Changes between Initial Version and Version 1 of SphericalHarmonics

Timestamp:

Aug 28, 2020, 11:47:34 AM (6 years ago)

Author:

goddard

Comment:

--

SphericalHarmonics

@@ +1 @@
+= Making a Spherical Harmonic Surface =
+
+Here is some Python code when opened in ChimeraX creates spherical harmonic surfaces.  The real part of the spherical harmonic is the surface radius.
+
+    r = Ylm(theta, phi) where Ylm is a spherical harmonic, l = 2, m=0,1,2.
+
+[[Image(harmonics.png)]]
+
+Python code for ChimeraX 1.0:
+
+
+{{{
+# Make a spherical harmonic surface.
+
+from math import sin, cos, pi, sqrt
+
+def spherical_surface(session,
+                      radius_function,
+                      theta_steps = 100,
+                      phi_steps = 50,
+                      positive_color = (255,100,100,255), # red, green, blue, alpha, 0-255 
+                      negative_color = (100,100,255,255)):
+
+    # Compute vertices and vertex colors
+    vertices = []
+    colors = []
+    for t in range(theta_steps):
+        theta = (t/theta_steps) * 2*pi
+        ct, st = cos(theta), sin(theta)
+        for p in range(phi_steps):
+            phi = (p/(phi_steps-1)) * pi
+            cp, sp = cos(phi), sin(phi)
+            r = radius_function(theta, phi)
+            xyz = (r*sp*ct, r*sp*st, r*cp)
+            vertices.append(xyz)
+            color = positive_color if r >= 0 else negative_color
+            colors.append(color)
+
+    # Compute triangles, triples of vertex indices
+    triangles = []
+    for t in range(theta_steps):
+        for p in range(phi_steps-1):
+            i = t*phi_steps + p
+            t1 = (t+1)%theta_steps
+            i1 = t1*phi_steps + p
+            triangles.append((i,i+1,i1+1))
+            triangles.append((i,i1+1,i1))
+
+    # Create numpy arrays
+    from numpy import array, float32, uint8, int32
+    va = array(vertices, float32)
+    ca = array(colors, uint8)
+    ta = array(triangles, int32)
+
+    # Compute average vertex normal vectors
+    from chimerax.surface import calculate_vertex_normals
+    na = calculate_vertex_normals(va, ta)
+
+    # Create ChimeraX surface model
+    from chimerax.core.models import Surface
+    s = Surface('surface', session)
+    s.set_geometry(va, na, ta)
+    s.vertex_colors = ca
+    session.models.add([s])
+
+    return s
+
+# Example spherical harmonic function Y(l=2,m=0) real part.
+def y20_re(theta, phi):
+    return 0.25*sqrt(5/pi) * (3*cos(phi)**2 - 1)
+def y21_re(theta, phi):
+    return -0.5*sqrt(15/(2*pi)) * sin(phi)*cos(phi) * cos(theta)
+def y22_re(theta, phi):
+    return 0.25*sqrt(15/(2*pi)) * sin(phi)**2 * cos(2*theta)
+
+# Create 3 surfaces
+spherical_surface(session, y20_re)
+
+s1 = spherical_surface(session, y21_re)
+from chimerax.geometry import translation
+s1.position = translation((1,0,0))
+
+s2 = spherical_surface(session, y22_re)
+s2.position = translation((2,0,0))
+
+}}}