Ellipsoid - Revision history

Cchem: 5 revisions

2016-09-19T02:19:31Z

5 revisions

Pyadmin: 1 revision

2014-03-28T02:16:23Z

1 revision

New page

This script provides methods that create [[cgo]]s as triangles. It uses code that is ported from [http://www.gamedev.net/reference/articles/article1172.asp 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'.

<source lang="python">
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')
</source>
[[Category:Script_Library|Ellipsoid]]
[[Category:Math_Scripts]]

Gilleain at 02:28, 20 July 2005

2005-07-20T02:28:35Z

Show changes

Gilleain at 22:03, 11 July 2005

2005-07-11T22:03:07Z

Gilleain at 22:02, 11 July 2005

2005-07-11T22:02:26Z

Gilleain at 21:27, 11 July 2005

2005-07-11T21:27:42Z

New page

This script provides a class called "SimpleEllipsoid" that can be created and [[load]]ed into pymol as a [[callback object]]. It uses code that is ported from [http://www.gamedev.net/reference/articles/article1172.asp this c++ code] and seems to be correct! In theory, this could be extended to make toroidal objects, as well as cylinders, spheres, and 'pillows'. Probably not very useful, though.

Here is the script. The last four lines show this in use, by making two ellipses and loading them into pymol.

<source lang="python">
from pymol.opengl.gl import *
from pymol.callback import Callback
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(a1, a2, a3, u, v, n, e):
x = a1 * sqC(u, n) * sqC(v, e)
y = a2 * sqC(u, n) * sqS(v, e)
z = a3 * sqS(u, n)
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(a1, a2, a3, u, v, n, e, alpha):
a1prime = 1 / (a1 + alpha)
a2prime = 1 / (a2 + alpha)
a3prime = 1 / (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

class SuperQuadricEllipsoid(Callback):

def __init__(self, a1, a2, a3, n, e, u1, u2, v1, v2, u_segs, v_segs, alpha=0):

# Calculate delta variables */
dU = (u2 - u1) / u_segs
dV = (v2 - v1) / v_segs

# Initialize variables for loop */
U = u1
self.points = []
self.normals = []
for Y in range(0, u_segs):
# Initialize variables for loop */
V = v1
for X in range(0, v_segs):
# VERTEX #1 */
x, y, z, nx, ny, nz = sqEllipsoid(a1, a2, a3, U, V, n, e)
self.points.append((x, y, z))
self.normals.append((nx, ny, nz))

# VERTEX #2 */
x, y, z, nx, ny, nz = sqEllipsoid(a1, a2, a3, U + dU, V, n, e)
self.points.append((x, y, z))
self.normals.append((nx, ny, nz))

# VERTEX #3 */
x, y, z, nx, ny, nz = sqEllipsoid(a1, a2, a3, U + dU, V + dV, n, e)
self.points.append((x, y, z))
self.normals.append((nx, ny, nz))

# VERTEX #4 */
x, y, z, nx, ny, nz = sqEllipsoid(a1, a2, a3, U, V + dV, n, e)
self.points.append((x, y, z))
self.normals.append((nx, ny, nz))

# Update variables for next loop */
V += dV
# Update variables for next loop */
U += dU

def get_extent(self):
return [[-10.0, -10.0, -10.0], [10.0, 10.0, 10.0]]

def __call__(self):
glBegin(GL_QUADS)
glColor3f(1.0, 1.0, 0.0)
for i in range(0, u_segs * v_segs * 4):
x, y, z = self.points[i]
nx, ny, nz = self.normals[i]
glNormal3f(nx, ny, nz)
glVertex3f(x, y, z)
glEnd()

class SimpleEllipsoid(SuperQuadricEllipsoid):

def __init__(self, a1, a2, a3):
SuperQuadricEllipsoid.__init__(self, a1, a2, a3, 1.0, 1.0, -math.pi / 2, math.pi / 2, -math.pi, math.pi, 10, 10)

rx, ry, rz = 1, 2, 3
cmd.load_callback(SimpleEllipsoid(rx, ry, rz), 'ellipsoid1')
rx, ry, rz = 2, 1, 3
cmd.load_callback(SimpleEllipsoid(rx, ry, rz), 'ellipsoid2')
</source>

← Older revision	Revision as of 02:19, 19 September 2016
(No difference)

@@ Line 112: / Line 112: @@
 x, y, z = 1, 1, 1
 rx, ry, rz = 1, 2, 3
-cmd.load_callback(SimpleEllipsoid(rx, ry, rz), 'ellipsoid1')
+cmd.load_callback(SimpleEllipsoid(x, y, z, rx, ry, rz), 'ellipsoid1')
 x, y, z = 2, 2, 2
 rx, ry, rz = 2, 1, 3
-cmd.load_callback(SimpleEllipsoid(rx, ry, rz), 'ellipsoid2')
+cmd.load_callback(SimpleEllipsoid(x, y, z, rx, ry, rz), 'ellipsoid2')
 </source>

@@ Line 45: / Line 45: @@
 class SuperQuadricEllipsoid(Callback):
-         def __init__(self, a1, a2, a3, n, e, u1, u2, v1, v2, u_segs, v_segs, alpha=0):
+         def __init__(self, x, y, z, a1, a2, a3, n, e, u1, u2, v1, v2, u_segs, v_segs, alpha=0):
-                 # Calculate delta variables */
+                 # Calculate delta variables
                  dU = (u2 - u1) / u_segs
                  dV = (v2 - v1) / v_segs
-                 # Initialize variables for loop */
+                 # Setup storage for data
                  self.points = []
                  self.normals = []
                  for Y in range(0, u_segs):
-                         # Initialize variables for loop */
+                         # Initialize variables for loop
                          V = v1
                          for X in range(0, v_segs):
@@ Line 88: / Line 93: @@
          def __call__(self):
                  glBegin(GL_QUADS)
                  glColor3f(1.0, 1.0, 0.0)
@@ Line 96: / Line 103: @@
                          glVertex3f(x, y, z)
                  glEnd()
 class SimpleEllipsoid(SuperQuadricEllipsoid):
-         def __init__(self, a1, a2, a3):
+         def __init__(self, x, y, z, a1, a2, a3):
-                 SuperQuadricEllipsoid.__init__(self, a1, a2, a3, 1.0, 1.0, -math.pi / 2, math.pi / 2, -math.pi, math.pi, 10, 10)
+                 SuperQuadricEllipsoid.__init__(self, x, y, z, a1, a2, a3, 1.0, 1.0, -math.pi / 2, math.pi / 2, -math.pi, math.pi, 10, 10)
 rx, ry, rz = 1, 2, 3
 cmd.load_callback(SimpleEllipsoid(rx, ry, rz), 'ellipsoid1')
 rx, ry, rz = 2, 1, 3
 cmd.load_callback(SimpleEllipsoid(rx, ry, rz), 'ellipsoid2')
 </source>