1. 1 Polygonal Techniques 2002. 5. 15 이영건

2. 2 Introduction This chapter –Discuss a variety of problems that are encountered within polygonal data sets The goal for polygonal representation –Accuracy and speed The three topic –Tessellation, consolidation, simplification

3. 3 Term definition Tessellation –Polygonal of the different forms have to split into more tractable primitives Displayed correctly Consolidation –The process which encompasses merging and linking polygonal data Improve data display Simplification –Attempting to remove unnecessary or insignificant features More speed

4. 4 Three-Dimensional Data - 1 Deferent representation for deferent types of objects –Solid-base modelers Voxels (fig – a) Constructive solid geometry (fig – b) Fig - a Fig - b

5. 5 Three-Dimensional Data - 2 –Surface-base modelers Mesh (fig – b) Subdivision (fig – c) Parametric surface (fig – a) Implicit surface –f(x, y, z) = 0 Fig - bFig - cFig - a

6. 6 Tessellation - 1 Tessellation –The process of splitting a polygon into a set of polygons Reasons –Triangle : optimization for Many graphics APIs and hardware (triangulation) –Renderer : handling convex polygons (convex partitioning) –In order to catch shadows and reflected light The different types of tessellation (b. convex partition, c. triangulation, d. uniformly meshed) abcd

7. 7 Tessellation - 2 Process of tessellation –How best to project a three-dimensional polygon into two dimensions Best plane –Selection the largest projected area among the xy, the yz, the zx –Using the greatest magnitude in the polygonal’s normal

8. 8 Tessellation - 3 –Problems Polygon facets by creating the modelers can be badly warped –produce an hourglass or bowtie quadrilateral (fig-a) –Using line / line intersection test (section 10.12) Polygons are not always made of a single outline –Using the join edge (fig-b) Fig - a Fig - b

9. 9 Shading problems Split the quadrilateral into the triangles –Provide proper input to the renderer –Avoid bowtie problems –Notice Select the good diagonal edge for renderer The different ways –Using the minimized differences (between color)

10. 10 Shading problems The different ways –Using the diagonal that gives the largest angle between the two triangles Left : each quadrilateral split along the same diagonal Right : the split is made using the diagonal whose corners are closer in height

11. 11 Shading problems Problem of warped quadrilateral –Texture is applied –When tessellation apply, distort texture –Requirement Fine meshing of surface Use texture-coordinate interpolation scheme

12. 12 Edge cracking and T-Vertices Producing the NURBS by modeler –Happen the edge cracking at the shared edge by the two surface –Solution Edge stitching –When joining flat surface is that of T-vertices, happen to related problem

13. 13 Consolidation –To find and adjust the links between polygons for rendering Advantage –Improve efficiency The display polygon meshes The area of backface culling Quality-related problem –Face orientation Use a right-handed orientation (counter-clockwise direction) Problem : When model has the only surface normal. Left : don’t have the normal per vertex Right : have the normal per vertex

14. 14 Consolidation Solution for forming polygonal meshes 1.Form edge-face structure 2.Find groups of polygons (determine solidity) 3.For each group, flip faces to gain consistency 4.Determine what the inside of the mesh is 5.Find smoothing groups and compute vertex normals 6.Find boundaries 7.Create polygonal meshes

15. 15 Consolidation –Form edge-face structure Form a list of all edges in the entire set of polygons Sorting by vertex coordinates Ex) v1(-3,5,2), v2(-3,6,-8)  v1 => v2 sorting –Find groups of polygons (determine solidity) A group consist of polygons which are connected by edges Ex) two group of the teapot : the pot and the lib –For each group, flip faces to gain consistency Ensure orientation consistency (counter-clockwise outlines) Select an arbitrary starting polygon Traversal neighbor polygons No consistency, apply flipping

16. 16 Simplification - 1 Simplification –The process of taking a complex model and reducing complexity –Data reduction or decimation The main advantage –Be quicker to render

17. 17 Simplification - 2 The operation of simplification –Edge collapse The strategy for new vertex placement –Select one vertex or the other vertex [Melax] Faster, Lower-quality –Check the midpoint on the edge [Hoppe] –Check both vertices on the edge [Garland and Heckbert] Higher-quality, Extra processing, code and momory

18. 18 Simplification - 3 Problem of edge collapse –Happen to edge crossing –Solution Using of the best cost function –Happen to ambiguous edge collapse

19. 19 The extension of the cost function –by Garland and Heckbert –Be to weight the value by the areas of the triangles associated with each plane –Be to use a cost function based on maintaining other surface features –Be to preserve the material changes, texture map edges, color-per-vertex changes Simplification - 4

20. 20 Simplification - 5 The simplification of LOD –Problem Happen to “Popping effect” –Solution Be to use alpha blending to cross-fade between model representation Be to use geomorphs to increase or decrease the level of detail