1 / 46

Chap.5 Geometric Modeling System

Chap.5 Geometric Modeling System. Geometric modeling? Classification of geometric modeling Solid modeling functions (from text) Feature based modeling functions (in SolidWorks) Assembly modeling Solid representation : B-Rep data structure Euler operator. Geometric Modeling?. Model

kalonice-cleatus
Download Presentation

Chap.5 Geometric Modeling System

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chap.5 Geometric Modeling System • Geometric modeling? • Classification of geometric modeling • Solid modeling functions (from text) • Feature based modeling functions (in SolidWorks) • Assembly modeling • Solid representation : B-Rep data structure • Euler operator

  2. Geometric Modeling? • Model • 대상에 대한 간략화된 표현 • 단순하면서도 • 관심있는 특성을 잘 표현할 것 • 예 • Fashion model • Role model • Geometric model == Shape model • 형상에 대한 model • Physical model • Computational model • Wide range of application incl. CAD/CAM

  3. SW Components of typical 3D CAD/CAM Data Exchange API (Application Program Interface) User Interface GUI, Command • CAD Module • - Part modeling • Assy modeling • Drafting • etc • CAM Module • tool path gen. • cutting simulation • post processing • etc External application Other CAD/CAM system Geometric Modeling Kernel Windows Graphic Lib. Operating System

  4. Classification of Geometric Model • By dimensionality • 2D • 3D • 2-Manifold vs Non-manifold • Precision • Exact • Approximation • What to store? • Procedure • Result • Hybrid

  5. By dimensionality • 2D model • Point, line, circular arc, planar curve • Poly line • PS (Point Sequence) curve : PwL • Area, Island • 3D model • Wire frame • Surface • Solid

  6. 2-Manifold vs Non-manifold • 2-Manifold • 2 dimensional manifold • 모델의 표면상의 임의 점에 대해 작은 rubber disk를 mapping가능한 물체 • 현존하는 모든 물체 • Bounded 2-manifold • Half disk mapping이 가능한 물체 • incomplete 2-manifold • Non-manifold model : 2D manifold가 아닌 상황도 표현할 수 있도록 하는 model • Mixed dimensional model • Dangling edge, isolated vertex, vertex contact, more than 2 faces sharing an edge, …

  7. Non-manifold model

  8. Precision • Exact (?) model : to be covered extensively during the course • Continuous/Smooth representation • Explicit / implicit / parametric curves / surfaces • Approximation model • Cloud of points (point cloud) • Height field • Z-map, Z-buffer, G-buffer : Rays at Uniform/non-uniform grid • Voxel model, dexel model • Quad tree, Oct tree • BSP (Binary space partitioning tree) • Mesh : Triangular, Rectangular, Polygonal r(u,v)

  9. Cloud of points • The simplest form • Unorganized / organized points • Too many points to represent the desired shape • Hard to handle  further processing is required • Obtained by digitizing • CMM (coordinate measuring machine) • Scanner using structured light (Moire, …) • Laser range scanner • CT, MRI • Computational result • …

  10. z(i,j) z y y(i) x(i) x Single valued Z-map model Height field over surface (Discrete vector model) Height field • Z-map, Z-buffer, G-buffer, Depth-buffer등으로 불리움 • z = f(x,y) : height field over xy plane • Uniform grid • Non-uniform grid • Very simple and efficient • Difficulties in representing vertical element and overhang • r(u,v) = r0(u,v) + f(u,v)N(u,v) : height field over surface • Cutting simulation model에 많이 사용됨

  11. Voxel model • Partition space into uniform grid cubical voxel (cf. pixel) • Stores properties at each voxel : occupancy, color, … • O(n3) storage for n x n x n grid, O(1) access time (random access) • Easy & fast Boolean operation, Slicing

  12. z(k,l,5) z z(i,j,1) y z(m,n,3) z(m,n,2) z(m,n,1) y(n) x(m) x Multi-valued Z-map model (dexel) Dexel model • Multi-valued Z-map model • Run-length encoded voxel model • Compromises speed and storage • O(kn2) storage for n x n grid & avg. k elements per pixel • O(k) access time

  13. Adaptive partition w/ Quadtree Uniform partition (pixel) Quad tree, Oct tree • Adaptive space partitioning • Generally more storage efficient than voxel or dexel at the same level of granularity(accuracy) • Relatively easy to handle

  14. 1 a b 1 g g a a 6 c 2 f f 3 d 3 5 e e 7 e 4 d c 4 d c b b f 5 2 6 7 BSP (Binary Space Partitioning) Tree • Recursively partition of space by hyper-planes • Efficient near-to-far ordering from a view point • real-time rendering • Efficient point membership classification Object Binary Spatial Partition BSP Tree

  15. Polygonal mesh • Most popular approximation model • Graphics, RP, CAD/CAM, DMU, CAE등에 두루 활용됨 • Hard to handle • Triangular mesh, Quad mesh, General polygonal mesh • Create mesh by • triangulating cloud of points • faceting exact surface model • interactive/iterative refining/decimating the initial mesh model • and so on

  16. What to store : Modeling procedure • Procedural model • Modeling에 사용된 procedure를 저장 • CSG (Constructive Solid Geometry) • Primitive solid들의 Boolean operation tree를 저장 • Fractal • Recursive self-similar shape • Parts are scaled copy of the original • 주로 graphics의 용도로 사용 • Terrain, plants, clouds, features, …

  17. What to store : result • B-Rep (Boundary representation) model • Modeling의 결과로 얻어진 형상의 bounding element를 저장 • Topology : element들간의 인접관계 • Geometry : element들의 실제 위치/모양

  18. B-Rep model • Topological element • Vertex • Edge • Loop (Edge list) • Face • Lump • Body • Geometrical element • Point • Curve • Composite curve • Surface, trimmed surface • N/A • N/A • Trimmed surface = • surface + trimming boundary curve

  19. What to store : hybrid model • Store both of procedure and result • Procedure : modeling sequence such as feature tree • Result : B-rep model • B-rep elements are associated with the modeling step • Modeling steps have the pointer to their resulting B-rep elements • 현재 사용되는 대부분의 CAD시스템이 채택 • Undo / Redo 용이 • Feature based modeling • Modeling step을 designer에게 의미있는 단위로 구성한 Hybrid modeler • ‘Hole’ instead of ‘subtracting cylinder’ • 하지만 범용 CAD시스템들은 그 단위가 form feature 중심 • 진정한 의미의 design feature / manufacturing feature는 적용하고자 하는 domain에 따라 다르기 때문.

  20. Chap.5 Geometric Modeling System • Geometric modeling? • Classification of geometric modeling • Solid modeling functions (from text) • Feature based modeling functions (in SolidWorks) • Assembly modeling • Solid representation : B-Rep data structure • Euler operator

  21. Solid modeling functions (from text A) • Create a simple shape • Primitive creation, Boolean operations • Create a solid from curves • Extrusion/Revolution(Sweeping), Lofting(Skinning) • Modifying • filleting, face lifting • Boundary modeling & tweaking • Feature-based modeling • Using familiar shapes (ex: hole, chamfer, slot, etc) • Parametric modeling • Changing the geometric constraints and/or dimension data,…

  22. Primitive creation, Boolean operations Solid Primitives

  23. Extrusion / Revolution (sweeping) Revolution (swinging) (text에서는 rotational sweeping 이라고 부름) Extrusion (text에서는 translational sweeping 이라고 부름)

  24. Lofting (Skinning)

  25. Blending (Rounding/Filleting), Face Lifting Rounding Filleting Face Lifting

  26. Boundary Modeling • Add, delete, modify entities such as vertices, edges, and faces directly • Construct solid from boundary surfaces

  27. Vertex Tweaking Edge Tweaking Modification by vertex moving Modification by edge replacement Tweaking • Face Tweaking Modification by face replacement

  28. Feature-based modeling Hole Chamfer Hole Slot Pocket (돌출컷) Fillet

  29. Parametric modeling • Models a shape by using geometric constraints and dimension data on its elements. • Geometric constraints • describing the relation between elements • (ex) 2 faces are parallel, 2 edges lie in a plane, etc. • Dimension data • Shape dimension, relations between the dimensions. • Parametric modeling constructs the required shape by solving the equations that express the geometric constraints - from dimensions, from the dimensional relations.

  30. Chap.5 Geometric Modeling System • Geometric modeling? • Classification of geometric modeling • Solid modeling functions (from text) • Feature based modeling functions (in SolidWorks) • Assembly modeling • Solid representation : B-Rep data structure • Euler operator

  31. Solid modeling features in SolidWorks-1 • Extrusion, Revolution • Extrusion cut, Revolution cut, Hole

  32. Solid modeling features in SolidWorks-2 • Fillet, Chamfer • Variable radius fillet

  33. Lofting, Sweeping • Lofting : 여러 단면곡선 • Sweeping : Section curve(s) + Guide curve

  34. Drafting(구배주기), Thick, Shell • Draft, Shell • Pattern (반복하기) : 선형, 원형, 대칭

  35. 그외 다수 • Sketch 정의 • Dimension & Constraints • Sheet metal modeling functions • Bending, .. • 전개도 만들기 • Mold modeling functions • Cavity • Parting surface 만들기 • 곡선/곡면 modeling

  36. Chap.5 Geometric Modeling System • Geometric modeling? • Classification of geometric modeling • Solid modeling functions (from text) • Feature based modeling functions (in SolidWorks) • Assembly modeling • Solid representation : B-Rep data structure • Euler operator

  37. Assembly modeling • Part model간의 상호 관계 형성 • Mating condition • Exploded view

  38. Chap.5 Geometric Modeling System • Geometric modeling? • Classification of geometric modeling • Solid modeling functions (from text) • Feature based modeling functions (in SolidWorks) • Assembly modeling • Solid representation : B-Rep data structure • Euler operator

  39. B-Rep (Boundary Representation) model review • Topological element • Vertex • Edge • Loop (Edge list) • Face • Lump • Body • 물체의 boundary를 저장 • Boundary element 들 • Geometrical element • Point • Curve • Composite curve • Surface, trimmed surface • N/A • N/A

  40. Connection table structure

  41. Problems of connection table • Simple Polyhedron only • Planar face • Linear edge • No hole  simple polyhedron • Face table에서 모서리 list의 길이가 variable → Face table의 관리가 번거롭다 • Vertex, Edge, Face간의 adjacency에 대한 정보 유도가 불편 • 한 edge를 공유하는 모든 face? • 한 vertex을 공유하는 모든 edge?  Edge-based structure • Winged edge structure • Half edge structure

  42. Doubly linked list for face F1 Doubly linked list for face F2 Edge-based structure? • Variable edge list length  linked list !! • Face는 하나의 edge만 point, 각각의 edge는 next edge를 point → Face를 이루는 모서리의 개수에 무관 • 같은 edge E6의 next edge가 어느 Face를 기준으로 하는가에 따라 달라짐 → F3를 저장할 때 F2에 대한 정보가 훼손 • 하나의 edge를 둘로 쪼개서 각각의 Face 에 대해 한번만 나타나도록 함 → half edge !!

  43. V5 E5 h9 h12 h14 E7 F1 E6 E6 h2 F2 E1 h11 Doubly linked list using half edges h4 V3 V2 E2 Half edge? • Edge : 두 face에 의해 공유 • Half edge : edge의 한 face내에서의 표현

  44. How about a hole on a face? • 구멍이 있는 face는 외부와 내부의 boundary  Loop의 개념을 도입 • 1st loop : periphery(outer) loop • Next loops : hole(inner) loops • Periphery loop (CCW)과 hole loop(CW)은 방향이 반대  진행방향의 왼쪽에 face의 내부 존재  face의 내부, 외부의 정보를 제공 L1 L2 L3 F1

  45. Half-edge data structure 1st face Parent solid 1st loop Parent face 1st HalfEdge Parent loop Shared edge Edge HalfEdge Any halfedge adj. to vertex Mate halfedge Start vertex

  46. Chap.5 Geometric Modeling System • Geometric modeling? • Classification of geometric modeling • Solid modeling functions (from text) • Feature based modeling functions (in SolidWorks) • Assembly modeling • Solid representation : B-Rep data structure • Euler operator

More Related