## 3D-XplorMath

### Summary

The primary goal of 3D-XplorMath is to allow users with little or no

programming experience to see, with minimal effort, concrete visual

representations of many different categories of mathematical objects

and processes. To accomplish this, objects from each category are

described internally by well-designed, parameterized data structures,

and for each category a variety of rendering methods is provided to

permit visualization of objects of the category in ways that are

appropriate for various purposes. Each of the hundreds of built-in

objects known to the program is assigned carefully chosen defaults so

that, when the object is selected from a menu, the program can immediately

construct a standard example of the object and render it in an optimized

view. The user may then use various menus and dialogs to alter the parameters

describing the shape and coloration of the object, change the viewpoint

from which it is seen, select different rendering methods, etc. Moreover,

as its name suggests, the program can display objects such as surfaces,

space curves and polyhedra using various stereo techniques. In addition

to the many built-in objects known to the program, a user can create

“user-defined” objects by entering formulas using standard mathematical

notation. Visualizations created by the program can be saved in jpeg and

other graphic formats and the data defining 3D objects can be exported to

other 3D programs (e.g., Bryce or POV-Ray) in formats such as .obj and .inc.

Both built-in and user-defined objects can depend on parameters, and the

program can create morphing animations by moving along a path in the

parameter space, and these animations can then be saved as QuickTime

movies. Each of the built-in objects has associated to it a so-called

ATO (About This Object) file that provides documentation for the object.

An early and more developed version of the program, written in Object

Pascal, runs under the Macintosh Operating System and a Java-based

cross-platform version is now also available.

### Authors

David Eck, Hermann Karcher, Richard Palais

### Vendor

3D-XplorMath Consortium

### Links

### Status

officially approved by the authors### Aims and scope

### Mathematical Classification

### Keywords

- animation
- astroid
- breather
- buckyball
- cardioid
- Catalan surface
- catenary
- central forces
- chaos theory
- cinquefoil knot
- circle
- cissoid
- Clifford-Hopf Torus
- Clifford Torus
- clothoid
- cones
- conformal maps
- conic section
- cuboctahedron
- curves
- cyclide
- cycloid
- differential equations
- Dini surface
- dodecahedron
- double Enneper
- dragon curve
- ellipse
- ellipsoid
- Enneper surface
- folium
- fractals
- geometry
- granny knot
- gyroid
- helicoid-catenoid
- helix
- Henneberg surface
- hexahedron
- hyperbola
- icosahedron
- icosidodecahedron
- Julia set
- Kepler orbits
- Klein bottle
- Koch snowflake
- Kuen surface
- lattice models
- lemniscate
- lidinoid
- limacon
- lissajous surface
- logarithmic spiral
- Mandelbrot set
- mathematical visualization
- minimal surfaces
- Moebius Strip
- monkey-saddle
- morphing
- nephroid
- octahedron
- ordinary differential equations
- oscillation
- parabola
- paraboloid
- planar Enneper
- plane curve
- planes
- polyhedra
- pseudosphere
- rhombic dodecahedron
- rhombohedron
- Riemann surface
- right conoid
- rotation
- saddle tower
- Scherk surface
- sine curve
- space curves
- spheres
- square knot
- Steiner surface
- surfaces
- tetrahedron
- torus
- torus knot
- tractrix
- trefoil knot
- twisted Scherk
- visualization
- Viviani
- Ward solitons
- wave equations
- waves
- Whitney umbrelle