[2528] | 1 | |
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| 2 | from coordinate_transforms.geo_reference import Geo_reference |
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| 3 | |
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| 4 | class General_mesh: |
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| 5 | """Collection of triangular elements (purely geometric) |
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| 6 | |
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| 7 | A triangular element is defined in terms of three vertex ids, |
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| 8 | ordered counter clock-wise, |
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| 9 | each corresponding to a given coordinate set. |
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| 10 | Vertices from different elements can point to the same |
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| 11 | coordinate set. |
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| 12 | |
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| 13 | Coordinate sets are implemented as an N x 2 Numeric array containing |
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| 14 | x and y coordinates. |
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| 15 | |
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| 16 | |
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| 17 | To instantiate: |
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| 18 | Mesh(coordinates, triangles) |
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| 19 | |
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| 20 | where |
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| 21 | |
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| 22 | coordinates is either a list of 2-tuples or an Mx2 Numeric array of |
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| 23 | floats representing all x, y coordinates in the mesh. |
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| 24 | |
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| 25 | triangles is either a list of 3-tuples or an Nx3 Numeric array of |
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| 26 | integers representing indices of all vertices in the mesh. |
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| 27 | Each vertex is identified by its index i in [0, M-1]. |
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| 28 | |
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| 29 | |
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| 30 | Example: |
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| 31 | a = [0.0, 0.0] |
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| 32 | b = [0.0, 2.0] |
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| 33 | c = [2.0,0.0] |
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| 34 | e = [2.0, 2.0] |
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| 35 | |
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| 36 | points = [a, b, c, e] |
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| 37 | triangles = [ [1,0,2], [1,2,3] ] #bac, bce |
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| 38 | mesh = Mesh(points, triangles) |
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| 39 | |
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| 40 | #creates two triangles: bac and bce |
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| 41 | |
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| 42 | Other: |
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| 43 | |
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| 44 | In addition mesh computes an Nx6 array called vertex_coordinates. |
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| 45 | This structure is derived from coordinates and contains for each |
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| 46 | triangle the three x,y coordinates at the vertices. |
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| 47 | |
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| 48 | |
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| 49 | This is a cut down version of mesh from pyvolution mesh.py |
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| 50 | """ |
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| 51 | |
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| 52 | #FIXME: It would be a good idea to use geospatial data as an alternative |
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| 53 | #input |
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| 54 | def __init__(self, coordinates, triangles, |
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[2866] | 55 | geo_reference=None, |
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| 56 | verbose=False): |
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[2528] | 57 | """ |
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| 58 | Build triangles from x,y coordinates (sequence of 2-tuples or |
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| 59 | Mx2 Numeric array of floats) and triangles (sequence of 3-tuples |
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| 60 | or Nx3 Numeric array of non-negative integers). |
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| 61 | |
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| 62 | origin is a 3-tuple consisting of UTM zone, easting and northing. |
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| 63 | If specified coordinates are assumed to be relative to this origin. |
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| 64 | """ |
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| 65 | |
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[2866] | 66 | if verbose: print 'General_mesh: Building basic mesh structure' |
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| 67 | |
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[2778] | 68 | from Numeric import array, zeros, Int, Float, sqrt, sum |
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[2528] | 69 | |
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[2778] | 70 | self.triangles = array(triangles,Int) |
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| 71 | self.coordinates = array(coordinates,Float) |
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| 72 | |
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[2528] | 73 | |
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[2694] | 74 | # FIXME: this stores a geo_reference, but when coords are returned |
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| 75 | # This geo_ref is not taken into account! |
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[2528] | 76 | if geo_reference is None: |
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| 77 | self.geo_reference = Geo_reference() #Use defaults |
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| 78 | else: |
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| 79 | self.geo_reference = geo_reference |
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| 80 | |
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| 81 | #Input checks |
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| 82 | msg = 'Triangles must an Nx3 Numeric array or a sequence of 3-tuples' |
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| 83 | assert len(self.triangles.shape) == 2, msg |
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| 84 | |
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| 85 | msg = 'Coordinates must an Mx2 Numeric array or a sequence of 2-tuples' |
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| 86 | assert len(self.coordinates.shape) == 2, msg |
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| 87 | |
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| 88 | msg = 'Vertex indices reference non-existing coordinate sets' |
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| 89 | assert max(max(self.triangles)) <= self.coordinates.shape[0], msg |
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| 90 | |
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| 91 | |
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| 92 | #Register number of elements (N) |
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| 93 | self.number_of_elements = N = self.triangles.shape[0] |
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| 94 | |
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[2532] | 95 | #FIXME: Maybe move to statistics? |
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[2778] | 96 | |
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[2528] | 97 | xy_extent = [ min(self.coordinates[:,0]), min(self.coordinates[:,1]) , |
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| 98 | max(self.coordinates[:,0]), max(self.coordinates[:,1]) ] |
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| 99 | |
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| 100 | self.xy_extent = array(xy_extent, Float) |
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| 101 | |
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| 102 | |
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| 103 | #Allocate space for geometric quantities |
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| 104 | self.normals = zeros((N, 6), Float) |
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| 105 | self.areas = zeros(N, Float) |
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| 106 | self.edgelengths = zeros((N, 3), Float) |
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| 107 | |
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| 108 | #Get x,y coordinates for all triangles and store |
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| 109 | self.vertex_coordinates = V = self.compute_vertex_coordinates() |
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| 110 | |
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[2778] | 111 | |
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[2528] | 112 | #Initialise each triangle |
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[2866] | 113 | if verbose: |
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| 114 | print 'General_mesh: Computing areas, normals and edgelenghts' |
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| 115 | |
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[2528] | 116 | for i in range(N): |
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[2866] | 117 | if verbose and i % ((N+10)/10) == 0: print '(%d/%d)' %(i, N) |
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| 118 | |
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[2528] | 119 | |
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| 120 | x0 = V[i, 0]; y0 = V[i, 1] |
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| 121 | x1 = V[i, 2]; y1 = V[i, 3] |
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| 122 | x2 = V[i, 4]; y2 = V[i, 5] |
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| 123 | |
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| 124 | #Area |
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| 125 | self.areas[i] = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
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| 126 | |
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| 127 | msg = 'Triangle (%f,%f), (%f,%f), (%f, %f)' %(x0,y0,x1,y1,x2,y2) |
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| 128 | msg += ' is degenerate: area == %f' %self.areas[i] |
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| 129 | assert self.areas[i] > 0.0, msg |
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| 130 | |
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| 131 | |
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| 132 | #Normals |
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| 133 | #The normal vectors |
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| 134 | # - point outward from each edge |
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| 135 | # - are orthogonal to the edge |
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| 136 | # - have unit length |
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| 137 | # - Are enumerated according to the opposite corner: |
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| 138 | # (First normal is associated with the edge opposite |
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| 139 | # the first vertex, etc) |
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| 140 | # - Stored as six floats n0x,n0y,n1x,n1y,n2x,n2y per triangle |
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| 141 | |
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| 142 | n0 = array([x2 - x1, y2 - y1]) |
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| 143 | l0 = sqrt(sum(n0**2)) |
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| 144 | |
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| 145 | n1 = array([x0 - x2, y0 - y2]) |
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| 146 | l1 = sqrt(sum(n1**2)) |
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| 147 | |
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| 148 | n2 = array([x1 - x0, y1 - y0]) |
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| 149 | l2 = sqrt(sum(n2**2)) |
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| 150 | |
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| 151 | #Normalise |
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| 152 | n0 /= l0 |
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| 153 | n1 /= l1 |
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| 154 | n2 /= l2 |
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| 155 | |
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| 156 | #Compute and store |
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| 157 | self.normals[i, :] = [n0[1], -n0[0], |
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| 158 | n1[1], -n1[0], |
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| 159 | n2[1], -n2[0]] |
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| 160 | |
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| 161 | #Edgelengths |
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| 162 | self.edgelengths[i, :] = [l0, l1, l2] |
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| 163 | |
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[2778] | 164 | |
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[2528] | 165 | #Build vertex list |
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[2866] | 166 | if verbose: print 'Building vertex list' |
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[2528] | 167 | self.build_vertexlist() |
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| 168 | |
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[2532] | 169 | |
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| 170 | |
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[2528] | 171 | def __len__(self): |
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| 172 | return self.number_of_elements |
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| 173 | |
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| 174 | def __repr__(self): |
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| 175 | return 'Mesh: %d triangles, %d elements'\ |
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| 176 | %(self.coordinates.shape[0], len(self)) |
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| 177 | |
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| 178 | def get_normals(self): |
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| 179 | """Return all normal vectors. |
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| 180 | Return normal vectors for all triangles as an Nx6 array |
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| 181 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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| 182 | """ |
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| 183 | return self.normals |
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| 184 | |
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| 185 | |
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| 186 | def get_normal(self, i, j): |
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| 187 | """Return normal vector j of the i'th triangle. |
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| 188 | Return value is the numeric array slice [x, y] |
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| 189 | """ |
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| 190 | return self.normals[i, 2*j:2*j+2] |
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| 191 | |
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| 192 | |
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| 193 | |
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| 194 | def get_vertex_coordinates(self, obj = False): |
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| 195 | """Return all vertex coordinates. |
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| 196 | Return all vertex coordinates for all triangles as an Nx6 array |
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| 197 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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| 198 | |
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| 199 | if obj is True, the x/y pairs are returned in a 3*N x 2 array. |
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| 200 | FIXME, we might make that the default. |
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| 201 | FIXME Maybe use keyword: continuous = False for this condition? |
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| 202 | FIXME - Maybe use something referring to unique vertices? |
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| 203 | |
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| 204 | |
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| 205 | """ |
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| 206 | |
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| 207 | if obj is True: |
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| 208 | from Numeric import concatenate, reshape |
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| 209 | V = self.vertex_coordinates |
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| 210 | #return concatenate( (V[:,0:2], V[:,2:4], V[:,4:6]), axis=0) |
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| 211 | |
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| 212 | N = V.shape[0] |
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| 213 | return reshape(V, (3*N, 2)) |
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| 214 | else: |
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| 215 | return self.vertex_coordinates |
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| 216 | |
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| 217 | |
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| 218 | def get_vertex_coordinate(self, i, j): |
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| 219 | """Return coordinates for vertex j of the i'th triangle. |
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| 220 | Return value is the numeric array slice [x, y] |
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| 221 | """ |
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| 222 | return self.vertex_coordinates[i, 2*j:2*j+2] |
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| 223 | |
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| 224 | |
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| 225 | def compute_vertex_coordinates(self): |
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| 226 | """Return vertex coordinates for all triangles as an Nx6 array |
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| 227 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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| 228 | """ |
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| 229 | |
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| 230 | #FIXME (Ole): Perhaps they should be ordered as in obj files?? |
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| 231 | #See quantity.get_vertex_values |
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| 232 | #FIXME (Ole) - oh yes they should |
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| 233 | |
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| 234 | from Numeric import zeros, Float |
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| 235 | |
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| 236 | N = self.number_of_elements |
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| 237 | vertex_coordinates = zeros((N, 6), Float) |
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| 238 | |
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| 239 | for i in range(N): |
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| 240 | for j in range(3): |
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| 241 | k = self.triangles[i,j] #Index of vertex 0 |
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| 242 | v_k = self.coordinates[k] |
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| 243 | vertex_coordinates[i, 2*j+0] = v_k[0] |
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| 244 | vertex_coordinates[i, 2*j+1] = v_k[1] |
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| 245 | |
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| 246 | return vertex_coordinates |
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| 247 | |
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| 248 | def get_vertices(self, indices=None): |
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| 249 | """Get connectivity |
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| 250 | indices is the set of element ids of interest |
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| 251 | """ |
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| 252 | |
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| 253 | from Numeric import take |
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| 254 | |
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| 255 | if (indices == None): |
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| 256 | indices = range(len(self)) #len(self)=number of elements |
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| 257 | |
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| 258 | return take(self.triangles, indices) |
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| 259 | |
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| 260 | #FIXME - merge these two (get_vertices and get_triangles) |
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| 261 | def get_triangles(self, obj = False): |
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| 262 | """Get connetivity |
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| 263 | Return triangles (triplets of indices into point coordinates) |
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| 264 | |
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| 265 | If obj is True return structure commensurate with replicated |
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| 266 | points, allowing for discontinuities |
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| 267 | (FIXME: Need good name for this concept) |
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| 268 | """ |
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| 269 | |
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| 270 | if obj is True: |
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| 271 | from Numeric import array, reshape, Int |
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| 272 | m = len(self) #Number of triangles |
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| 273 | M = 3*m #Total number of unique vertices |
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| 274 | T = reshape(array(range(M)).astype(Int), (m,3)) |
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| 275 | else: |
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| 276 | T = self.triangles |
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| 277 | |
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| 278 | return T |
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| 279 | |
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| 280 | |
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| 281 | |
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| 282 | def get_unique_vertices(self, indices=None): |
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| 283 | triangles = self.get_vertices(indices=indices) |
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| 284 | unique_verts = {} |
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| 285 | for triangle in triangles: |
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| 286 | unique_verts[triangle[0]] = 0 |
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| 287 | unique_verts[triangle[1]] = 0 |
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| 288 | unique_verts[triangle[2]] = 0 |
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| 289 | return unique_verts.keys() |
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| 290 | |
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| 291 | def build_vertexlist(self): |
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| 292 | """Build vertexlist index by vertex ids and for each entry (point id) |
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| 293 | build a list of (triangles, vertex_id) pairs that use the point |
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| 294 | as vertex. |
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| 295 | |
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| 296 | Preconditions: |
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| 297 | self.coordinates and self.triangles are defined |
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| 298 | |
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| 299 | Postcondition: |
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| 300 | self.vertexlist is built |
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| 301 | """ |
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| 302 | |
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| 303 | vertexlist = [None]*len(self.coordinates) |
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| 304 | for i in range(self.number_of_elements): |
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| 305 | |
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| 306 | a = self.triangles[i, 0] |
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| 307 | b = self.triangles[i, 1] |
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| 308 | c = self.triangles[i, 2] |
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| 309 | |
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| 310 | #Register the vertices v as lists of |
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| 311 | #(triangle_id, vertex_id) tuples associated with them |
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[2808] | 312 | #This is used for averaging multiple vertex values. |
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[2528] | 313 | for vertex_id, v in enumerate([a,b,c]): |
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| 314 | if vertexlist[v] is None: |
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| 315 | vertexlist[v] = [] |
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| 316 | |
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| 317 | vertexlist[v].append( (i, vertex_id) ) |
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| 318 | |
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| 319 | self.vertexlist = vertexlist |
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| 320 | |
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| 321 | |
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| 322 | def get_extent(self): |
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| 323 | """Return min and max of all x and y coordinates |
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| 324 | """ |
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| 325 | |
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| 326 | |
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| 327 | C = self.get_vertex_coordinates() |
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| 328 | X = C[:,0:6:2].copy() |
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| 329 | Y = C[:,1:6:2].copy() |
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| 330 | |
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| 331 | xmin = min(X.flat) |
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| 332 | xmax = max(X.flat) |
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| 333 | ymin = min(Y.flat) |
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| 334 | ymax = max(Y.flat) |
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| 335 | |
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| 336 | return xmin, xmax, ymin, ymax |
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| 337 | |
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| 338 | |
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| 339 | def get_area(self): |
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| 340 | """Return total area of mesh |
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| 341 | """ |
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| 342 | |
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| 343 | return sum(self.areas) |
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[2532] | 344 | |
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| 345 | |
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