Ray Tracing

Question 1

Helmhotz Reciprocity Rule

Answer 1

We can trace rays backwards as well as forwards.

BRDF(x, ψ’, ψ, λ) = BRDF(x, ψ, ψ’, λ)

Question 2

How do we order the basis of the View and World coordinate systems?

Answer 2

View = Left Hand Rule
World = Right Hand Rule

Question 3

4 Steps to translate pixel locations to world space for ray tracing

Answer 3

1. Translate the pixel (x, y, 0) by (-hx / 2, -hy / 2, d)
2. Preserve aspect ratio with a scale (-w / nx, -h /ny, 1)
3. Rotate to look at correct direction
4. Translate to origin of view

P = (T_y R_z) S_z T_I
T_y R_z = M_vw

Question 4

What does pixel translation look like if

d=1, lookfrom = (0s), look at = (0s) and up = (0, 1, 0)?

Answer 4

?

Question 5

Texture Mapping

Answer 5

A way of adding surface detail without increasing model complexity

Paper: Blinn & Newell 1976

Question 6

UV Mapping

Answer 6

Convert (x, y, z) -> (u, v) unit square. Retrieve (u, v) from (di, dj) in the texture and map it back to the original 3D point.

Different projections: Plane, Sphere, Cube, Cylinder

Question 7

Bump Mapping

Answer 7

Perturb normal with image by taking difference between pixels in texture as the change in u and v and applying that change to the normal.

Paper: Blinn 1978 “Wrinkled Surfaces”

Question 8

Solid Texture

Answer 8

3D Textures to replicate wood, marble, and other textured objects with volume.

Paper: Perlin 1985 “Image Synthesizer”

Question 9

Computational Solid Geometry

Answer 9

Allow for intersections, unions, and boolean operations of models/geometry to create new shapes. With raytracing, find the near and far points of intersection with every object and then calculate appropriate point based on type of operation.

Question 10

Bounding box

Answer 10

Surround each complex geometry with a box so ray intersection only has to check the more complex intersection if it intesects the box. Use box aligned with coordinate axes.

Tradeoff with bounding box construction time.

Question 11

Spatial Subdivision

Answer 11

Split space into subregions so only subregions through which the ray passes need to be checked for intersections.

Use voxels or trees. Useful with lots of small objects in scene.

Question 12

Grid Acceleration

Answer 12

Good: if occupancy does not vary significantly
Bad: Stepping through empty cells
Use: Bressenham’s line algorithm
O( c_1 cubedroot(n) )

Question 13

Octree Acceleration

Answer 13

Good: if Occupancy varies
Bad: Must traverse height of tree
O( log n )