Background
Looking to create interesting video transitions (in grayscale).
Problem
Given equations that represent a closed, symmetrical shape, plot the outline and concentrically shade the shape towards its centre.
Example
Consider the following equations:
x = 16 * sin(t)^3
y = 13 * cos(t) - 5 * cos(2 * t) - 2 * cos(3 * t) - cos(4 * t)
t = [0:2 * pi]
When plotted:
When shaded, it would resemble (not shown completely shaded, but sufficient to show the idea):
Notice that shading is darkest on the outside (e.g., #000000 RGB hex), then lightens as it fills to the centre. The centre would be a white (e.g., #FFFFFF) dot.
Questions
- What would be the most expedient way to produce high-resolution, concentrically shaded grayscale images, such as the shaded heart above?
- What are such closed, symmetrical shapes formally called?
Thank you!
Ideas
- Use a library such as http://code.google.com/p/jmathplot/
- Use GNUPlot
- Use R
- Plot using Wolfram Alpha, use ImageMagick to create smaller concentric versions