Subdivision theory
1 like973 views
This document summarizes key concepts in subdivision surface theory, including: - Subdivision surfaces generate smooth surfaces from coarse polygonal meshes by recursively subdividing polygons. - Schemes like Catmull-Clark and Butterfly determine how vertices are positioned during subdivision and control properties like continuity. - Extraordinary vertices near non-quadrilateral mesh structures require special handling. - Evaluation masks specify how nearby vertices influence a vertex's final position in the smooth limit surface.
![AnyDesk Pro 3.7.0 Crack License Key Free Download 2025 [Latest]](https://cdn.slidesharecdn.com/ss_thumbnails/tighteningeverybolt-fosdem2025-250224092147-cc175839-250305170448-f3a5e54e-250307111927-ff339e62-thumbnail.jpg?width=560&fit=bounds)
More Related Content
Similar to Subdivision theory (15)
Recently uploaded (20)
![AVG Antivirus Crack With Free version Download 2025 [Latest]](https://cdn.slidesharecdn.com/ss_thumbnails/tighteningeverybolt-fosdem2025-250224092147-cc175839-250305170448-f3a5e54e-250307161054-70f02df2-thumbnail.jpg?width=560&fit=bounds)
![EASEUS Partition Master Crack with License Code [Latest]](https://cdn.slidesharecdn.com/ss_thumbnails/untitleddesign2-250305050346-6916c049-thumbnail.jpg?width=560&fit=bounds)
Subdivision theory
- 1. Subdivision Theory By Brian Sharp (GAMASUTRA) 伎
- 2. Geris Game Pixar, Siggraph98 + 蠍一レ讀 Subdivision Surfaces 伎ろ襴2蠍一覦螻 http://www.youtube.com/watch?v=9IYRC7g2ICg
- 3. Subdivision Surfaces Polygonal Model 伎surface 襯狩覦 覈: 启Μ螻Polygon讌蟯+ NURBS覿 (Poly. Model豌)手/ 螳启Μ螻る螳 (Poly. Model螻朱るゴ蟆) 覯渚蟆覿危覃危螳 Coarse / deltailedlevel 襦蟆蠏手
- 4. In this Entirely theory! 襴讀覓朱Implementation .. ∬碓谿渚覈螻朱襴覈蠍磯蓋企企る讌 磯Μ蟆讌覈詩.. But, れ覈語螳螻殊曙蟆磯Μ螳れ蟆襷る覦襯瑚屋蟆譴
- 5. The What and the why What? Surface generated through subdivision. Control net 企手覿襯企original polygonal surface Surface 豢螳polygon碁 覈vertices 伎襭一磯殊企 企覦scheme 襷るるゴ螻, 企逢surface property 襯手屋
- 6. Topology Control net 螻eventual surface(朱limit surface)topology Topology? Surface 蟲譟磯ゼ覓覦覯譴 Stretching 企twisting 企讌 Ex : 螻(′願襴) 襾瑚係Topology http://en.wikipedia.org/wiki/Topology#mediaviewer/File:Mug_and_Torus_morph.gif
- 7. Topology , Subdivision surfaces B-spline 企Besizer豺襦覘螳覲旧″surface れ覈碁蟆曙蟇磯覿螳ロ. ∬り願姥覃伎蟆continuity 襯殊讌蠍一企糾, 覈詩覃patch 螳seam creases 蠍壱artifacts 覦螳 Subdivision surfaces mesh(closed覃企譬)伎煙願モtopology 襦蟲焔伎 Mesh surface 襯朱れ企願鍵覓語continuity 伎seam覿襯手臼control net 覃伎
- 8. The basics Continuity Interpolate / Approximate Uniform / Non-uniform Stationary / Non-stationary Subdivision shape Extraordinary vertices
- 9. The basics : Continuity CnContinuity : 朱襷覩碁一瑚襯狩 C0: 一碁碁伎. C1: 1谿覩碁一. Surface. Tangent 螳一 Sharp seam 伎ヾ讌 る覿覿scheme C1 continuity 襯手讌螻 C2: 2谿覩碁一. 轟豺C2cont. 襯手讌朱, 覿覿C1cont. 襯殊狩轟煙朱螳讌 Subdivision surfaces 蠍一螳ル┝螻ろ煙continuity
- 10. The basics : Continuity CnContinuity : 朱襷覩碁一瑚襯狩 C0: 一碁碁伎. C1: 1谿覩碁一. Surface. Tangent 螳一 Sharp seam 伎ヾ讌 る覿覿scheme C1 continuity 襯手讌螻 C2: 2谿覩碁一. 轟豺C2cont. 襯手讌朱, 覿覿C1cont. 襯殊狩轟煙朱螳讌 Subdivision surfaces 蠍一螳ル┝螻ろ煙continuity
- 11. The basics : Continuity CnContinuity : 朱襷覩碁一瑚襯狩 C0: 一碁碁伎. C1: 1谿覩碁一. Surface. Tangent 螳一 Sharp seam 伎ヾ讌 る覿覿scheme C1 continuity 襯手讌螻 C2: 2谿覩碁一. 轟豺C2cont. 襯手讌朱, 覿覿C1cont. 襯殊狩轟煙朱螳讌 Subdivision surfaces 蠍一螳ル┝螻ろ煙continuity
- 12. The basics : Continuity Subdivision surfaces 螳Continuity襯殊讌蠍磯覓語 覈語朱襷启Μ螻れ朱襷れ蟯, 豺企手朱覈瑚蟾企り螳蟯, Display resolution 伎朱讌蟯 伎limit surface 襯殊詞.
- 13. The basics : To interpolate or not Interpolate Approximate Controlpoint 豺 Limit surface 譟伎 Limit surface 碁譟伎 Controlpoint 企 企 limit surfaces螳蟾讌 Smoothness 觜蟲讌 Undulation, ripple 伎伎 ->螻朱伎 蟆郁骸覓殊豸 豕譬limit surface豢豸′ 豕譬limit surface豢豸′企れ
- 14. The basics : Uniform, Stationary Uniform : 覈Control point 螳狩蠏豺朱subdivided Non-uniform : edge 襷ろ磯朱るジ蠏豺螳 Stationary : 覈step 狩蠏豺朱subdivided Non-stationary : step 襷ろ磯朱るジ蠏豺螳 Non-uniform 企non-stationary scheme覲襦. 螻手伎rule set 朱覦蠑瑚鍵企れ
- 15. The basics : Subdivision shape Triangular or Quadrilateral Quadrilateral : 覿覿n-sided subdivide rule螳讌螻 Triangular : 朱覿手朱讓手subdivide 讓手蟇伎曙襷, 讓手覦覯磯殊譬蟆郁骸覓朱殊
- 16. The basics : Extraordinary vertices Vertex Valance : vertex 覲郁屋edge Subdivision scheme 覲一Vertex valance 譴 Extraordinary vertex(valance, 蟲譟一磯)譯朱limit surface煙レ譴 覿覿scheme れExtraordinary vertex襯手ろ讌 豌覿一ヾEV 螳豕譬蟆郁骸覓殊蟾讌覲讌螻
- 17. The basics : Surface evaluation Limit surface polygonal approximation谿剰鍵 Control net 企り, Vertices 襯殊螳螻, Faces 襯朱襷, 蟆讓手 朱襦語
- 18. The basics : Surface evaluation 覈scheme recursive 蟆evaluation , 覿覿scheme 覈朱control pointevaluation Interpolating schemes 蟆曙vertex tangent mask 襯殊伎企朱surface normal 蟲る蟆覩 Approximating scheme 蟆曙Evaluation mask 襯殊伎企朱vertex limit position 蟲る蟆覩 襷ろろり骸企, 譯朱朱襷vertex 螳豕譬蟆郁骸(豺, 碁押)レ殊讌襯狩
- 19. 1. The Polyhedral Scheme
- 20. The Polyhedral Scheme ∬リsubdivision scheme Triangular, interpolating, uniform, stationary Edge 譴螳襦vertices 豢螳企ゼedge 襦郁屋手り襦碁 : smooth surface 焔螳 Control net 襯殊覲蟆渚讌 C0continuity Valance : 6
- 21. The Polyhedral Scheme Point 螳企limit surfaces 蠍磯覓語evaluation mask 螳 Surface螳smooth 讌蠍磯覓語tangent mask 覩語
- 22. 2. The Butterfly Subdivision Scheme
- 23. Butterfly subdivision scheme Polyhedral scheme 螻殊, but C1continuity ≒A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control, 1990, Dyn, Levin and Gregory Evaluation mask 螳觜覈 Interpolating, Triangular W : tension parameter
- 24. Butterfly subdivision scheme 襷, vertices 蟲譟郁butterfly 螳覃(N less than 5)? ∬係譯朱w = -1/16蟆語覲るジ覦覯伎 企一譯朱smooth 讌螳覦 一ろ碁ゼ觜′蟆
- 25. 2.2. Modified Butterfly Scheme
- 26. Modified Butterfly Scheme 1993, Dynand his colleagues ∬鍵覲瑚絵Original 螻殊 Regular valence of vertices -6 覈豺C1 continuity 焔 8-point stencil 10-point stencil襦 豢螳d weight 襷a 谿螳 豐weight 1
- 27. Modified Butterfly Scheme Extraordinary vertex care 伎 Edge 讓暑Extraordinary vertex 手化 ∬end point 願壱蠏螳
- 29. Catmull-Clark surfaces Quadrilateral and approximating Regular vertices : valence 4 (朱quadrilateral surfacerectangular grid)
- 30. Catmull-Clark surfaces Vertex Addition (3 steps) 1.りcontrol point 蠏螳朱蟲譴FacePoints豢螳 a b c d e f g h
- 31. Catmull-Clark surfaces Vertex Addition (3 steps) 1.りcontrol point 蠏螳朱蟲譴FacePoints豢螳 2.螳old edge 襷, end vertices 襷譯狩FacePoints蠏螳朱蟲譴edge points 豢螳 a b c d e f g h i
- 32. Catmull-Clark surfaces Vertex Addition (3 steps) 1.りcontrol point 蠏螳朱蟲譴FacePoints豢螳 2.螳old edge 襷, end vertices 襷譯狩FacePoints蠏螳朱蟲譴edge points 豢螳 a b c d e f g h i j l k
- 33. Catmull-Clark surfaces Vertex Addition (3 steps) 2.螳old edge 襷, end vertices 襷譯狩FacePoints蠏螳朱蟲譴edge points 豢螳 3.Old vertices れ譯殊伎磯殊企覈vertices れ襦edge 襦郁屋
- 34. Catmull-Clark surfaces 轟伎1.-Quadrilateral 伎螻褐subdivision 襦蠍face vertex k( !=4 ) 螳襦edge vertices 郁屋 -> extraordinary vertices 螳subdivision 譴覦 ∬係覲伎企蟆襷朱讌. 轟伎2. Single step 覈control net faces quadrilateral 企 -> 豌step覯襷extraordinary vertex 螳豢螳
- 36. Catmull-Clark surfaces Evaluation mask For vertex of valence N Tangent mask Surface normal : cross product of t0and t1 * 豌subdivision e, f 覿螳
- 37. Catmull-Clark surfaces 覈step 讌Catmull-clarksubdivision surfaces
- 39. Catmull-Clark Extended 曙Geris game 覃伎original 襷蟆 Subdivision 轟譟郁唄磯sharp semi-sharp crease 螳讌 一ろ瑚覈碁覈朱edge vertex 讌螳 Geri 朱(譯朱螳暑)譯朱蠍一伎 旧豢螳磯, scheme 焔殊 Non-uniform, non-stationary 企一煙覲覓語In game 蠍一企れ
- 40. れ覦(襷..) Implementing Subdivision Surface Theory 殊碁殊るジ壱in GAMASUTRA 轟, るジsubdivision scheme螳 Loop subdivision, Doo-sabinsubdivision