For the final exam a student should be able to…
Describe the geometric basis for efficient collision detection.
Explain the basics of ray tracing, including the ray tree and the basics of refractive materials.
State how ray-object interactions are determined using methods similar to collision detection.
Define a shadow ray and describe how it is used in ray tracing.
Define reverse ray tracing and state a use for it.
Define constructive solid geometry and contrast it to surface-based geometric modeling.
State at least two anti-aliasing methods that can be used in ray tracing (or rendering of 3-D models in general).
Apply blending to simulate transparency and related effects.
Describe the basics of real shadows for point and non-point sources (not in w0405: including the umbra and penumbra.
Describe the 2-pass shadow algorithm and how it uses visible surface detection methods.
Describe the shadow volume approach to rendering shadows and state how it falls short of real shadows.
Explain the basics of bump mapping, including why it perturbs normals without perturbing vertices.
Discuss the basic approach of using texture maps with accumulation (or blending) to efficiently implement bump mapping.
State the basic properties of quaternions and their use in rotations.
(not in w0405) Define a “great circle” and its relationship to the slerp (spherical linear interpolation) function.
Describe the various buffers that constitute the OpenGL framebuffer and the related tests.
Define fractal dimension and calculate it for basic examples.
Describe simple fractals having dimension 1 < D = ln N / ln M < 2, where N and M are natural numbers.
(not in w0405) Explain the 2-D midpoint displacement algorithm for terrain generation.
(not in w0405) Describe the basics of the Julia-Fatou sets and the Mandlebröt set.
Define an affine map in terms of either Cartesian or homogeneous coordinates.
Implement a fractal generator given a probabilistic affine map parameter set.