I'm trying to get a neat slice-off of a torus along the plane of the Villarceau circles. One way to do this seems to be to find the equation for the curve...
Since the height can be expressed in terms of the projected distance to a point and the wheel-radius ("c" here) and tube-diameter ("a") of the torus, we can...
Haven't quite got the bottom half working, and this is pretty kludgy, but it points the way to taking general sections of a torus. Change "m" to change the...
There hasn't been anything on the site lately, so just thought I'd pass this along. Still plugging away at graphing toruses. Can't find the notes that I got...
I think I'm most of the way to being able to cut off a torus cleanly with an intersecting plane. Here's a step on the way: cutting off a parametric cylinder...
Almost there. One general approach is to find the parametric equation of the intersection curve from the two parametric equations for the surface. I'm not sure...
Not quite perfect, but seems to achieve the goal of slicing off a cylinder cleanly with an inclined cutting plane, whatever the angle. Angle of cutting plane...
Here, the surface has been colored by the value of the parameter u. It would seem better to me to be able to color the surface with cleanly cut-off,...
Got it simplified. All the drawing uses two functions, for the left and right halves of the cylinder: Different forms and combinations of parameters let you do...
Sorry, the last version didn't have the degree mark put in for the angle of rotation. Here's the fixed version. If you rotate to minus the angle of the cutting...
Aiming to rotate the cones around and up and down, like search lights, to illustrate conic sections as projections more vividly. The cone function has been...
Here are some linear algebra examples where you can experiment with the different effects of doing transformations in different orders. You have to be careful...
Just trying to figure out if the intersection of two circular cones is always two straight lines, even if they have different slant angles. Looks like it. Also...
... This is based on the file in the "Examples" menu, in the "2. Two dimensions sub-menu". Here's something, anyway: Did you make sure that "t" runs through...
Some tips for investigating parametric 2D plots. You can eliminate the irritating "jump line" for the discontinuity by taking a small section out of the...
Still cleaning up the functions. Sorry they still look complicated, but I'm trying to make them as versatile as possible, so that transformaitons on them can...
At last, conic sections with actual sliced-off cones. Not that this is necessarily the best way to do it, but I was able to use the same definition as for a...
I'm trying to find a way to plot the curve for a generalized conic surface so that I can match it up to the implict plot. A generalized conic surface is the...
I just posted this to sci.math, but I'll take help anywhere I can find it: I'm trying to find parametric equations for Clairaut's cubic cone, z y^2 = a x^3 +...
Some more plots of generalized conic surfaces, made from polynomials. Just change the expression for the generatrix (= "directing curve") to try more. A...
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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