Great Math Software for Curves and Surfaces

By Xah Lee. Date: . Last updated:

This page lists some great math programs that i've used.


Mathematica icon

Mathematica from Mathematica is famous for the book A New Kind of Science, and Wolfram alpha. Most images at Visual Dictionary of Special Plane Curves are created with Mathematica in 1997.

Mathematica comes free bundled with Raspberry Pi Raspberry Pi

Graphing Calculator

Graphing Calculator

Graphing Calculator by Ron Avitzur. Imagine your hand-held graphing calculator with the power of a desktop computer, then you get the idea of what this program is about.

Out of 10 or 20 programs that plots curves and surfaces i've tried, I think this is the best. Most versatile and most easy to use. Go download a demo and see for yourself. If you want a plotting program for your highschool or college installation, I suggest this one. URL: Mac OSX Win

The website A Visual Dictionary of Famous Plane Curve includes many files of Graphing Calculator.



K3DSurf. A program that plots surfaces or higher-dimensional manifolds. It can plot equations of 3 variables and parametric formulas for higher-dimension surfaces, and can do morph based on a variable. OSX Win linux


3dxm screenshot

3D-XplorMath, by mathematician Richard Palais. 3D-XplorMath is a program for visualization of objects and processes in geometry. It can plot and animate surfaces, 2D/3D curves, complex valued functions, differential equations and others. The most eye-catching is its rendering of over 100 curious surfaces in differential geometry.

3D-XplorMath also includes some over one hundred expositions in PDF on various geometry topics on curves, surfaces, comlex mappings, fractals. The flaw with 3DXM is that it is very difficult to use. The menus are overflowing and non-standard, and user must read a big documentation to learn what various parameters mean and how to use them.

If you study or teach differential geometry, differential equations, or minimal surfaces, this is a excellent program. (Note: I'm a member of the 3D-XploreMath Consortium.)


• Mathematica package for converting 3D-XplorMath surface files to Mathematica graphics:


PlanarCurveExplorer screenshot
PlanarCurveExplorer. Is a excellent Java Applet that does plane curves. One particular aspect of this program is that it is written by and for mathematicians.… Java


SpaceCurveExplorer screenshot
SpaceCurveExplorer. Is a excellent Java Applet that does space curves. By and for mathematicians.… Java
SurfaceExplorer screenshot
SurfaceExplorer. Is a excellent Java Applet that does surfaces for the study of differential geometry. By and for mathematicians.… Java


ParametricSurfaceViewer screenshot
ParametricSurfaceViewer. Is a excellent Java Applet that does parametric surfaces for the study of differential geometry. Author is Markus Schmies.… On their site, they also have quite a few other apps related to differential geometry. Java



Spivak is a surface plotter by Jacob Siehler. One interesting feature is that users can drag a point inside a box, and the corresponding point on the surface moves dynamically. User can also turn on the drawing of tangent plane, tangent line, geodesic, and principal curvature lines at that point. There is also SpaceCurve program by the author. Website: (2005-11,2006-06) OSX



app icon GrafEQ GrafEQ is a plane curve plotting program especially good at plotting implicit equations. Available for Mac and Windows. Fully functional demo is available at Pedagoguery Software Mac Win (2004-10)

2004-01. The mathematician Paul Bourke has written a (commercial) app called SuperShape, that creates various odd-shaped 3-d models. Mac Linux

Here is a list of Curves and Surface plotters for Windows