What Well Be Covering Today: Modified Butterfly Subdivision Texturing and Antialiasing Global Illumination via Radiosity

Modified Butterfly Subdivision Based on Dyn/Levin/Gregory Butterfly Subdivision Adds rules for non-regular vertices –Standard Butterfly is not C 1 at k=3 or k>7

Mesh Data Structure List of vertices Each vertex has a set edges (vertices it is connected to) –sorted in order around vertex –Not guaranteed CCW (normal problems)

Vertex Normals Formulas from SIG2000 course notes Problems with boundary edge rules –Possibly due to bad vertex orientation

Starfish-like Thing

Frog-ish Head

Anti-Aliasing Standard OpenGL Accumulation Buffer techniques Helpful Tip: Dont save your antialiasing example pictures as JPEGs

Texture Mapping Calculate vertex texture coordinates using spherical projection Issues to Deal with: –Texture coordinate problems –Polar Distortion

Wrapped Texture Coordinates Vertices can only have one texture coordinate –Some need two Two Solutions: –Duplicate vertices (bad, fast) –Detect & Fix at render time (good, slow)

At-Pole Texture Coordinates Singularity at poles –entire line of texture on one point –OpenGL cannot handle this gracefully Again, can be detected and corrected at render-time

Polar Distortion Problem Texture mapped like lines of lattitude / longitude Lines get closer at poles Distort texture to counter this effect WARNING: distorted texture will not tile!

Polar Distortion Solution

Son Of Frog-ish Head

Radiosity Progressive Refinement (Shooting) –My machine only has 256 MB of RAM –Large Scenes == Thrashing –Throw away form factors after each shot Use hemicube to calculate form factors –Projecting faces – easy way and hard way

Form Factors the Hard Way Clip and project each poly onto faces of hemicube (geometrically) Find pixels that intersect projected poly A HUGE WASTE OF PROGRAMMING EFFORT (and its really slow, too)

Form Factors the Easy Way Use OpenGLs Z-buffer –Encode each face with a color –Graphics Hardware speeds this up Can be less accurate than geometric method –Standard Z-Buffer accuracy problem

Other Implementation Issues Use double precision! –Dealing with summation of lots of tiny values –Single precision loses light –Particularly for Fqs in HemiCube OpenGL and multi-threading do not really mix together so nicely…

Progressive Refinement

Low Hemicube Resolution

Radiosity On Butterfly Surfaces