Ellipsoid
From PyMolWiki
This script provides methods that create cgos as triangles. It uses code that is ported from this c++ code and seems to be correct!
Here is the script. The last four lines show this in use, by making an ellipse and a toroid and loading them into pymol. This is done most easily by something like "cmd.load_cgo(makeEllipsoid(1, 1, 1, 2, 3, 4), 'ellipsoid')" which makes an ellipsoid at x, y, z = 1, 1, 1 and dimensions 2, 3, 4 and called 'ellipsoid'.
from pymol.cgo import BEGIN, COLOR, TRIANGLES, VERTEX, NORMAL, END from pymol import cmd def signOfFloat(f): if f < 0: return -1 if f > 0: return 1 return 0 def sqC(v, n): return signOfFloat(math.cos(v)) * math.pow(math.fabs(math.cos(v)), n) def sqCT(v, n, alpha): return alpha + sqC(v, n) def sqS(v, n): return signOfFloat(math.sin(v)) * math.pow(math.fabs(math.sin(v)), n) def sqEllipsoid(x, y, z, a1, a2, a3, u, v, n, e): x = a1 * sqC(u, n) * sqC(v, e) + x y = a2 * sqC(u, n) * sqS(v, e) + y z = a3 * sqS(u, n) + z nx = sqC(u, 2 - n) * sqC(v, 2 - e) / a1 ny = sqC(u, 2 - n) * sqS(v, 2 - e) / a2 nz = sqS(u, 2 - n) / a3 return x, y, z, nx, ny, nz def sqToroid(x, y, z, a1, a2, a3, u, v, n, e, alpha): a1prime = 1.0 / (a1 + alpha) a2prime = 1.0 / (a2 + alpha) a3prime = 1.0 / (a3 + alpha) x = a1prime * sqCT(u, e, alpha) * sqC(v, n) y = a2prime * sqCT(u, e, alpha) * sqS(v, n) z = a3prime * sqS(u, e) nx = sqC(u, 2 - e) * sqC(v, 2 - n) / a1prime ny = sqC(u, 2 - e) * sqS(v, 2 - n) / a2prime nz = sqS(u, 2 - e) / a3prime return x, y, z, nx, ny, nz def makeSuperQuadricEllipsoid(x, y, z, a1, a2, a3, n, e, u1, u2, v1, v2, u_segs, v_segs, color=[0.5, 0.5, 0.5]): r, g, b = color # Calculate delta variables */ dU = (u2 - u1) / u_segs dV = (v2 - v1) / v_segs o = [ BEGIN, TRIANGLES ] U = u1 for Y in range(0, u_segs): # Initialize variables for loop */ V = v1 for X in range(0, v_segs): # VERTEX #1 */ x1, y1, z1, n1x, n1y, n1z = sqEllipsoid(x, y, z, a1, a2, a3, U, V, n, e) x2, y2, z2, n2x, n2y, n2z = sqEllipsoid(x, y, z, a1, a2, a3, U + dU, V, n, e) x3, y3, z3, n3x, n3y, n3z = sqEllipsoid(x, y, z, a1, a2, a3, U + dU, V + dV, n, e) x4, y4, z4, n4x, n4y, n4z = sqEllipsoid(x, y, z, a1, a2, a3, U, V + dV, n, e) o.extend([COLOR, r, g, b, NORMAL, n1x, n1y, n1z, VERTEX, x1, y1, z1]) o.extend([COLOR, r, g, b, NORMAL, n2x, n2y, n2z, VERTEX, x2, y2, z2]) o.extend([COLOR, r, g, b, NORMAL, n4x, n4y, n4z, VERTEX, x4, y4, z4]) o.extend([COLOR, r, g, b, NORMAL, n2x, n2y, n2z, VERTEX, x2, y2, z2]) o.extend([COLOR, r, g, b, NORMAL, n3x, n3y, n3z, VERTEX, x3, y3, z3]) o.extend([COLOR, r, g, b, NORMAL, n4x, n4y, n4z, VERTEX, x4, y4, z4]) # Update variables for next loop */ V += dV # Update variables for next loop */ U += dU o.append(END) return o def makeSuperQuadricToroid(x, y, z, a1, a2, a3, alpha, n, e, u1, u2, v1, v2, u_segs, v_segs, color=[0.5, 0.5, 0.5]): r, g, b = color # Calculate delta variables */ dU = (u2 - u1) / u_segs dV = (v2 - v1) / v_segs o = [ BEGIN, TRIANGLES ] U = u1 for Y in range(0, u_segs): # Initialize variables for loop */ V = v1 for X in range(0, v_segs): # VERTEX #1 */ x1, y1, z1, n1x, n1y, n1z = sqToroid(x, y, z, a1, a2, a3, U, V, n, e, alpha) x2, y2, z2, n2x, n2y, n2z = sqToroid(x, y, z, a1, a2, a3, U + dU, V, n, e, alpha) x3, y3, z3, n3x, n3y, n3z = sqToroid(x, y, z, a1, a2, a3, U + dU, V + dV, n, e, alpha) x4, y4, z4, n4x, n4y, n4z = sqToroid(x, y, z, a1, a2, a3, U, V + dV, n, e, alpha) o.extend([COLOR, r, g, b, NORMAL, n1x, n1y, n1z, VERTEX, x1, y1, z1]) o.extend([COLOR, r, g, b, NORMAL, n2x, n2y, n2z, VERTEX, x2, y2, z2]) o.extend([COLOR, r, g, b, NORMAL, n4x, n4y, n4z, VERTEX, x4, y4, z4]) o.extend([COLOR, r, g, b, NORMAL, n2x, n2y, n2z, VERTEX, x2, y2, z2]) o.extend([COLOR, r, g, b, NORMAL, n3x, n3y, n3z, VERTEX, x3, y3, z3]) o.extend([COLOR, r, g, b, NORMAL, n4x, n4y, n4z, VERTEX, x4, y4, z4]) # Update variables for next loop */ V += dV # Update variables for next loop */ U += dU o.append(END) return o def makeEllipsoid(x, y, z, a1, a2, a3): return makeSuperQuadricEllipsoid(x, y, z, a1, a2, a3, 1.0, 1.0, -math.pi / 2, math.pi / 2, -math.pi, math.pi, 10, 10) def makeCylinder(x, y, z, a1, a2, a3): return makeSuperQuadricEllipsoid(x, y, z, a1, a2, a3, 0.0, 1.0, -math.pi / 2, math.pi / 2, -math.pi, math.pi, 10, 10) def makeSpindle(x, y, z, a1, a2, a3): return makeSuperQuadricEllipsoid(x, y, z, a1, a2, a3, 2.0, 1.0, -math.pi / 2, math.pi / 2, -math.pi, math.pi, 10, 10) def makeDoublePyramid(x, y, z, a1, a2, a3): return makeSuperQuadricEllipsoid(x, y, z, a1, a2, a3, 2.0, 2.0, -math.pi / 2, math.pi / 2, -math.pi, math.pi, 10, 10) def makePillow(x, y, z, a1, a2, a3): return makeSuperQuadricEllipsoid(x, y, z, a1, a2, a3, 1.0, 0.0, -math.pi, math.pi, -math.pi, math.pi, 10, 10) def makeRoundCube(x, y, z, a1, a2, a3): return makeSuperQuadricEllipsoid(x, y, z, a1, a2, a3, 0.2, 0.2, -math.pi / 2, math.pi / 2, -math.pi, math.pi, 10, 10) def makeToroid(x, y, z, a1, a2, a3, alpha): return makeSuperQuadricToroid(x, y, z, a1, a2, a3, alpha, 1.0, 1.0, -math.pi, math.pi, -math.pi, math.pi, 10, 10) x, y, z, rx, ry, rz = 1, 1, 1, 1, 2, 3 cmd.load_cgo(makeEllipsoid(x, y, z, rx, ry, rz), 'ellipsoid-cgo') x, y, z, rx, ry, rz = 1, 1, 1, 8, 2, 2 cmd.load_cgo(makeToroid(x, y, z, rx, ry, rz, 3), 'toroid-cgo')
