Math
Supershapes and parametric surfaces
Gielis supershapes, supertoroids, a Calabi-Yau slice, knots.
What happens
Gielis' superformula turns four exponents into an entire family of shapes: raise m and the arms multiply, drop n1 and they sharpen into a star. The presets glide into each other rather than cutting, so you watch the arms grow out of a sphere. Alongside it: supertoroids with a twisting cross-section, torus knots, the Klein bottle's figure-8 immersion, and Hanson's Calabi-Yau slice - a 2D slice in C2, projected for display, not the full six-dimensional manifold.
Equations used in the module
Equations r(φ) = [ |cos(mφ/4)/a|^n₂ + |sin(mφ/4)/b|^n₃ ]^(−1/n₁) (Gielis) x = r(θ) cos θ · r(φ) cos φ, y = r(θ) sin θ · r(φ) cos φ, z = r(φ) sin φ morph: parameters interpolated, mesh re-lathed
