Programmable Tessellation on the GPU Over the past five years many researchers have used the programmable features of the GPU to implement high-quality tessellation Patney and Owens's adaptive subdivision on the GPU [2008] transformed the typical depth-first recursive traversal of split surfaces into a breadth-first operation While this performs well on the GPU using a breadth-first Subdivision surfaces: Each polygonal mesh has a well-defined smooth surface associated with it A refinement algorithm computes the smooth surface as the limit of a recursive process (the exact surface depends on the method used) One such method is Catmull-Clark subdivision A popular approach by Loop and Schaefer [2] is suited for the GPU and approximates the surface with bicubic patches

Motivation

Evaluation Example: Catmull-Clark Subdivision • Most popular scheme • Based on B-Spline subdivision • Evaluation through recursive refinement • Add one new vertex for every face and every edge Example: Catmull-Clark Subdivision 4 1 4 1 4 1 4 1 Example: Catmull-Clark Subdivision 8 3 16 1 16 1 8 3 16 1 16 1 Example: Catmull-Clark Subdivision n n 4 4 −7 2 2 3 n 4 2 1 n 2 2 3 n 2 2 3 n 2

Computer Graphics assignment help tutors are writing Computer Graphics assignments from years with excellent command on the Computer Graphics are able to work on Computer Graphics research projects thesis or Computer Graphics dissertation writing help for complex topics like Back face culling Shadow volumes Shadow buffer Shadow mapping nature of light Transport theory radiance

25/10/2007Adaptive computation of subdivision surfaces United States Patent Application 20070247458 Kind Code: A1 Abstract: A method for the computation of a subdivision surface from a base mesh of coarse faces which requires no dynamic allocations is performed as follows First a static data structure is allocated The static data structure includes a hierarchy of data arrays where each of

Rapid Evaluation of Catmull-Clark Subdivision Surfaces by Jeffrey Bolz Peter Schrder 2002 Using subdivision as a basic primitive for the construction of arbitrary topology smooth free-form surfaces is attractive for content destined for display on devices with greatly varying rendering performance

Figure 1: Comparison of evaluation order of patches for different batch sizes Surfaces that are created in the same iteration are shaded in the same color This shows the locality-preserving property of our subdivision algorithm: surfaces that are spatially close together are evaluated in the same iteration

Exact Evaluation of Subdivision Surfaces

Exact Evaluation of Subdivision Surfaces Jos Stam Alias | wavefront Seattle WA USA Evaluation of Surfaces Mapping a 2D square in 3D u v f(u v) Example: bicubic B-splines Example bicubic B-splines Example: bicubic B-splines Example: bicubic B-splines C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 C 11 C 12 C 13 C 14 C 15 C 16 f(u v) = Σ Ci Bi (u v) i=1 16 Piece-wise B-splines Piece-wise B

These subdivision surfaces are commonly defined recursively [Catmull and Clark 1978] To be implemented in a GPU tessellator a limit-surface representation [Stam 1998] is common as new points can be generated in a single pass However a limit-surface method involves pre- computation on the mesh before tessellation has issues at extraordinary vertices and can be quite slow when

same evaluation shader in lock-step We expect tessellation hardware to become standard in the near future [Blythe 2006 Boyd 2007] 1 1 Catmull-Clark Surfaces on Tessellation Hardware Catmull-Clark subdivision surfaces are in fact piecewise parametric and therefore amenable to hardware tessellation Each quadrilateral face in a Catmull-Clark

Subdividing a subdivision surface includes traversing the subdivision surface to locate a target polygon on the subdivision surface partially subdividing the target polygon re-traversing the subdivision surface to locate the target polygon on the subdivision surface and additionally subdividing the target polygon Data is stored indicating a point in a subdividing process where the

Subdivision surfaces can be naturally edited at different levels of subdivision Starting with basic shapes you can use binary operators to create the correct topology Then edit the coarse mesh to create the basic shape then edit the offsets for the next subdivision step then repeat this at finer and finer levels You can always see how your edit effect the limit surface via GPU evaluation

Surface Quality Assessment of Subdivision Surfaces on Programmable Graphics Hardware Yusuke Yasui Takashi Kanai Keio UniversitySFC Faculty of Environmental Information 5322 Endo Fujisawa Kanagawa 252-8520 JAPAN {t00950yy/kanai}sfc keio ac jp Abstract In this paper we propose a method of subdivision surface quality assessment by reflection lines on pro- grammable graphics hardware

1 1 Fast Evaluation of Subdivision Surfaces on Direct3D 10 Graphics Hardware by Gyrgy Antal and Lszl Szirmay-Kalos 1 2 Improved Appearance Variety for Geometry Instancing by Jonathan Mam and Daniel Thalmann 1 3 Implementing Real-Time Mesh Simplification Using Programmable Geometry Pipeline on GPU by Christopher DeCoro and Natalya Tatarchuk 2 Rendering Techniques 2 1 Care and

Evaluation of Subdivision Surfaces on Programmable Graphics Hardware By Jeff Bolz and Peter Schrder Abstract High-order smooth surface primitives such as subdivision patches for example are attractive for the modeling of free-form surfaces In contrast to meshes they require only a few control points to specify large sections of a surface Unfortunately much of this bandwidth

Real

Clark subdivision surfaces Furthermore the newly generated surface positions and their vertex attributes are not stored explicitly in video memory which improves the overall performance Figure 4 Comparison between the standard DirectX 9 graphics pipeline (left) and corresponding graphics pipeline with tessellation support (right also representing Xbox 360 graphics pipeline) /ote that

programmable shaders 26 Why Catmull-Clark? Quads are better than tris at capturing the symmetries of natural and man-made objects Tube like surfaces (arms legs fingers) are easier to model Generalize uniform tensor product cubic B-splines makes it easier to use in-house and commercial systems (Renderman and Alias-Wavefront) 27 Hybrid subdivision Hoppe wrote about smooth surfaces with

Evaluation of Subdivision Surfaces on Programmable Graphics Hardware 2003 1 3 Correction of Local Irregularities Using Reflection Lines KLASS R Computer Aided Design 12(7) 411-420 1980 1 4 Smooth Subdivision Surfaces Based on Triangles LOOP C Master's thesis University of Utah Department of Mathematics 1987 1 5 Surface

expose a programmable tessellation unit 1 Introduction Catmull-Clark subdivision surfaces [4] have become a standard modeling prim- itive in computer generated motion pictures and 3D games To create a sub-division surface an artist constructs a coarse polygon mesh that approximates the shape of the desired surface A subdivision algorithm recursively refines this shape to produce a

a programmable tessellation unit Categories and Subject Descriptors: I 3 5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve surface solid and object representations General Terms: Performance Additional Key Words and Phrases: Catmull-Clark subdivision GPU tessellation subdivision surfaces ACM Reference Format:

Clark subdivision surfaces Furthermore the newly generated surface positions and their vertex attributes are not stored explicitly in video memory which improves the overall performance Figure 4 Comparison between the standard DirectX 9 graphics pipeline (left) and corresponding graphics pipeline with tessellation support (right also representing Xbox 360 graphics pipeline) /ote that

Programmable Tessellation on the GPU Over the past five years many researchers have used the programmable features of the GPU to implement high-quality tessellation Patney and Owens's adaptive subdivision on the GPU [2008] transformed the typical depth-first recursive traversal of split surfaces into a breadth-first operation While this performs well on the GPU using a breadth-first

A Basic Evaluation Method of Subdivision Surfaces Yasushi Yamaguchi Dept of Graphics and Computer Sciences Graduate School of Arts and Sciences The University of Tokyo 3-8-1 Komaba Meguro-ku Tokyo 153-8902 Japan email: yamagraco c u-tokyo ac jp Abstract A subdivision surface is a powerful tool to represent a smooth sur- face with arbitrary topology It starts with a control polyhedron

For surfaces built through linear combination of basis functions it is possible to precompute tessellations and use these to evaluate the surface at runtime in a simple computation performed entirely on a programmable graphics processor (GPU) The improved bandwidth requirements---only control points need transmission during animation for example---coupled with the high performance of GPUs