starfish

This example creates a starfish with five arms.

Each arm is represented as a Bezier curve eminating from the origin. At the origin, the thickness of each arm is at its maximum, and it linearly decreases throughout the length of the arm until a minimum value at the end of the Bezier curve. We then turn this 2D structure into a 3D structure.

Given a 3D point c, we project it onto the xy plane (p) and then further project this point onto the Bezier curve (p1). The thickness for p1 is then calculated. For c to be in the solid, abs(||p-p1||) + abs(c.z) must be less than the thickness. This produces a triangular shape, while still maintaining smoothness along Z cross-sections. Projections and thickness calculations are performed on a discretized version of the Bezier curves, for ease of computation.

Rendering