Saddle Surfaces

简介

Monkey Saddle, Dog Saddle, Starfish Saddle, Octopus Saddle! In my Calculus III class we often use a hyperbolic paraboloid ("Basic Saddle") in our examples. We also look at a "Monkey Saddle" and a "Dog Saddle" and I have an animation that goes up to eight which we like to call the "Octopus Saddle." I used Wolfram Mathematica to make this set of "Saddle Surfaces" for numbers 2 through 8. 2 - Basic Saddle 3 - Monkey Saddle 4 - Dog Saddle 5 - Starfish Saddle 6 - Six Saddle 7 - Seven Saddle 8 - Octopus Saddle For each surface above, I included two versions. The regular version has the entire surface on a circular domain and the "Cut" version has the z-range restricted for a shorter, more easily printable model. If you want a different height variation, choose the regular version for the model and cut it as desired in your slicer. Note that the full surfaces would require a significant amount of support to print and they have very little contact with the build plate. Contour Map Surfaces The prints with the stripes illustrate the relationship between a surface and its contour map. The prints are set up using the saddle surface model and a second model "Contour Creator." I used PrusaSlicer to import the surface and then selected "Add Modifier..." to load the STL file for the "Contour Creator." This allowed me to set a different extruder for the stripes. Three different versions of "Contour Creator" are included: 0.1, 0.2, and 0.3 Stripes. I used the "0.3 Stripes" and printed with a…