Mathematica Packages for Plane Curves

Throughout this site you'll find downloadable Mathematica notebooks with this icon. Mathematica is a technical computing system sold by Wolfram Research Inc. All artistic images and curve construction animations on this site are generated using Mathematica version 4 and the following packages.

As of 2009, Mathematica is at version 7. However, the packages here should work with Mathematica 7. (please write to me at xahlee@gmail.com if you find any problems.)

You can download MathPlayer http://www.wolfram.com/products/player/ to view images and animations in the following notebooks if you do not have Mathematica.

Mathematica Packages

ParaPlot

ParaPlot does ParametricPlot with extended capabilities. All artistic images on this site are created by ParaPlot.

• Varing the curve color with t. (from gray to blue by default)
• Plot curves without drawing their asymptotes.
• Optional list of t rendered as red dots on the curve and its value superscribed.
• Plot tangent, secant, or normal lines at these points.
• Plot parallel, caustic, conchoid, evolute, involute, pedal, and inversion of a curve.
• User have full control over these options and their PlotStyle. Fully documented on-line.

PlaneCurveFormulas

This package exports three category of functions:

• Parametric formulas of about 50 special plane curves. For example, Ellipse[e][t] would return a parametric formula for a ellipse with eccentricity e and dummy parameter t.
• Functions returning formulas for derived curves, such as Evolute, Involute, Parallel, Conchoid, Inversion, etc.
• Functions useful for study of plane curves such as ArcLength and Curvature, and functions for affine transformation such as Mirror, Scale, Rotate.

PlaneCurveGenerator

This package exports about 30 functions that generate animations showing various ways to trace special plane curves. A typical function looks like EllipseGenerator[NumberOfFrames→30, LastFrameOnly→False] This package is designed to visually demonstrate various properties of special plane curves.

TrochoidPlot

This package contain six graphics functions. TrochoidPlot, HypoTrochoidPlot, EpiTrochoidPlot, TrochoidGenerator, HypoTrochoidGenerator, and EpiTrochoidGenerator. The *Plot functions draw trochoid curves. The *Generator functions generates animation.

Some examples of graphics and movies generated by this package can be seen here: Epicycloid and Hypocycloid

TrochoidShow

This package define two graphic functions: MultiTrochoidPlot and TrochoidMovie. MultiTrochoidPlot plots multiple hypotrochoid and epitrochoids of various parameter settings, TrochoidMovie[] generates animations showing the effect of gradually varing one or more parameter on the curve generated. In other words, this package will draw SpiralGraphs and its mathematical variations.

Some examples of graphics and movies generated by this package can be seen here: Epicycloid and Hypocycloid .

RuledSurfacePlot

Ruled surface are surfaces that can be generated by moving a line in space. This package exports several functions that plot ruled surfaces, including: RuledSurfacePlot[], CylinderPlot[], Oloid[], RegularTetrahedron[], Cube[], RightCircularCone[], HyperboloidOfOneSheet[], Helicoid[], HyperbolicParaboloid[]. The RuledSurfacePlot[] takes two space curves and connect them by lines to form a ruled surface.

Other Mathematica packages:

• A package for graphing complex functions and planar transformations. See Geometric Transformation on the Plane.
• A packge for graphing nested inversion of circles. See Geometric Transformation on the Plane.
• A package for graphing plane tiling and symmetry. See Plane Tiling Mathematica Package.