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.
Full size: Polar Plotting.
- 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