CS488 - Introduction to Computer Graphics - Lecture 24

Comments and Questions


  1. Surface normals
  2. Constructive Solid Geometry
  3. Office hours

More Ray Tracing

Speeding Up Intersection Tests

  1. Bounding Volumes (usually Boxes)
    1. Find the smallest - or close to smallest - regular volume that encloses the object
    2. Use ray-intersect-volume as a pretest for fast negative results.
    3. Trade-off between
      • benefit of quicker `miss'detection
      • cost of getting a good bounding surface
      • Both increase as complexity of primitive increases

    Scene subdision

    1. Divide the scene volume into sub-volumes: many ways to do it, such as
      • quad-trees
      • oct-trees
      • BSP trees
      • ...
    2. List all primitives by sub-volume.
    3. Only test primitives in the sub-volumes through which a ray passes.


Two different, but linked, types of artifacts

  1. Spatial (or temporal) frequency aliasing,
  2. Reconstruction aliasing

Exact solutions are simple in principle

  1. Remove high spatial frquencies by filtering
    1. Fourier transform in image space: remember that you need to keep both amplitude and phase.
    2. Filter
    3. Inverse transform in image space

    Filtering is the tricky part.

  2. Use a sampling filter that is the inverse of the reconstruction filter
    1. For the display to be used find the pixel shape
    2. Construct a sampling filter appropriate for the pixel shape
    3. Do ray-tracing calculating over a weighted area

    Finding the pixel shape is the hard part.

These are the things that apply to images where you end up with a bunch of graphical primitives on the image plane, so that you image is effectively designed at infinite resolution. A similar effect is produced when ray tracing, but has different types of solution, which are

  1. Beam tracing
  2. Super sampling
  3. Stochastic sampling
  4. Importance sampling


Bidirectional Ray Tracing

The `caustic' project

Participating Media




Texture Mapping

  1. Basic
    1. Start with a 2D image: pixellated or procedural
    2. Map 2D image onto primitive using a 2D affine transformation
      • Simple if the surface of the primitive is flat
      • otherwise, ...
      • Texture pixels normally do not match display pixels, so some image processing may be needed.
    3. Backwards map intersection point with ray into the image to get the surface properties
  2. Normal Mapping (Bump mapping)
    1. Start with a difference surface, defined with respect to the surface
    2. Calculate the normals to the difference surface and map them onto the surface of the primitive
    3. Use the mapped surface models for lighting
    4. No occlusion, shadows are wrong, silhouettes are wrong, nobody notices!
  3. Solid Textures
    1. Solution to mapping texture onto curved surfaces
    2. Usually procedural

(Un)natural Phenomena

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