A surface of revolution is generated by rotating a curve around an axis. Rotating a polynomial profile around the z-axis produces a mushroom-like form: the profile controls radius as height changes, while rotation supplies the circular direction. section 8.2.2
For computation, represent the surface parametrically over a UV square: S(u, v) → (x, y, z), with both parameters ranging from 0 to 1. A sampled grid then provides points that can be connected into triangles. section 8.2.2
A practical construction separates the profile from the rotation:
- Triangulate the sampled points rather than attempting to render a continuous surface directly; increasing the grid density produces a smoother approximation. section 8.2.2
A low-poly mushroom
Profile samples such as z = [0, 0.25, 0.5, 0.75, 1] and radii [0.2, 0.4, 0.2, 0.8, 0] define a cap-and-stem silhouette. Rotating that profile creates a low-polygon mushroom; perturbing radii and height produces randomized variants.
