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script/DropDeform_poly.py

+"""
+Droplet Deformation (DropDeform)
+
+Determine droplet deformation into Polyhedron Shape.
+
+Source code of DropDeform: https://git.rwth-aachen.de/avt-fvt/public/droplet-deformation/
+
+The source code of DropDeform is licensed under the Eclipse Public License v2.0 (EPL 2.0).
+Copyright (c) 2025 Fluid Process Engineering (AVT.FVT), RWTH Aachen University.
+Written by Stepan Sibirtsev
+
+The coyprights and license terms are given in LICENSE.
+
+In this script polyhedral shape parameters for the DropDeform_main.py script are set.
+Script version date: 06.01.2025
+""" 
+
+""" Import packages """
+import numpy as np
+""" Define Polyhedral shape parameters """
+# Predefine polyhedron shape specific constants for:
+# Polyhedron volume
+C_V = np.zeros(5)
+# Polygon face area
+C_A = np.zeros(5)
+# Polygon incircle radius
+C_rc = np.zeros(5)
+# Polyhedron midsphere radius
+C_rm = np.zeros(5)
+# Polyhedron insphere radius
+C_rs = np.zeros(5)
+# Number of edges
+n_e = np.zeros(5)
+# Number of corners
+n_c = np.zeros(5)
+# Number of polygon faces
+n_f = np.zeros(5)
+# Iterate through the five polyhedron shapes and assign the polyhedral shape parameters
+for ish in range(5):
+    # Tetrahedron
+    if ish == 0:
+        # Polyhedron volume
+        C_V[ish] = 1.0 / (6.0 * 2.0**0.5)
+        # Polygon face area
+        C_A[ish] = (3.0**0.5) / 4.0
+        # Polygon incircle radius
+        C_rc[ish] = (3.0**0.5) / 6.0
+        # Polyhedron midsphere radius
+        C_rm[ish] = 1.0 / (8.0**0.5)
+        # Polyhedron insphere radius 
+        C_rs[ish] = 1.0 / (24.0**0.5)  
+        # Number of edges 
+        n_e[ish] = 6.0
+        # Number of corners
+        n_c[ish] = 4.0
+        # Number of polygon faces
+        n_f[ish] = 4.0
+    # Cube       
+    elif ish == 1:
+        # Polyhedron volume
+        C_V[ish] = 1.0 
+        # Polygon face area
+        C_A[ish] = 1.0
+        # Polygon incircle radius
+        C_rc[ish] = 0.5
+        # Polyhedron midsphere radius
+        C_rm[ish] = 1.0 / (2.0**0.5)
+        # Polyhedron insphere radius 
+        C_rs[ish] = 0.5
+        # Number of edges 
+        n_e[ish] = 12.0
+        # Number of corners
+        n_c[ish] = 8.0
+        # Number of polygon faces
+        n_f[ish] = 6.0
+    # Octahedron
+    elif ish == 2:
+        # Polyhedron volume
+        C_V[ish] = (2.0**0.5) / 3.0
+        # Polygon face area
+        C_A[ish] = (3.0**0.5) / 4.0
+        # Polygon incircle radius
+        C_rc[ish] = (3.0**0.5) / 6.0
+        # Polyhedron midsphere radius
+        C_rm[ish] = 0.5
+        # Polyhedron insphere radius 
+        C_rs[ish] = 1.0 / (6.0**0.5)
+        # Number of edges 
+        n_e[ish] = 12.0
+        # Number of corners
+        n_c[ish] = 6.0
+        # Number of polygon faces
+        n_f[ish] = 8.0
+    # Dodecahedron
+    elif ish == 3:
+        # Polyhedron volume
+        C_V[ish] = (15.0 + 7.0*(5.0**0.5)) / 4.0            
+        # Polygon face area
+        C_A[ish] = ((5.0*(5.0+2.0*(5.0**0.5)))**0.5) / 4.0
+        # Polygon incircle radius
+        C_rc[ish] = ((1.0+2.0/(5.0**0.5))**0.5) / 2.0
+        # Polyhedron midsphere radius
+        C_rm[ish] = (3.0+5.0**0.5) / 4.0
+        # Polyhedron insphere radius 
+        C_rs[ish] = ((10.0*(25.0+11.0*(5.0**0.5)))**0.5) / 20.0
+        # Number of edges 
+        n_e[ish] = 30.0
+        # Number of corners
+        n_c[ish] = 20.0
+        # Number of polygon faces
+        n_f[ish] = 12.0
+    # Icosahedron
+    elif ish == 4:
+        # Polyhedron volume
+        C_V[ish] = 5.0 * (3.0 + 5.0**0.5) / 12.0
+        # Polygon face area
+        C_A[ish] = (3.0**0.5) / 4.0
+        # Polygon incircle radius
+        C_rc[ish] = (3.0**0.5) / 6.0
+        # Polyhedron midsphere radius
+        C_rm[ish] = (1.0+5.0**0.5) / 4.0
+        # Polyhedron insphere radius 
+        C_rs[ish] = ((3.0**0.5)*(3.0+5.0**0.5)) / 12.0
+        # Number of edges 
+        n_e[ish] = 30.0
+        # Number of corners
+        n_c[ish] = 12.0
+        # Number of polygon faces
+        n_f[ish] = 20.0
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