Ray Tracing II

HW1 Part A due October 10

• Camera module

• Object module– Read from a file– Sphere and Light only

• Ray tracer module: – No shading. No reflection and refraction.

• Display module (in text mode)

Ray-Object Intersection

• For example: sphere(x-x0)2+(y-y0)2+(z-z0)2=r2

• Ray: (x,y,z)=(x1,y1,z1)+t(xd,yd,zd)

• Find t that satisfy (x-x0)2+(y-y0)2+(z-z0)2=r2

• Normal vector?

• Also easy for planes, cones, …etc.

Ray-Triangle Intersection

• Ray: (x,y,z)=(x1,y1,z1)+t(xd,yd,zd)

• Triangle:

(x,y,z)=(x1,y1,z1)+u(x01,y01,z01)+v(x02,y02,z02)

• Find t, u, v that produce the same (x,y,z)• Intersection found if:

t > 0

0 ≦ u, v 1, and≦u + v 1≦

V0V1

V2

Part B due October 24

• Object module– Add at least a plane type.

• Ray tracer module: – Add shading, reflection, and refraction.

• Display module:– PPM library will be provided.

• Add a demo scene of your own.

Lighting (Shading) & Shadow

• Point light is easy to implement.

• How to determine a surface point is in the shadow? Use a shadow ray (from intersection point to light).

• Shading will be introduced in the next lecture.

Reflection and Refraction

• Reflected ray is determined by:– incoming ray and normal vector.

• Refracted ray is determined by:– Incoming ray– Normal vector– And density

• Snell’s law: I sin i = t sin t

i t

Advanced Ray Tracing

• Make it fast.

• Make it better.– Anti-aliasing– Distributed Ray Tracing

Make It Fast

• From Pharr’s Chapter 4– Object subdivision (i.e., bounding volume)– Spatial subdivision (e.g., grid, octree, kd-

tree)– Ray coherence.

Anti-Aliasing

• Super(or Over)-sampling

• Adaptive vs. Non-adaptive

• Uniform vs. Jittered

• Detail coming in a future lecture

Distributed Ray Tracing

• Published by R. L. Cook in 1984.

• Antialiasing

• Motion blur

• Depth of field (camera)

• Ideas behind other so-called Monte Carlo methods.

Space Partitions

Common Operations in 3D

• Line/object intersection– Given a ray or line, which object will it

intersect?

• View frustum culling

• Collision detection

Sorting/Indexing in 3D

• Sequential search is too slow for large models.

• How about storing them in a 3D array?– Size will be overwhelming

• Think “hierarchy”

Octree

• Divide the space in halves in X/Y/Z.– Always split in the middle.– You may also consider them as splitting in

X, then in Y, then in Z.

• If too many objects are in a partition, divide them again (recursively).

K-D Tree

• More flexible than octree:– Not always splitted in the middle.– Split in X, then in Y, then in Z, or any order.

Kd-tree Example

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2 3

2

3

4 5 6 7

4

5

6

7

8 9 10 11 12 13

8

9

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Figure Source: CS638 slides by Stephen Chenney, University of Wisconsin – Madison,

BSP Trees

• From the paper by Fuchs et al, “On visible surface generation by a priori tree structures” SIGGRAPH 80.

• Binary Space Partition trees– A sequence of cuts that divide a region of

space into two

• Cutting planes can be of any orientation

Drawing Order from BSP Trees

• BSP tress can be used to order polygons from back to front, or visa-versa– Descend tree with viewpoint– Things on the same side of a splitting plane as the

viewpoint are always in front of things on the far side

• Can draw from back to front– Gives the correct order for rendering transparent

objects with a z-buffer, and by far the best way to do it

• Can draw front to back too.

BSP Example1

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3 75

BA out8

D out

6

C out

12

3

4

56

78

outA

outBC

D Figure Source: CS638 slides by Stephen Chenney, University of Wisconsin – Madison,

OBB Tree

• OBB stands for Oriented Bounding Box.

• OBB is a rectangular bounding box at an arbitrary orientation.

• Asymptotically faster for close proximity situations.