物；选择对象的中心旋转视图Arc Rotate SubObject弧形旋转于次物体；选择次对象的中心旋转视图Arc ShapeArc Subdivision弧细分；圆弧细分Archive文件归档Area区域Array阵列Array Dimensions阵列尺寸;阵列维数Array Transformation阵列变换ASCII Export输出ASCII文件Aspect Ratio纵横比Asset Browser资源浏览器Assign指定Assign Controller分配控制器Assign Float Controller分配浮动控制器Assign Position Controller赋予控制器Assign Random Colors随机指定颜色Assigned Controllers指定控制器At All Vertices在所有的顶点上At Distinct Points在特殊的点上At Face Centers 在面的中心At Point在点上Atmosphere氛围；大气层；大气，空气;环境Atmospheres氛围Attach连接;结合；附加Attach Modifier结合修改器Attach Multiple多项结合控制;多重连接Attach To连接到Attach To RigidBody Modifier连接到刚性体编辑器Attachment连接；附件Attachment Constraint连接约束Attenuation衰减AudioClip音频剪切板AudioFloat浮动音频Audio Position Controller音频位置控制器AudioPosition音频位置Audio Rotation Controller音频旋转控制器AudioRotation音频旋转Audio Scale Controller音频缩放控制器AudioScale音频缩放；声音缩放Auto自动Auto Align Curve Starts自动对齐曲线起始节点Auto Arrange自动排列Auto Arrange Graph Nodes自动排列节点Auto Expand自动扩展Auto Expand Base Objects自动扩展基本物体Auto Expand Children自动扩展子级Auto Expand Materials自动扩展材质Auto Expand Modifiers自动扩展修改器Auto Expand Selected Only自动扩展仅选择的Auto Expand Transforms自动扩展变换Auto Expand XYZ Components自动扩展坐标组成Auto Key自动关键帧Auto-Rename Merged Material自动重命名合并材质Auto Scroll自动滚屏Auto Select自动选择Auto Select Animated自动选择动画Auto Select Position自动选择位置bitsCN#com中国网管联盟Auto Select Rotation自动选择旋转Auto Select Scale自动选择缩放Auto Select XYZ Components自动选择坐标组成Auto—Smooth自动光滑AutoGrid自动网格；自动栅格AutoKey Mode Toggle自动关键帧模式开关Automatic自动Automatic Coarseness自动粗糙Automatic Intensity Calculation自动亮度计算Automatic Reinitialization自动重新载入Automatic Reparam.自动重新参数化Automatic Reparamerization自动重新参数化Automatic Update自动更新Axis轴;轴向;坐标轴Axis Constraints轴向约束Axis Scaling轴向比率Back后视图Back Length后面长度Back Segs后面片段数Back View背视图Back Width后面宽度Backface Cull背面忽略显示；背面除去;背景拣出Backface Cull Toggle背景拣出开关Background背景Background Display Toggle背景显示开关Background Image背景图像Background Lock Toggle背景锁定开关Background Texture Size背景纹理尺寸；背景纹理大小Backgrounds背景Backside ID内表面材质号Backup Time One Unit每单位备份时间Banking倾斜Banyan榕树Banyan tree榕树Base基本；基部；基点；基本色；基色Base/Apex基点/顶点Base Color基准颜色；基本颜色Base Colors基准颜色Base Curve基本曲线Base Elev基准海拔；基本海拔Base Objects导入基于对象的参数，例如半径、高度和线段的数目;基本物体Base Scale基本比率Base Surface基本表面;基础表面Base To Pivot中心点在底部Bevel Profile轮廓倒角Bevel Profile Modifier轮廓倒角编辑器;轮廓倒角修改器Bezier贝塞尔曲线Bezier Color贝塞尔颜色bbs。

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Geometric ModelingGeometric modeling is a fundamental concept in the field of computer graphics and design. It involves the creation and manipulation of digital representations of objects and environments using geometric shapes and mathematical equations. This process is essential for various applications, including animation, virtual reality, architectural design, and manufacturing. Geometric modeling plays a crucial role in bringing creative ideas to life and enabling the visualization of complex concepts. In this article, we will explore the significance of geometric modeling from multiple perspectives, including its technical aspects, creative potential, and real-world applications. From a technical standpoint, geometric modeling relies on mathematical principles to define and represent shapes, surfaces, and volumes in a digital environment. This involves the use of algorithms to generate and manipulate geometric data, enabling the creation of intricate and realistic 3D models. The precision and accuracy of geometric modeling are essential for engineering, scientific simulations, and industrial design. Engineers and designers utilize geometric modeling software to develop prototypes, analyze structural integrity, and simulate real-world scenarios. The ability to accurately model physical objects and phenomena in a virtual space is invaluable for testing and refining concepts before they are realized in the physical world. Beyond its technical applications, geometric modeling also offers immense creative potential. Artists and animators use geometric modeling tools to sculpt, texture, and animate characters and environments for films, video games, and virtual experiences. The ability to manipulate geometric primitives and sculpt organic forms empowers creatives to bring their imaginations to life in stunning detail. Geometric modeling software provides a canvas for artistic expression, enabling artists to explore new dimensions of creativity and visual storytelling. Whether it's crafting fantastical creatures or architecting futuristic cityscapes, geometric modeling serves as a medium for boundless creativity and artistic innovation. In the realm of real-world applications, geometric modeling has a profound impact on various industries and disciplines. In architecture and urban planning, geometric modeling software is used to design and visualize buildings, landscapes, and urban developments. This enables architects and urban designers toconceptualize and communicate their ideas effectively, leading to the creation of functional and aesthetically pleasing spaces. Furthermore, geometric modelingplays a critical role in medical imaging and scientific visualization, allowing researchers and practitioners to study complex anatomical structures and visualize scientific data in meaningful ways. The ability to create accurate and detailed representations of biological and physical phenomena contributes to advancementsin healthcare, research, and education. Moreover, geometric modeling is integral to the manufacturing process, where it is used for product design, prototyping,and production. By creating digital models of components and assemblies, engineers can assess the functionality and manufacturability of their designs, leading tothe development of high-quality and efficient products. Geometric modeling also facilitates the implementation of additive manufacturing technologies, such as 3D printing, by providing the digital blueprints for creating physical objects layer by layer. This convergence of digital modeling and manufacturing technologies is revolutionizing the production landscape and enabling rapid innovation across various industries. In conclusion, geometric modeling is a multifaceteddiscipline that intersects technology, creativity, and practicality. Its technical foundations in mathematics and algorithms underpin its applications in engineering, design, and scientific research. Simultaneously, it serves as a creative platform for artists and animators to realize their visions in virtual spaces. Moreover,its real-world applications extend to diverse fields such as architecture, medicine, and manufacturing, where it contributes to innovation and progress. The significance of geometric modeling lies in its ability to bridge the digital and physical worlds, facilitating the exploration, creation, and realization of ideas and concepts. As technology continues to advance, geometric modeling will undoubtedly play an increasingly pivotal role in shaping the future of design, visualization, and manufacturing.。

A Practical Guide to Parametric Drawing in AutoCAD Rick Ellis – Cadapult Software Solutions, Inc.Parametric design tools aren’t just for programs like Inventor software, Revit software, or AutoCAD Civil 3D software; there is also a set of parametric drawing tools that you can use to create dynamic relationships and constraints between objects in AutoCAD software. The parametric drawing tools will revolutionize the way that you draw and edit objects in AutoCAD software. This class will introduce you to parametric drawing in AutoCAD software by using both geometric and dimensional constraints to add intelligence to your objects. You will learn how using Auto Constrain and Inferred Constraints can help you quickly add constraints and change your process from drafting to modeling. If you’ve ever wanted geometry in your drawing to update based on changes that you’ve made to other objects, or if you’ve wanted to type a new value into a dimension and have the object update based on this new value, this class is for you.Learning ObjectivesAt the end of this class, you will be able to:1. Learn how to create geometric relationships between objects by adding constraints2. Learn how to define dimensional constraints3. Learn how to identity and edit constrained objects4. Learn how to use inferred constraints to have AutoCAD automatically define constraints for you Your AU ExpertsRick Ellis is the President of CADapult Software Solutions, Inc., where he provides training and consulting services to clients around the country, helping them get the most out of their design software investment. Rick specializes in AutoCAD® Civil 3D®, AutoCAD® Map 3D, Autodesk® InfraWorks™, AutoCAD® Raster Design, and AutoCAD®. He is a member of the Autodesk Developer Network, and author of several critically acclaimed books on AutoCAD Civil3D, and AutoCAD Map 3D; including the Practical Guide series. Rick continues to use AutoCAD Civil 3D on projects in a production environment, in addition to teaching classes to organizations both large and small around the country. This practical background and approach has made him a sought after instructor by organizations around the world.**************************@theRickEllisOverviewWhat is parametric drawing?The Autodesk Definition: “Feature in AutoCAD that assigns constraints to objects, establishing the distance, location, and orientation of objects with respect to other objects.”If the defini tion above didn’t answer all of your questions about parametric drawing, I’ll expand on that and go into a bit more detail. AutoCAD 2010 introduced Parametric drawing. This is not only a relatively new feature for AutoCAD, it is a new concept that will change the way that you create and edit drawings in AutoCAD. While this is a somewhat new feature for AutoCAD, similar tools for parametric design have been in other products like Inventor, Revit, and Civil 3D for some time and you may be familiar with them. Put simply, the idea of parametric drawing is that objects can be related to each other. For example, if you want two lines to be parallel, they would always be parallel. If you change one line then the other will update to match it. This is just one example. However, if you think about all the possibilities, and all the time that you have spent editing drawings to make sure that all the necessary and related changes have been made for a simple change to the design, these tools have the potential to revolutionize the way that you work.AutoCAD uses two types of Parametric Constraints:▪Geometric Constraints∙The Autodesk Definition: “Rules that define the geometric relationships of objects (or points of objects) elements and control how an object can change shape or size.Geometric constraints are coincident, collinear, concentric, equal, fix, horizontal, parallel,perpendicular, tangent, and vertical.”∙Sticky Object Snaps. They maintain the geometric relationship between objects rather than setting it once at the time you use the object snap and then allowing it to change inthe future.∙Add intelligence to your drawings.∙Allow you to think more about modeling and less about drafting.▪Dimensional Constraints∙The Autodesk Definition: “Parametric dimensions tha t control the size, angle, or position of geometry relative to the drawing or other objects. When dimensions are changed, theobject resizes.”∙You can type the value into a dimension and the object updates. It’s the opposite of associative dimensions. With Dimensional Constraints the dimension value drives thegeometry rather than the geometry driving the dimension.∙Can include equations.∙Can even reference other objects. For example, line 1 is twice the length of line 2.Exercise 1 – Working with Existing Constraints1. Open the drawing Widget Assembly complete.dwg from the folder called Completed Assemblyin the dataset.2. Select the block representing the slider on the shaft (identified by callout number 2).3. Move the block.4. Notice the block can only move along the shaft and the arm rotates as it moves.5. Double click the dimension d1 and change the value to 1.56. Notice that changing the value of the dimension moves the block.7. Select and move one of the callouts.8. Notice the entire row of callouts moves together.9. Try moving other pieces of this assembly to see the different constraints in action.10. Open the drawing Parametric - geometric.dwg from the dataset.11. Move and stretch different pieces of the orthographic projection to see how constraints have beenset up within it.Geometric ConstraintsGeometric Constraints maintain the geometric relationship between objects based on basic geometric properties of the entity or entities you apply them to. AutoCAD supports the following geometric constraint types:▪Coincident▪Co-linear▪Tangent▪Perpendicular▪Parallel▪Horizontal (relative to the current UCS X axis)▪Vertical (relative to the current UCS Y axis)▪Concentric▪Equal▪Symmetric▪Smooth▪FixedThe commands to create and manage Geometric Constraints can be found on the Parametric tab of the ribbon.The table below shows the types of objects that can be used to create geometric constraints and their constraint points.Tips when creating geometric constraints:▪When applying constraints between two entities AutoCAD modifies the second entity selected, leaving the first entity unmodified.▪If you convert an object that has constraints to a ployline the constraints are lost.▪If you explode a polyline that has constraints the constraints are lost.▪If you copy an object with constraints the constraints are copied if all the objects involved in the constraint are copied.Constraint BarsConstraint Bars provide a heads-up interface to help you manage geometric constraints in your drawings. Constraint Bars look and behave a lot like transparent floating tool bars, except that each button on a bar represents a single geometric constraint.When you place your cursor over individual constraints on a constraint bar AutoCAD highlights the button, the entity the constraint applies to, and the corresponding button and entity participating in the constraint.When you right-click on a constraint on the constraint bar there are several commands which you can perform on the constraint, including deleting the constraint, hiding the bar, or managing the constraint bar settings.To delete all constraints on an entity use the Delete Constraints command. Ribbon: Parametric tab >> Manage panel >> Delete Constraints.Exercise 2 – Working with Geometric Constraints1. Open the drawing Parametric - geometric.dwg from the dataset.2. Pan to a blank area of the drawing.3. Draw 4 individual lines similar to the graphic below.4. Add Geometric Constraints to make this a dynamic rectangle.a. Use the Coincident, Parallel, and Perpendicular constraints.5. Zoom extents to find the bracket in the drawing as displayed below.6. Add Geometric Constraints to make the bracket hinge at the corner while keeping both sides ofthe part the same size.7. Zoom extents to find the orthographic projection.8. Copy the orthographic projection.9. Remove all the constraints from the orthographic projection.10. Add geometric constraints to the orthographic projection to make it behave as the original.Auto ConstrainIf applying geometric constraints one at a times seems like a tedious task there is an option to let AutoCAD look for objects that can be constrained and add them for you. Auto Constrain examines entities you select and attempts to automatically constrain the geometry based on its current position.You can control the settings for the Auto Constrain command in the Constraint Settings dialog box. Ribbon: Parametric tab >> Geometric panel >> >> Constraint Settings.Here you can select the type(s) of constraints that you want the Auto Constrain command to apply. You can also set Tolerances for distance and angle. These tolerances will determine if constraints are applied and objects are modified when they are “close” to geometrica lly accurate. When used properly this can help clean up a drawing that was created without using object snaps. However, you want to choose your tolerances carefully as it will allow the Auto Constrain command to modify geometry. If you only want the Auto Constrain command to apply constraints where the geometry is perfect and not modify any geometry, set the tolerances to 0.Inferred ConstraintsInferred constraints automatically apply geometric constraints while creating and editing geometric objects, removing the need for you to add constraints later. The Infer Constraints mode works with your object snaps and is enabled with a toggle on the status bar.Once enabled object snaps that are used when creating or editing objects are also used to infer geometric constraints. Objects are not modified by inferred constraints.Exercise 3 – Working with Auto Constrain and Inferred Constraints1. Open the drawing Parametric – Inferred.dwg from the dataset.2. Pan to a blank area of the drawing.3. Draw a rectangle using the rectangle command.4. Use the Auto Constrain command to add constraints.5. Notice what constraints are added.6. Zoom extents to find the bracket in the drawing as displayed below.7. Use the Auto Constrain command to add constraints.8. Notice what constraints are added.9. Turn on Inferred constraints.10. Draw a rectangle using the rectangle command.11. Notice what constraints are added.Dimensional ConstraintsDimensional Constraints constrain objects by allowing you to enter values or formulas. They work similar to associative dimensions, just in reverse. While associative dimensions update the value of the dimension as the object changes, dimensional constraints update the object when the value of the dimension changes. The dimensions drive the geometry rather than the geometry driving the dimensions. Dimensional constraints come in the following types:▪Aligned▪Horizontal▪Vertical▪Radial▪Diameter▪AngularDimensional constraints can constrain the following properties:▪Distances between objects, or between points on objects▪Angles between objects, or between points on objects▪Sizes of arcs and circlesThere two different kinds of dimensional constraints:▪Dynamic∙Maintain the same size regardless of zoom level∙Can easily be turned on or off globally in the drawing∙Display using a fixed, predefined dimension style∙Position the textual information automatically, and provide triangle grips with which you can change the value of a dimensional constraint∙Do not display when the drawing is plotted▪Annotational∙Change their size when zooming in or out∙Display individually with layers∙Display using the current dimension style∙Provide grip capabilities that are similar to those on dimensions∙Display when the drawing is plottedIf you need to control the dimension style of dynamic constraints, or if you need to plot dimensional constraints, use the Properties palette to change dynamic constraints to annotational constraints.The commands to create and manage Dimensional Constraints can be found on the Parametric tab of the ribbon.Tips when creating dimensional constraints:▪When applying dimensional constraints AutoCAD modifies the constrained geometry to satisfy the new constraint.▪If you convert an object that has constraints to a ployline the constraints are lost.▪If you explode a polyline that has constraints the constraints are lost.▪If you copy an object with dimensional constraints the constraints are copied.▪Dimensional constraints can contain equations.The example above contains a rectangle with two basic dimensional constraints.The example above contains a rectangle with two dimensional constraints where the length (d1) is equal to twice the height (d2).You can manage all the values of your dimensional constraints with the Parameters Manager. Ribbon: Parametric tab >> Manage panel >> Parameters Manager.In the Parameters Manager you can edit expressions and even add user defined variables that you can use in expressions.Exercise 4 – Working with Dimensional Constraints1. Open the drawing Parametric - dimensions.dwg from the dataset.2. Zoom to the rectangle.a. It already has geometric constraints.3. Add Dimensional Constraints for the width and length.4. Edit the width to be 3.5. Edit the length to be twice the width by editing the expression.6. Zoom extents to find the bracket in the drawing as displayed below.a. It already has geometric constraints.7. Add a dimensional constraint to control the angle.8. Draw circles at each end of the part.9. Use a concentric geometric constraint to position them10. Add a dimensional constraint that makes them half the outer radius of the part.Constraints in Dynamic BlocksIntroduced in AutoCAD 2005, Dynamic Blocks extend the capabilities of traditional blocks by providing the ability to define custom grips and properties for your blocks which affect the geometry for the block. You create dynamic blocks by combining Block Actions and Block Action Parameters within the block definition. Now you can extend the power of blocks even further by adding geometric and dimensional constraints to your dynamic blocks.When you add geometric and dimensional constraints to dynamic blocks it is best to add them in the block editor using the commands on the Block Editor tab of the Ribbon.A Block Properties table allows you to define and control values for parameters and properties within a block definition. This will become the list of selectable values in the dynamic block.Exercise 5 – Working Constraints in Dynamic Blocks1. Open the drawing Parametric - blocks.dwg from the dataset.2. Open the block editor.a. Ribbon: Insert tab >> Block panel >> Block Editor.b. Name the new block AUParametric.3. Draw a rectangle using the rectangle command starting the lower left corner of the rectangle at0,0.4. Add Geometric Constraints to make this a dynamic rectangle.5. Add Dimensional Constraints for the width and length.6. Edit the width to be 5.7. Edit the length to be twice the width by editing the expression.8. Add a Block Table.a. Place the block table near the origin of the block.b. Placement of the block table does not need to be exact. It will be the location of a grip onthe block that can be used to select standard sizes.9. Enter 1 for the number of grips.10. Click the Add Properties button11. Select the d1 parameter and Click <<OK>>.12. Enter values for d1 as shown above.13. Click <<OK>> when finished.14. Close the block editor and save the changes.15. Insert the block anywhere in your drawing.16. Select the block and notice the available grips.a. You will be able to stretch it in the vertical direction and the rectangle will keep the 2:1ratio of length to width.b. Select the block table grip and you will see the predefined widths.c. Select one of the values and notice how the block resizes.ConclusionParametric drawing in AutoCAD with geometric and dimensional constraints is a powerful set of tools that may drastically change the way that you create and edit drawings. I hope that this introduction to these exciting features has got you thinking about ways that you can apply it to your own drawings and projects.I encourage you to try it out, start small at first, but I am confident that you fill not only find these tools a powerful time saver but also intuitive and easy to learn.。