Computer Graphics Normal, Texture, Supersampling Exercises

1
Computer Graphics- Normal, Texture,
Supersampling Exercises -

• Marcus Magnor

2
Vertex Normals

• Normal vector per vertex
• E.g., averaged orientations of adjoining
  triangles
• Normalized
• Normal interpolation in triangle
• Hitpoint position in barycentric coordinates
  (u,v,1-u-v)
• Barycentric interpolation cf. lecture
  raytrace1, slide 36
• Re-normalize interpolated normal vector

3
Surface Parameterization

• Some objects have a natural parameterization
• Sphere spherical coordinates (?,f) (2p u, p v)
• Cylinder cylindrical coordinates (?,z) (2p u,
  H v)
• Parametric surfaces (such as B-spline or Bezier
  surfaces)
• Parametrization less obvious for
• Polygons
• Implicit surfaces

4
Triangle Parameterization

• Piecewise planar object surface patches
• To each vertex (xo,yo,zo) assign texture
  coordinates (u,v)
• Viewing projection (xo,yo,zo) ? (x,y)
• Yields warping operation (u,v)?(x,y)
• In homogeneous coordinates
• Transformation coefficients determined by 3 pairs
  (u,v)?(x,y)
• Invertible if points are non-collinear

5
Triangle Parameterization II

• Inverse transform (x,y)?(u,v)
• Transformation coefficients must be calculated
  for each triangle
• Scan-line rendering
• Bilinear interpolation of (u,v,q) in screen
  space
• Ray tracing
• Evaluation at each intersection

6
Supersampling

• Regular
• Subdivide pixel into sub-areas
• Send one ray through each sub-areas center
• Average
• Random
• N rays through pixel area at (quasi-)random 2D
  positions
• average
• Stratified
• Combination of former two
• Subdivide pixel into sub-areas
• Send one ray through each sub-area at (quasi-)
  random 2D position
• average