• electromagnetic wave
• frequency (f) and wavelength (lambda) : c = f * lambda
• white light: contains all visible frequencies 400 nm < l < 700 nm
• Color: a particular frequency.
• Red = 700, green = 546.1, blue = 435.8

• Brightness or luminance: total energy of the light
• Hue: the dominant wavelength
• Saturation: the percentage of luminance which is taken by the dominant wavelength.
• The color sensation or intensity I = r × I_red + g × I_green + b × I_blue

Light sources

Ambient light:

• Illuminates the entire scene uniformly.
• The light of the sun on a cloudy day.
• Does not produce shadow.
• Its intensity is constant.

• A light source situated at the infinity, that arrives everywhere along the same direction.
• The sun on a sunny day.
• Produces a shadow.
• The intensity is constant.

• Light sources situated at a perceptible distance that illuminate the scene radially.
• An uncovered lamp.
• Produces shadow.
• The intensity can depend on the closeness to the source.
• It illuminates along a direction going from the light source to the current point.

• Similar to the point light sources, but they don't illuminate in every direction.
• It has an illumination range, which is usually inside a cone centered on the light source.

Ambient light	Directional light source	Point light source	Projection light source

General principle
The intensity of what we see from a ray of light depends on the angle between it and the view vector.

Note that the normal to any planar polygon (triangle) is constant on the polygon.

If I_p is the intensity of the light, L the opposite of the direction of the light, and N is the normal to the surface, we can compute the intensity of the light on that polygon as

I = I_p cos (N, L)

The color will be constant on the surface of the polygon.

Notations (all the vectors are unit vectors):

Q - the point to draw.

V - the viewpoint vector, going from the point Q to the viewer's eye for the perspective projection, or perpendicular to the projection plane for the parallel projection.

N - the normal to the surface in the point Q.

L - a vector going from the point Q to the light source.

R - the reflection of L in the point Q: L, N, and R are co-planar, L and R make the same angle with N.

theta - the angle between L or R and N: cos theta = L × N.

phi - the angle between R and V: cos phi = R × V.

General idea: split the ray L into two reflected rays:

• diffuse reflection, going equally in all directions, of factor k_d .
• specular reflection, going in the R direction, of factor k_s.
• add the ambient component of factor k_a.
• if k_a+ k_s+ k_d < 1, part of the ray is absorbed by the material.

I_d = Sum_iⁿ₌₁ I_pi cos theta_i
I_s = Sum_iⁿ₌₁ I_pi cos^k phi_i

For point light sources with intensity decreasing with distance:

For projection light source: if Phi = angle(L, light source direction)

I_p = I_pc * cos Phi, if Phi < Phi₀
I_p = 0, if Phi > Phi₀

Surface properties:

• For metallic surface: increase k_s and k.
• For velvet-looking surface: increase k_d.
• Surface irregularities: introduce a random factor in the reflected components.

• Can produce stone surfaces, orange skin, fabrics, journal paper, wood, etc.

Distance Term in the Phong Model

• To include a term depending on the distance to the light source, if we denote by
  d = distance (light source, Q)
  I = k_aI_a + factor *(k_dI_d + k_sI_s)
  where factor = 1/(a + bd + cd²)
• The factor is know as the quadratic attenuation term.