POVDISPLAY is a set of functions in Maple to handle curves, filaments ribbons and surfaces.
The main graphical function produces a POV file. POV is a ray-tracing program producing stunning 3D photo-realistic pictures.
Once the library is loaded (See How to load POVDISPLAY), the following command line in Maple
>povdisplay(surface,sin(X)*X*Y*sin(Y),[[-2,2],[-2,2]],povname=`example1`, scene=16,radius=0.2,color=`Gold`,precision=`0.05`,camera=[0,-10,0]);
produces a POV files (the file example1.pov) that generates the following picture:
POVDISPLAY was written mainly to handle curves in 3D. Here is an example of a curve with superimposed twist represented as a simple curve, a curve with twist and as a ribbon:
>povdisplay(curve,knot(4,1),[0,2*Pi],povname=`example2`, background=Blue,orientation=[-90,90]);
>povdisplay(vector,knot(4,1),[0,2*Pi,3],povname=`example3`, ribbon=`yes`,radius=1,scene=3,twist=1,orientation=[-90,90]);
>povdisplay(vector,knot(4,1),[0,2*Pi,300],povname=`example4`,ribbonstyle=2, ribbon=`yes`,radius=1.5,color=Orange,ribbondistance=0.25, scene=14,twist=1,orientation=[-90,90]);
POVDISPLAY also contains a library of prime knot of up to 8 crossings. The parameterization used is the harmonic parameterization due to A. Trautwein. To call one of such knot (say the fifth knot with 7 crossing in our knot table), just type:
>povdisplay(curve,knot(7,3),[0,2*Pi],povname=`example5`, radius=1,numberofpoints=800,scene=12,orientation=[-99,38]);
To learn more about knots and stuff visit the KnotPlot site.
Many pre-defined background scenes are available. Here we call the scene number 15 with a trefoil knot:
>povdisplay(knot,[3,1],[0,2*Pi],povname=`example6`,radius=1.5,numberofpoints=600,scene=15,color=`checker color Yellow color Green`,orientation=[-37,-120],preview=no);
One of the main interesting features of POVDISPLAY is that it uses the orientation of Maple 3D graphics. It is then easy to use Maple to find the best possible view of a 3D object before producing the POV file.
POVDISPLAY allows to handle different curves. It can from the curves find their curvature, torsion or compute the Frenet basis. Given the curvature or torsion it can also reconstruct the curves and so on.
POVDISPLAY manipulates both curves given by an analytical representation or a list of points.
POVDISPLAY can compute the Link, Twist and writhe of a given curve.
For instance let us study a knot with 4 crossing:
>k41:=knot(4,1);
The link between the knot and the curves obtained by following the extremity of its normal vector is:
>Link1(k41,k41+d1(k41,0),0,2*Pi,100);
The writhe of the same knot:
>Writhe1(k41,0,2*Pi,100);
