[5897] | 1 | """Library of standard meshes and facilities for reading various |
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| 2 | mesh file formats |
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| 3 | """ |
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| 4 | |
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[7317] | 5 | import anuga.utilities.log as log |
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[7276] | 6 | import numpy as num |
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[5897] | 7 | |
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[6145] | 8 | |
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[5897] | 9 | def rectangular_old(m, n, len1=1.0, len2=1.0, origin = (0.0, 0.0)): |
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| 10 | |
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| 11 | """Setup a rectangular grid of triangles |
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| 12 | with m+1 by n+1 grid points |
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| 13 | and side lengths len1, len2. If side lengths are omitted |
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| 14 | the mesh defaults to the unit square. |
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| 15 | |
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| 16 | len1: x direction (left to right) |
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| 17 | len2: y direction (bottom to top) |
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| 18 | |
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| 19 | Return to lists: points and elements suitable for creating a Mesh or |
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| 20 | FVMesh object, e.g. Mesh(points, elements) |
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| 21 | """ |
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| 22 | |
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| 23 | from anuga.config import epsilon |
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| 24 | |
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| 25 | deltax = float(len1)/m |
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| 26 | deltay = float(len2)/n |
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| 27 | |
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| 28 | #Dictionary of vertex objects |
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| 29 | vertices = {} |
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| 30 | points = [] |
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| 31 | |
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| 32 | for i in range(m+1): |
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| 33 | for j in range(n+1): |
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| 34 | vertices[i,j] = len(points) |
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| 35 | points.append([i*delta1 + origin[0], j*delta2 + origin[1]]) |
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| 36 | |
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| 37 | |
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| 38 | #Construct 2 triangles per rectangular element and assign tags to boundary |
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| 39 | elements = [] |
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| 40 | boundary = {} |
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| 41 | for i in range(m): |
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| 42 | for j in range(n): |
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| 43 | v1 = vertices[i,j+1] |
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| 44 | v2 = vertices[i,j] |
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| 45 | v3 = vertices[i+1,j+1] |
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| 46 | v4 = vertices[i+1,j] |
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| 47 | |
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| 48 | #Update boundary dictionary and create elements |
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| 49 | if i == m-1: |
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| 50 | boundary[(len(elements), 2)] = 'right' |
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| 51 | if j == 0: |
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| 52 | boundary[(len(elements), 1)] = 'bottom' |
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| 53 | elements.append([v4,v3,v2]) #Lower element |
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| 54 | |
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| 55 | if i == 0: |
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| 56 | boundary[(len(elements), 2)] = 'left' |
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| 57 | if j == n-1: |
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| 58 | boundary[(len(elements), 1)] = 'top' |
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| 59 | elements.append([v1,v2,v3]) #Upper element |
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| 60 | |
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| 61 | return points, elements, boundary |
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| 62 | |
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| 63 | def rectangular(m, n, len1=1.0, len2=1.0, origin = (0.0, 0.0)): |
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| 64 | |
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| 65 | """Setup a rectangular grid of triangles |
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| 66 | with m+1 by n+1 grid points |
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| 67 | and side lengths len1, len2. If side lengths are omitted |
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| 68 | the mesh defaults to the unit square. |
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| 69 | |
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| 70 | len1: x direction (left to right) |
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| 71 | len2: y direction (bottom to top) |
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| 72 | |
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| 73 | Return to lists: points and elements suitable for creating a Mesh or |
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| 74 | FVMesh object, e.g. Mesh(points, elements) |
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| 75 | """ |
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| 76 | |
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| 77 | from anuga.config import epsilon |
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| 78 | |
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| 79 | delta1 = float(len1)/m |
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| 80 | delta2 = float(len2)/n |
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| 81 | |
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| 82 | #Calculate number of points |
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| 83 | Np = (m+1)*(n+1) |
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| 84 | |
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| 85 | class Index: |
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| 86 | |
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| 87 | def __init__(self, n,m): |
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| 88 | self.n = n |
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| 89 | self.m = m |
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| 90 | |
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| 91 | def __call__(self, i,j): |
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| 92 | return j+i*(self.n+1) |
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| 93 | |
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| 94 | |
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| 95 | index = Index(n,m) |
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| 96 | |
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[7276] | 97 | points = num.zeros((Np, 2), num.float) |
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[5897] | 98 | |
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| 99 | for i in range(m+1): |
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| 100 | for j in range(n+1): |
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| 101 | |
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| 102 | points[index(i,j),:] = [i*delta1 + origin[0], j*delta2 + origin[1]] |
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| 103 | |
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| 104 | #Construct 2 triangles per rectangular element and assign tags to boundary |
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| 105 | #Calculate number of triangles |
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| 106 | Nt = 2*m*n |
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| 107 | |
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| 108 | |
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[7276] | 109 | elements = num.zeros((Nt, 3), num.int) |
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[5897] | 110 | boundary = {} |
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| 111 | nt = -1 |
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| 112 | for i in range(m): |
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| 113 | for j in range(n): |
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| 114 | nt = nt + 1 |
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| 115 | i1 = index(i,j+1) |
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| 116 | i2 = index(i,j) |
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| 117 | i3 = index(i+1,j+1) |
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| 118 | i4 = index(i+1,j) |
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| 119 | |
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| 120 | |
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| 121 | #Update boundary dictionary and create elements |
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| 122 | if i == m-1: |
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| 123 | boundary[nt, 2] = 'right' |
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| 124 | if j == 0: |
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| 125 | boundary[nt, 1] = 'bottom' |
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| 126 | elements[nt,:] = [i4,i3,i2] #Lower element |
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| 127 | nt = nt + 1 |
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| 128 | |
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| 129 | if i == 0: |
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| 130 | boundary[nt, 2] = 'left' |
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| 131 | if j == n-1: |
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| 132 | boundary[nt, 1] = 'top' |
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| 133 | elements[nt,:] = [i1,i2,i3] #Upper element |
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| 134 | |
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| 135 | return points, elements, boundary |
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| 136 | |
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| 137 | |
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| 138 | def rectangular_cross(m, n, len1=1.0, len2=1.0, origin = (0.0, 0.0)): |
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| 139 | |
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| 140 | """Setup a rectangular grid of triangles |
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| 141 | with m+1 by n+1 grid points |
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| 142 | and side lengths len1, len2. If side lengths are omitted |
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| 143 | the mesh defaults to the unit square. |
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| 144 | |
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| 145 | len1: x direction (left to right) |
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| 146 | len2: y direction (bottom to top) |
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| 147 | |
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| 148 | Return to lists: points and elements suitable for creating a Mesh or |
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| 149 | FVMesh object, e.g. Mesh(points, elements) |
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| 150 | """ |
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| 151 | |
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| 152 | from anuga.config import epsilon |
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| 153 | |
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| 154 | delta1 = float(len1)/m |
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| 155 | delta2 = float(len2)/n |
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| 156 | |
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| 157 | #Dictionary of vertex objects |
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| 158 | vertices = {} |
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| 159 | points = [] |
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| 160 | |
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| 161 | for i in range(m+1): |
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| 162 | for j in range(n+1): |
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| 163 | vertices[i,j] = len(points) |
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| 164 | points.append([delta1*i + origin[0], delta2*j + origin[1]]) |
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| 165 | |
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| 166 | # Construct 4 triangles per element |
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| 167 | elements = [] |
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| 168 | boundary = {} |
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| 169 | for i in range(m): |
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| 170 | for j in range(n): |
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| 171 | v1 = vertices[i,j+1] |
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| 172 | v2 = vertices[i,j] |
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| 173 | v3 = vertices[i+1,j+1] |
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| 174 | v4 = vertices[i+1,j] |
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| 175 | x = (points[v1][0]+points[v2][0]+points[v3][0]+points[v4][0])*0.25 |
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| 176 | y = (points[v1][1]+points[v2][1]+points[v3][1]+points[v4][1])*0.25 |
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| 177 | |
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| 178 | # Create centre point |
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| 179 | v5 = len(points) |
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| 180 | points.append([x, y]) |
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| 181 | |
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| 182 | #Create left triangle |
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| 183 | if i == 0: |
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| 184 | boundary[(len(elements), 1)] = 'left' |
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| 185 | elements.append([v2,v5,v1]) |
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| 186 | |
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| 187 | #Create bottom triangle |
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| 188 | if j == 0: |
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| 189 | boundary[(len(elements), 1)] = 'bottom' |
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| 190 | elements.append([v4,v5,v2]) |
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| 191 | |
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| 192 | #Create right triangle |
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| 193 | if i == m-1: |
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| 194 | boundary[(len(elements), 1)] = 'right' |
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| 195 | elements.append([v3,v5,v4]) |
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| 196 | |
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| 197 | #Create top triangle |
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| 198 | if j == n-1: |
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| 199 | boundary[(len(elements), 1)] = 'top' |
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| 200 | elements.append([v1,v5,v3]) |
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| 201 | |
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| 202 | |
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| 203 | return points, elements, boundary |
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| 204 | |
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[6717] | 205 | |
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| 206 | def rectangular_periodic(m_g, n_g, len1_g=1.0, len2_g=1.0, origin_g = (0.0, 0.0)): |
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| 207 | |
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| 208 | |
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| 209 | """Setup a rectangular grid of triangles |
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| 210 | with m+1 by n+1 grid points |
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| 211 | and side lengths len1, len2. If side lengths are omitted |
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| 212 | the mesh defaults to the unit square, divided between all the |
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| 213 | processors |
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| 214 | |
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| 215 | len1: x direction (left to right) |
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| 216 | len2: y direction (bottom to top) |
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| 217 | |
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| 218 | """ |
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| 219 | |
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| 220 | processor = 0 |
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| 221 | numproc = 1 |
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| 222 | |
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| 223 | |
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| 224 | n = n_g |
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| 225 | m_low = -1 |
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| 226 | m_high = m_g +1 |
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| 227 | |
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| 228 | m = m_high - m_low |
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| 229 | |
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| 230 | delta1 = float(len1_g)/m_g |
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| 231 | delta2 = float(len2_g)/n_g |
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| 232 | |
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| 233 | len1 = len1_g*float(m)/float(m_g) |
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| 234 | len2 = len2_g |
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| 235 | origin = ( origin_g[0]+float(m_low)/float(m_g)*len1_g, origin_g[1] ) |
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| 236 | |
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| 237 | #Calculate number of points |
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| 238 | Np = (m+1)*(n+1) |
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| 239 | |
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| 240 | class VIndex: |
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| 241 | |
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| 242 | def __init__(self, n,m): |
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| 243 | self.n = n |
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| 244 | self.m = m |
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| 245 | |
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| 246 | def __call__(self, i,j): |
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| 247 | return j+i*(self.n+1) |
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| 248 | |
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| 249 | class EIndex: |
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| 250 | |
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| 251 | def __init__(self, n,m): |
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| 252 | self.n = n |
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| 253 | self.m = m |
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| 254 | |
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| 255 | def __call__(self, i,j): |
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| 256 | return 2*(j+i*self.n) |
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| 257 | |
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| 258 | |
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| 259 | I = VIndex(n,m) |
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| 260 | E = EIndex(n,m) |
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| 261 | |
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[7276] | 262 | points = num.zeros( (Np,2), num.float) |
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[6717] | 263 | |
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| 264 | for i in range(m+1): |
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| 265 | for j in range(n+1): |
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| 266 | |
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| 267 | points[I(i,j),:] = [i*delta1 + origin[0], j*delta2 + origin[1]] |
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| 268 | |
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| 269 | #Construct 2 triangles per rectangular element and assign tags to boundary |
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| 270 | #Calculate number of triangles |
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| 271 | Nt = 2*m*n |
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| 272 | |
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| 273 | |
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[7276] | 274 | elements = num.zeros( (Nt,3), num.int) |
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[6717] | 275 | boundary = {} |
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| 276 | Idgl = [] |
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| 277 | Idfl = [] |
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| 278 | Idgr = [] |
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| 279 | Idfr = [] |
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| 280 | |
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| 281 | full_send_dict = {} |
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| 282 | ghost_recv_dict = {} |
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| 283 | nt = -1 |
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| 284 | for i in range(m): |
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| 285 | for j in range(n): |
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| 286 | |
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| 287 | i1 = I(i,j+1) |
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| 288 | i2 = I(i,j) |
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| 289 | i3 = I(i+1,j+1) |
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| 290 | i4 = I(i+1,j) |
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| 291 | |
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| 292 | #Lower Element |
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| 293 | nt = E(i,j) |
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| 294 | if i == 0: |
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| 295 | Idgl.append(nt) |
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| 296 | |
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| 297 | if i == 1: |
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| 298 | Idfl.append(nt) |
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| 299 | |
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| 300 | if i == m-2: |
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| 301 | Idfr.append(nt) |
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| 302 | |
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| 303 | if i == m-1: |
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| 304 | Idgr.append(nt) |
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| 305 | |
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| 306 | if i == m-1: |
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| 307 | if processor == numproc-1: |
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| 308 | boundary[nt, 2] = 'right' |
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| 309 | else: |
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| 310 | boundary[nt, 2] = 'ghost' |
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| 311 | |
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| 312 | if j == 0: |
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| 313 | boundary[nt, 1] = 'bottom' |
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| 314 | elements[nt,:] = [i4,i3,i2] |
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| 315 | |
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| 316 | #Upper Element |
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| 317 | nt = E(i,j)+1 |
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| 318 | if i == 0: |
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| 319 | Idgl.append(nt) |
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| 320 | |
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| 321 | if i == 1: |
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| 322 | Idfl.append(nt) |
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| 323 | |
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| 324 | if i == m-2: |
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| 325 | Idfr.append(nt) |
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| 326 | |
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| 327 | if i == m-1: |
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| 328 | Idgr.append(nt) |
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| 329 | |
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| 330 | if i == 0: |
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| 331 | if processor == 0: |
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| 332 | boundary[nt, 2] = 'left' |
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| 333 | else: |
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| 334 | boundary[nt, 2] = 'ghost' |
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| 335 | if j == n-1: |
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| 336 | boundary[nt, 1] = 'top' |
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| 337 | elements[nt,:] = [i1,i2,i3] |
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| 338 | |
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| 339 | Idfl.extend(Idfr) |
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| 340 | Idgr.extend(Idgl) |
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| 341 | |
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[7276] | 342 | Idfl = num.array(Idfl, num.int) |
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| 343 | Idgr = num.array(Idgr, num.int) |
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[6717] | 344 | |
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| 345 | full_send_dict[processor] = [Idfl, Idfl] |
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| 346 | ghost_recv_dict[processor] = [Idgr, Idgr] |
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| 347 | |
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| 348 | |
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| 349 | return points, elements, boundary, full_send_dict, ghost_recv_dict |
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| 350 | |
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| 351 | |
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[5897] | 352 | def oblique(m, n, lenx = 1.0, leny = 1.0, theta = 8.95, origin = (0.0, 0.0)): |
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| 353 | """Setup a oblique grid of triangles |
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| 354 | with m segments in the x-direction and n segments in the y-direction |
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| 355 | |
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| 356 | """ |
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| 357 | |
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| 358 | import math |
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| 359 | |
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| 360 | from anuga.config import epsilon |
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| 361 | |
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| 362 | |
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| 363 | deltax = lenx/float(m) |
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| 364 | deltay = leny/float(n) |
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| 365 | a = 0.75*lenx*math.tan(theta/180.*math.pi) |
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| 366 | x1 = lenx |
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| 367 | y1 = 0 |
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| 368 | x2 = lenx |
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| 369 | y2 = leny |
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| 370 | x3 = 0.25*lenx |
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| 371 | y3 = leny |
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| 372 | x4 = x3 |
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| 373 | y4 = 0 |
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| 374 | a2 = a/(x1-x4) |
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| 375 | a1 = -a2*x4 |
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| 376 | a4 = ((a1 + a2*x3)/y3-(a1 + a2*x2)/y2)/(x2-x3) |
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| 377 | a3 = 1. - (a1 + a2*x3)/y3 - a4*x3 |
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| 378 | |
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| 379 | # Dictionary of vertex objects |
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| 380 | vertices = {} |
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| 381 | points = [] |
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| 382 | |
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| 383 | for i in range(m+1): |
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| 384 | x = deltax*i |
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| 385 | for j in range(n+1): |
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| 386 | y = deltay*j |
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| 387 | if x > 0.25*lenx: |
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| 388 | y = a1 + a2*x + a3*y + a4*x*y |
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| 389 | |
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| 390 | vertices[i,j] = len(points) |
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| 391 | points.append([x + origin[0], y + origin[1]]) |
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| 392 | |
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| 393 | # Construct 2 triangles per element |
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| 394 | elements = [] |
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| 395 | boundary = {} |
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| 396 | for i in range(m): |
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| 397 | for j in range(n): |
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| 398 | v1 = vertices[i,j+1] |
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| 399 | v2 = vertices[i,j] |
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| 400 | v3 = vertices[i+1,j+1] |
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| 401 | v4 = vertices[i+1,j] |
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| 402 | |
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| 403 | #Update boundary dictionary and create elements |
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| 404 | if i == m-1: |
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| 405 | boundary[(len(elements), 2)] = 'right' |
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| 406 | if j == 0: |
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| 407 | boundary[(len(elements), 1)] = 'bottom' |
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| 408 | elements.append([v4,v3,v2]) #Lower |
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| 409 | |
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| 410 | if i == 0: |
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| 411 | boundary[(len(elements), 2)] = 'left' |
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| 412 | if j == n-1: |
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| 413 | boundary[(len(elements), 1)] = 'top' |
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| 414 | |
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| 415 | elements.append([v1,v2,v3]) #Upper |
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| 416 | |
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| 417 | return points, elements, boundary |
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| 418 | |
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| 419 | |
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| 420 | def circular(m, n, radius=1.0, center = (0.0, 0.0)): |
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| 421 | """Setup a circular grid of triangles with m concentric circles and |
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| 422 | with n radial segments. If radius is are omitted the mesh defaults to |
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| 423 | the unit circle radius. |
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| 424 | |
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| 425 | radius: radius of circle |
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| 426 | |
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| 427 | #FIXME: The triangles become degenerate for large values of m or n. |
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| 428 | """ |
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| 429 | |
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| 430 | |
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| 431 | |
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| 432 | from math import pi, cos, sin |
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| 433 | |
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| 434 | radius = float(radius) #Ensure floating point format |
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| 435 | |
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| 436 | #Dictionary of vertex objects and list of points |
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| 437 | vertices = {} |
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| 438 | points = [[0.0, 0.0]] #Center point |
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| 439 | vertices[0, 0] = 0 |
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| 440 | |
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| 441 | for i in range(n): |
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| 442 | theta = 2*i*pi/n |
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| 443 | x = cos(theta) |
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| 444 | y = sin(theta) |
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| 445 | for j in range(1,m+1): |
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| 446 | delta = j*radius/m |
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| 447 | vertices[i,j] = len(points) |
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| 448 | points.append([delta*x, delta*y]) |
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| 449 | |
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| 450 | #Construct 2 triangles per element |
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| 451 | elements = [] |
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| 452 | for i in range(n): |
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| 453 | for j in range(1,m): |
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| 454 | |
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| 455 | i1 = (i + 1) % n #Wrap around |
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| 456 | |
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| 457 | v1 = vertices[i,j+1] |
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| 458 | v2 = vertices[i,j] |
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| 459 | v3 = vertices[i1,j+1] |
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| 460 | v4 = vertices[i1,j] |
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| 461 | |
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| 462 | elements.append([v4,v2,v3]) #Lower |
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| 463 | elements.append([v1,v3,v2]) #Upper |
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| 464 | |
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| 465 | |
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| 466 | #Do the center |
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| 467 | v1 = vertices[0,0] |
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| 468 | for i in range(n): |
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| 469 | i1 = (i + 1) % n #Wrap around |
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| 470 | v2 = vertices[i,1] |
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| 471 | v3 = vertices[i1,1] |
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| 472 | |
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| 473 | elements.append([v1,v2,v3]) #center |
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| 474 | |
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| 475 | return points, elements |
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| 476 | |
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| 477 | |
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| 478 | def from_polyfile(name): |
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| 479 | """Read mesh from .poly file, an obj like file format |
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| 480 | listing first vertex coordinates and then connectivity |
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| 481 | """ |
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| 482 | |
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| 483 | from anuga.utilities.numerical_tools import anglediff |
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| 484 | from math import pi |
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| 485 | import os.path |
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| 486 | root, ext = os.path.splitext(name) |
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| 487 | |
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| 488 | if ext == 'poly': |
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| 489 | filename = name |
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| 490 | else: |
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| 491 | filename = name + '.poly' |
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| 492 | |
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| 493 | |
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| 494 | fid = open(filename) |
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| 495 | |
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| 496 | points = [] #x, y |
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| 497 | values = [] #z |
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| 498 | ##vertex_values = [] #Repeated z |
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| 499 | triangles = [] #v0, v1, v2 |
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| 500 | |
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| 501 | lines = fid.readlines() |
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| 502 | |
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| 503 | keyword = lines[0].strip() |
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| 504 | msg = 'First line in .poly file must contain the keyword: POINTS' |
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| 505 | assert keyword == 'POINTS', msg |
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| 506 | |
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| 507 | offending = 0 |
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| 508 | i = 1 |
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| 509 | while keyword == 'POINTS': |
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| 510 | line = lines[i].strip() |
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| 511 | i += 1 |
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| 512 | |
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| 513 | if line == 'POLYS': |
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| 514 | keyword = line |
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| 515 | break |
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| 516 | |
---|
| 517 | fields = line.split(':') |
---|
| 518 | assert int(fields[0]) == i-1, 'Point indices not consecutive' |
---|
| 519 | |
---|
| 520 | #Split the three floats |
---|
| 521 | xyz = fields[1].split() |
---|
| 522 | |
---|
| 523 | x = float(xyz[0]) |
---|
| 524 | y = float(xyz[1]) |
---|
| 525 | z = float(xyz[2]) |
---|
| 526 | |
---|
| 527 | points.append([x, y]) |
---|
| 528 | values.append(z) |
---|
| 529 | |
---|
| 530 | |
---|
| 531 | k = i |
---|
| 532 | while keyword == 'POLYS': |
---|
| 533 | line = lines[i].strip() |
---|
| 534 | i += 1 |
---|
| 535 | |
---|
| 536 | if line == 'END': |
---|
| 537 | keyword = line |
---|
| 538 | break |
---|
| 539 | |
---|
| 540 | |
---|
| 541 | fields = line.split(':') |
---|
| 542 | assert int(fields[0]) == i-k, 'Poly indices not consecutive' |
---|
| 543 | |
---|
| 544 | #Split the three indices |
---|
| 545 | vvv = fields[1].split() |
---|
| 546 | |
---|
| 547 | i0 = int(vvv[0])-1 |
---|
| 548 | i1 = int(vvv[1])-1 |
---|
| 549 | i2 = int(vvv[2])-1 |
---|
| 550 | |
---|
| 551 | #Check for and exclude degenerate areas |
---|
| 552 | x0 = points[i0][0] |
---|
| 553 | y0 = points[i0][1] |
---|
| 554 | x1 = points[i1][0] |
---|
| 555 | y1 = points[i1][1] |
---|
| 556 | x2 = points[i2][0] |
---|
| 557 | y2 = points[i2][1] |
---|
| 558 | |
---|
| 559 | area = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
---|
| 560 | if area > 0: |
---|
| 561 | |
---|
| 562 | #Ensure that points are arranged in counter clock-wise order |
---|
| 563 | v0 = [x1-x0, y1-y0] |
---|
| 564 | v1 = [x2-x1, y2-y1] |
---|
| 565 | v2 = [x0-x2, y0-y2] |
---|
| 566 | |
---|
| 567 | a0 = anglediff(v1, v0) |
---|
| 568 | a1 = anglediff(v2, v1) |
---|
| 569 | a2 = anglediff(v0, v2) |
---|
| 570 | |
---|
| 571 | |
---|
| 572 | if a0 < pi and a1 < pi and a2 < pi: |
---|
| 573 | #all is well |
---|
| 574 | j0 = i0 |
---|
| 575 | j1 = i1 |
---|
| 576 | j2 = i2 |
---|
| 577 | else: |
---|
| 578 | #Swap two vertices |
---|
| 579 | j0 = i1 |
---|
| 580 | j1 = i0 |
---|
| 581 | j2 = i2 |
---|
| 582 | |
---|
| 583 | triangles.append([j0, j1, j2]) |
---|
| 584 | ##vertex_values.append([values[j0], values[j1], values[j2]]) |
---|
| 585 | else: |
---|
| 586 | offending +=1 |
---|
| 587 | |
---|
[7317] | 588 | log.critical('Removed %d offending triangles out of %d' |
---|
| 589 | % (offending, len(lines))) |
---|
[5897] | 590 | return points, triangles, values |
---|
| 591 | |
---|
| 592 | |
---|
| 593 | |
---|
| 594 | def strang_mesh(filename): |
---|
| 595 | """Read Strang generated mesh. |
---|
| 596 | """ |
---|
| 597 | |
---|
| 598 | from math import pi |
---|
| 599 | from anuga.utilities.numerical_tools import anglediff |
---|
| 600 | |
---|
| 601 | |
---|
| 602 | fid = open(filename) |
---|
| 603 | points = [] # List of x, y coordinates |
---|
| 604 | triangles = [] # List of vertex ids as listed in the file |
---|
| 605 | |
---|
| 606 | for line in fid.readlines(): |
---|
| 607 | fields = line.split() |
---|
| 608 | if len(fields) == 2: |
---|
| 609 | # we are reading vertex coordinates |
---|
| 610 | points.append([float(fields[0]), float(fields[1])]) |
---|
| 611 | elif len(fields) == 3: |
---|
| 612 | # we are reading triangle point id's (format ae+b) |
---|
| 613 | triangles.append([int(float(fields[0]))-1, |
---|
| 614 | int(float(fields[1]))-1, |
---|
| 615 | int(float(fields[2]))-1]) |
---|
| 616 | else: |
---|
| 617 | raise 'wrong format in ' + filename |
---|
| 618 | |
---|
| 619 | elements = [] #Final list of elements |
---|
| 620 | |
---|
| 621 | for t in triangles: |
---|
| 622 | #Get vertex coordinates |
---|
| 623 | v0 = t[0] |
---|
| 624 | v1 = t[1] |
---|
| 625 | v2 = t[2] |
---|
| 626 | |
---|
| 627 | x0 = points[v0][0] |
---|
| 628 | y0 = points[v0][1] |
---|
| 629 | x1 = points[v1][0] |
---|
| 630 | y1 = points[v1][1] |
---|
| 631 | x2 = points[v2][0] |
---|
| 632 | y2 = points[v2][1] |
---|
| 633 | |
---|
| 634 | #Check that points are arranged in counter clock-wise order |
---|
| 635 | vec0 = [x1-x0, y1-y0] |
---|
| 636 | vec1 = [x2-x1, y2-y1] |
---|
| 637 | vec2 = [x0-x2, y0-y2] |
---|
| 638 | |
---|
| 639 | a0 = anglediff(vec1, vec0) |
---|
| 640 | a1 = anglediff(vec2, vec1) |
---|
| 641 | a2 = anglediff(vec0, vec2) |
---|
| 642 | |
---|
| 643 | if a0 < pi and a1 < pi and a2 < pi: |
---|
| 644 | elements.append([v0, v1, v2]) |
---|
| 645 | else: |
---|
| 646 | elements.append([v0, v2, v1]) |
---|
| 647 | |
---|
| 648 | return points, elements |
---|
| 649 | |
---|
| 650 | # #Map from edge number to indices of associated vertices |
---|
| 651 | # edge_map = ((1,2), (0,2), (0,1)) |
---|
| 652 | |
---|
| 653 | def contracting_channel(m, n, W_upstream = 1., W_downstream = 0.75, |
---|
| 654 | L_1 = 5.0, L_2 = 2.0, L_3 = 10, origin = (0.0, 0.0)): |
---|
| 655 | """Setup a contracting channel grid of triangles |
---|
| 656 | with m segments in the x-direction and n segments in the y-direction |
---|
| 657 | |
---|
| 658 | """ |
---|
| 659 | |
---|
| 660 | import math |
---|
| 661 | |
---|
| 662 | from anuga.config import epsilon |
---|
| 663 | |
---|
| 664 | |
---|
| 665 | lenx = L_1 + L_2 + L_3 |
---|
| 666 | leny = W_upstream |
---|
| 667 | deltax = lenx/float(m) |
---|
| 668 | deltay = leny/float(n) |
---|
| 669 | |
---|
| 670 | x1 = 0 |
---|
| 671 | y1 = 0 |
---|
| 672 | x2 = L_1 |
---|
| 673 | y2 = 0 |
---|
| 674 | x3 = L_1 + L_2 |
---|
| 675 | y3 = (W_upstream - W_downstream)/2 |
---|
| 676 | x4 = L_1 + L_2 + L_3 |
---|
| 677 | y4 = y3 |
---|
| 678 | x5 = x4 |
---|
| 679 | y5 = y4 + W_downstream |
---|
| 680 | x6 = L_1 + L_2 |
---|
| 681 | y6 = y5 |
---|
| 682 | x7 = L_1 |
---|
| 683 | y7 = W_upstream |
---|
| 684 | x8 = 0 |
---|
| 685 | y8 = W_upstream |
---|
| 686 | a1 = 0 |
---|
| 687 | a2 = (W_upstream - W_downstream)/(2*L_2) |
---|
| 688 | a3 = 1 |
---|
| 689 | a4 = (W_downstream - W_upstream)/(L_2*W_upstream) |
---|
| 690 | |
---|
| 691 | # Dictionary of vertex objects |
---|
| 692 | vertices = {} |
---|
| 693 | points = [] |
---|
| 694 | |
---|
| 695 | for i in range(m+1): |
---|
| 696 | x = deltax*i |
---|
| 697 | for j in range(n+1): |
---|
| 698 | y = deltay*j |
---|
| 699 | if x > L_1 and x <= (L_1 + L_2): |
---|
| 700 | y = a1 + a2*(x - L_1) + a3*y + a4*(x - L_1)*y |
---|
| 701 | elif x > L_1 + L_2: |
---|
| 702 | y = (W_upstream - W_downstream)/2 + deltay*j*W_downstream/W_upstream |
---|
| 703 | |
---|
| 704 | vertices[i,j] = len(points) |
---|
| 705 | points.append([x + origin[0], y + origin[1]]) |
---|
| 706 | |
---|
| 707 | # Construct 2 triangles per element |
---|
| 708 | elements = [] |
---|
| 709 | boundary = {} |
---|
| 710 | for i in range(m): |
---|
| 711 | for j in range(n): |
---|
| 712 | v1 = vertices[i,j+1] |
---|
| 713 | v2 = vertices[i,j] |
---|
| 714 | v3 = vertices[i+1,j+1] |
---|
| 715 | v4 = vertices[i+1,j] |
---|
| 716 | |
---|
| 717 | #Update boundary dictionary and create elements |
---|
| 718 | if i == m-1: |
---|
| 719 | boundary[(len(elements), 2)] = 'right' |
---|
| 720 | if j == 0: |
---|
| 721 | boundary[(len(elements), 1)] = 'bottom' |
---|
| 722 | elements.append([v4,v3,v2]) #Lower |
---|
| 723 | |
---|
| 724 | if i == 0: |
---|
| 725 | boundary[(len(elements), 2)] = 'left' |
---|
| 726 | if j == n-1: |
---|
| 727 | boundary[(len(elements), 1)] = 'top' |
---|
| 728 | |
---|
| 729 | elements.append([v1,v2,v3]) #Upper |
---|
| 730 | |
---|
| 731 | return points, elements, boundary |
---|
| 732 | |
---|
| 733 | |
---|
| 734 | def contracting_channel_cross(m, n, W_upstream = 1., W_downstream = 0.75, |
---|
| 735 | L_1 = 5.0, L_2 = 2.0, L_3 = 10, origin = (0.0, 0.0)): |
---|
| 736 | """Setup a contracting channel grid of triangles |
---|
| 737 | with m segments in the x-direction and n segments in the y-direction |
---|
| 738 | |
---|
| 739 | """ |
---|
| 740 | |
---|
| 741 | import math |
---|
| 742 | |
---|
| 743 | from anuga.config import epsilon |
---|
| 744 | |
---|
| 745 | |
---|
| 746 | lenx = L_1 + L_2 + L_3 |
---|
| 747 | leny = W_upstream |
---|
| 748 | deltax = lenx/float(m) |
---|
| 749 | deltay = leny/float(n) |
---|
| 750 | |
---|
| 751 | x1 = 0 |
---|
| 752 | y1 = 0 |
---|
| 753 | x2 = L_1 |
---|
| 754 | y2 = 0 |
---|
| 755 | x3 = L_1 + L_2 |
---|
| 756 | y3 = (W_upstream - W_downstream)/2 |
---|
| 757 | x4 = L_1 + L_2 + L_3 |
---|
| 758 | y4 = y3 |
---|
| 759 | x5 = x4 |
---|
| 760 | y5 = y4 + W_downstream |
---|
| 761 | x6 = L_1 + L_2 |
---|
| 762 | y6 = y5 |
---|
| 763 | x7 = L_1 |
---|
| 764 | y7 = W_upstream |
---|
| 765 | x8 = 0 |
---|
| 766 | y8 = W_upstream |
---|
| 767 | a1 = 0 |
---|
| 768 | a2 = (W_upstream - W_downstream)/(2*L_2) |
---|
| 769 | a3 = 1 |
---|
| 770 | a4 = (W_downstream - W_upstream)/(L_2*W_upstream) |
---|
| 771 | |
---|
| 772 | # Dictionary of vertex objects |
---|
| 773 | vertices = {} |
---|
| 774 | points = [] |
---|
| 775 | |
---|
| 776 | for i in range(m+1): |
---|
| 777 | x = deltax*i |
---|
| 778 | for j in range(n+1): |
---|
| 779 | y = deltay*j |
---|
| 780 | if x > L_1 and x <= (L_1 + L_2): |
---|
| 781 | y = a1 + a2*(x - L_1) + a3*y + a4*(x - L_1)*y |
---|
| 782 | elif x > L_1 + L_2: |
---|
| 783 | y = (W_upstream - W_downstream)/2 + deltay*j*W_downstream/W_upstream |
---|
| 784 | |
---|
| 785 | vertices[i,j] = len(points) |
---|
| 786 | points.append([x + origin[0], y + origin[1]]) |
---|
| 787 | |
---|
| 788 | # Construct 4 triangles per element |
---|
| 789 | elements = [] |
---|
| 790 | boundary = {} |
---|
| 791 | for i in range(m): |
---|
| 792 | for j in range(n): |
---|
| 793 | v1 = vertices[i,j+1] |
---|
| 794 | v2 = vertices[i,j] |
---|
| 795 | v3 = vertices[i+1,j+1] |
---|
| 796 | v4 = vertices[i+1,j] |
---|
| 797 | x = (points[v1][0]+points[v2][0]+points[v3][0]+points[v4][0])*0.25 |
---|
| 798 | y = (points[v1][1]+points[v2][1]+points[v3][1]+points[v4][1])*0.25 |
---|
| 799 | v5 = len(points) |
---|
| 800 | points.append([x, y]) |
---|
| 801 | |
---|
| 802 | #Create left triangle |
---|
| 803 | if i == 0: |
---|
| 804 | boundary[(len(elements), 1)] = 'left' |
---|
| 805 | elements.append([v2,v5,v1]) |
---|
| 806 | |
---|
| 807 | #Create bottom triangle |
---|
| 808 | if j == 0: |
---|
| 809 | boundary[(len(elements), 1)] = 'bottom' |
---|
| 810 | elements.append([v4,v5,v2]) |
---|
| 811 | |
---|
| 812 | #Create right triangle |
---|
| 813 | if i == m-1: |
---|
| 814 | boundary[(len(elements), 1)] = 'right' |
---|
| 815 | elements.append([v3,v5,v4]) |
---|
| 816 | |
---|
| 817 | #Create top triangle |
---|
| 818 | if j == n-1: |
---|
| 819 | boundary[(len(elements), 1)] = 'top' |
---|
| 820 | elements.append([v1,v5,v3]) |
---|
| 821 | |
---|
| 822 | |
---|
| 823 | return points, elements, boundary |
---|
| 824 | |
---|
| 825 | |
---|
| 826 | |
---|
| 827 | |
---|
| 828 | def oblique_cross(m, n, lenx = 1.0, leny = 1.0, theta = 8.95, origin = (0.0, 0.0)): |
---|
| 829 | """Setup a oblique grid of triangles |
---|
| 830 | with m segments in the x-direction and n segments in the y-direction |
---|
| 831 | |
---|
| 832 | """ |
---|
| 833 | |
---|
| 834 | import math |
---|
| 835 | |
---|
| 836 | from anuga.config import epsilon |
---|
| 837 | |
---|
| 838 | |
---|
| 839 | deltax = lenx/float(m) |
---|
| 840 | deltay = leny/float(n) |
---|
| 841 | a = 0.75*lenx*math.tan(theta/180.*math.pi) |
---|
| 842 | x1 = lenx |
---|
| 843 | y1 = 0 |
---|
| 844 | x2 = lenx |
---|
| 845 | y2 = leny |
---|
| 846 | x3 = 0.25*lenx |
---|
| 847 | y3 = leny |
---|
| 848 | x4 = x3 |
---|
| 849 | y4 = 0 |
---|
| 850 | a2 = a/(x1-x4) |
---|
| 851 | a1 = -a2*x4 |
---|
| 852 | a4 = ((a1 + a2*x3)/y3-(a1 + a2*x2)/y2)/(x2-x3) |
---|
| 853 | a3 = 1. - (a1 + a2*x3)/y3 - a4*x3 |
---|
| 854 | |
---|
| 855 | # Dictionary of vertex objects |
---|
| 856 | vertices = {} |
---|
| 857 | points = [] |
---|
| 858 | |
---|
| 859 | for i in range(m+1): |
---|
| 860 | x = deltax*i |
---|
| 861 | for j in range(n+1): |
---|
| 862 | y = deltay*j |
---|
| 863 | if x > 0.25*lenx: |
---|
| 864 | y = a1 + a2*x + a3*y + a4*x*y |
---|
| 865 | |
---|
| 866 | vertices[i,j] = len(points) |
---|
| 867 | points.append([x + origin[0], y + origin[1]]) |
---|
| 868 | |
---|
| 869 | # Construct 4 triangles per element |
---|
| 870 | elements = [] |
---|
| 871 | boundary = {} |
---|
| 872 | for i in range(m): |
---|
| 873 | for j in range(n): |
---|
| 874 | v1 = vertices[i,j+1] |
---|
| 875 | v2 = vertices[i,j] |
---|
| 876 | v3 = vertices[i+1,j+1] |
---|
| 877 | v4 = vertices[i+1,j] |
---|
| 878 | x = (points[v1][0]+points[v2][0]+points[v3][0]+points[v4][0])*0.25 |
---|
| 879 | y = (points[v1][1]+points[v2][1]+points[v3][1]+points[v4][1])*0.25 |
---|
| 880 | v5 = len(points) |
---|
| 881 | points.append([x, y]) |
---|
| 882 | |
---|
| 883 | #Update boundary dictionary and create elements |
---|
| 884 | #Create left triangle |
---|
| 885 | if i == 0: |
---|
| 886 | boundary[(len(elements), 1)] = 'left' |
---|
| 887 | elements.append([v2,v5,v1]) |
---|
| 888 | |
---|
| 889 | #Create bottom triangle |
---|
| 890 | if j == 0: |
---|
| 891 | boundary[(len(elements), 1)] = 'bottom' |
---|
| 892 | elements.append([v4,v5,v2]) |
---|
| 893 | |
---|
| 894 | #Create right triangle |
---|
| 895 | if i == m-1: |
---|
| 896 | boundary[(len(elements), 1)] = 'right' |
---|
| 897 | elements.append([v3,v5,v4]) |
---|
| 898 | |
---|
| 899 | #Create top triangle |
---|
| 900 | if j == n-1: |
---|
| 901 | boundary[(len(elements), 1)] = 'top' |
---|
| 902 | elements.append([v1,v5,v3]) |
---|
| 903 | |
---|
| 904 | |
---|
| 905 | return points, elements, boundary |
---|