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Plot3D

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Plot3D[f, {x, xmin, xmax}, {y, ymin, ymax}]
generates a three-dimensional plot of f as a function of x and y.
Plot3D[{f1, f2, ...}, {x, xmin, xmax}, {y, ymin, ymax}]
plots several functions.
  • Holes are left at any positions where the fi evaluate to None, or anything other than real numbers.
  • Plot3D treats the variables x and y as local, effectively using Block.
  • Plot3D has attribute HoldAll, and evaluates f only after assigning specific numerical values to x and y.
  • In some cases it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to x and y.
  • Plot3D has the same options as Graphics3D, with the following additions and changes:
AxesTruewhether to draw axes
BoundaryStyleAutomatichow to draw boundary lines for surfaces
BoxRatios{1,1,0.4}bounding 3D box ratios
ClippingStyleAutomatichow to draw clipped parts of surfaces
ColorFunctionAutomatichow to determine the color of surfaces
ColorFunctionScalingTruewhether to scale arguments to ColorFunction
EvaluationMonitorNoneexpression to evaluate at every function evaluation
ExclusionsAutomaticx, y curves to exclude
ExclusionsStyleNonewhat to draw at excluded curves
FillingNonefilling under each surface
FillingStyleOpacity[0.5]style to use for filling
MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
MeshAutomatichow many mesh lines in each direction to draw
MeshFunctions{#1&,#2&}how to determine the placement of mesh lines
MeshShadingNonehow to shade regions between mesh lines
MeshStyleAutomaticthe style for mesh lines
MethodAutomaticthe method to use for refining surfaces
NormalsFunctionAutomatichow to determine effective surface normals
PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
PlotPointsAutomaticthe initial number of sample points in each direction
PlotRange{Full,Full,Automatic}the range of z or other values to include
PlotStyleAutomaticgraphics directives for the style for each surface
RegionFunction(True&)how to determine whether a point should be included
WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • Plot3D[Tooltip[{f1, f2, ...}], ...] specifies that the fi should be displayed as tooltip labels for the corresponding surfaces.
  • Tooltip[f, label] specifies an explicit tooltip label for a surface.
  • PlotStyle->None draws no surface, so effectively does not eliminate hidden surfaces.
  • Plot3D initially evaluates each function at a grid of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing at most MaxRecursion times.
  • You should realize that with the finite number of sample points used, it is possible for Plot3D to miss features in your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.
  • With the setting Mesh->All, Plot3D draws mesh lines to show all subdivisions it makes.
  • The default setting MeshFunctions->{{#1&, #2&}} draws an x, y mesh on each surface.
  • By default, surfaces are treated as uniform white diffuse reflectors, corresponding to ColorFunction->(White&).
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