[5897] | 1 | """Classes implementing general 2D triangular mesh with neighbour structure. |
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| 2 | |
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| 3 | This structure is purely geometrical. Anything relating to quantities |
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| 4 | or timestepping is implemented in subclass domain.py. |
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| 5 | |
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| 6 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 7 | Geoscience Australia, 2004 |
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| 8 | """ |
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| 9 | |
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| 10 | from general_mesh import General_mesh |
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| 11 | from anuga.caching import cache |
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[7317] | 12 | import anuga.utilities.log as log |
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| 13 | |
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[5897] | 14 | from math import pi, sqrt |
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[6145] | 15 | |
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[7276] | 16 | import numpy as num |
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[5897] | 17 | |
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[7276] | 18 | |
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[5897] | 19 | class Mesh(General_mesh): |
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| 20 | """Collection of triangular elements (purely geometric) |
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| 21 | |
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| 22 | A triangular element is defined in terms of three vertex ids, |
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| 23 | ordered counter clock-wise, |
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| 24 | each corresponding to a given coordinate set. |
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| 25 | Vertices from different elements can point to the same |
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| 26 | coordinate set. |
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| 27 | |
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[7276] | 28 | Coordinate sets are implemented as an N x 2 numeric array containing |
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[5897] | 29 | x and y coordinates. |
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| 30 | |
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| 31 | |
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| 32 | To instantiate: |
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| 33 | Mesh(coordinates, triangles) |
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| 34 | |
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| 35 | where |
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| 36 | |
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[7276] | 37 | coordinates is either a list of 2-tuples or an Mx2 numeric array of |
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[5897] | 38 | floats representing all x, y coordinates in the mesh. |
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| 39 | |
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[7276] | 40 | triangles is either a list of 3-tuples or an Nx3 numeric array of |
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[5897] | 41 | integers representing indices of all vertices in the mesh. |
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| 42 | Each vertex is identified by its index i in [0, M-1]. |
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| 43 | |
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| 44 | |
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| 45 | Example: |
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| 46 | a = [0.0, 0.0] |
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| 47 | b = [0.0, 2.0] |
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| 48 | c = [2.0,0.0] |
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| 49 | e = [2.0, 2.0] |
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| 50 | |
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| 51 | points = [a, b, c, e] |
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| 52 | triangles = [ [1,0,2], [1,2,3] ] #bac, bce |
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| 53 | mesh = Mesh(points, triangles) |
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| 54 | |
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| 55 | #creates two triangles: bac and bce |
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| 56 | |
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| 57 | |
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| 58 | Mesh takes the optional third argument boundary which is a |
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| 59 | dictionary mapping from (element_id, edge_id) to boundary tag. |
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| 60 | The default value is None which will assign the default_boundary_tag |
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| 61 | as specified in config.py to all boundary edges. |
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| 62 | """ |
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| 63 | |
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| 64 | #FIXME: Maybe rename coordinates to points (as in a poly file) |
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| 65 | #But keep 'vertex_coordinates' |
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| 66 | |
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| 67 | #FIXME: Put in check for angles less than a set minimum |
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| 68 | |
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| 69 | |
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| 70 | def __init__(self, coordinates, triangles, |
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| 71 | boundary=None, |
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| 72 | tagged_elements=None, |
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| 73 | geo_reference=None, |
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| 74 | use_inscribed_circle=False, |
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| 75 | verbose=False): |
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| 76 | """ |
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| 77 | Build triangles from x,y coordinates (sequence of 2-tuples or |
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[7276] | 78 | Mx2 numeric array of floats) and triangles (sequence of 3-tuples |
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| 79 | or Nx3 numeric array of non-negative integers). |
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[5897] | 80 | """ |
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| 81 | |
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| 82 | |
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| 83 | |
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| 84 | |
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| 85 | General_mesh.__init__(self, coordinates, triangles, |
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| 86 | geo_reference=geo_reference, |
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| 87 | verbose=verbose) |
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| 88 | |
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[7317] | 89 | if verbose: log.critical('Initialising mesh') |
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[5897] | 90 | |
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| 91 | N = len(self) #Number_of_triangles |
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| 92 | |
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| 93 | self.use_inscribed_circle = use_inscribed_circle |
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| 94 | |
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| 95 | #Allocate space for geometric quantities |
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[7276] | 96 | self.centroid_coordinates = num.zeros((N, 2), num.float) |
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[5897] | 97 | |
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[7276] | 98 | self.radii = num.zeros(N, num.float) |
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[5897] | 99 | |
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[7276] | 100 | self.neighbours = num.zeros((N, 3), num.int) |
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| 101 | self.neighbour_edges = num.zeros((N, 3), num.int) |
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| 102 | self.number_of_boundaries = num.zeros(N, num.int) |
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| 103 | self.surrogate_neighbours = num.zeros((N, 3), num.int) |
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[5897] | 104 | |
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| 105 | #Get x,y coordinates for all triangles and store |
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| 106 | V = self.vertex_coordinates # Relative coordinates |
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| 107 | |
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| 108 | #Initialise each triangle |
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[7317] | 109 | if verbose: log.critical('Mesh: Computing centroids and radii') |
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[5897] | 110 | for i in range(N): |
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[7317] | 111 | if verbose and i % ((N+10)/10) == 0: log.critical('(%d/%d)' % (i, N)) |
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[5897] | 112 | |
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| 113 | x0, y0 = V[3*i, :] |
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| 114 | x1, y1 = V[3*i+1, :] |
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[7276] | 115 | x2, y2 = V[3*i+2, :] |
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[5897] | 116 | |
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| 117 | #x0 = V[i, 0]; y0 = V[i, 1] |
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| 118 | #x1 = V[i, 2]; y1 = V[i, 3] |
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| 119 | #x2 = V[i, 4]; y2 = V[i, 5] |
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| 120 | |
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| 121 | #Compute centroid |
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[7276] | 122 | centroid = num.array([(x0 + x1 + x2)/3, (y0 + y1 + y2)/3], num.float) |
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[5897] | 123 | self.centroid_coordinates[i] = centroid |
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| 124 | |
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| 125 | |
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| 126 | if self.use_inscribed_circle == False: |
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| 127 | #OLD code. Computed radii may exceed that of an |
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| 128 | #inscribed circle |
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| 129 | |
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| 130 | #Midpoints |
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[7276] | 131 | m0 = num.array([(x1 + x2)/2, (y1 + y2)/2], num.float) |
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| 132 | m1 = num.array([(x0 + x2)/2, (y0 + y2)/2], num.float) |
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| 133 | m2 = num.array([(x1 + x0)/2, (y1 + y0)/2], num.float) |
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[5897] | 134 | |
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| 135 | #The radius is the distance from the centroid of |
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| 136 | #a triangle to the midpoint of the side of the triangle |
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| 137 | #closest to the centroid |
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[6145] | 138 | d0 = num.sqrt(num.sum( (centroid-m0)**2 )) |
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| 139 | d1 = num.sqrt(num.sum( (centroid-m1)**2 )) |
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| 140 | d2 = num.sqrt(num.sum( (centroid-m2)**2 )) |
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[5897] | 141 | |
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| 142 | self.radii[i] = min(d0, d1, d2) |
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| 143 | |
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| 144 | else: |
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| 145 | #NEW code added by Peter Row. True radius |
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| 146 | #of inscribed circle is computed |
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| 147 | |
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[6145] | 148 | a = num.sqrt((x0-x1)**2+(y0-y1)**2) |
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| 149 | b = num.sqrt((x1-x2)**2+(y1-y2)**2) |
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| 150 | c = num.sqrt((x2-x0)**2+(y2-y0)**2) |
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[5897] | 151 | |
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| 152 | self.radii[i]=2.0*self.areas[i]/(a+b+c) |
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| 153 | |
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| 154 | |
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| 155 | #Initialise Neighbours (-1 means that it is a boundary neighbour) |
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| 156 | self.neighbours[i, :] = [-1, -1, -1] |
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| 157 | |
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| 158 | #Initialise edge ids of neighbours |
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| 159 | #In case of boundaries this slot is not used |
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| 160 | self.neighbour_edges[i, :] = [-1, -1, -1] |
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| 161 | |
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| 162 | |
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| 163 | #Build neighbour structure |
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[7317] | 164 | if verbose: log.critical('Mesh: Building neigbour structure') |
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[5897] | 165 | self.build_neighbour_structure() |
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| 166 | |
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| 167 | #Build surrogate neighbour structure |
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[7317] | 168 | if verbose: log.critical('Mesh: Building surrogate neigbour structure') |
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[5897] | 169 | self.build_surrogate_neighbour_structure() |
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| 170 | |
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| 171 | #Build boundary dictionary mapping (id, edge) to symbolic tags |
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[7317] | 172 | if verbose: log.critical('Mesh: Building boundary dictionary') |
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[5897] | 173 | self.build_boundary_dictionary(boundary) |
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| 174 | |
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[8154] | 175 | #Update boundary_enumeration |
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| 176 | self.build_boundary_neighbours() |
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| 177 | |
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[5897] | 178 | #Build tagged element dictionary mapping (tag) to array of elements |
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[7317] | 179 | if verbose: log.critical('Mesh: Building tagged elements dictionary') |
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[5897] | 180 | self.build_tagged_elements_dictionary(tagged_elements) |
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| 181 | |
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| 182 | # Build a list of vertices that are not connected to any triangles |
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| 183 | self.lone_vertices = [] |
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| 184 | #Check that all vertices have been registered |
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[7276] | 185 | for node, count in enumerate(self.number_of_triangles_per_node): |
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[5897] | 186 | #msg = 'Node %d does not belong to an element.' %node |
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| 187 | #assert count > 0, msg |
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| 188 | if count == 0: |
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| 189 | self.lone_vertices.append(node) |
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[7276] | 190 | |
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[5897] | 191 | #Update boundary indices FIXME: OBSOLETE |
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| 192 | #self.build_boundary_structure() |
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| 193 | |
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| 194 | #FIXME check integrity? |
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[7317] | 195 | if verbose: log.critical('Mesh: Done') |
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[5897] | 196 | |
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| 197 | def __repr__(self): |
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| 198 | return General_mesh.__repr__(self) + ', %d boundary segments'\ |
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| 199 | %(len(self.boundary)) |
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| 200 | |
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| 201 | |
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| 202 | def set_to_inscribed_circle(self,safety_factor = 1): |
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| 203 | #FIXME phase out eventually |
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| 204 | N = self.number_of_triangles |
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| 205 | V = self.vertex_coordinates |
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| 206 | |
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| 207 | #initialising min and max ratio |
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| 208 | i=0 |
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| 209 | old_rad = self.radii[i] |
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| 210 | x0 = V[i, 0]; y0 = V[i, 1] |
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| 211 | x1 = V[i, 2]; y1 = V[i, 3] |
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| 212 | x2 = V[i, 4]; y2 = V[i, 5] |
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[6145] | 213 | a = num.sqrt((x0-x1)**2+(y0-y1)**2) |
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| 214 | b = num.sqrt((x1-x2)**2+(y1-y2)**2) |
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| 215 | c = num.sqrt((x2-x0)**2+(y2-y0)**2) |
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[5897] | 216 | ratio = old_rad/self.radii[i] |
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| 217 | max_ratio = ratio |
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| 218 | min_ratio = ratio |
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| 219 | |
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| 220 | for i in range(N): |
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| 221 | old_rad = self.radii[i] |
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| 222 | x0 = V[i, 0]; y0 = V[i, 1] |
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| 223 | x1 = V[i, 2]; y1 = V[i, 3] |
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| 224 | x2 = V[i, 4]; y2 = V[i, 5] |
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[6145] | 225 | a = num.sqrt((x0-x1)**2+(y0-y1)**2) |
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| 226 | b = num.sqrt((x1-x2)**2+(y1-y2)**2) |
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| 227 | c = num.sqrt((x2-x0)**2+(y2-y0)**2) |
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[5897] | 228 | self.radii[i]=self.areas[i]/(2*(a+b+c))*safety_factor |
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| 229 | ratio = old_rad/self.radii[i] |
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| 230 | if ratio >= max_ratio: max_ratio = ratio |
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| 231 | if ratio <= min_ratio: min_ratio = ratio |
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| 232 | return max_ratio,min_ratio |
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| 233 | |
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| 234 | |
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| 235 | |
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| 236 | def build_neighbour_structure(self): |
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| 237 | """Update all registered triangles to point to their neighbours. |
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| 238 | |
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| 239 | Also, keep a tally of the number of boundaries for each triangle |
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| 240 | |
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| 241 | Postconditions: |
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| 242 | neighbours and neighbour_edges is populated |
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| 243 | number_of_boundaries integer array is defined. |
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| 244 | """ |
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| 245 | |
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| 246 | #Step 1: |
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| 247 | #Build dictionary mapping from segments (2-tuple of points) |
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| 248 | #to left hand side edge (facing neighbouring triangle) |
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| 249 | |
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| 250 | N = len(self) #Number_of_triangles |
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| 251 | neighbourdict = {} |
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| 252 | for i in range(N): |
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| 253 | |
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| 254 | #Register all segments as keys mapping to current triangle |
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| 255 | #and segment id |
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| 256 | a = self.triangles[i, 0] |
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| 257 | b = self.triangles[i, 1] |
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| 258 | c = self.triangles[i, 2] |
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| 259 | if neighbourdict.has_key((a,b)): |
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| 260 | msg = "Edge 2 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[a,b][1],neighbourdict[a,b][0]) |
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[8124] | 261 | raise Exception(msg) |
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[5897] | 262 | if neighbourdict.has_key((b,c)): |
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| 263 | msg = "Edge 0 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[b,c][1],neighbourdict[b,c][0]) |
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[8124] | 264 | raise Exception(msg) |
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[5897] | 265 | if neighbourdict.has_key((c,a)): |
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| 266 | msg = "Edge 1 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[c,a][1],neighbourdict[c,a][0]) |
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[8124] | 267 | raise Exception(msg) |
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[5897] | 268 | |
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| 269 | neighbourdict[a,b] = (i, 2) #(id, edge) |
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| 270 | neighbourdict[b,c] = (i, 0) #(id, edge) |
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| 271 | neighbourdict[c,a] = (i, 1) #(id, edge) |
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| 272 | |
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| 273 | |
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| 274 | #Step 2: |
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| 275 | #Go through triangles again, but this time |
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| 276 | #reverse direction of segments and lookup neighbours. |
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| 277 | for i in range(N): |
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| 278 | a = self.triangles[i, 0] |
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| 279 | b = self.triangles[i, 1] |
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| 280 | c = self.triangles[i, 2] |
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| 281 | |
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| 282 | self.number_of_boundaries[i] = 3 |
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| 283 | if neighbourdict.has_key((b,a)): |
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| 284 | self.neighbours[i, 2] = neighbourdict[b,a][0] |
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| 285 | self.neighbour_edges[i, 2] = neighbourdict[b,a][1] |
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| 286 | self.number_of_boundaries[i] -= 1 |
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| 287 | |
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| 288 | if neighbourdict.has_key((c,b)): |
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| 289 | self.neighbours[i, 0] = neighbourdict[c,b][0] |
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| 290 | self.neighbour_edges[i, 0] = neighbourdict[c,b][1] |
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| 291 | self.number_of_boundaries[i] -= 1 |
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| 292 | |
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| 293 | if neighbourdict.has_key((a,c)): |
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| 294 | self.neighbours[i, 1] = neighbourdict[a,c][0] |
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| 295 | self.neighbour_edges[i, 1] = neighbourdict[a,c][1] |
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| 296 | self.number_of_boundaries[i] -= 1 |
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| 297 | |
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| 298 | |
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| 299 | def build_surrogate_neighbour_structure(self): |
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| 300 | """Build structure where each triangle edge points to its neighbours |
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| 301 | if they exist. Otherwise point to the triangle itself. |
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| 302 | |
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| 303 | The surrogate neighbour structure is useful for computing gradients |
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| 304 | based on centroid values of neighbours. |
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| 305 | |
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| 306 | Precondition: Neighbour structure is defined |
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| 307 | Postcondition: |
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| 308 | Surrogate neighbour structure is defined: |
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| 309 | surrogate_neighbours: i0, i1, i2 where all i_k >= 0 point to |
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| 310 | triangles. |
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| 311 | |
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| 312 | """ |
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| 313 | |
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| 314 | N = len(self) #Number of triangles |
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| 315 | for i in range(N): |
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| 316 | #Find all neighbouring volumes that are not boundaries |
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| 317 | for k in range(3): |
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| 318 | if self.neighbours[i, k] < 0: |
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| 319 | self.surrogate_neighbours[i, k] = i #Point this triangle |
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| 320 | else: |
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| 321 | self.surrogate_neighbours[i, k] = self.neighbours[i, k] |
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| 322 | |
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| 323 | |
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| 324 | |
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| 325 | def build_boundary_dictionary(self, boundary = None): |
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| 326 | """Build or check the dictionary of boundary tags. |
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| 327 | self.boundary is a dictionary of tags, |
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| 328 | keyed by volume id and edge: |
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| 329 | { (id, edge): tag, ... } |
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| 330 | |
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| 331 | Postconditions: |
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| 332 | self.boundary is defined. |
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| 333 | """ |
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| 334 | |
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| 335 | from anuga.config import default_boundary_tag |
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| 336 | |
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| 337 | if boundary is None: |
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| 338 | boundary = {} |
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| 339 | for vol_id in range(len(self)): |
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| 340 | for edge_id in range(0, 3): |
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| 341 | if self.neighbours[vol_id, edge_id] < 0: |
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| 342 | boundary[(vol_id, edge_id)] = default_boundary_tag |
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| 343 | else: |
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| 344 | #Check that all keys in given boundary exist |
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| 345 | for vol_id, edge_id in boundary.keys(): |
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| 346 | msg = 'Segment (%d, %d) does not exist' %(vol_id, edge_id) |
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| 347 | a, b = self.neighbours.shape |
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| 348 | assert vol_id < a and edge_id < b, msg |
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| 349 | |
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| 350 | #FIXME: This assert violates internal boundaries (delete it) |
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| 351 | #msg = 'Segment (%d, %d) is not a boundary' %(vol_id, edge_id) |
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| 352 | #assert self.neighbours[vol_id, edge_id] < 0, msg |
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| 353 | |
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| 354 | #Check that all boundary segments are assigned a tag |
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| 355 | for vol_id in range(len(self)): |
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| 356 | for edge_id in range(0, 3): |
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| 357 | if self.neighbours[vol_id, edge_id] < 0: |
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| 358 | if not boundary.has_key( (vol_id, edge_id) ): |
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| 359 | msg = 'WARNING: Given boundary does not contain ' |
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| 360 | msg += 'tags for edge (%d, %d). '\ |
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| 361 | %(vol_id, edge_id) |
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| 362 | msg += 'Assigning default tag (%s).'\ |
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| 363 | %default_boundary_tag |
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| 364 | |
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| 365 | #FIXME: Print only as per verbosity |
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| 366 | |
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| 367 | #FIXME: Make this situation an error in the future |
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| 368 | #and make another function which will |
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| 369 | #enable default boundary-tags where |
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| 370 | #tags a not specified |
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| 371 | boundary[ (vol_id, edge_id) ] =\ |
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| 372 | default_boundary_tag |
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| 373 | |
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| 374 | |
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| 375 | |
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| 376 | self.boundary = boundary |
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| 377 | |
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| 378 | |
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| 379 | def build_tagged_elements_dictionary(self, tagged_elements = None): |
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| 380 | """Build the dictionary of element tags. |
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| 381 | self.tagged_elements is a dictionary of element arrays, |
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| 382 | keyed by tag: |
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| 383 | { (tag): [e1, e2, e3..] } |
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| 384 | |
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| 385 | Postconditions: |
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| 386 | self.element_tag is defined |
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| 387 | """ |
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| 388 | |
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| 389 | if tagged_elements is None: |
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| 390 | tagged_elements = {} |
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| 391 | else: |
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| 392 | #Check that all keys in given boundary exist |
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| 393 | for tag in tagged_elements.keys(): |
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[7276] | 394 | tagged_elements[tag] = num.array(tagged_elements[tag], num.int) |
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[5897] | 395 | |
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| 396 | msg = 'Not all elements exist. ' |
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| 397 | assert max(tagged_elements[tag]) < len(self), msg |
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| 398 | self.tagged_elements = tagged_elements |
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[7276] | 399 | |
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[6191] | 400 | def get_tagged_elements(self): |
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| 401 | return self.tagged_elements |
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[5897] | 402 | |
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| 403 | def build_boundary_structure(self): |
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| 404 | """Traverse boundary and |
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| 405 | enumerate neighbour indices from -1 and |
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| 406 | counting down. |
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| 407 | |
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| 408 | Precondition: |
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| 409 | self.boundary is defined. |
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| 410 | Post condition: |
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| 411 | neighbour array has unique negative indices for boundary |
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| 412 | boundary_segments array imposes an ordering on segments |
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| 413 | (not otherwise available from the dictionary) |
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| 414 | |
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| 415 | Note: If a segment is listed in the boundary dictionary |
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| 416 | it *will* become a boundary - even if there is a neighbouring triangle. |
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| 417 | This would be the case for internal boundaries |
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| 418 | """ |
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| 419 | |
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| 420 | #FIXME: Now Obsolete - maybe use some comments from here in |
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| 421 | #domain.set_boundary |
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| 422 | |
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| 423 | if self.boundary is None: |
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| 424 | msg = 'Boundary dictionary must be defined before ' |
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| 425 | msg += 'building boundary structure' |
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[8124] | 426 | raise Exception(msg) |
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[5897] | 427 | |
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| 428 | |
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| 429 | self.boundary_segments = self.boundary.keys() |
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| 430 | self.boundary_segments.sort() |
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| 431 | |
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| 432 | index = -1 |
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| 433 | for id, edge in self.boundary_segments: |
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| 434 | |
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| 435 | #FIXME: One would detect internal boundaries as follows |
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| 436 | #if self.neighbours[id, edge] > -1: |
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[7317] | 437 | # log.critical('Internal boundary') |
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[5897] | 438 | |
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| 439 | self.neighbours[id, edge] = index |
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[8154] | 440 | |
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| 441 | self.boundary_enumeration[id,edge] = index |
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| 442 | |
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[5897] | 443 | index -= 1 |
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| 444 | |
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[8164] | 445 | |
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| 446 | |
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[8154] | 447 | def build_boundary_neighbours(self): |
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| 448 | """Traverse boundary and |
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| 449 | enumerate neighbour indices from -1 and |
---|
| 450 | counting down. |
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[5897] | 451 | |
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[8154] | 452 | Precondition: |
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| 453 | self.boundary is defined. |
---|
| 454 | Post condition: |
---|
| 455 | neighbours array has unique negative indices for boundary |
---|
| 456 | boundary_segments array imposes an ordering on segments |
---|
| 457 | (not otherwise available from the dictionary) |
---|
| 458 | |
---|
| 459 | """ |
---|
| 460 | |
---|
| 461 | if self.boundary is None: |
---|
| 462 | msg = 'Boundary dictionary must be defined before ' |
---|
| 463 | msg += 'building boundary structure' |
---|
| 464 | raise Exception(msg) |
---|
| 465 | |
---|
| 466 | self.boundary_enumeration = {} |
---|
| 467 | |
---|
| 468 | X = self.boundary.keys() |
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| 469 | X.sort() |
---|
| 470 | |
---|
| 471 | index = -1 |
---|
| 472 | for id, edge in X: |
---|
| 473 | self.neighbours[id, edge] = index |
---|
| 474 | |
---|
| 475 | self.boundary_enumeration[id,edge] = -index -1 |
---|
| 476 | |
---|
| 477 | index -= 1 |
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| 478 | |
---|
[8164] | 479 | # Now we know number of boundaries |
---|
| 480 | M = len(self.boundary_enumeration) |
---|
| 481 | self.boundary_cells = num.zeros((M,),num.int) |
---|
| 482 | self.boundary_edges = num.zeros((M,),num.int) |
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[8154] | 483 | |
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[8164] | 484 | for id, edge in X: |
---|
[8154] | 485 | |
---|
[8164] | 486 | j = self.boundary_enumeration[id,edge] |
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| 487 | self.boundary_cells[j] = id |
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| 488 | self.boundary_edges[j] = edge |
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| 489 | |
---|
| 490 | |
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[5897] | 491 | def get_boundary_tags(self): |
---|
| 492 | """Return list of available boundary tags |
---|
| 493 | """ |
---|
| 494 | |
---|
| 495 | tags = {} |
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| 496 | for v in self.boundary.values(): |
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| 497 | tags[v] = 1 |
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| 498 | |
---|
| 499 | return tags.keys() |
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| 500 | |
---|
| 501 | |
---|
| 502 | def get_boundary_polygon(self, verbose=False): |
---|
| 503 | """Return bounding polygon for mesh (counter clockwise) |
---|
| 504 | |
---|
| 505 | Using the mesh boundary, derive a bounding polygon for this mesh. |
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[7276] | 506 | If multiple vertex values are present (vertices stored uniquely), |
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| 507 | the algorithm will select the path that contains the entire mesh. |
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[5897] | 508 | |
---|
| 509 | All points are in absolute UTM coordinates |
---|
| 510 | """ |
---|
| 511 | |
---|
[7276] | 512 | from anuga.utilities.numerical_tools import angle, ensure_numeric |
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[5897] | 513 | |
---|
| 514 | # Get mesh extent |
---|
| 515 | xmin, xmax, ymin, ymax = self.get_extent(absolute=True) |
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| 516 | pmin = ensure_numeric([xmin, ymin]) |
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[7276] | 517 | pmax = ensure_numeric([xmax, ymax]) |
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[5897] | 518 | |
---|
| 519 | # Assemble dictionary of boundary segments and choose starting point |
---|
| 520 | segments = {} |
---|
| 521 | inverse_segments = {} |
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| 522 | p0 = None |
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[7276] | 523 | |
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| 524 | # Start value across entire mesh |
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| 525 | mindist = num.sqrt(num.sum((pmax-pmin)**2)) |
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[5897] | 526 | for i, edge_id in self.boundary.keys(): |
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| 527 | # Find vertex ids for boundary segment |
---|
| 528 | if edge_id == 0: a = 1; b = 2 |
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| 529 | if edge_id == 1: a = 2; b = 0 |
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| 530 | if edge_id == 2: a = 0; b = 1 |
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| 531 | |
---|
[7276] | 532 | A = self.get_vertex_coordinate(i, a, absolute=True) # Start |
---|
| 533 | B = self.get_vertex_coordinate(i, b, absolute=True) # End |
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[5897] | 534 | |
---|
| 535 | # Take the point closest to pmin as starting point |
---|
| 536 | # Note: Could be arbitrary, but nice to have |
---|
| 537 | # a unique way of selecting |
---|
[6145] | 538 | dist_A = num.sqrt(num.sum((A-pmin)**2)) |
---|
| 539 | dist_B = num.sqrt(num.sum((B-pmin)**2)) |
---|
[5897] | 540 | |
---|
| 541 | # Find lower leftmost point |
---|
| 542 | if dist_A < mindist: |
---|
| 543 | mindist = dist_A |
---|
| 544 | p0 = A |
---|
| 545 | if dist_B < mindist: |
---|
| 546 | mindist = dist_B |
---|
| 547 | p0 = B |
---|
| 548 | |
---|
| 549 | # Sanity check |
---|
| 550 | if p0 is None: |
---|
[7276] | 551 | msg = 'Impossible: p0 is None!?' |
---|
[8124] | 552 | raise Exception(msg) |
---|
[5897] | 553 | |
---|
| 554 | # Register potential paths from A to B |
---|
| 555 | if not segments.has_key(tuple(A)): |
---|
[7276] | 556 | segments[tuple(A)] = [] # Empty list for candidate points |
---|
[5897] | 557 | |
---|
[7276] | 558 | segments[tuple(A)].append(B) |
---|
[5897] | 559 | |
---|
| 560 | # Start with smallest point and follow boundary (counter clock wise) |
---|
| 561 | polygon = [list(p0)]# Storage for final boundary polygon |
---|
[7276] | 562 | point_registry = {} # Keep track of storage to avoid multiple runs |
---|
| 563 | # around boundary. This will only be the case if |
---|
| 564 | # there are more than one candidate. |
---|
[5897] | 565 | # FIXME (Ole): Perhaps we can do away with polygon |
---|
| 566 | # and use only point_registry to save space. |
---|
| 567 | |
---|
[7276] | 568 | point_registry[tuple(p0)] = 0 |
---|
| 569 | |
---|
[5897] | 570 | while len(point_registry) < len(self.boundary): |
---|
| 571 | candidate_list = segments[tuple(p0)] |
---|
| 572 | if len(candidate_list) > 1: |
---|
[7276] | 573 | # Multiple points detected (this will be the case for meshes |
---|
| 574 | # with duplicate points as those used for discontinuous |
---|
| 575 | # triangles with vertices stored uniquely). |
---|
| 576 | # Take the candidate that is furthest to the clockwise |
---|
| 577 | # direction, as that will follow the boundary. |
---|
| 578 | # |
---|
| 579 | # This will also be the case for pathological triangles |
---|
| 580 | # that have no neighbours. |
---|
[5897] | 581 | |
---|
| 582 | if verbose: |
---|
[7317] | 583 | log.critical('Point %s has multiple candidates: %s' |
---|
| 584 | % (str(p0), candidate_list)) |
---|
[5897] | 585 | |
---|
| 586 | # Check that previous are not in candidate list |
---|
| 587 | #for p in candidate_list: |
---|
| 588 | # assert not allclose(p0, p) |
---|
| 589 | |
---|
| 590 | # Choose vector against which all angles will be measured |
---|
[7276] | 591 | if len(polygon) > 1: |
---|
| 592 | v_prev = p0 - polygon[-2] # Vector that leads to p0 |
---|
| 593 | # from previous point |
---|
[5897] | 594 | else: |
---|
[7276] | 595 | # FIXME (Ole): What do we do if the first point has |
---|
| 596 | # multiple candidates? |
---|
[5897] | 597 | # Being the lower left corner, perhaps we can use the |
---|
[7276] | 598 | # vector [1, 0], but I really don't know if this is |
---|
| 599 | # completely watertight. |
---|
[5897] | 600 | v_prev = [1.0, 0.0] |
---|
| 601 | |
---|
[7276] | 602 | # Choose candidate with minimum angle |
---|
[5897] | 603 | minimum_angle = 2*pi |
---|
| 604 | for pc in candidate_list: |
---|
[7276] | 605 | vc = pc-p0 # Candidate vector (from p0 to candidate pt) |
---|
[5897] | 606 | |
---|
| 607 | # Angle between each candidate and the previous vector |
---|
| 608 | # in [-pi, pi] |
---|
| 609 | ac = angle(vc, v_prev) |
---|
| 610 | if ac > pi: |
---|
[7276] | 611 | # Give preference to angles on the right hand side |
---|
| 612 | # of v_prev |
---|
[5897] | 613 | ac = ac-2*pi |
---|
| 614 | |
---|
[7276] | 615 | # Take the minimal angle corresponding to the |
---|
| 616 | # rightmost vector |
---|
[5897] | 617 | if ac < minimum_angle: |
---|
| 618 | minimum_angle = ac |
---|
[7276] | 619 | p1 = pc # Best candidate |
---|
[5897] | 620 | |
---|
| 621 | if verbose is True: |
---|
[7317] | 622 | log.critical(' Best candidate %s, angle %f' |
---|
| 623 | % (p1, minimum_angle*180/pi)) |
---|
[5897] | 624 | else: |
---|
| 625 | p1 = candidate_list[0] |
---|
| 626 | |
---|
| 627 | if point_registry.has_key(tuple(p1)): |
---|
[7276] | 628 | # We have reached a point already visited. |
---|
| 629 | if num.allclose(p1, polygon[0]): |
---|
| 630 | # If it is the initial point, the polygon is complete. |
---|
[5897] | 631 | if verbose is True: |
---|
[7317] | 632 | log.critical(' Stop criterion fulfilled at point %s' |
---|
| 633 | % str(p1)) |
---|
| 634 | log.critical(str(polygon)) |
---|
[7276] | 635 | |
---|
[5897] | 636 | # We have completed the boundary polygon - yeehaa |
---|
[7276] | 637 | break |
---|
| 638 | else: |
---|
| 639 | # The point already visited is not the initial point |
---|
| 640 | # This would be a pathological triangle, but the |
---|
| 641 | # algorithm must be able to deal with this |
---|
| 642 | pass |
---|
| 643 | |
---|
[5897] | 644 | else: |
---|
[7276] | 645 | # We are still finding new points on the boundary |
---|
[5897] | 646 | point_registry[tuple(p1)] = len(point_registry) |
---|
[7276] | 647 | |
---|
| 648 | polygon.append(list(p1)) # De-numeric each point :-) |
---|
[5897] | 649 | p0 = p1 |
---|
| 650 | |
---|
| 651 | return polygon |
---|
| 652 | |
---|
| 653 | def check_integrity(self): |
---|
| 654 | """Check that triangles are internally consistent e.g. |
---|
| 655 | that area corresponds to edgelengths, that vertices |
---|
| 656 | are arranged in a counter-clockwise order, etc etc |
---|
| 657 | Neighbour structure will be checked by class Mesh |
---|
| 658 | """ |
---|
| 659 | |
---|
| 660 | from anuga.config import epsilon |
---|
| 661 | from anuga.utilities.numerical_tools import anglediff |
---|
| 662 | |
---|
| 663 | N = len(self) |
---|
| 664 | |
---|
| 665 | # Get x,y coordinates for all vertices for all triangles |
---|
| 666 | V = self.get_vertex_coordinates() |
---|
| 667 | |
---|
| 668 | # Check each triangle |
---|
| 669 | for i in range(N): |
---|
| 670 | |
---|
| 671 | x0, y0 = V[3*i, :] |
---|
| 672 | x1, y1 = V[3*i+1, :] |
---|
| 673 | x2, y2 = V[3*i+2, :] |
---|
[7276] | 674 | |
---|
[5897] | 675 | # Check that area hasn't been compromised |
---|
| 676 | area = self.areas[i] |
---|
[8219] | 677 | ref = -((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
---|
| 678 | msg = 'Triangle %i (%f,%f), (%f,%f), (%f, %f)' % (i, x0,y0,x1,y1,x2,y2) |
---|
| 679 | msg += 'Wrong area: %f %f'\ |
---|
| 680 | %(area, ref) |
---|
[5897] | 681 | assert abs((area - ref)/area) < epsilon, msg |
---|
| 682 | |
---|
[8219] | 683 | msg = 'Triangle %i (%f,%f), (%f,%f), (%f, %f)' % (i, x0,y0,x1,y1,x2,y2) |
---|
[8070] | 684 | msg += ' is degenerate: area == %f' % self.areas[i] |
---|
| 685 | assert area > 0.0, msg |
---|
| 686 | |
---|
[5897] | 687 | # Check that points are arranged in counter clock-wise order |
---|
| 688 | v0 = [x1-x0, y1-y0] |
---|
| 689 | v1 = [x2-x1, y2-y1] |
---|
| 690 | v2 = [x0-x2, y0-y2] |
---|
| 691 | a0 = anglediff(v1, v0) |
---|
| 692 | a1 = anglediff(v2, v1) |
---|
| 693 | a2 = anglediff(v0, v2) |
---|
| 694 | |
---|
| 695 | msg = '''Vertices (%s,%s), (%s,%s), (%s,%s) are not arranged |
---|
| 696 | in counter clockwise order''' %(x0, y0, x1, y1, x2, y2) |
---|
| 697 | assert a0 < pi and a1 < pi and a2 < pi, msg |
---|
| 698 | |
---|
| 699 | # Check that normals are orthogonal to edge vectors |
---|
| 700 | # Note that normal[k] lies opposite vertex k |
---|
| 701 | |
---|
| 702 | normal0 = self.normals[i, 0:2] |
---|
| 703 | normal1 = self.normals[i, 2:4] |
---|
| 704 | normal2 = self.normals[i, 4:6] |
---|
| 705 | |
---|
| 706 | for u, v in [ (v0, normal2), (v1, normal0), (v2, normal1) ]: |
---|
| 707 | |
---|
| 708 | # Normalise |
---|
[6145] | 709 | l_u = num.sqrt(u[0]*u[0] + u[1]*u[1]) |
---|
| 710 | l_v = num.sqrt(v[0]*v[0] + v[1]*v[1]) |
---|
[5897] | 711 | |
---|
| 712 | msg = 'Normal vector in triangle %d does not have unit length' %i |
---|
[6145] | 713 | assert num.allclose(l_v, 1), msg |
---|
[5897] | 714 | |
---|
| 715 | x = (u[0]*v[0] + u[1]*v[1])/l_u # Inner product |
---|
[7276] | 716 | |
---|
[5897] | 717 | msg = 'Normal vector (%f,%f) is not perpendicular to' %tuple(v) |
---|
| 718 | msg += ' edge (%f,%f) in triangle %d.' %(tuple(u) + (i,)) |
---|
[7276] | 719 | msg += ' Inner product is %e.' %x |
---|
[5897] | 720 | assert x < epsilon, msg |
---|
| 721 | |
---|
| 722 | |
---|
| 723 | |
---|
| 724 | |
---|
[6654] | 725 | # Check neighbour structure |
---|
[5897] | 726 | for i in range(N): |
---|
| 727 | # For each triangle |
---|
[7276] | 728 | |
---|
[5897] | 729 | for k, neighbour_id in enumerate(self.neighbours[i,:]): |
---|
| 730 | |
---|
| 731 | #Assert that my neighbour's neighbour is me |
---|
| 732 | #Boundaries need not fulfill this |
---|
| 733 | if neighbour_id >= 0: |
---|
| 734 | edge = self.neighbour_edges[i, k] |
---|
| 735 | msg = 'Triangle %d has neighbour %d but it does not point back. \n' %(i,neighbour_id) |
---|
| 736 | msg += 'Only points to (%s)' %(self.neighbours[neighbour_id,:]) |
---|
| 737 | assert self.neighbours[neighbour_id, edge] == i ,msg |
---|
| 738 | |
---|
| 739 | |
---|
| 740 | |
---|
| 741 | #Check that all boundaries have |
---|
| 742 | # unique, consecutive, negative indices |
---|
| 743 | |
---|
| 744 | #L = len(self.boundary) |
---|
| 745 | #for i in range(L): |
---|
| 746 | # id, edge = self.boundary_segments[i] |
---|
| 747 | # assert self.neighbours[id, edge] == -i-1 |
---|
| 748 | |
---|
| 749 | |
---|
| 750 | #NOTE: This assert doesn't hold true if there are internal boundaries |
---|
| 751 | #FIXME: Look into this further. |
---|
| 752 | #FIXME (Ole): In pyvolution mark 3 this is OK again |
---|
| 753 | #NOTE: No longer works because neighbour structure is modified by |
---|
| 754 | # domain set_boundary. |
---|
| 755 | #for id, edge in self.boundary: |
---|
| 756 | # assert self.neighbours[id,edge] < 0 |
---|
| 757 | # |
---|
| 758 | #NOTE (Ole): I reckon this was resolved late 2004? |
---|
| 759 | # |
---|
| 760 | #See domain.set_boundary |
---|
| 761 | |
---|
| 762 | |
---|
| 763 | |
---|
| 764 | #Check integrity of inverted triangle structure |
---|
| 765 | |
---|
| 766 | V = self.vertex_value_indices[:] #Take a copy |
---|
[6145] | 767 | V = num.sort(V) |
---|
| 768 | assert num.allclose(V, range(3*N)) |
---|
[5897] | 769 | |
---|
[6145] | 770 | assert num.sum(self.number_of_triangles_per_node) ==\ |
---|
| 771 | len(self.vertex_value_indices) |
---|
[5897] | 772 | |
---|
| 773 | # Check number of triangles per node |
---|
| 774 | count = [0]*self.number_of_nodes |
---|
| 775 | for triangle in self.triangles: |
---|
| 776 | for i in triangle: |
---|
| 777 | count[i] += 1 |
---|
| 778 | |
---|
[6145] | 779 | assert num.allclose(count, self.number_of_triangles_per_node) |
---|
[5897] | 780 | |
---|
| 781 | |
---|
| 782 | # Check integrity of vertex_value_indices |
---|
| 783 | current_node = 0 |
---|
| 784 | k = 0 # Track triangles touching on node |
---|
| 785 | for index in self.vertex_value_indices: |
---|
| 786 | |
---|
| 787 | if self.number_of_triangles_per_node[current_node] == 0: |
---|
| 788 | # Node is lone - i.e. not part of the mesh |
---|
| 789 | continue |
---|
[7276] | 790 | |
---|
[5897] | 791 | k += 1 |
---|
[7276] | 792 | |
---|
[5897] | 793 | volume_id = index / 3 |
---|
| 794 | vertex_id = index % 3 |
---|
[7276] | 795 | |
---|
[5897] | 796 | msg = 'Triangle %d, vertex %d points to %d. Should have been %d'\ |
---|
| 797 | %(volume_id, vertex_id, self.triangles[volume_id, vertex_id], current_node) |
---|
| 798 | assert self.triangles[volume_id, vertex_id] == current_node, msg |
---|
[7276] | 799 | |
---|
[5897] | 800 | if self.number_of_triangles_per_node[current_node] == k: |
---|
| 801 | # Move on to next node |
---|
| 802 | k = 0 |
---|
| 803 | current_node += 1 |
---|
| 804 | |
---|
| 805 | |
---|
| 806 | def get_lone_vertices(self): |
---|
| 807 | """Return a list of vertices that are not connected to any triangles. |
---|
| 808 | |
---|
| 809 | """ |
---|
| 810 | return self.lone_vertices |
---|
| 811 | |
---|
| 812 | def get_centroid_coordinates(self, absolute=False): |
---|
| 813 | """Return all centroid coordinates. |
---|
| 814 | Return all centroid coordinates for all triangles as an Nx2 array |
---|
| 815 | (ordered as x0, y0 for each triangle) |
---|
| 816 | |
---|
| 817 | Boolean keyword argument absolute determines whether coordinates |
---|
| 818 | are to be made absolute by taking georeference into account |
---|
| 819 | Default is False as many parts of ANUGA expects relative coordinates. |
---|
| 820 | """ |
---|
| 821 | |
---|
| 822 | V = self.centroid_coordinates |
---|
| 823 | if absolute is True: |
---|
| 824 | if not self.geo_reference.is_absolute(): |
---|
| 825 | V = self.geo_reference.get_absolute(V) |
---|
[7276] | 826 | |
---|
[5897] | 827 | return V |
---|
| 828 | |
---|
[7276] | 829 | |
---|
[5897] | 830 | def get_radii(self): |
---|
| 831 | """Return all radii. |
---|
| 832 | Return radius of inscribed cirle for all triangles |
---|
| 833 | """ |
---|
[7276] | 834 | return self.radii |
---|
[5897] | 835 | |
---|
| 836 | |
---|
| 837 | |
---|
| 838 | def statistics(self): |
---|
| 839 | """Output statistics about mesh |
---|
| 840 | """ |
---|
| 841 | |
---|
| 842 | from anuga.utilities.numerical_tools import histogram, create_bins |
---|
| 843 | |
---|
| 844 | vertex_coordinates = self.vertex_coordinates # Relative coordinates |
---|
| 845 | areas = self.areas |
---|
| 846 | x = vertex_coordinates[:,0] |
---|
| 847 | y = vertex_coordinates[:,1] |
---|
| 848 | |
---|
| 849 | |
---|
| 850 | #Setup 10 bins for area histogram |
---|
| 851 | bins = create_bins(areas, 10) |
---|
| 852 | #m = max(areas) |
---|
| 853 | #bins = arange(0., m, m/10) |
---|
| 854 | hist = histogram(areas, bins) |
---|
| 855 | |
---|
| 856 | str = '------------------------------------------------\n' |
---|
| 857 | str += 'Mesh statistics:\n' |
---|
| 858 | str += ' Number of triangles = %d\n' %len(self) |
---|
| 859 | str += ' Extent [m]:\n' |
---|
| 860 | str += ' x in [%f, %f]\n' %(min(x), max(x)) |
---|
| 861 | str += ' y in [%f, %f]\n' %(min(y), max(y)) |
---|
| 862 | str += ' Areas [m^2]:\n' |
---|
| 863 | str += ' A in [%f, %f]\n' %(min(areas), max(areas)) |
---|
[7276] | 864 | str += ' number of distinct areas: %d\n' %(len(areas)) |
---|
[5897] | 865 | str += ' Histogram:\n' |
---|
| 866 | |
---|
| 867 | hi = bins[0] |
---|
| 868 | for i, count in enumerate(hist): |
---|
| 869 | lo = hi |
---|
| 870 | if i+1 < len(bins): |
---|
[7276] | 871 | #Open upper interval |
---|
[5897] | 872 | hi = bins[i+1] |
---|
[7276] | 873 | str += ' [%f, %f[: %d\n' %(lo, hi, count) |
---|
[5897] | 874 | else: |
---|
| 875 | #Closed upper interval |
---|
| 876 | hi = max(areas) |
---|
| 877 | str += ' [%f, %f]: %d\n' %(lo, hi, count) |
---|
| 878 | |
---|
| 879 | N = len(areas) |
---|
| 880 | if N > 10: |
---|
| 881 | str += ' Percentiles (10%):\n' |
---|
| 882 | areas = areas.tolist() |
---|
| 883 | areas.sort() |
---|
| 884 | |
---|
| 885 | k = 0 |
---|
| 886 | lower = min(areas) |
---|
[7276] | 887 | for i, a in enumerate(areas): |
---|
| 888 | if i % (N/10) == 0 and i != 0: #For every 10% of the sorted areas |
---|
[5897] | 889 | str += ' %d triangles in [%f, %f]\n' %(i-k, lower, a) |
---|
| 890 | lower = a |
---|
| 891 | k = i |
---|
[7276] | 892 | |
---|
[5897] | 893 | str += ' %d triangles in [%f, %f]\n'\ |
---|
[7276] | 894 | %(N-k, lower, max(areas)) |
---|
| 895 | |
---|
| 896 | |
---|
[5897] | 897 | str += ' Boundary:\n' |
---|
| 898 | str += ' Number of boundary segments == %d\n' %(len(self.boundary)) |
---|
[7276] | 899 | str += ' Boundary tags == %s\n' %self.get_boundary_tags() |
---|
[5897] | 900 | str += '------------------------------------------------\n' |
---|
| 901 | |
---|
[7276] | 902 | |
---|
[5897] | 903 | return str |
---|
| 904 | |
---|
[7276] | 905 | |
---|
[5897] | 906 | def get_triangle_containing_point(self, point): |
---|
[6654] | 907 | """Return triangle id for triangle containing specified point (x,y) |
---|
[5897] | 908 | |
---|
| 909 | If point isn't within mesh, raise exception |
---|
| 910 | |
---|
| 911 | """ |
---|
[7276] | 912 | |
---|
[5897] | 913 | # FIXME(Ole): This function is currently brute force |
---|
| 914 | # because I needed it for diagnostics. |
---|
| 915 | # We should make it fast - probably based on the |
---|
| 916 | # quad tree structure. |
---|
[7711] | 917 | from anuga.geometry.polygon import is_outside_polygon,\ |
---|
[5897] | 918 | is_inside_polygon |
---|
| 919 | |
---|
| 920 | polygon = self.get_boundary_polygon() |
---|
[7276] | 921 | |
---|
[5897] | 922 | if is_outside_polygon(point, polygon): |
---|
| 923 | msg = 'Point %s is outside mesh' %str(point) |
---|
[8124] | 924 | raise Exception(msg) |
---|
[5897] | 925 | |
---|
| 926 | |
---|
| 927 | V = self.get_vertex_coordinates(absolute=True) |
---|
| 928 | |
---|
| 929 | # FIXME: Horrible brute force |
---|
| 930 | for i, triangle in enumerate(self.triangles): |
---|
| 931 | poly = V[3*i:3*i+3] |
---|
| 932 | |
---|
| 933 | if is_inside_polygon(point, poly, closed=True): |
---|
| 934 | return i |
---|
[7276] | 935 | |
---|
[7968] | 936 | msg = 'Point %s not found within a triangle' %str(point) |
---|
[8124] | 937 | raise Exception(msg) |
---|
[5897] | 938 | |
---|
| 939 | |
---|
| 940 | |
---|
[7968] | 941 | |
---|
[5897] | 942 | def get_intersecting_segments(self, polyline, |
---|
| 943 | use_cache=False, |
---|
| 944 | verbose=False): |
---|
| 945 | """Find edges intersected by polyline |
---|
| 946 | |
---|
| 947 | Input: |
---|
| 948 | polyline - list of points forming a segmented line |
---|
| 949 | use_cache |
---|
| 950 | verbose |
---|
| 951 | |
---|
| 952 | Output: |
---|
| 953 | list of instances of class Triangle_intersection |
---|
| 954 | |
---|
| 955 | The polyline may break inside any triangle causing multiple |
---|
| 956 | segments per triangle - consequently the same triangle may |
---|
| 957 | appear in several entries. |
---|
| 958 | |
---|
| 959 | If a polyline segment coincides with a triangle edge, |
---|
| 960 | the the entire shared segment will be used. |
---|
| 961 | Onle one of the triangles thus intersected will be used and that |
---|
| 962 | is the first one encountered. |
---|
| 963 | |
---|
| 964 | Intersections with single vertices are ignored. |
---|
| 965 | |
---|
| 966 | Resulting segments are unsorted |
---|
| 967 | """ |
---|
[7276] | 968 | |
---|
[5897] | 969 | V = self.get_vertex_coordinates() |
---|
| 970 | N = len(self) |
---|
[7276] | 971 | |
---|
[5897] | 972 | # Adjust polyline to mesh spatial origin |
---|
| 973 | polyline = self.geo_reference.get_relative(polyline) |
---|
| 974 | |
---|
| 975 | if use_cache is True: |
---|
| 976 | segments = cache(get_intersecting_segments, |
---|
[7276] | 977 | (V, N, polyline), |
---|
[5897] | 978 | {'verbose': verbose}, |
---|
| 979 | verbose=verbose) |
---|
[7276] | 980 | else: |
---|
[5897] | 981 | segments = get_intersecting_segments(V, N, polyline, |
---|
| 982 | verbose=verbose) |
---|
| 983 | |
---|
[7276] | 984 | |
---|
[5897] | 985 | return segments |
---|
| 986 | |
---|
[7276] | 987 | |
---|
| 988 | |
---|
[5897] | 989 | def get_triangle_neighbours(self, tri_id): |
---|
| 990 | """ Given a triangle id, Return an array of the |
---|
| 991 | 3 neighbour triangle id's. |
---|
| 992 | |
---|
| 993 | Negative returned triangle id's represent a boundary as a neighbour. |
---|
[7276] | 994 | |
---|
[5897] | 995 | If the given triangle id is bad, return an empty list. |
---|
| 996 | """ |
---|
| 997 | |
---|
| 998 | try: |
---|
| 999 | return self.neighbours[tri_id,:] |
---|
| 1000 | except IndexError: |
---|
| 1001 | return [] |
---|
| 1002 | |
---|
[7276] | 1003 | |
---|
[5897] | 1004 | def get_interpolation_object(self): |
---|
| 1005 | """Get object I that will allow linear interpolation using this mesh |
---|
[7276] | 1006 | |
---|
| 1007 | This is a time consuming process but it needs only to be |
---|
[5897] | 1008 | once for the mesh. |
---|
[7276] | 1009 | |
---|
| 1010 | Interpolation can then be done using |
---|
| 1011 | |
---|
| 1012 | result = I.interpolate_block(vertex_values, interpolation_points) |
---|
| 1013 | |
---|
[5897] | 1014 | where vertex values have been obtained from a quantity using |
---|
| 1015 | vertex_values, triangles = self.get_vertex_values() |
---|
| 1016 | """ |
---|
| 1017 | |
---|
| 1018 | if hasattr(self, 'interpolation_object'): |
---|
| 1019 | I = self.interpolation_object |
---|
| 1020 | else: |
---|
| 1021 | from anuga.fit_interpolate.interpolate import Interpolate |
---|
[7276] | 1022 | |
---|
| 1023 | # Get discontinuous mesh - this will match internal |
---|
[5897] | 1024 | # representation of vertex values |
---|
| 1025 | triangles = self.get_disconnected_triangles() |
---|
| 1026 | vertex_coordinates = self.get_vertex_coordinates() |
---|
| 1027 | |
---|
| 1028 | I = Interpolate(vertex_coordinates, triangles) |
---|
| 1029 | self.interpolation_object = I |
---|
| 1030 | |
---|
[7276] | 1031 | return I |
---|
| 1032 | |
---|
| 1033 | |
---|
[5897] | 1034 | class Triangle_intersection: |
---|
| 1035 | """Store information about line segments intersecting a triangle |
---|
[7276] | 1036 | |
---|
[5897] | 1037 | Attributes are |
---|
| 1038 | |
---|
| 1039 | segment: Line segment intersecting triangle [[x0,y0], [x1, y1]] |
---|
| 1040 | normal: [a,b] right hand normal to segment |
---|
| 1041 | length: Length of intersecting segment |
---|
| 1042 | triangle_id: id (in mesh) of triangle being intersected |
---|
| 1043 | |
---|
| 1044 | """ |
---|
| 1045 | |
---|
| 1046 | |
---|
| 1047 | def __init__(self, |
---|
| 1048 | segment=None, |
---|
| 1049 | normal=None, |
---|
| 1050 | length=None, |
---|
| 1051 | triangle_id=None): |
---|
[7276] | 1052 | self.segment = segment |
---|
[5897] | 1053 | self.normal = normal |
---|
| 1054 | self.length = length |
---|
| 1055 | self.triangle_id = triangle_id |
---|
| 1056 | |
---|
[7276] | 1057 | |
---|
[5897] | 1058 | def __repr__(self): |
---|
| 1059 | s = 'Triangle_intersection(' |
---|
| 1060 | s += 'segment=%s, normal=%s, length=%s, triangle_id=%s)'\ |
---|
| 1061 | %(self.segment, |
---|
| 1062 | self.normal, |
---|
| 1063 | self.length, |
---|
| 1064 | self.triangle_id) |
---|
[7276] | 1065 | |
---|
[5897] | 1066 | return s |
---|
| 1067 | |
---|
| 1068 | |
---|
[7276] | 1069 | |
---|
[5897] | 1070 | def _get_intersecting_segments(V, N, line, |
---|
| 1071 | verbose=False): |
---|
| 1072 | """Find edges intersected by line |
---|
| 1073 | |
---|
| 1074 | Input: |
---|
| 1075 | V: Vertex coordinates as obtained by mesh.get_vertex_coordinates() |
---|
| 1076 | N: Number of triangles in mesh |
---|
| 1077 | line - list of two points forming a segmented line |
---|
| 1078 | verbose |
---|
| 1079 | Output: |
---|
| 1080 | list of instances of class Triangle_intersection |
---|
| 1081 | |
---|
| 1082 | This method is used by the public method |
---|
| 1083 | get_intersecting_segments(self, polyline) which also contains |
---|
| 1084 | more documentation. |
---|
| 1085 | """ |
---|
| 1086 | |
---|
[7711] | 1087 | from anuga.geometry.polygon import intersection |
---|
| 1088 | from anuga.geometry.polygon import is_inside_polygon |
---|
[7276] | 1089 | |
---|
[5897] | 1090 | msg = 'Line segment must contain exactly two points' |
---|
| 1091 | assert len(line) == 2, msg |
---|
| 1092 | |
---|
| 1093 | # Origin of intersecting line to be used for |
---|
| 1094 | # establishing direction |
---|
| 1095 | xi0 = line[0][0] |
---|
| 1096 | eta0 = line[0][1] |
---|
| 1097 | |
---|
[7276] | 1098 | |
---|
[5897] | 1099 | # Check intersection with edge segments for all triangles |
---|
| 1100 | # FIXME (Ole): This should be implemented in C |
---|
| 1101 | triangle_intersections={} # Keep track of segments already done |
---|
| 1102 | for i in range(N): |
---|
| 1103 | # Get nodes and edge segments for each triangle |
---|
| 1104 | x0, y0 = V[3*i, :] |
---|
| 1105 | x1, y1 = V[3*i+1, :] |
---|
| 1106 | x2, y2 = V[3*i+2, :] |
---|
| 1107 | |
---|
[7276] | 1108 | |
---|
[5897] | 1109 | edge_segments = [[[x0,y0], [x1, y1]], |
---|
| 1110 | [[x1,y1], [x2, y2]], |
---|
| 1111 | [[x2,y2], [x0, y0]]] |
---|
| 1112 | |
---|
| 1113 | # Find segments that are intersected by line |
---|
[7276] | 1114 | |
---|
[5897] | 1115 | intersections = {} # Use dictionary to record points only once |
---|
| 1116 | for edge in edge_segments: |
---|
| 1117 | |
---|
| 1118 | status, value = intersection(line, edge) |
---|
[7317] | 1119 | #if value is not None: log.critical('Triangle %d, status=%s, ' |
---|
| 1120 | # 'value=%s' |
---|
| 1121 | # % (i, str(status), str(value))) |
---|
[7276] | 1122 | |
---|
[5897] | 1123 | if status == 1: |
---|
| 1124 | # Normal intersection of one edge or vertex |
---|
[7276] | 1125 | intersections[tuple(value)] = i |
---|
[5897] | 1126 | |
---|
| 1127 | # Exclude singular intersections with vertices |
---|
| 1128 | #if not(allclose(value, edge[0]) or\ |
---|
| 1129 | # allclose(value, edge[1])): |
---|
| 1130 | # intersections.append(value) |
---|
| 1131 | |
---|
| 1132 | if status == 2: |
---|
| 1133 | # Edge is sharing a segment with line |
---|
| 1134 | |
---|
| 1135 | # This is usually covered by the two |
---|
| 1136 | # vertices that would have been picked up |
---|
| 1137 | # under status == 1. |
---|
| 1138 | # However, if coinciding line stops partway |
---|
| 1139 | # along this edge, it will be recorded here. |
---|
| 1140 | intersections[tuple(value[0,:])] = i |
---|
[7276] | 1141 | intersections[tuple(value[1,:])] = i |
---|
[5897] | 1142 | |
---|
[7276] | 1143 | |
---|
[5897] | 1144 | if len(intersections) == 1: |
---|
| 1145 | # Check if either line end point lies fully within this triangle |
---|
| 1146 | # If this is the case accept that as one end of the intersecting |
---|
| 1147 | # segment |
---|
| 1148 | |
---|
| 1149 | poly = V[3*i:3*i+3] |
---|
| 1150 | if is_inside_polygon(line[1], poly, closed=False): |
---|
| 1151 | intersections[tuple(line[1])] = i |
---|
| 1152 | elif is_inside_polygon(line[0], poly, closed=False): |
---|
[7276] | 1153 | intersections[tuple(line[0])] = i |
---|
[5897] | 1154 | else: |
---|
[7276] | 1155 | # Ignore situations where one vertex is touch, for instance |
---|
[5897] | 1156 | continue |
---|
| 1157 | |
---|
| 1158 | |
---|
| 1159 | msg = 'There can be only two or no intersections' |
---|
| 1160 | assert len(intersections) in [0,2], msg |
---|
| 1161 | |
---|
| 1162 | |
---|
| 1163 | if len(intersections) == 2: |
---|
| 1164 | |
---|
| 1165 | # Calculate attributes for this segment |
---|
| 1166 | |
---|
| 1167 | |
---|
| 1168 | # End points of intersecting segment |
---|
| 1169 | points = intersections.keys() |
---|
| 1170 | x0, y0 = points[0] |
---|
| 1171 | x1, y1 = points[1] |
---|
| 1172 | |
---|
| 1173 | |
---|
| 1174 | # Determine which end point is closer to the origin of the line |
---|
| 1175 | # This is necessary for determining the direction of |
---|
| 1176 | # the line and the normals |
---|
| 1177 | |
---|
| 1178 | # Distances from line origin to the two intersections |
---|
[7276] | 1179 | z0 = num.array([x0 - xi0, y0 - eta0], num.float) |
---|
| 1180 | z1 = num.array([x1 - xi0, y1 - eta0], num.float) |
---|
| 1181 | d0 = num.sqrt(num.sum(z0**2)) |
---|
[6145] | 1182 | d1 = num.sqrt(num.sum(z1**2)) |
---|
[7276] | 1183 | |
---|
[5897] | 1184 | if d1 < d0: |
---|
| 1185 | # Swap |
---|
| 1186 | xi, eta = x0, y0 |
---|
| 1187 | x0, y0 = x1, y1 |
---|
| 1188 | x1, y1 = xi, eta |
---|
| 1189 | |
---|
| 1190 | # (x0,y0) is now the origin of the intersecting segment |
---|
| 1191 | |
---|
[7276] | 1192 | |
---|
[5897] | 1193 | # Normal direction: |
---|
| 1194 | # Right hand side relative to line direction |
---|
[7276] | 1195 | vector = num.array([x1 - x0, y1 - y0], num.float) # Segment vector |
---|
[6145] | 1196 | length = num.sqrt(num.sum(vector**2)) # Segment length |
---|
[7276] | 1197 | normal = num.array([vector[1], -vector[0]], num.float)/length |
---|
[5897] | 1198 | |
---|
| 1199 | |
---|
[7276] | 1200 | segment = ((x0,y0), (x1, y1)) |
---|
[5897] | 1201 | T = Triangle_intersection(segment=segment, |
---|
| 1202 | normal=normal, |
---|
| 1203 | length=length, |
---|
| 1204 | triangle_id=i) |
---|
| 1205 | |
---|
| 1206 | |
---|
| 1207 | # Add segment unless it was done earlier |
---|
[7276] | 1208 | if not triangle_intersections.has_key(segment): |
---|
[5897] | 1209 | triangle_intersections[segment] = T |
---|
| 1210 | |
---|
| 1211 | |
---|
[7276] | 1212 | # Return segments as a list |
---|
[5897] | 1213 | return triangle_intersections.values() |
---|
| 1214 | |
---|
| 1215 | |
---|
| 1216 | def get_intersecting_segments(V, N, polyline, |
---|
[7276] | 1217 | verbose=False): |
---|
[5897] | 1218 | """Internal function to find edges intersected by Polyline |
---|
[7276] | 1219 | |
---|
[5897] | 1220 | Input: |
---|
| 1221 | V: Vertex coordinates as obtained by mesh.get_vertex_coordinates() |
---|
| 1222 | N: Number of triangles in mesh |
---|
[7276] | 1223 | polyline - list of points forming a segmented line |
---|
[5897] | 1224 | verbose |
---|
| 1225 | Output: |
---|
| 1226 | list of instances of class Triangle_intersection |
---|
| 1227 | |
---|
| 1228 | This method is used by the public method |
---|
| 1229 | get_intersecting_segments(self, polyline) which also contains |
---|
[7276] | 1230 | more documentation. |
---|
[5897] | 1231 | """ |
---|
| 1232 | |
---|
| 1233 | msg = 'Polyline must contain at least two points' |
---|
| 1234 | assert len(polyline) >= 2, msg |
---|
[7276] | 1235 | |
---|
| 1236 | |
---|
[5897] | 1237 | # For all segments in polyline |
---|
| 1238 | triangle_intersections = [] |
---|
| 1239 | for i, point0 in enumerate(polyline[:-1]): |
---|
| 1240 | |
---|
| 1241 | point1 = polyline[i+1] |
---|
| 1242 | if verbose: |
---|
[7317] | 1243 | log.critical('Extracting mesh intersections from line:') |
---|
| 1244 | log.critical('(%.2f, %.2f) - (%.2f, %.2f)' |
---|
| 1245 | % (point0[0], point0[1], point1[0], point1[1])) |
---|
[7276] | 1246 | |
---|
[5897] | 1247 | line = [point0, point1] |
---|
| 1248 | triangle_intersections += _get_intersecting_segments(V, N, line, |
---|
| 1249 | verbose=verbose) |
---|
| 1250 | |
---|
| 1251 | |
---|
| 1252 | msg = 'No segments found' |
---|
| 1253 | assert len(triangle_intersections) > 0, msg |
---|
[7276] | 1254 | |
---|
| 1255 | |
---|
[5897] | 1256 | return triangle_intersections |
---|
| 1257 | |
---|
[7276] | 1258 | |
---|
| 1259 | |
---|
| 1260 | |
---|
| 1261 | |
---|
[5897] | 1262 | def segment_midpoints(segments): |
---|
| 1263 | """Calculate midpoints of all segments |
---|
[7276] | 1264 | |
---|
[5897] | 1265 | Inputs: |
---|
| 1266 | segments: List of instances of class Segment |
---|
[7276] | 1267 | |
---|
[5897] | 1268 | Ouputs: |
---|
| 1269 | midpoints: List of points |
---|
| 1270 | """ |
---|
[7276] | 1271 | |
---|
[5897] | 1272 | midpoints = [] |
---|
| 1273 | msg = 'Elements of input list to segment_midpoints must be of class Triangle_intersection' |
---|
| 1274 | for segment in segments: |
---|
| 1275 | assert isinstance(segment, Triangle_intersection), msg |
---|
[7276] | 1276 | |
---|
| 1277 | midpoint = num.sum(num.array(segment.segment, num.float), axis=0)/2 |
---|
[5897] | 1278 | midpoints.append(midpoint) |
---|
| 1279 | |
---|
| 1280 | return midpoints |
---|
[7276] | 1281 | |
---|
| 1282 | |
---|
| 1283 | |
---|