Instructions - Isocontour plotting tool

Purpose

Fundamentals

The box in the upper left corner is the viewscreen for the plot. It can be rotated by clicking and dragging on the box.

Enter the function you wish to plot in the function box, the contour of that function to be plotted in the text area below, and press plot.

You may enter your function in terms of x, y, and z. In addition you may also enter your function in terms of r, theta, and phi, where they are defined such that:

x = r sin(phi) cos(theta)
y = r sin(phi) sin(theta)
z = r cos(phi)

Features

The applet will solve for the solution of f(x,y,z)=c along the edges of a grid of cubes filling the viewing area using a root-finding method. For each cube, the solution of the contour in 3 dimensions is approximated by a polygon with vertices along those edges;

You can control the resolution of the image. It is recommended that you start with the lowest resolution and without any adaptive "cleanup" iterations, and gradually increase the resolution to the level desired. The higher the resolution of the solution, the longer it will take to render the image.

You may view the image as filled polygons or as a mesh. Polygons and mesh lines are colored to represent depth on a ranbow spectrum, with red representing features closer to the viewer and blue representing features further from the viewer. As such, it is possible to increase the 3-D effect of the image through viewing the images with Chromadepth glasses.

Things to try

   x*x + y*y + z*z = 1

(z-
y*((sqrt(x*x+y*y)-1)/
(sqrt(x*x+y*y)+x)))*step(1.5-r)