Calculating Illumination

This section explains the way in which the various lighting parameters are used to characterize the illumination of the scene.

The lighting model is used to calculate the the color of every point on a surface under illumination. It is defined to be the sum of the illuminations from each individual light source.

The following symbols are used in all the lighting calculations below:

• d : the distance from the light source to the point under consideration.
• C : a color triple. Each of the equations below involving C or any subscripted C, can be decomposed into three equivalent equations for the red, green and blue color components. Each of the color values must lie between 0 and 1. If in any of the calculations a color value falls outside this range, it must be normalized.
• C_diff : The diffuse color of a surface - given by the color parameter in a surface statement.
• C_spec : The specular color of a surface - calculated from C_diff and C_light.
• C_light : The color of the illuminating light - given by the color parameter in any light statement.
• I : a color triple representing illumination or perceived color. Each of the equations below involving I or any subscripted I, can be decomposed into red, green and blue color components and must be normalized in the same manner as a color triple, C.
• D : the direction vector for a directional light or spot light.
• P : the position of a point light or a spot light.
• L : the light vector - has direction opposite to the direction of incident light.
• V : the vector from the point under consideration to the eye.
• N : the surface normal on the same side of the surface as V. Note that this is not necessarily the outward surface normal.
• R : the reflection vector that defines the reflection direction of the light ray in the ideal case of a planar mirror. It is calculated as R = 2(N ^. L)N - L.

Note: L, V, N, and R are all unit vectors

The illumination at a point on a surface is dependent on both the properties of the surface and those of the illuminating light sources. The parameters of the surface statement define the various surface properties.

The (C_r C_g C_b) triple specifies the diffuse color of the surface - i.e. the color of the surface when viewed under diffuse illumination or the normal color of the surface. This is C_diff.

K_amb, K_diff, and K_spec are the ambient, diffuse, and specular reflection coefficients respectively. All should be between 0 and 1. Each is multiplied by the three color values of the surface to provide the reflectance properties of the surface for each of the three colors. The K_amb coeffiecient controls the fraction of ambient light that is reflected from the surface. This coefficient can be raised or lowered to match the general reflectivity of the surface (i.e. K_amb = K_diff) or to represent the amount of ambient light that affects the object (i.e. the ambient light coefficient may be lowered if the object is believed to be in a dark corner of the scene.) The K_diff coeffiecient controls the fraction of light that is reflected diffusely from the surface. This diffuse reflection is calculated with Lambert's law. The K_spec coeffiecient controls the fraction of light that is reflected specularly from the surface. This specular reflection is calculated according to the Phong illumination model.

N_phong is the exponent in Phong's specular term.

Lighting calculations should be performed in the light's coordinate system. The point being lit and its normal vector should be transformed to the light's coordinate system using Q_{light<-object} and Q_{object<-light}^T respectively. This will enable correct calculations for falloff in the case of a light that has been scaled and will allow for spotlights or point lights to be nonuniformly scaled in the world.

Metallic Surfaces

m is the metallic factor of the surface and is used to calculate C_spec, the specular color of the surface. The value of m should be between 0 and 1. The more metallic a surface is, the more of its natural color is reflected in specular reflections. If a surface is purely metallic (m=1) then specular reflections off the surface will have the same color as diffuse reflections; if a surface is purely plastic (m=0) then specular reflections will be exactly the color of the incoming light. If C_light is the color of the illuminating light, then

Ambient Light

light  id
  type  SLF_AMBIENT
  color (Cr Cg Cb)

endlight

An ambient light defines non-directional background illumination. The color of a surface illuminated by ambient light is

For example:

light bg
  type  SLF_AMBIENT
  color (0.86 0.2 0)
endlight

Directional Light

light  id

  type  SLF_DIRECTIONAL
  color (Cr Cg Cb)
endlight

A directional light is a light source at infinity with light being radiated in one principal direction, D = (x_d y_d z_d). By default that direction is (0 0 -1), along the -z-axis, but it can be changed by the transformations that place the light in the scene. If Q_world<-light is the light's transformation then

Similarly, the surface and its normal could be transformed to the light's coordinate system using Q_light<-world and Q_world<-light^T respectively. Then the default light vector, (0 0 -1), is used. This method will give correct results in the case of a scaled light source.

For a directional light, the normalized light vector, L, is constant for all points under consideration.

The color of a point on a surface illuminated by a directional light source is

Point Light

light  id
  type         SLF_POINT
  color        (Cr Cg Cb)
  deaddistance (d0)
  falloff      (n1)

endlight

A point light source is located at a point P = (x_p y_p z_p), and radiates light equally in all directions. By default that position is at the origin, (0 0 0), but it can be changed by the transformations that place the light in the scene. If Q_world<-light is the light's transformation then

is the position of the light source in world coordinates.

Similarly, the surface and its normal could be transformed to the light's coordinate system using Q_light<-world and Q_world<-light^T respectively. Then the default light position, (0 0 0), is used. This method will give correct results in the case of a scaled light source.

The light vector, L, is different for each point on the surface and is the vector from the point under consideration to the light source. d₀ is the dead distance and n₁ is the exponent in the falloff factor.

The color of a point on a surface illuminated by a point light source is the same as for a directional light source except that it is attenuated with distance by a factor 1/(d₀ + d)^n₁. If d is the distance from the light source to the point under consideration, the color of a point on a surface illuminated by a point light source is:

Spot Light

light  id
  type           SLF_SPOT
  color          (Cr Cg Cb)
  deaddistance   (d0)
  falloff        (n1)
  angularfalloff (n2)

endlight

The light vector, L, is different for each point on the surface and is the unit vector from the point under consideration to P. d is the distance from the light source to the point. d₀ and n₁ are the same as for a point light and n₂ is the exponent of the angular falloff between D and -L. The color of a point on a surface illuminated by a spot light source is the same as for a point light source except that it is attenuated with angle out of the beam by a factor [D ^. (-L)]^n₂. The color of a point on a surface illuminated by a spotlight is