Polar Plotting: Newton Graphics App

Polar Plotting was a Newton application I wrote in 1993 for exploring polar coordinate curves. It plots r = f(θ) for 14 classic mathematical curves and allows user-defined expressions.

The original NewtonScript source code has been translated into HTML5 Canvas and TypeScript, faithfully recreating the Newton’s visual style and interactivity.

Usage
Tap the function selector (top dropdown) to choose from 14 predefined polar curves or select “User Defined” to enter a custom expression.
Predefined Curves
  • Circle: cos(θ)
  • Parabolic Spiral: √(1/θ)
  • Archimedean Spiral: √θ
  • Equiangular Spiral: eθ
  • Rhodonea: cos(4θ) — a rose curve
  • Reciprocal Spiral: 1/θ
  • Ellipse: 1/(1+0.5cosθ)
  • Cardioid: 1+cosθ
  • Parabola: 1/(1+cosθ)
  • Limaçon without loop: 1+0.5cosθ
  • Limaçon with loop: 0.5+cosθ
  • Rectangular Hyperbola: √|1/cos(2θ)|
  • Lemniscate of Bernoulli: √|cos(2θ)|
  • Line: 1/cosθ
Rendering Styles
Four rendering styles are available via the style dropdown:
  • Lines — connecting line segments (default)
  • Filled — triangle fan from origin (solid fill)
  • Points — discrete sample points
  • Vector — line segments from origin to each point
Scale
Drag the scale slider to zoom in or out. A fast preview is drawn while dragging; the full-quality 100-step plot is rendered on release.
User-Defined Functions
Select “User Defined” from the function menu, then tap the expression area to enter a custom formula. Use theta as the variable. Supported functions: sin, cos, tan, sqrt, abs, exp, log, pow, atan2, and more. Press Go to re-evaluate.
History
Written in NewtonScript in 1993 as “Polar Plotting” (©1993 Freed Enterprises). This web edition is a faithful translation of the original source code.
See Also
Time To Go: Newton Clock Suite