is Parametric description Parametric equations in terms of surface parameters u and v (equivalent to longitude and latitude if m equals 2) are where the auxiliary functions are and the sign function sgn(x) is Spherical product Barr introduces the spherical product which given two plane curves produces a 3D surface. If are two plane curves then the spherical product is This is similar to the typical parametric equation of a sphere: which give rise to the name spherical product. Barr uses the spherical product to define quadric surfaces, like ellipsoids, and hyperboloids as well as the torus, superellipsoid, superquadric hyperboloids of one and two sheets, and supertoroids. Plotting code The following GNU Octave code generates a mesh approximation of a superquadric: function superquadric(epsilon,a) n = 50; etamax = pi/2; etamin = -pi/2; wmax = pi; wmin = -pi; deta = (etamax-etamin)/n; dw = (wmax-wmin)/n; [i,j] = meshgrid(1:n+1,1:n+1) eta = etamin + (i-1) * deta; w = wmin + (j-1) * dw; x = a(1) .* sign(cos(eta)) .* abs(cos(eta)).^epsilon(1) .* sign(cos(w)) .* abs(cos(w)).^epsilon(1); y = a(2) .* sign(cos(eta)) .* abs(cos(eta)).^epsilon(2) .* sign(sin(w)) .* abs(sin(w)).^epsilon(2); z = a(3) .* sign(sin(eta)) .* abs(sin(eta)).^epsilon(3); mesh(x,y,z); end See also Superegg Superellipsoid Ellipsoid References External links Bibliography: SuperQuadric Representations Superquadric Tensor Glyphs SuperQuadric Ellipsoids and Toroids, OpenGL Lighting, and Timing Superquadrics by Robert Kragler, The Wolfram Demonstrations Project. Superquadrics in Python Superquadrics recovery algorithm in Python and MATLAB Computer graphics Computer vision Robotics Geometry Geometry in computer vision