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Three-Dimensional Graphics
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The next example shows how an increase in the value of PlotPoints affects the smoothness of the resulting graph.
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f[x_, y_] = x2y2 Exp[ (x2 + y2)]; Plot3D[f[x, y], {x, 2, 2}, {y, 2, 2}]
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Plot3D[f[x, y], {x, 2, 2}, {y, 2, 2}, PlotPoints 40]
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Most of the two-dimensional graphics options discussed in 4 will work with Plot3D. There are a few extra options that are new as well. The most popular ones are:
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Axes False will suppress the axes from being drawn. Axes {true_or_ false, true_or_ false, true_or_ false}, where true_or_ false is either True or False, will determine which axes will be drawn. Boxed False will suppress the bounding box containing the graph from being drawn. BoxRatios {sx, sy, sz} specifies the ratios of side lengths for the bounding box of the threedimensional picture. Mathematica s default is BoxRatios {1, 1, 0.4}. BoxRatios 1 is equivalent to BoxRatios {1, 1, 1}. Ticks False will eliminate tick marks and corresponding labeling along the axes. Ticks {true_or_ false, true_or_ false, true_or_ false}, where true_or_ false is either True or False, will control ticks on individual axes.
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FaceGrids is an option that draws grid lines on the faces of the bounding box.
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FaceGrids All draws grid lines on all six faces of the bounding box. FaceGrids None (default) draws no grid lines.
Three-Dimensional Graphics
FaceGrids {{x1, y1, z1}, {x2, y2, z2},. . . , {x6, y6, z6}} allows gridlines to be drawn on individual faces. Two of the three numbers in each sublist must be 0 and the third 1 to indicate which of the six possible faces will contain grid lines.
AxesEdge is an option that specifies on which edges of the bounding box axes should be drawn.
AxesEdge Automatic (default) lets Mathematica decide on which edges axes should be drawn. AxesEdge {{y1, z1 }, {x2, z2 }, {x3, y3 }} is where each of the x, y, and z values are either 1 or 1, to indicate on which edges of the bounding box the axes are to be drawn. 1 indicates that the axes will be drawn on the edge with the larger coordinate value, 1 indicates the smaller coordinate value. Any of the three lists {x, y} can be replaced by Automatic, in which case Mathematica decides where to place the axis, or None, in which case the axis is not drawn. BoxStyle is an option that specifies how the bounding box is to be drawn. BoxStyle can be set to a list of style options such as Dashing, Thickness, GrayLevel, or RGBColor. Mesh is an option that determines whether a mesh should be drawn on the graphic surface. The default is Mesh True; Mesh False or Mesh None eliminates the mesh.
The next example plots the parabolic cylinder z = x2 using different options.
EXAMPLE 3 (Graphs are grouped together for easy comparison.)
Plot3D[x2, {x, 2, 2}, {y, 2, 2}] Plot3D[x2, {x, 2, 2}, {y, 2, 2}, Mesh False] Plot3D[x2, {x, 2, 2}, {y, 2, 2}, BoxRatios 1] Plot3D[x2, {x, 2, 2}, {y, 2, 2}, FaceGrids {{1, 0, 0}, {0, 1, 0}}] Plot3D[x2, {x, 2, 2}, {y, 2, 2}, AxesEdge {{ 1, 1}, {1, 1}, {1, 1}}]
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Three-Dimensional Graphics
Three-dimensional graphics are generated as a sequence of polygons shaded to create a pleasing threedimensional affect. The polygons are drawn opaque so that surfaces behind other surfaces are hidden. The following option can be used to draw the surface transparent.
PlotStyle FaceForm[ ] draws the polygons transparent (only the connecting lines are drawn) so that all surfaces are visible.
EXAMPLE 4 (Graphs are grouped together for easy comparison.)
Plot3D[1 y2, {x, 5, 5}, {y, 5, 5}, BoxRatios {1, 1, 2}, Boxed False, Axes False] Plot3D[1 y2, {x, 5, 5}, {y, 5, 5}, BoxRatios {1, 1, 2}, Boxed False, Axes False, PlotStyle FaceForm[ ]]
There are many different ways to view a three-dimensional drawing. ViewPoint is an option that views the surface from a specified fixed point outside the box that contains it.
ViewPoint {x,y,z} gives the position of the viewpoint relative to the center of the box that contains the surface being plotted. The values of x, y, and z may be .
The viewpoint coordinates are scaled in such a way that the longest side of the bounding box is 1. The viewpoint must be located outside the bounding box. Generally, the further from the surface the viewpoint is selected, the less the distortion. The default Viewpoint parameters are {1.3, 2.4, 2.0}. In addition, the following symbolic forms are permitted. Their meanings are self explanatory.
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