13 - Mappings and Shadows

ucla | CS 174A | 2024-03-19 01:50

Table of Contents

Texture Mapping

  • pasttern mapping: wrap a pattern across a surface
  • individual texture elements are Texels
  • use texel color as diffuse color, index using (s,t) texture coords
  • index the surface using (u,v) coords and map (s,t)→(u,v)

    Aliasing

  • usually due to sampling too few points per pixel
  • due to points sharing texels, we might miss the texture map and end up with useless colors:
    • in this example we mapepd directly and everythign ended up white:
  • we can anti-alias using area average sampling
    • e.g., take a square and color the average of that texel:
  • or MipMap:
    • bilinear interp the (u,v) coord of the object and map from (s,t):
    • setting the u,v coords of the image to different values allows different layouts of texture mapping:

      • Bump and Displacement Mapping

  • displacement maps actually displace the objects a little based on the map
    • B is the bump param that will usualyl given as a map per pixel or can be interp
    • B>0 => raise it up
    • B<0 => push it down
    • changes the actual geometry of the object:
  • bump mapping only changes the direction of the normals
    • uses partial derivatives wrt to the surface/pixel index and point index

Environmental Mapping

  • reflection mapping
  • use polar/spherical coords of reflected ray to map environment
  • use the reflected ray R (vector) to map based on the direction of R
  • maps are usually cubic or spherical

Shadow Algos

  • if a light ray does not touch the surface of a polygon/object, that point is in a shadow
  • for object precision: shadow volume algo (old)
  • for image precision: 2-pass z-buffer algo
  • render shadows with ambient light
  • mark shadows for specific light sources by running HSR from eye position

    Shadow Volume Method

  • create shadow volumes by tracing the 3d object made by the 2d front facing faces
  • add this shadow volume to database
  • then do parity check to remove unnecessary volumes

    2-Pass Z-buffer

  • treat each light source as a spotlight
  • then calculate this z-buffers for each light
  • 1st pass
    • do z-buffer (2d full) from light position
    • this z-buffer will give us the z-value of the closest polygons to the light at each pixel
  • 2nd pass
    • do z-buffer (scanline or full) from eye position
    • for each visible pixel in scan line
      • check if the z-value that the poly’s object belongs to in WS is farther than the z-buffer at that coordinate
      • if so, then it is in a shadow
    • we check (x,y,z) and see that z > z_blue_polygon thus it is in shadow
  • e.g.

    • Tradeoff

  • simple to implement
  • BUT, regires large shadow buffer, depth buffer resolution usually 8-bit
  • umbra and penumbra aliasing may happen if shadows are far from the light