by wendy » Sat Jan 31, 2009 8:06 am
The response was picked up in 'search for un-answered questions'. I did not look at the dates :s
Spheration is an effect applied to the a partial construction. This is what the name of the article says.
The crind product is a product of form rss(), applied to a radiant form.
The radiant form of a surface and a centre, supposes that the centre is 0, and the surface is 1. Any line drawn from the centre that strikes the surface, is measured in a linear scale using these units. Should the line strike twice, then it is counted as two separate lines, with different measures. One can then draw smaller and larger copies, eg at 0.7 or 1.3, by linking all of the 0.7 &c points together.
The normal practice is to centre the 0-point. For example for a circle of radius 1, the radiant function is simply the true radius. For a square of edge 2, the radiant function is max(abs(x), abs(y)).
An example of spheration applied to a figure of 2d is the crossing of two equal cylinders, being {[x,y],z}. For any plane containing the z axis, it strikes the square at some angle, giving a line somewhat longer than 2 units. The section in this axis and z, gives an ellipse of height z, and length longer than 2. For example, the one through the long diagonal gives an ellipse of axies 2 (z), and 2.828 (x+y). This is the crind-product of lines 2, 2.828.