By entering in any space curve in the expression C_d(s), you get a generalized cone traced around it. http://mathworld.wolfram.com/GeneralizedCone.html ... By...
Polar coordinate plots will show up on top of any kind of background you make with an [h s v] color map in 2D. Handy for seeing light colors like yellow...
Trying to understand these geometrically and relate them to slices through a generalized cone. It looks like we've got expressions for lines in the numerator...
Some general functions for drawing a triangle given three points. You can drag the points around and the triangle border will be drawn by a single function, as...
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Just scratching the surface of what can be done with this. You can make as many copies as you want of the original triangle function, using subscripts, and...
Not too useful, yet, I suppose, but shows how you can combine functions. There are probably much simpler ways to do this. Could be used to make perspective...
This obviously can be simplified a lot, but it's another example of how to "share a parameter" in order to use a single function to draw a shape consisting of...
There are some problems with subscripts that should be fixed in the next release that should make doing this kind of thing a lot easier. Ought to be possible...
Due to a GC quirk, you have to use "if" statements within a vector expression (the "[h s v]" color-mapping vector, in this case), or at least I haven't figured...
This uses the triangle function in the previous e-mail, except converted to 3D, to plot a general "pyramidal cone". Like the previous files, this is in large...
Hope nobody minds all the files. Hoping something is of interest here (and maybe get a little assistance). I'm plugging away at trying to understand...
This is part of some work-in-progress for illustrating parameterization, following a number of good text-books. You can do very intricate things with color...
The idea is to use the "normal form" of the line: Just divide through by the "modulus" of the coefficients. E.g., for the line: we end up with: The "0.8"...
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Jun 19, 2006 8:42 pm
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Still not quite finished, but in trying to get functions to color in parallelograms in both positive and negative orientations (counter-clockwise vs....
Amazingly, you can form complicated functions that draw the interior of a figure, or part of a line or other shape going through it, just by forming the right...
I forgot to mention that if the parallelogram vertices are in counter-clockwise order, the sign of the area changes and the colors change to their complements...
... Hank, If you could give me a few more specifics, I might be able to help out more. Is this the kind of thing you had in mind? Here's something that does a...
As long as you make sure all your parameters---the "n" parameter and the "t" parameter---run in synch, you can get the trace of a curve as you animate it just...
Not quite a general-purpose tool, but getting there. The idea is to get something where you only have to change the lines for the radial and angular...
Log spiral where start and stop angles can be changed. I believe log spirals are "self-similar" at different scales. Might be interesting to take different...
By setting the k_2 and k_5 constants you can get the compound-harmonic-motion Lissajous curves in both polar and rectangular coordinates. These may seem like...
... I managed to plot the points and lines, but I'm at a loss as to how to do best-fit plotting for polar coordinates (or in general, for that matter). Any...
