CISC 454 Goals for Test 3

Updated April 2 at 23:20.
Bump mapping is not on the test.

Ray tracing

  what happens at each ray bounce
    shadow rays to all point lights
    recursive ray in ideal reflection direction
    apply Phong to every incoming ray

  Ray/triangle intersection
    ray parameterization: p + td
    plane equation for plane of triangle: n dot x = d
    Barycentric coordinates
      p = alpha v1 + beta v2 + gamma v0
      for points inside triangle :
        alpha + beta + gamma = 1 
        alpha, beta, gamma >= 0
        idea that alpha, beta, gamma are the SIGNED areas of sub-triangles

  Acceleration techniques
    axis-aligned bounding boxes (AABBs)
      how to find whether ray intersects AABB
      following a ray through an octtree
    k-d trees
      how to choose the separating plane: even vs. median vs. SAH
      SAH algorithm       

    what does aliasing look like
    how to reduce aliasing
    jittered sampling

  Analysis of random sampling
    what is an estimator and an estimate
    how to know if an estimator is biased
    how to analyse the variance of an estimator
    the effect of variance on the image
    how stratified sampling can reduce variance

  Glossy reflections
    sample multiple rays
    generate random points on disk
    average the outgoing light after applying Phong to each ray

    hard shadows from point light sources
      requires only a single ray to test if source is blocked
    soft shadows from area light sources
      generate random points on the area source
      how to generate UNIFORM random points on a triangle (Barycentric coords)

  Bias in ray tracing
    weight of ray = factor by which ray's light is attenuated at the eye
    cut off ray after weight < threshold
    why this causes bias in the resulting image
    how to avoid bias with Russian Roulette

Volume Rendering

  Rendering equations
    exponential attenuation through a volume
    volume rendering integral
    discrete volume rendering integral
      appoximations and discretizations that are made (e.g. delta s, constant tau and C, Taylor series)

    axis-aligned slices with 2D textures
    viewpoint-aligned slices with 3D textures
    back-to-front in software
    front-to-back in software with early termination

  Transfer functions
    1D: tau -> (kd, tau')

  Surface shading
    use of emission to fake light reflection
    Computing C(p) and alpha(p) at position p on ray
    gradient computation (intermediate, central, Sobel, Zucker-Hummel)
    use of negative normalized gradient with Phong

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