1. Introduction to Ray Tracing
CSE 681

2. Ray Tracing Shoot a ray through each pixel;
Find first object intersected by ray.
Image plane
Eye
Compute ray. (More linear algebra.)
Compute ray-object intersection.
CSE 681

3. Ray Tracing For each pixel Form ray from eye through pixel
For each object
Intersection ray with object
If intersection is closer than any other so far, save it
Color pixel with shade of object at point of intersection
CSE 681

4. Example
CSE 681

5. Shade of Object at Point
Ambient
Diffuse
Specular
Shadows
Material properties
Texture
Reflections
Transparency (refraction)
CSE 681

6. Diffuse Reflection Light that gets absorbed into the objects surface
Gets reflected equally in all directions
Need to calculate angle of incoming light to surface
CSE 681

7. Diffuse Reflection
Calculate amount/color of light shining on an object.
Depends on angle between light ray and surface normal.
CSE 681

8. Example: Diffuse reflection
What about shiny objects?
CSE 681

9. Specular Reflection Calculate light bouncing off object to your eye;
Angle of incidence = angle of reflection.
Most intense at angle of reflection; falls off from there
Angle of incidence
Angle of reflection
Eye
CSE 681

10. Example: Specular Reflection
CSE 681

11. What’s wrong with this picture?
No shadows.
CSE 681

12. Shadows Determine when light ray is blocked from reaching object.
Ray-object intersection calculation
For each pixel
for each object
for each light source
CSE 681

13. Reflection
Image plane
Eye
CSE 681

14. Transparency
Transparency
CSE 681

15. Transparency & Refraction
Ray changes direction in transition between materials
Material properties give ratio of in/out angles
CSE 681

16. Transparency & Refraction
CSE 681

17. Recursive Ray Tracing
Image plane
Eye
CSE 681

18. Polyhedral Models
Polyhedral models
CSE 681

19. Texture Mapping
Texture mapping.
CSE 681

20. Sampling and Aliasing Problem: Representing pixel by a single ray.
Using higher resolution won’t solve problem.
No matter how small pixels are, objects can be smaller.
CSE 681

21. Anti-Aliasing Solution: Use multiple rays;
Average values calculated by rays.
Image plane
Eye
CSE 681

22. Sampling and Aliasing
Problem: Sampling frequency may match image frequency.
Image plane
Eye
Viewport
CSE 681

23. Random/Stochastic Sampling
Randomly sample rays through pixel.
Image plane
Eye
Viewport
CSE 681

24. Efficiency 1280 x 1024 = 1,310,720  106 pixels. 106 initial rays.
106 reflection rays.
Potentially 106 refraction rays.
3 x 106 shadow rays (3 lights.)
Next level:
Potentially 4 x 106 refraction/reflection rays.
1,000,000 polygons.
107 x 106 = 1013 ray-polygon intersection calculations.
No anti-aliasing.
CSE 681

25. Intersection Data Structures
Coarse test to see if ray could *possibly* intersection object
Divide space up - sort objects into spatial buckets – trace ray from bucket to bucket
CSE 681

26. Bounding Boxes
CSE 681

27. Spatial Subdivision
CSE 681

28. Theory: sampling the environment
Rendering as sampling problem
Expected value & variance
Techniques to efficiently reduce variance
CSE 681

29. Major Course Topics Object & coordinate transformations.
Ray-object intersections.
Diffuse & specular reflection.
Shadows.
Opacity & refraction.
Recursive ray tracing.
Polyhedral models.
Texture mapping.
Anti-aliasing and sampling.
Bounding boxes and spatial subdivision.
Sampling theory.
CSE 681