Simulating the Physics of Pool using RenerMan

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/s2. • 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...)