Great Software For 3D Visualization Of Geometry

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This page lists some fun geometry software i've used. Usually they are visualization software for non-Euclidean geometry or higher-dimensional geometry.

Curved Space

curved space screenshot
“Curved Space” screenshot.

Curved Space Jeff Weeks wrote a wondrous program that lets you fly thru various “warped” geometric spaces (3-manifolds). Source code and tutorial are included for programers. Home page: http://www.geometrygames.org/CurvedSpaces/index.html. OSX Win

Jeff Weeks wrote a excellent book to accompany the program. 《The Shape of Space》 amazon.

KriviznaPlus And KriDva

KriviznaPlus screenshot KriDva screenshot
“KriviznaPlus” and “KriDva”

KriviznaPlus and KriDva by Viktor Massalogin. KriviznaPlus draws the Stereographic Projection from 3D to plane. KriDva draws the stereographic projection of S^3 sphere (x^2+y^2+z^2+z^2==r^2) to the 3D space. These programs are extremely fun and beautiful. I hope the author adds more explanations on the math. As of 2004, he added another version CPace. Home page: http://www.hot.ee/bntren/Program.html. Win

stereop

Stereographic Projection of a icosahedron, by John M Sullivan
Partial screenshot of “stereop”, by John M Sullivan.

stereop by mathematician John M Sullivan. This applet does Stereographic Projection of regular polyhedrons. User can choose any of cube, tetrahedron, octahedron, dodecahedron, icosahedron, and they are centrally projected onto a sphere. This sphere, is then stereo-graphically projected onto a plane. User can rotate the polyhedron, and see its image on the plane change accordingly. Home page: http://torus.math.uiuc.edu/jms/java/stereop/. Java

SeifertView

interf26 trefoilmoebius trefoilseifert trefoilside
Seifert surfaces from SeifertView.

SeifertView by Jack van Wijk, is a software to visualize Knot-rim Surfaces (aka Seifert surface). A knot-rim surface is a surface such that its edge is a knot or link. Home page: http://www.win.tue.nl/~vanwijk/seifertview/ Win

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