3-D CURVES: Executable or Text Version

Draws curves of the form y = F ( x , z ) in 3-D. y is "up" the screen, x is across the screen, and z appears to go "into" the screen.

• Functions must be entered in ALL UPPER CASE or ALL LOWER CASE. Example z*sin(x) + (1-z)*tan(1/x).


• You need to play around with the scale (typically in the range 0.1 to 10) and the ranges until you like the picture.

CATACAUSTIC CURVES: Executable or Text Version

As illustrated by the screen dump picture below, with this program you can select a point light-source with the mouse (just left-click where you want when the mouse cross-hairs appear), and you will see the curve created by the envelope of reflected light rays from the surface of the chosen curve.

I achieve this by accurately estimating the derivative of the curve at each point the light hits it, from which I calculate the Unit Normal vector to the curve at that point, from which I can work out the correct reflected ray.

For further inspiration of which curves to draw, Jan Wassenaar's website has 667 different curves to choose from.

Return to Top Page                                                                                                         Next Page