Simulating the Physics of Pool using RenerMan

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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

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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

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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

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Light Shaders (contd)

• Light Shaders used in project include
• ambient light
• three point light sources

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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

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Surface Shaders (contd)

• Surface Shaders used in project include
• felt
• wood
• pool ball texture map

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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

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Spherical Texture Maps (contd)

• The original image has the size of 2h x h.
• Then scale the images x-axis by half

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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

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How Shaders All Come Together

• Draw Picture

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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.)

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Physics (contd)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

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Physics (contd)Deflection

• The actual equations of deflection, in
  components, are(where the subscripts o and c
  refer to the object ball and cue ball,
  respectively)

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Physics (contd)Angular Velocity

• To make the billiard balls roll correctly, the
  angular velocity is needed.
• The equation for angular velocity is

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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...)