## Three-Dimensional PlotsIn three dimensions the domain is not a single interval, but a Cartesian product of two intervals.
We have already designed our code to work with lists of intervals that are applied to functions of
several arguments using and replacing rectangles by cuboids and
`Distribute` by `Graphics` . The code of
`Graphics3D` `IntervalPlot[` expr{`, ` x```
,
``` }
`, ` {`, ` y`, ` }
`, ` is shown in Listing 2.`]` Options[IntervalPlot3D] = { Tolerance -> 0.05 } split[l_List] := Distribute[split /@ l, List, List] rect[l:{_,_,_}] := Cuboid[Min /@ l, Max /@ l] RectangleGraph[l:{{_,_,_}..}] := Graphics3D[{EdgeForm[Thickness[0]], rect /@ l}] IntervalPlot3D[expr_, {x_Symbol, x0_, x1_}, {y_Symbol, y0_, y1_}, opts___?OptionQ]:= With[{tol = (x1-x0)Tolerance /. {opts} /. Options[IntervalPlot3D]}, Module[{finals}, finals = refine[Function[{x,y},expr], Interval /@ N[{{x0, x1}, {y0, y1}}], tol]; Show[RectangleGraph[finals], Evaluate[FilterOptions[Graphics3D,opts]], PlotRange -> {{x0, x1}, {y0, y1}, Automatic}, Axes -> True, BoxRatios -> {1,1,0.5}] ] ]
Cuboids truncated at the box boundary have an open top which makes them easy to distinguish from the closed ones. The different-sized domains, resulting from the adaptive algorithm, are clearly visible.
All values in the following picture are finite, but along the line the cuboids extend from to even for very fine subdivisions.
This investigation is continued in the next issue of Converted by Mathematica
October 15, 1999
[Prev Page][Next Page] |