Advanced topics Advanced Multimedia Technology: Computer Graphics Yung-Yu Chuang 2006/01/04 with slides by Brian Curless, Zoran Popovic, Mario Costa Sousa and Robin Chen

Outline Mapping techniques –Texture mapping –Displacement mapping –Bump mapping Shadows Ray tracing

Texture maps How is texture mapped to the surface? –Dimensionality: 1D, 2D, 3D –Texture coordinates (s,t) Surface parameters (u,v) Projection: spherical, cylindrical, planar Reparameterization What does texture control? –Surface color and transparency –Illumination: environment maps, shadow maps –Reflection function: reflectance maps –Geometry: displacement and bump maps

Texture

History 1974 basic idea (Catmull/Williams) 1976 reflection maps (Blinn/Newell) 1978 bump mapping (Blinn) 1983 mipmap (Williams) 1984 illumination (Miller/Hoffman) 1985 solid texture (Perlin)

Texture maps

Reflection maps

Environment maps

Bump/displacement maps

Illumination maps

Solid textures

Texture mapping

(u,v) sphericalcylindricalplanar

Spherical mapping

Cylindrical mapping

Planar mapping

Spherical mapping

Cylindrical mapping

Planar mapping

Aliasing

Antialiasing

Mip maps A mipmap takes at most 1/3 more memory

Sum area table

Antialiasing

Displacement mapping

Bump mapping

Bump v.s. displacement mapping

Shadow buffer

Forward ray tracing

Precursors to ray tracing local illumination cast one ray, then shade according to light ray casting (Appel 1968) cast one eye ray + one ray to light

Whitted ray tracing algorithm

Ray tree

Shading

Outer loop

traceRay

Reflection

Refraction

Ray-sphere intersection

Ray-plane intersection

Ray-triangle intersection

Acceleration techniques Object subdivision: hierarchical bounding volume Space subdivision: –Uniform: uniform grid –Adaptive: kd-tree, octree…

Bounding volume hierarchy

1)Find bounding box of objects Bounding volume hierarchy

1)Find bounding box of objects 2)Split objects into two groups Bounding volume hierarchy

1)Find bounding box of objects 2)Split objects into two groups 3)Recurse Bounding volume hierarchy

1)Find bounding box of objects 2)Split objects into two groups 3)Recurse Bounding volume hierarchy

1)Find bounding box of objects 2)Split objects into two groups 3)Recurse Bounding volume hierarchy

1)Find bounding box of objects 2)Split objects into two groups 3)Recurse Bounding volume hierarchy

At midpoint Sort, and put half of the objects on each side Use modeling hierarchy Where to split?

BVH traversal If hit parent, then check all children (from the closer to the further?)

BVH traversal Don't return intersection immediately because the other subvolumes may have a closer intersection

Bounding volume hierarchy

Space subdivision approaches KD tree Unifrom grid

Space subdivision approaches BSP tree Quadtree (2D) Octree (3D)

Uniform grid

Preprocess scene 1.Find bounding box

Uniform grid Preprocess scene 1.Find bounding box 2.Determine grid resolution

Uniform grid Preprocess scene 1.Find bounding box 2.Determine grid resolution 3.Place object in cell if its bounding box overlaps the cell

Uniform grid Preprocess scene 1.Find bounding box 2.Determine grid resolution 3.Place object in cell if its bounding box overlaps the cell 4.Check that object overlaps cell (expensive!)

Uniform grid traversal Preprocess scene Traverse grid 3D line = 3D-DDA

A A Leaf nodes correspond to unique regions in space K-d tree

A A Leaf nodes correspond to unique regions in space B K-d tree

A B A B Leaf nodes correspond to unique regions in space K-d tree

A B A B C

A B C A B C

A B C A B C D

A B C D A B C D

A B C D A B C D Leaf nodes correspond to unique regions in space K-d tree

A B C D A B C D Leaf nodes correspond to unique regions in space K-d tree traversal

Antialiasing with supersampling

Result

Advanced ray tracing