1. Simulating the Physics of Pool using RenerMan ● Shaders and Texture Mapping ● Spherical Texture Maps ● Rotating the Balls ● Lighting ● Physics Equations ● Functions Yet to Be Implemented

2. Shaders and Texture Maps ● Shaders are a part of the rendering program that calculates the appearance of visible surfaces in the scene. In RenderMan, a written procedure is used as a shader. ● There are three types of shaders: – Light Shaders – Surface Shaders – Volume Shaders

3. Light Shaders ● Light Source Shaders calculates the intensity and color of light sent by a light source to a point on a surface ● Basic light source shaders include: – ambient light – distant light – point light – spotlight

4. Light Shaders (cont’d) ● Light Shaders used in project include: – ambient light – three point light sources

5. Surface Shaders ● A surface shader calculates the color of light reflecting from a point on a surface in a particular direction ● Basic Surface Shaders Include: – constant – matte – metal – plastic – texture map

6. Surface Shaders (cont’d) ● Surface Shaders used in project include: – felt – wood – pool ball texture map

7. Spherical Texture Maps ● Applying texture maps to spheres is a special case ● When a texture is applied to a sphere, the texture will be stretched horizontally

8. Spherical Texture Maps (cont’d) ● The original image has the size of 2h x h. ● Then scale the image’s x-axis by half

9. Volume Shaders ● Volume Shaders calculates the color and intensity of light as it passes through a volume (a region of space). ● Volume Shaders include: – Fog – Jell-O ● I intend to use fog to simulate the smoky environment of a pool hall

10. How Shaders All Come Together ● Draw Picture

11. Physics Equations ● Most pool applications use the ninety degree rule to simulate the deflection of pool balls, even those that claim to simulate the actual physics of the game. ● Just because you used physics equations, does not mean you used the correct equations. ● The ninety degree rule holds true only in frictionless environments (air hockey, collisions in space, etc.)

12. Physics (cont’d) Friction, and Deceleration ● Most people assume the friction between a billiard ball and the table is so small, friction can be ignored. ● This is not true, friction does exist on a pool table, causing an average deceleration of 0.21 m/s 2. ● Since friction does exist, the ninety degree rule does NOT hold true for pool

13. Physics (cont’d) Deflection ● The actual equations of deflection, in components, are: (where the subscripts o and c refer to the object ball and cue ball, respectively)

14. Physics (cont’d) Angular Velocity ● To make the billiard balls roll correctly, the angular velocity is needed. ● The equation for angular velocity is:

15. Functions Yet to Be Implemented ● Smoky Environment ● Motion Blur ● Camera Motion ● Pockets, and other pool accessories. ● Ball deflection off of wall ● Ball Falling In Pocket (maybe...)