Three-Dimensional Mathematica Graphics (Section 4.2)

Extract from Mathematica Graphics: An Intensive Tutorial

by Tom Wickham-Jones

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4.2 Using Color and Lighting

Mathematica graphics have many features designed to use color. Some of these examples will not look so interesting on a monochrome display; however, in color some of them are quite striking.

4.2.1 Directives

There are a number of directives to color primitives.

GrayLevel[g]

RGBColor[r, g, b]

Hue[h]

Hue[h, s, b]

CMYKColor[c, m, y, k]

Mathematica color directives.

The directives GrayLevel, RGBColor and CMYKColor take as arguments numbers between 0 and 1 inclusive. Thus GrayLevel[0] is black, RGBColor[1, 0, 0] is a red and CMYKColor[0, 1, 0, 0] is a magenta.

The directive Hue is special; it can take one or three arguments. The latter, Hue[h, s, b], describes the hue, saturation and brightness. There is also a one-argument form, Hue[h], which is equivalent to Hue[h, 1, 1]. The arguments for saturation and brightness must be numbers between 0 and 1 inclusive. However the first argument, that for hue, is taken modulo 1. Thus Hue[0], Hue[1] and Hue[2] are all the same color, namely a red. This wrapping around makes Hue a versatile command for introducing color into the graphics.

4.2.2 Lighting

The lighting of three-dimensional Mathematica graphics is set by a number of options.

The lighting model used in Mathematica is not a photo-realistic ray tracer. It provides simulated light sources which do not diverge and do not cast shadows. To use the simulated light sources it is necessary to set the option Lighting -> True, which is set by default. The direction of the lights are determined by the setting of the LightSources options.

The coordinates of these light sources are in display coordinates. Thus the default setting gives lights which are on the right, top and top-right of the screen. The parts of the object which are not illuminated by the light sources are colored by the AmbientLight option. To make a more complex type of surface one can use the SurfaceColor directive.

4.2.3 Function Evaluation

Mathematica provides a number of ways to color a function according to an evaluation.

ColorFunction

ColorFunction is an option for SurfaceGraphics, DensityGraphics, ContourGraphics and related commands. It also exists for the Graphics primitive Raster. It must be set to a function of one argument. This is given the height at each point of the array scaled to run from 0 to 1. It must return a color directive.

4.2.4 ColorOutput

ColorOutput is an option for all graphics commands. It instructs Mathematica to filter through the PostScript as it is emitted and change color specifications. In this way color separations can be carried out.