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The option Mesh draws a rectangular mesh that subdivides the region.
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Mesh None (default) draws no mesh. Mesh n draws n equally spaced mesh divisions. Mesh Automatic draws automatically chosen mesh divisions. Mesh All draws mesh divisions between all elements. Mesh Full draws mesh divisions through regular data points.
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DensityPlot[x2 + y2, {x, 10, 10}, {y, 10, 10}] DensityPlot[x2 + y2, {x, 10, 10}, {y, 10, 10}, Mesh Automatic]
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The commands ListContourPlot and ListDensityPlot are the analogs of ContourPlot and DensityPlot for lists of numbers. These commands are appropriate for use with functions defined on a lattice of integer coordinates.
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ListContourPlot[array] generates a contour plot from a two-dimensional array of numbers. ListDensityPlot[array] generates a density plot from a two-dimensional array of numbers.
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array = {{z11, z12,...}, {z21, z22,...}, ...}, representing the heights of points in the x-y plane, must be a nested array of dimension 2 2 or larger. zij is the z-coordinate of the point ( j,i ). The options for ListContourPlot and ListDensityPlot are the same as for ContourPlot and DensityPlot, except that the axes are labeled, by default, with positive integers starting with 1. The option DataRange allows you to change the labeling of the axes to correspond to the actual values of the data.
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DataRange {{xmin, xmax}, {ymin, ymax}} labels the x and y axes from xmin to xmax and from ymin to ymax, respectively.
Three-Dimensional Graphics
EXAMPLE 13
list = Table[Random[], {x, 1, 10}, {y, 1, 10}]; ListContourPlot[list, DataRange {{ 5, 5}, {3, 7}}] ListDensityPlot[list, DataRange {{ 5, 5}, {3, 7}}]
Generates a 10 10 array of random numbers.
3 4 2 0 2 4
3 4 2 0 2 4
ContourPlot3D is the three-dimensional counterpart of ContourPlot. ContourPlot3D will sketch the level surfaces of f, i.e., the set of points (x, y, z) such that f(x, y, z) = k.
ContourPlot3D[f[x, y, z], {x, xmin, xmax}, {y, ymin, ymax},{z, zmin, zmax}] draws a three-dimensional contour plot of the level surface f(x, y, z) = 0 in a box determined by xmin, xmax, ymin, ymax, zmin, and zmax. Contours {k1, k2,...} draws level surfaces corresponding to k1, k2, . . . PlotPoints {nx, ny} determines the initial number of evaluation points that will be used in the x and y directions, respectively. PlotPoints n is equivalent to PlotPoints {n, n}.
The most commonly used options for ContourPlot3D are
EXAMPLE 14
ContourPlot3D[z x2 y2, {x, 5, 5}, {y, 5, 5}, {z, 0, 10}, Contours {0, 5}, Mesh None]
5 10
0 5 0 5
Three-Dimensional Graphics
ListPlot3D is the three-dimensional analog of ListPlot.
ListPlot3D[{{z11, z12,...}, {z21, z22,...},...}] generates a three-dimensional surface based upon a given array of heights, zij (must be a nested array of dimension at least 2 2). The x- and y-coordinate values for each data point are taken to be consecutive integers beginning with 1. ListPlot3D[{{x1, y1, z1}, {x2, y2, z2},...}] generates a three-dimensional surface based upon a given array of heights, zj which are the z-coordinates corresponding to the points {xi, yi}. MeshShading shades generates a surface shaded according to the descriptions in the array shades (GrayLevel, Hue, RGBColor, etc.). If array has dimensions m n, then shades must have dimensions (m 1) (n 1) . DataRange {{xmin, xmax}, {ymin, ymax}} labels the x- and y-axes from xmin to xmax and from ymin to ymax, respectively. The default is DataRange Automatic, which assigns values starting with 1.
Some options for ListPlot3D include:
Mesh is an option that specifies how mesh divisions should be drawn. The default is Mesh Automatic.
Mesh n specifies that n equally spaced mesh divisions (lines) should be drawn in each direction. Mesh All specifies that mesh divisions should be drawn between all elements. Mesh None eliminates all mesh divisions from being drawn.
EXAMPLE 15 (Graphs are grouped together for easy comparison.)
list = {{1, 5, 2, 2}, {3, 6, 1, 4}, {3, 1, 7, 2}};
ListPlot3D[list] ListPlot3D[list, Mesh None] shades = {{Red, Orange, Green}, {Cyan, Yellow, Magenta}}; ListPlot3D[list, MeshShading shades]
6 4 2 1 2 3 4 1.0 1.5 2.0
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