NAME

LiveGraphicsRectangularPlot3D.pl - provide an interactive 3D rectangular plot.

DESCRIPTION

LiveGraphicsRectangularPlot3D.pl provides two macros for creating an interactive plot of a function of two variables z = f(x,y) in Rectangular (Cartesian) coordinates via the LiveGraphics3D Javascript applet. The routine RectangularDomainPlot3D() takes a MathObject Formula of two variables defined over a rectangular domain and some plot options as input and returns a string of plot data that can be displayed using the Live3Ddata() routine of the LiveGraphics3D.pl macro. The routine AnnularDomainPlot3D works similarly for a function z = f(x,y) over an annular domain specified in polar by rmin < r < rmax and tmin < theta < tmax.

USAGE

RectangularPlot3DRectangularDomain(options)

Options are:

function => $f,        $f is a MathObjects Formula
                       For example, in the setup section define

                       Context("Numeric");
                       Context()->variables->add(s=>"Real",t=>"Real");
                       $a = random(1,3,1);
                       $f = Formula("$a*s^2-2*t"); # use double quotes!

                       before calling RectangularPlot3DRectangularDomain()

xvar => "s",           independent variable name, default "x"
yvar => "t",           independent variable name, default "y"

xmin => -3,            domain for xvar
xmax =>  3,

ymin => -3,            domain for yvar
ymax =>  3,

xsamples => 20,        deltax = (xmax - xmin) / xsamples
ysamples => 20,        deltay = (ymax - ymin) / ysamples

axesframed => 1,       1 displays framed axes, 0 hides framed axes

xaxislabel => "S",     Capital letters may be easier to read
yaxislabel => "T",
zaxislabel => "Z",

outputtype => 1,       return string of only polygons (or mesh)
              2,       return string of only plotoptions
              3,       return string of polygons (or mesh) and plotoptions
              4,       return complete plot

RectangularPlot3DAnnularDomain(options)

Options are:

function => $f,        $f is a MathObjects Formula
                       For example, in the setup section define

                       Context("Numeric");
                       Context()->variables->add(y=>"Real",r=>"Real",t=>"Real");
                       $a = random(1,3,1);
                       $f = Formula("$a*e^(- x^2 - y^2)"); # use double quotes!

                       before calling RectangularPlot3DAnnularDomain()

xvar => "x",           independent variable name, default "x"
yvar => "y",           independent variable name, default "y"

rvar => "r",           independent variable name, default "r"
tvar => "t",           independent variable name, default "t" (for theta)

rmin => -3,            domain for rvar
rmax =>  3,

tmin => -3,            domain for tvar
tmax =>  3,

rsamples => 20,        deltar = (rmax - rmin) / rsamples
tsamples => 20,        deltat = (tmax - tmin) / tsamples

axesframed => 1,       1 displays framed axes, 0 hides framed axes

xaxislabel => "X",     Capital letters may be easier to read
yaxislabel => "Y",
zaxislabel => "Z",

outputtype => 1,       return string of only polygons (or mesh)
              2,       return string of only plotoptions
              3,       return string of polygons (or mesh) and plotoptions
              4,       return complete plot