Re: Cropping a surface to a sphere

*To*: mathgroup at smc.vnet.net*Subject*: [mg88246] Re: Cropping a surface to a sphere*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Tue, 29 Apr 2008 06:51:01 -0400 (EDT)*Organization*: University of Bergen*References*: <fv1ff5$es6$1@smc.vnet.net> <fv42fb$5q4$1@smc.vnet.net>

David Park wrote: > > Here is a second version of the surface cropped to a sphere using a number > of options. > > ContourPlot3D[-x^4 y^2 + x^2 y^4 + x^4 z^2 - y^4 z^2 - x^2 z^4 + > y^2 z^4 == 1, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}, > RegionFunction -> Function[{x, y, z, f}, x^2 + y^2 + z^2 <= 9], > ContourStyle -> {FaceForm[ColorData["Legacy"]["DarkSeaGreen"], > GrayLevel[.7]]}, > PlotPoints -> 25, > Mesh -> False, > > (* Use white lights instead of colored lights *) > Lighting -> "Neutral", > Axes -> False, > Boxed -> False, > > (* The following options provide a smooth rotation with the mouse *) > SphericalRegion -> True, > RotationAction -> Clip, > > (* The following option causes the plot to fill the viewing area *) > PlotRegion -> {{-.3, 1.3}, {-.3, 1.3}}, > Background -> ColorData["Legacy"]["LightBeige"], > ImageSize -> 500] > > It's not clear that we need the bounding box or the axes. We might just say > it is the surface out to a radius of 3. The colored lights add nothing to > the plot. They only introduce confusion so we use Neutral lighting. We then > use the ContourStyle option to give different colors to the inside and > outside of the surface. If you don't like the image jumping around when you > use the mouse to rotate, you can use the SphericalRegion and RotationAction > options. The PlotRegion option gives us an initial view such that the object > fills the viewing area. You can also use the mouse zoom function to control > this. Then we use a Background to tone down the plot and ImageSize to > control the initial size. There are many other options that might be used. > > I hope you will agree that this is a much better presentation of the surface > than my previous reply without all the options. This looks very nice indeed---thank you for this demonstration of how to make great looking graphics! and sorry for not paying attention to the obviously outstanding option RegionFunction ...