Mathematica Tutorial: Visualization And Graphics - Wolfram Research

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94 Visualization and Graphics In diffuse reflection, light incident on a surface is scattered equally in all directions. When this kind of reflection occurs, a surface has a "dull" or "matte" appearance. Diffuse reflectors obey Lambert's law of light reflection, which states that the intensity of reflected light is cosHaL times the intensity of the incident light, where a is the angle between the incident light direction and the surface normal vector. Note that when a > 90 È , there is no reflected light. In specular reflection, a surface reflects light in a mirror-like way. As a result, the surface has a “shiny” or “gloss” appearance. With a perfect mirror, light incident at a particular angle is reflected at exactly the same angle. Most materials, however, scatter light to some extent, and so lead to reflected light that is distributed over a range of angles. Mathematica allows you to specify how broad the distribution is by giving a specular exponent, defined according to the Phong lighting model. With specular exponent n, the intensity of light at an angle q away from the mirror reflection direction is assumed to vary like cos HqL n . As n Ø , therefore, the surface behaves like a perfect mirror. As n decreases, however, the surface becomes less “shiny”, and for n = 0, the surface is a completely diffuse reflector. Typical values of n for actual materials range from about 1 to several hundred. Glow is light radiated from a surface at a certain color and intensity of light that is independent of incident light. Most actual materials show a mixture of diffuse and specular reflection, and some objects glow in addition to reflecting light. For each kind of light emission, an object can have an intrinsic color. For diffuse reflection, when the incident light is white, the color of the reflected light is the material's intrinsic color. When the incident light is not white, each color component in the reflected light is a product of the corresponding component in the incident light and in the intrinsic color of the material. Similarly, an object may have an intrinsic specular reflection color, which may be different from its diffuse reflection color, and the specularly reflected light is a component-wise product of the incident light and the intrinsic specular color. For glow, the color emitted is determined by intrinsic properties alone, with no dependence on incident light. In Mathematica, you can specify light properties by giving any combination of diffuse reflection, specular reflection, and glow directives. To get no reflection of a particular kind, you may give the corresponding intrinsic color as Black, or GrayLevel@0D. For materials that are effectively “white”, you can specify intrinsic colors of the form GrayLevel@aD, where a is the reflectance or albedo of the surface.
Visualization and Graphics 95 GrayLevel@aD RGBColor@r,g,bD Specularity@spec,nD Glow@colD matte surface with albedo a matte surface with intrinsic color surface with specularity spec and specular exponent n; spec can be a number between 0 and 1 or an RGBColor specification glowing surface with color col Specifying surface properties of lighted objects. In[9]:= This shows a sphere with the default matte white surface, illuminated by several colored light sources. Graphics3D@Sphere@DD Out[9]= In[10]:= This makes the sphere have low diffuse reflectance, but high specular reflectance. As a result, the sphere has a “specular highlight” near the light sources, and is quite dark elsewhere. Graphics3D@8GrayLevel@0.2D, Specularity@0.8, 5D, Sphere@D
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Mathematica Tutorial: Visualization And Graphics - Wolfram Research

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