A material based on the Phong shading model. This material has several independent components that together give an object its appearance using the Phong shading model. The material interacts with each illuminating light separately, and the contribution from each light is summed.

The diffuse and specular components can be specified by a (solid) color and/or a texture map (represented as an image). If both are applied, their values are multiplied. For example:
Color#LIMEGREEN * =

Color#CYAN * =

PhongMaterial is not suitable for surfaces that act like mirrors and reflect their environment, such as reflective metals, water, and reflective ceramics. Neither does light refract (bend) when passing through transparent or translucent materials such as water, glass, or ice. These materials rely on Fresnel effects that are not implemented for this material.

Components

While in the physical world each light ray goes through a single path of reflection, transmission, or absorption, in the computational world a number of adjacent rays are averaged into a single one that can split into multiple paths. This approximation simplifies the computation model greatly while still allowing realistic rendering. The validity of this approximation depends on microscopic details of the material, but it holds well for the vast majority of cases. When an averaged incident ray (blue) hits the surface, it can split into many rays depending on the values of the components of the material: rays that are either transmitted through the material (green) or reflected in all directions via scattering (purple) depend on the diffuse component; rays that are reflected (orange), which depend on the incident angle, are controlled by the specular component.

Diffuse

The diffuse component, sometimes called albedo, serves as the base color of the surface. It represents light that is not reflected directly from the surface and instead enters the material.
The alpha channel of the diffuse component controls the light that passes through it (transmitted). Decreasing the alpha value increases the transparency of the material and causes the object to appear translucent, and ultimately makes it transparent. Materials such as glass and plastics can be simulated with a low alpha value.
Light that isn't transmitted undergoes subsurface scattering that causes it to be absorbed in the material or be reflected back to the surface, exiting in (approximately) all directions (irrespective of the incident angle). The RGB channels of the diffuse component controls which colors are absorbed and which are reflected, giving the material its base color. The higher one of the RGB values is, the more that material reflects that color.

The diffuse component interacts with all lights - both those that have directionality and AmbientLight, which simulates a light that comes from all directions.

Specular

The specular component represents light that is reflected directly from the surface. For most materials, the color of the specular component is on the gray scale regardless of the diffuse component's color. This means that the specular highlight will be the light's color and not the material's color. These materials are sometimes called dielectrics. Metals, on the other hand, reflect a color similar to their diffuse color (like yellow for gold or reddish for copper) and get most of their appearance from the specular color. These materials are sometimes called conductors.

The spread of the surface-reflected rays simulates the microgeometry that causes adjacent beams to be reflected in different directions. Smooth surfaces' microgeometry varies little, causing them to have a strong specular component that results in a glossy look, such as plastics, finished wood, and polished metals. Conversely, rough surfaces have a varying microgeometry, weak specular component, and a matte look, such as unfinished wood, fabric, and cardboard. This spread is controlled by the specular power, sometimes called smoothness or, conversely, roughness. A larger specular power simulates a smoother object, which results in a smaller reflection.

The specular component interacts only with lights that have directionality (not AmbientLight) as it depends on the incident ray direction, and also on the viewer (camera) position since it depends on the reflectance direction.

The alpha component of the specular color is not used at this time.

Self-Illumination

The self-illumination component, also called emissive, represents light emitted by the object. It does not interact with light sources and as such the viewer position does not matter. Specifying this component does not cause the object to serve as a light source - a light has to be added at the position of the object with a color that matches this color. If a multi-colored map is used, several lights of matching colors can be positioned appropriately in the object's volume to give a realistic appearance.

The alpha component of the self-illumination color is not used at this time.

Bump

The bump component gives the illusion of small height changes on the surface, like bumps and ridges. It is a normal map (not a height map or a displacement map), which works by modifying the normals of surfaces on the object, causing light to interact differently with the surface than it would have without it. Tree trunks and rough stones can be simulated with a bump map.

Bump maps are less expensive than changing a mesh by subdividing a surface into many polygons facing different ways. If the physical geometry of the surface is not important (for example, for intersection calculations), it's advised to use a bump map.

The alpha component of the bump map is not used at this time.

Mathematical Model

Bump

The default normal vector of a point on the polygon is N=(0, 0, 1) (facing away from the surface). If a bump map is specified, this vector will have a different value based on the RGB values in the bump map: N=2 * RGB - 1. The default value for a bump map (corresponding to the default normal) is RGB=(0.5, 0.5, 1), which is why bump maps tend to be blueish.

We will treat N as the normal vector after applying a bump map, if available.

Diffuse

The diffuse component represents light scattered from the surface in all directions, hence, it depends on the interaction between the light and the surface (and independent of the viewer position): L⋅N. L⋅N is the geometric factor of the diffuse component. It moderates the intensity of the color resulting from the light hitting the surface at different angles. If the light ray is parallel to the surface, L⋅N=0 and the diffuse contribution of the light will be 0; if the light ray is perpendicular to the surface (coincides with the normal vector), L⋅N=1 and no reduction in intensity occurs.

Defining the light's color as C_L, and the material's diffuse color as C_DM, we multiply the 3 factors described above: L⋅N * C_L * C_DM. For i lights illuminating the surface, the contribution of each light is summed:
Σ_i(L_i⋅N * C_Li * C_DM) = Σ_i(L_i⋅N * C_Li) * C_DM (since C_DM is a property of the material and is the same for all lights).

Since AmbientLight simulates a light coming from and scattered in all directions, it contributes fully to the diffuse component (L⋅N=1). We will define all the ambient lights' contribution as A=Σ_i(C_Li) and all the other lights' (that have a light vector) as D=Σ_i(L_i⋅N * C_Li). The total diffuse component contribution is then (A+D) * C_DM.

Specular

The specular component represents light reflected from the surface in a mirror-like reflection, hence, it depends on the interaction between the reflected light and the viewer position: R⋅V. As similarly explained in the diffuse component section, the geometric contribution is strongest when the viewer is aligned with the reflection vector and is non-existent when they are perpendicular.

The specular power, P, represents the smoothness of the surface. Smoother surfaces have more narrow reflections and their specular power is smaller (right image), while rougher surfaces have more dispersed reflections and their specular power is larger (left image). Since 0≤R⋅V≤1, the term (R⋅V)^P decreases as P increases, giving a smaller contribution.

Like with the diffuse component, the resulting specular color is computed by multiplying the geometric factor, the light's color, and the material's specular color, C_SM, for each light:
Σ_i((R_i⋅V)^P * C_Li) * C_SM, and defining the specular lights' contribution as S=Σ_i((R_i⋅V)^P * C_Li), the total specular component contribution is S * C_SM.

Self-Illumination

The self-illumination component represents light emanating from the surface, hence, it is not affected by lights, the geometry, or the viewer position. Its contribution is just the material's self-illumination color, C_LM.

Summary

The final color at the point of the computation is then: (A+D) * C_DM + S * C_SM + C_LM.

Examples

This section shows examples for simulating various common materials. Each image will be accompanied by the values used for the material. Values that aren't specified are the default ones.

Gloss

The specular power controls the size of specular highlights, which changes the gloss or smoothness look. Lower powers create larger highlights and vice versa. Some plastics and marble exhibit this behavior, as shown here with 2 billiard balls:

Materials values

Image
Diffuse color	Color.YELLOW.darker()	Color.RED.darker()
Specular color	Color.WHITE	Color.WHITE
Specular power	10	150

Transparency

Some materials are transparent/translucent, allowing most of the light through, like glass and plastics. This is achieved with low diffuse opacity (alpha) values. Tint can be achieved with small RGB values in addition. The smoothness of these materials also means a specular component is present with strength that depends on the finish/polish of the material. A high brightness specular color gives a more glossy look and a low brightness one gives a more matte look.

Material values

Image
Diffuse color	Color.rgb(0, 0, 0, 0.3)	Color.rgb(0, 0, 0, 0.3)	Color.rgb(0, 0, 0, 0.3)	Color.rgb(75, 0, 0, 0.15)
Specular color	Color.hsb(0, 0, 0)	Color.hsb(0, 0, 45)	Color.hsb(0, 0, 90)	Color.hsb(0, 0, 45)

Specular Color

Metals reflect their own color rather than the light's full color. In this case, the specular color should be similar to the diffuse color, with its brightness affecting the shininess/polish levels. Copper and gold are shown here.

Material values

Image
Diffuse color	Color.hsb(20, 85, 70)	Color.hsb(20, 85, 70)	Color.hsb(20, 85, 70)	Color.hsb(41, 82, 92)	Color.hsb(41, 82, 92)
Specular color	Color.hsb(20, 85, 40)	Color.hsb(20, 85, 70)	Color.hsb(20, 85, 100)	Color.hsb(41, 82, 30)	Color.hsb(41, 82, 92)

Maps and Surface Detail

The specular and bump maps can provide surface details that make the object look more realistic. A tree trunk, which has none-to-low specularity, has a lot of grooves that can be emphasized with a bump map:

Model with maps applied

Bump	Diffuse	Bump+Diffuse

A diffuse color of HSB=(0, 0, 60) has been used to darken the wood.

Polished wood, like that used in housing, has a strong specular component due to the finish and buff. A combination of a specular and a bump map highlights the details in the wood:

Model with maps applied

Diffuse	Diffuse+Specular	Diffuse+Bump	Diffuse+Specular+Bump

A specular power of 100 has been used to give a more smooth look.

Texture Animation

Texture animation and runtime effects can be achieved in different ways. Firstly, an animated GIF can be used as the Image for texture maps, as demonstrated here when used as a diffuse map:

Secondly, by using a WritableImage, the pixel values can be changed programmatically, creating a live texture as demonstrated for the diffuse map by this code snippet that repaints the image left to right and top to bottom:

Other maps can be modified as well, producing various effects.
Another way to animate textures is done through changing the texture coordinates of the mesh, the explanation for which is out of scope for this class.