[7276] | 1 | import copy |
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| 2 | import numpy as num |
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[5897] | 3 | |
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| 4 | from anuga.coordinate_transforms.geo_reference import Geo_reference |
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[7317] | 5 | import anuga.utilities.log as log |
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[5897] | 6 | |
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| 7 | class General_mesh: |
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| 8 | """Collection of 2D triangular elements |
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| 9 | |
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| 10 | A triangular element is defined in terms of three vertex ids, |
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| 11 | ordered counter clock-wise, each corresponding to a given node |
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| 12 | which is represented as a coordinate set (x,y). |
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| 13 | Vertices from different triangles can point to the same node. |
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[7276] | 14 | The nodes are implemented as an Nx2 numeric array containing the |
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[5897] | 15 | x and y coordinates. |
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| 16 | |
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| 17 | |
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| 18 | To instantiate: |
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| 19 | Mesh(nodes, triangles) |
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| 20 | |
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| 21 | where |
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| 22 | |
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[7276] | 23 | nodes is either a list of 2-tuples or an Nx2 numeric array of |
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[5897] | 24 | floats representing all x, y coordinates in the mesh. |
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| 25 | |
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[7276] | 26 | triangles is either a list of 3-tuples or an Mx3 numeric array of |
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[5897] | 27 | integers representing indices of all vertices in the mesh. |
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| 28 | Each vertex is identified by its index i in [0, N-1]. |
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| 29 | |
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| 30 | |
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| 31 | Example: |
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| 32 | |
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| 33 | a = [0.0, 0.0] |
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| 34 | b = [0.0, 2.0] |
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| 35 | c = [2.0,0.0] |
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| 36 | e = [2.0, 2.0] |
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| 37 | |
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| 38 | nodes = [a, b, c, e] |
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| 39 | triangles = [ [1,0,2], [1,2,3] ] # bac, bce |
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| 40 | |
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[7276] | 41 | # Create mesh with two triangles: bac and bce |
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[5897] | 42 | mesh = Mesh(nodes, triangles) |
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| 43 | |
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| 44 | |
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| 45 | |
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| 46 | Other: |
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| 47 | |
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| 48 | In addition mesh computes an Mx6 array called vertex_coordinates. |
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| 49 | This structure is derived from coordinates and contains for each |
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| 50 | triangle the three x,y coordinates at the vertices. |
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| 51 | |
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| 52 | See neighbourmesh.py for a specialisation of the general mesh class |
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| 53 | which includes information about neighbours and the mesh boundary. |
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| 54 | |
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| 55 | The mesh object is purely geometrical and contains no information |
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| 56 | about quantities defined on the mesh. |
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| 57 | |
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| 58 | """ |
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| 59 | |
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[7276] | 60 | # FIXME: It would be a good idea to use geospatial data as an alternative |
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| 61 | # input |
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| 62 | def __init__(self, |
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| 63 | nodes, |
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| 64 | triangles, |
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| 65 | geo_reference=None, |
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[5897] | 66 | verbose=False): |
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| 67 | """Build triangular 2d mesh from nodes and triangle information |
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| 68 | |
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| 69 | Input: |
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[7276] | 70 | |
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[5897] | 71 | nodes: x,y coordinates represented as a sequence of 2-tuples or |
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[7276] | 72 | a Nx2 numeric array of floats. |
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| 73 | |
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| 74 | triangles: sequence of 3-tuples or Mx3 numeric array of |
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[5897] | 75 | non-negative integers representing indices into |
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| 76 | the nodes array. |
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[7276] | 77 | |
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[5897] | 78 | georeference (optional): If specified coordinates are |
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| 79 | assumed to be relative to this origin. |
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| 80 | |
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| 81 | |
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| 82 | """ |
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| 83 | |
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[7317] | 84 | if verbose: log.critical('General_mesh: Building basic mesh structure ' |
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| 85 | 'in ANUGA domain') |
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[5897] | 86 | |
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[7276] | 87 | self.triangles = num.array(triangles, num.int) |
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| 88 | self.nodes = num.array(nodes, num.float) |
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[5897] | 89 | |
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[7276] | 90 | # Register number of elements and nodes |
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[5897] | 91 | self.number_of_triangles = N = self.triangles.shape[0] |
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[7276] | 92 | self.number_of_nodes = self.nodes.shape[0] |
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[5897] | 93 | |
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| 94 | |
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| 95 | # FIXME: this stores a geo_reference, but when coords are returned |
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| 96 | # This geo_ref is not taken into account! |
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| 97 | if geo_reference is None: |
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[7276] | 98 | self.geo_reference = Geo_reference() # Use defaults |
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[5897] | 99 | else: |
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| 100 | self.geo_reference = geo_reference |
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| 101 | |
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| 102 | # Input checks |
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[7276] | 103 | msg = ('Triangles must an Mx3 numeric array or a sequence of 3-tuples. ' |
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| 104 | 'The supplied array has the shape: %s' |
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| 105 | % str(self.triangles.shape)) |
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[5897] | 106 | assert len(self.triangles.shape) == 2, msg |
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| 107 | |
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[7276] | 108 | msg = ('Nodes must an Nx2 numeric array or a sequence of 2-tuples' |
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| 109 | 'The supplied array has the shape: %s' % str(self.nodes.shape)) |
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[5897] | 110 | assert len(self.nodes.shape) == 2, msg |
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| 111 | |
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| 112 | msg = 'Vertex indices reference non-existing coordinate sets' |
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[7276] | 113 | assert num.max(self.triangles) < self.nodes.shape[0], msg |
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[5897] | 114 | |
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| 115 | # FIXME: Maybe move to statistics? |
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| 116 | # Or use with get_extent |
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[7276] | 117 | xy_extent = [min(self.nodes[:,0]), min(self.nodes[:,1]), |
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| 118 | max(self.nodes[:,0]), max(self.nodes[:,1])] |
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[5897] | 119 | |
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[7276] | 120 | self.xy_extent = num.array(xy_extent, num.float) |
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[5897] | 121 | |
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| 122 | # Allocate space for geometric quantities |
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[7276] | 123 | self.normals = num.zeros((N, 6), num.float) |
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| 124 | self.areas = num.zeros(N, num.float) |
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| 125 | self.edgelengths = num.zeros((N, 3), num.float) |
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[5897] | 126 | |
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[7484] | 127 | # Get x,y coordinates for all triangle vertices and store |
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[5897] | 128 | self.vertex_coordinates = V = self.compute_vertex_coordinates() |
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| 129 | |
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[7484] | 130 | # Get x,y coordinates for all triangle edge midpoints and store |
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| 131 | self.edge_midpoint_coordinates = self.compute_edge_midpoint_coordinates() |
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| 132 | |
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[5897] | 133 | # Initialise each triangle |
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| 134 | if verbose: |
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[7317] | 135 | log.critical('General_mesh: Computing areas, normals ' |
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| 136 | 'and edgelengths') |
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[7276] | 137 | |
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[5897] | 138 | for i in range(N): |
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[7317] | 139 | if verbose and i % ((N+10)/10) == 0: log.critical('(%d/%d)' % (i, N)) |
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[7276] | 140 | |
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[5897] | 141 | x0, y0 = V[3*i, :] |
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| 142 | x1, y1 = V[3*i+1, :] |
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[7276] | 143 | x2, y2 = V[3*i+2, :] |
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[5897] | 144 | |
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[8105] | 145 | |
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| 146 | i0 = self.triangles[i][0] |
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| 147 | i1 = self.triangles[i][1] |
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| 148 | i2 = self.triangles[i][2] |
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| 149 | |
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| 150 | assert x0 == self.nodes[i0][0] |
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| 151 | assert y0 == self.nodes[i0][1] |
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| 152 | |
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| 153 | assert x1 == self.nodes[i1][0] |
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| 154 | assert y1 == self.nodes[i1][1] |
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| 155 | |
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| 156 | assert x2 == self.nodes[i2][0] |
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| 157 | assert y2 == self.nodes[i2][1] |
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| 158 | |
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[5897] | 159 | # Area |
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[7276] | 160 | self.areas[i] = abs((x1*y0-x0*y1) + (x2*y1-x1*y2) + (x0*y2-x2*y0))/2 |
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[5897] | 161 | |
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[8105] | 162 | msg = 'Triangle %g (%f,%f), (%f,%f), (%f, %f)' % (i,x0,y0,x1,y1,x2,y2) |
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[7276] | 163 | msg += ' is degenerate: area == %f' % self.areas[i] |
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[5897] | 164 | assert self.areas[i] > 0.0, msg |
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| 165 | |
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| 166 | # Normals |
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| 167 | # The normal vectors |
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| 168 | # - point outward from each edge |
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| 169 | # - are orthogonal to the edge |
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| 170 | # - have unit length |
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| 171 | # - Are enumerated according to the opposite corner: |
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| 172 | # (First normal is associated with the edge opposite |
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| 173 | # the first vertex, etc) |
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| 174 | # - Stored as six floats n0x,n0y,n1x,n1y,n2x,n2y per triangle |
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[7276] | 175 | n0 = num.array([x2-x1, y2-y1], num.float) |
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[6145] | 176 | l0 = num.sqrt(num.sum(n0**2)) |
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[5897] | 177 | |
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[7276] | 178 | n1 = num.array([x0-x2, y0-y2], num.float) |
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[6145] | 179 | l1 = num.sqrt(num.sum(n1**2)) |
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[5897] | 180 | |
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[7276] | 181 | n2 = num.array([x1-x0, y1-y0], num.float) |
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[6145] | 182 | l2 = num.sqrt(num.sum(n2**2)) |
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[5897] | 183 | |
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| 184 | # Normalise |
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| 185 | n0 /= l0 |
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| 186 | n1 /= l1 |
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| 187 | n2 /= l2 |
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| 188 | |
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| 189 | # Compute and store |
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| 190 | self.normals[i, :] = [n0[1], -n0[0], |
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| 191 | n1[1], -n1[0], |
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| 192 | n2[1], -n2[0]] |
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| 193 | |
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| 194 | # Edgelengths |
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| 195 | self.edgelengths[i, :] = [l0, l1, l2] |
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| 196 | |
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[7276] | 197 | # Build structure listing which triangles belong to which node. |
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[7317] | 198 | if verbose: log.critical('Building inverted triangle structure') |
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[5897] | 199 | self.build_inverted_triangle_structure() |
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| 200 | |
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| 201 | def __len__(self): |
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| 202 | return self.number_of_triangles |
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| 203 | |
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| 204 | def __repr__(self): |
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[7276] | 205 | return ('Mesh: %d vertices, %d triangles' |
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| 206 | % (self.nodes.shape[0], len(self))) |
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[5897] | 207 | |
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| 208 | def get_normals(self): |
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| 209 | """Return all normal vectors. |
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[7276] | 210 | |
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[5897] | 211 | Return normal vectors for all triangles as an Nx6 array |
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| 212 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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| 213 | """ |
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[7276] | 214 | |
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[5897] | 215 | return self.normals |
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| 216 | |
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| 217 | def get_normal(self, i, j): |
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| 218 | """Return normal vector j of the i'th triangle. |
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[7276] | 219 | |
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[5897] | 220 | Return value is the numeric array slice [x, y] |
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| 221 | """ |
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[7276] | 222 | |
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[5897] | 223 | return self.normals[i, 2*j:2*j+2] |
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[6654] | 224 | |
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| 225 | def get_edgelength(self, i, j): |
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| 226 | """Return length of j'th edge of the i'th triangle. |
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| 227 | Return value is the numeric array slice [x, y] |
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| 228 | """ |
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| 229 | return self.edgelengths[i, j] |
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| 230 | |
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[5897] | 231 | |
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[7519] | 232 | def get_number_of_triangles(self): |
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| 233 | return self.number_of_triangles |
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| 234 | |
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| 235 | |
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[6191] | 236 | def get_number_of_nodes(self): |
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| 237 | return self.number_of_nodes |
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[7276] | 238 | |
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[7519] | 239 | |
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[5897] | 240 | def get_nodes(self, absolute=False): |
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| 241 | """Return all nodes in mesh. |
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| 242 | |
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| 243 | The nodes are ordered in an Nx2 array where N is the number of nodes. |
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| 244 | This is the same format they were provided in the constructor |
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| 245 | i.e. without any duplication. |
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| 246 | |
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| 247 | Boolean keyword argument absolute determines whether coordinates |
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| 248 | are to be made absolute by taking georeference into account |
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| 249 | Default is False as many parts of ANUGA expects relative coordinates. |
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[7276] | 250 | (To see which, switch to default absolute=True and run tests). |
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[5897] | 251 | """ |
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| 252 | |
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[8200] | 253 | N = self.number_of_nodes |
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[5897] | 254 | V = self.nodes[:N,:] |
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| 255 | if absolute is True: |
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| 256 | if not self.geo_reference.is_absolute(): |
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| 257 | V = self.geo_reference.get_absolute(V) |
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[7276] | 258 | |
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[5897] | 259 | return V |
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[7276] | 260 | |
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| 261 | def get_node(self, i, absolute=False): |
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[5897] | 262 | """Return node coordinates for triangle i. |
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| 263 | |
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| 264 | Boolean keyword argument absolute determines whether coordinates |
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| 265 | are to be made absolute by taking georeference into account |
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| 266 | Default is False as many parts of ANUGA expects relative coordinates. |
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[7276] | 267 | (To see which, switch to default absolute=True and run tests). |
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| 268 | |
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| 269 | Note: This method returns a modified _copy_ of the nodes slice if |
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| 270 | absolute is True. If absolute is False, just return the slice. |
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| 271 | This is related to the ensure_numeric() returning a copy problem. |
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[5897] | 272 | """ |
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| 273 | |
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| 274 | V = self.nodes[i,:] |
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| 275 | if absolute is True: |
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| 276 | if not self.geo_reference.is_absolute(): |
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[7276] | 277 | # get a copy so as not to modify the internal self.nodes array |
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| 278 | V = copy.copy(V) |
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| 279 | V += num.array([self.geo_reference.get_xllcorner(), |
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| 280 | self.geo_reference.get_yllcorner()], num.float) |
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| 281 | return V |
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[5897] | 282 | |
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[7276] | 283 | def get_vertex_coordinates(self, triangle_id=None, absolute=False): |
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| 284 | """Return vertex coordinates for all triangles. |
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| 285 | |
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[5897] | 286 | Return all vertex coordinates for all triangles as a 3*M x 2 array |
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| 287 | where the jth vertex of the ith triangle is located in row 3*i+j and |
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| 288 | M the number of triangles in the mesh. |
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| 289 | |
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| 290 | if triangle_id is specified (an integer) the 3 vertex coordinates |
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| 291 | for triangle_id are returned. |
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[7276] | 292 | |
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[5897] | 293 | Boolean keyword argument absolute determines whether coordinates |
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| 294 | are to be made absolute by taking georeference into account |
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| 295 | Default is False as many parts of ANUGA expects relative coordinates. |
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| 296 | """ |
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[7276] | 297 | |
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[5897] | 298 | V = self.vertex_coordinates |
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| 299 | |
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[7276] | 300 | if triangle_id is None: |
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[5897] | 301 | if absolute is True: |
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| 302 | if not self.geo_reference.is_absolute(): |
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| 303 | V = self.geo_reference.get_absolute(V) |
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| 304 | return V |
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| 305 | else: |
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| 306 | i = triangle_id |
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| 307 | msg = 'triangle_id must be an integer' |
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| 308 | assert int(i) == i, msg |
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| 309 | assert 0 <= i < self.number_of_triangles |
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[7276] | 310 | |
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| 311 | i3 = 3*i |
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[5897] | 312 | if absolute is True and not self.geo_reference.is_absolute(): |
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[6145] | 313 | offset=num.array([self.geo_reference.get_xllcorner(), |
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[7276] | 314 | self.geo_reference.get_yllcorner()], num.float) |
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[7498] | 315 | |
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| 316 | return V[i3:i3+3,:] + offset |
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[5897] | 317 | else: |
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[7498] | 318 | return V[i3:i3+3,:] |
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[5897] | 319 | |
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| 320 | def get_vertex_coordinate(self, i, j, absolute=False): |
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| 321 | """Return coordinates for vertex j of the i'th triangle. |
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| 322 | Return value is the numeric array slice [x, y] |
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| 323 | """ |
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| 324 | |
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| 325 | msg = 'vertex id j must be an integer in [0,1,2]' |
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| 326 | assert j in [0,1,2], msg |
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[7276] | 327 | |
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| 328 | V = self.get_vertex_coordinates(triangle_id=i, absolute=absolute) |
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[5897] | 329 | return V[j,:] |
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| 330 | |
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[7484] | 331 | |
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| 332 | |
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[5897] | 333 | def compute_vertex_coordinates(self): |
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| 334 | """Return all vertex coordinates for all triangles as a 3*M x 2 array |
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| 335 | where the jth vertex of the ith triangle is located in row 3*i+j. |
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| 336 | |
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| 337 | This function is used to precompute this important structure. Use |
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| 338 | get_vertex coordinates to retrieve the points. |
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| 339 | """ |
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| 340 | |
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| 341 | M = self.number_of_triangles |
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[7276] | 342 | vertex_coordinates = num.zeros((3*M, 2), num.float) |
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[5897] | 343 | |
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| 344 | for i in range(M): |
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| 345 | for j in range(3): |
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| 346 | k = self.triangles[i,j] # Index of vertex j in triangle i |
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| 347 | vertex_coordinates[3*i+j,:] = self.nodes[k] |
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| 348 | |
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| 349 | return vertex_coordinates |
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| 350 | |
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[7484] | 351 | |
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| 352 | def get_edge_midpoint_coordinates(self, triangle_id=None, absolute=False): |
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| 353 | """Return edge midpoint coordinates for all triangles or from particular triangle. |
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| 354 | |
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| 355 | Return all edge midpoint coordinates for all triangles as a 3*M x 2 array |
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| 356 | where the jth midpoint of the ith triangle is located in row 3*i+j and |
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| 357 | M the number of triangles in the mesh. |
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| 358 | |
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| 359 | if triangle_id is specified (an integer) the 3 midpoint coordinates |
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| 360 | for triangle_id are returned. |
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| 361 | |
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| 362 | Boolean keyword argument absolute determines whether coordinates |
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| 363 | are to be made absolute by taking georeference into account |
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| 364 | Default is False as many parts of ANUGA expects relative coordinates. |
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| 365 | """ |
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| 366 | |
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| 367 | E = self.edge_midpoint_coordinates |
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| 368 | |
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| 369 | if triangle_id is None: |
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| 370 | if absolute is True: |
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| 371 | if not self.geo_reference.is_absolute(): |
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| 372 | E = self.geo_reference.get_absolute(E) |
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| 373 | return E |
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| 374 | else: |
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| 375 | i = triangle_id |
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| 376 | msg = 'triangle_id must be an integer' |
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| 377 | assert int(i) == i, msg |
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| 378 | assert 0 <= i < self.number_of_triangles |
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| 379 | |
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| 380 | i3 = 3*i |
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| 381 | if absolute is True and not self.geo_reference.is_absolute(): |
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| 382 | offset=num.array([self.geo_reference.get_xllcorner(), |
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| 383 | self.geo_reference.get_yllcorner()], num.float) |
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[7498] | 384 | |
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| 385 | return E[i3:i3+3,:] + offset |
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[7484] | 386 | else: |
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[7498] | 387 | return E[i3:i3+3,:] |
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[7484] | 388 | |
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| 389 | |
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| 390 | def get_edge_midpoint_coordinate(self, i, j, absolute=False): |
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| 391 | """Return coordinates for edge midpoint j of the i'th triangle. |
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| 392 | Return value is the numeric array slice [x, y] |
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| 393 | """ |
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| 394 | |
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| 395 | msg = 'edge midpoint id j must be an integer in [0,1,2]' |
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| 396 | assert j in [0,1,2], msg |
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| 397 | |
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| 398 | E = self.get_edge_midpoint_coordinates(triangle_id=i, absolute=absolute) |
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[7498] | 399 | return E[j,:] # Return (x, y) for edge mid point |
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[7484] | 400 | |
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| 401 | |
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| 402 | def compute_edge_midpoint_coordinates(self): |
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| 403 | """Return all edge midpoint coordinates for all triangles as a 3*M x 2 array |
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| 404 | where the jth edge midpoint of the ith triangle is located in row 3*i+j. |
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| 405 | |
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| 406 | This function is used to precompute this important structure. Use |
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| 407 | get_edge_midpoint_coordinates to retrieve the points. |
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| 408 | |
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| 409 | Assumes that vertex_coordinates have been computed |
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| 410 | """ |
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| 411 | |
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| 412 | M = self.number_of_triangles |
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| 413 | E = num.zeros((3*M, 2), num.float) |
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| 414 | |
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| 415 | V = self.vertex_coordinates |
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| 416 | |
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| 417 | V0 = V[0:3*M:3, :] |
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| 418 | V1 = V[1:3*M:3, :] |
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| 419 | V2 = V[2:3*M:3, :] |
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| 420 | |
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| 421 | |
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| 422 | #print V.shape, V0.shape, V1.shape, V2.shape |
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| 423 | |
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| 424 | #print E.shape, E[0:3*M:3, :].shape, E[1:3*M:3, :].shape, E[2:3*M:3, :].shape |
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| 425 | E[0:3*M:3, :] = 0.5*(V1+V2) |
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| 426 | E[1:3*M:3, :] = 0.5*(V2+V0) |
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| 427 | E[2:3*M:3, :] = 0.5*(V0+V1) |
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| 428 | |
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| 429 | return E |
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| 430 | |
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| 431 | |
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| 432 | |
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[5897] | 433 | def get_triangles(self, indices=None): |
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| 434 | """Get mesh triangles. |
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| 435 | |
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| 436 | Return Mx3 integer array where M is the number of triangles. |
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| 437 | Each row corresponds to one triangle and the three entries are |
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| 438 | indices into the mesh nodes which can be obtained using the method |
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| 439 | get_nodes() |
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| 440 | |
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| 441 | Optional argument, indices is the set of triangle ids of interest. |
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| 442 | """ |
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| 443 | |
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| 444 | |
---|
| 445 | if indices is None: |
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[6191] | 446 | return self.triangles |
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[5897] | 447 | |
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[7276] | 448 | return num.take(self.triangles, indices, axis=0) |
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[5897] | 449 | |
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| 450 | def get_disconnected_triangles(self): |
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| 451 | """Get mesh based on nodes obtained from get_vertex_coordinates. |
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| 452 | |
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| 453 | Return array Mx3 array of integers where each row corresponds to |
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| 454 | a triangle. A triangle is a triplet of indices into |
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| 455 | point coordinates obtained from get_vertex_coordinates and each |
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| 456 | index appears only once |
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| 457 | |
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| 458 | This provides a mesh where no triangles share nodes |
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| 459 | (hence the name disconnected triangles) and different |
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| 460 | nodes may have the same coordinates. |
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| 461 | |
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| 462 | This version of the mesh is useful for storing meshes with |
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| 463 | discontinuities at each node and is e.g. used for storing |
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| 464 | data in sww files. |
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| 465 | |
---|
| 466 | The triangles created will have the format |
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| 467 | [[0,1,2], |
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| 468 | [3,4,5], |
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| 469 | [6,7,8], |
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| 470 | ... |
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[7276] | 471 | [3*M-3 3*M-2 3*M-1]] |
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[5897] | 472 | """ |
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| 473 | |
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| 474 | M = len(self) # Number of triangles |
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| 475 | K = 3*M # Total number of unique vertices |
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[7276] | 476 | return num.reshape(num.arange(K, dtype=num.int), (M,3)) |
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[5897] | 477 | |
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[7276] | 478 | def get_unique_vertices(self, indices=None): |
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| 479 | """FIXME(Ole): This function needs a docstring""" |
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[5897] | 480 | |
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| 481 | triangles = self.get_triangles(indices=indices) |
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| 482 | unique_verts = {} |
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| 483 | for triangle in triangles: |
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[7276] | 484 | unique_verts[triangle[0]] = 0 |
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| 485 | unique_verts[triangle[1]] = 0 |
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| 486 | unique_verts[triangle[2]] = 0 |
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[5897] | 487 | return unique_verts.keys() |
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| 488 | |
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| 489 | def get_triangles_and_vertices_per_node(self, node=None): |
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| 490 | """Get triangles associated with given node. |
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| 491 | |
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| 492 | Return list of triangle_ids, vertex_ids for specified node. |
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| 493 | If node in None or absent, this information will be returned |
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[8200] | 494 | for all nodes in a list L where L[v] is the triangle |
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[5897] | 495 | list for node v. |
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| 496 | """ |
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| 497 | |
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| 498 | triangle_list = [] |
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| 499 | if node is not None: |
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| 500 | # Get index for this node |
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[6145] | 501 | first = num.sum(self.number_of_triangles_per_node[:node]) |
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[7276] | 502 | |
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[5897] | 503 | # Get number of triangles for this node |
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| 504 | count = self.number_of_triangles_per_node[node] |
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| 505 | |
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| 506 | for i in range(count): |
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| 507 | index = self.vertex_value_indices[first+i] |
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| 508 | |
---|
| 509 | volume_id = index / 3 |
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| 510 | vertex_id = index % 3 |
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| 511 | |
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| 512 | triangle_list.append( (volume_id, vertex_id) ) |
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| 513 | |
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[7276] | 514 | triangle_list = num.array(triangle_list, num.int) #array default# |
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[5897] | 515 | else: |
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| 516 | # Get info for all nodes recursively. |
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| 517 | # If need be, we can speed this up by |
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| 518 | # working directly with the inverted triangle structure |
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[8200] | 519 | for i in range(self.number_of_nodes): |
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[5897] | 520 | L = self.get_triangles_and_vertices_per_node(node=i) |
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| 521 | triangle_list.append(L) |
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| 522 | |
---|
| 523 | return triangle_list |
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| 524 | |
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| 525 | def build_inverted_triangle_structure(self): |
---|
| 526 | """Build structure listing triangles belonging to each node |
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| 527 | |
---|
| 528 | Two arrays are created and store as mesh attributes |
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| 529 | |
---|
| 530 | number_of_triangles_per_node: An integer array of length N |
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| 531 | listing for each node how many triangles use it. N is the number of |
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| 532 | nodes in mesh. |
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[7276] | 533 | |
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[5897] | 534 | vertex_value_indices: An array of length M listing indices into |
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| 535 | triangles ordered by node number. The (triangle_id, vertex_id) |
---|
| 536 | pairs are obtained from each index as (index/3, index%3) or each |
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| 537 | index can be used directly into a flattened triangles array. This |
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| 538 | is for example the case in the quantity.c where this structure is |
---|
| 539 | used to average vertex values efficiently. |
---|
| 540 | |
---|
| 541 | Example: |
---|
| 542 | a = [0.0, 0.0] # node 0 |
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| 543 | b = [0.0, 2.0] # node 1 |
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| 544 | c = [2.0, 0.0] # node 2 |
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| 545 | d = [0.0, 4.0] # node 3 |
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| 546 | e = [2.0, 2.0] # node 4 |
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| 547 | f = [4.0, 0.0] # node 5 |
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| 548 | nodes = array([a, b, c, d, e, f]) |
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| 549 | |
---|
[7276] | 550 | # bac, bce, ecf, dbe |
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| 551 | triangles = array([[1,0,2], [1,2,4], [4,2,5], [3,1,4]]) |
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[5897] | 552 | |
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[7276] | 553 | For this structure: |
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[5897] | 554 | number_of_triangles_per_node = [1 3 3 1 3 1] |
---|
| 555 | which means that node a has 1 triangle associated with it, node b |
---|
| 556 | has 3, node has 3 and so on. |
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[7276] | 557 | |
---|
[5897] | 558 | vertex_value_indices = [ 1 0 3 10 2 4 7 9 5 6 11 8] |
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| 559 | which reflects the fact that |
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| 560 | node 0 is used by triangle 0, vertex 1 (index = 1) |
---|
| 561 | node 1 is used by triangle 0, vertex 0 (index = 0) |
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| 562 | and by triangle 1, vertex 0 (index = 3) |
---|
| 563 | and by triangle 3, vertex 1 (index = 10) |
---|
| 564 | node 2 is used by triangle 0, vertex 2 (index = 2) |
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| 565 | and by triangle 1, vertex 1 (index = 4) |
---|
| 566 | and by triangle 2, vertex 1 (index = 7) |
---|
| 567 | node 3 is used by triangle 3, vertex 0 (index = 9) |
---|
| 568 | node 4 is used by triangle 1, vertex 2 (index = 5) |
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| 569 | and by triangle 2, vertex 0 (index = 6) |
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| 570 | and by triangle 3, vertex 2 (index = 11) |
---|
[7276] | 571 | node 5 is used by triangle 2, vertex 2 (index = 8) |
---|
[5897] | 572 | |
---|
| 573 | Preconditions: |
---|
| 574 | self.nodes and self.triangles are defined |
---|
| 575 | |
---|
| 576 | Postcondition: |
---|
| 577 | self.number_of_triangles_per_node is built |
---|
[7276] | 578 | self.vertex_value_indices is built |
---|
[5897] | 579 | """ |
---|
| 580 | |
---|
| 581 | # Count number of triangles per node |
---|
[8200] | 582 | number_of_triangles_per_node = num.zeros(self.number_of_nodes, |
---|
[7276] | 583 | num.int) #array default# |
---|
[5897] | 584 | for volume_id, triangle in enumerate(self.get_triangles()): |
---|
| 585 | for vertex_id in triangle: |
---|
| 586 | number_of_triangles_per_node[vertex_id] += 1 |
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| 587 | |
---|
| 588 | # Allocate space for inverted structure |
---|
[6145] | 589 | number_of_entries = num.sum(number_of_triangles_per_node) |
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[7276] | 590 | vertex_value_indices = num.zeros(number_of_entries, num.int) #array default# |
---|
[5897] | 591 | |
---|
| 592 | # Register (triangle, vertex) indices for each node |
---|
[8200] | 593 | vertexlist = [None] * self.number_of_nodes |
---|
| 594 | for volume_id in range(self.number_of_triangles): |
---|
[5897] | 595 | a = self.triangles[volume_id, 0] |
---|
| 596 | b = self.triangles[volume_id, 1] |
---|
| 597 | c = self.triangles[volume_id, 2] |
---|
| 598 | |
---|
[7276] | 599 | for vertex_id, node_id in enumerate([a, b, c]): |
---|
[5897] | 600 | if vertexlist[node_id] is None: |
---|
| 601 | vertexlist[node_id] = [] |
---|
[7276] | 602 | vertexlist[node_id].append((volume_id, vertex_id)) |
---|
[5897] | 603 | |
---|
| 604 | # Build inverted triangle index array |
---|
| 605 | k = 0 |
---|
| 606 | for vertices in vertexlist: |
---|
| 607 | if vertices is not None: |
---|
| 608 | for volume_id, vertex_id in vertices: |
---|
| 609 | vertex_value_indices[k] = 3*volume_id + vertex_id |
---|
| 610 | k += 1 |
---|
| 611 | |
---|
| 612 | # Save structure |
---|
| 613 | self.number_of_triangles_per_node = number_of_triangles_per_node |
---|
| 614 | self.vertex_value_indices = vertex_value_indices |
---|
| 615 | |
---|
| 616 | def get_extent(self, absolute=False): |
---|
| 617 | """Return min and max of all x and y coordinates |
---|
| 618 | |
---|
| 619 | Boolean keyword argument absolute determines whether coordinates |
---|
| 620 | are to be made absolute by taking georeference into account |
---|
| 621 | """ |
---|
| 622 | |
---|
| 623 | C = self.get_vertex_coordinates(absolute=absolute) |
---|
| 624 | X = C[:,0:6:2].copy() |
---|
| 625 | Y = C[:,1:6:2].copy() |
---|
| 626 | |
---|
[7276] | 627 | xmin = num.min(X) |
---|
| 628 | xmax = num.max(X) |
---|
| 629 | ymin = num.min(Y) |
---|
| 630 | ymax = num.max(Y) |
---|
| 631 | |
---|
[5897] | 632 | return xmin, xmax, ymin, ymax |
---|
| 633 | |
---|
| 634 | def get_areas(self): |
---|
[7276] | 635 | """Get areas of all individual triangles.""" |
---|
[5897] | 636 | |
---|
[7276] | 637 | return self.areas |
---|
| 638 | |
---|
[5897] | 639 | def get_area(self): |
---|
[7276] | 640 | """Return total area of mesh""" |
---|
[5897] | 641 | |
---|
[6145] | 642 | return num.sum(self.areas) |
---|
[5897] | 643 | |
---|
[6191] | 644 | def set_georeference(self, g): |
---|
| 645 | self.geo_reference = g |
---|
[7276] | 646 | |
---|
[6191] | 647 | def get_georeference(self): |
---|
| 648 | return self.geo_reference |
---|
[7276] | 649 | |
---|