| 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 math import pi, sqrt |
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| 12 | |
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| 13 | |
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| 14 | class Mesh(General_mesh): |
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| 15 | """Collection of triangular elements (purely geometric) |
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| 16 | |
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| 17 | A triangular element is defined in terms of three vertex ids, |
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| 18 | ordered counter clock-wise, |
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| 19 | each corresponding to a given coordinate set. |
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| 20 | Vertices from different elements can point to the same |
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| 21 | coordinate set. |
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| 22 | |
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| 23 | Coordinate sets are implemented as an N x 2 Numeric array containing |
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| 24 | x and y coordinates. |
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| 25 | |
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| 26 | |
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| 27 | To instantiate: |
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| 28 | Mesh(coordinates, triangles) |
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| 29 | |
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| 30 | where |
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| 31 | |
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| 32 | coordinates is either a list of 2-tuples or an Mx2 Numeric array of |
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| 33 | floats representing all x, y coordinates in the mesh. |
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| 34 | |
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| 35 | triangles is either a list of 3-tuples or an Nx3 Numeric array of |
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| 36 | integers representing indices of all vertices in the mesh. |
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| 37 | Each vertex is identified by its index i in [0, M-1]. |
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| 38 | |
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| 39 | |
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| 40 | Example: |
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| 41 | a = [0.0, 0.0] |
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| 42 | b = [0.0, 2.0] |
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| 43 | c = [2.0,0.0] |
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| 44 | e = [2.0, 2.0] |
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| 45 | |
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| 46 | points = [a, b, c, e] |
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| 47 | triangles = [ [1,0,2], [1,2,3] ] #bac, bce |
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| 48 | mesh = Mesh(points, triangles) |
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| 49 | |
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| 50 | #creates two triangles: bac and bce |
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| 51 | |
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| 52 | |
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| 53 | Mesh takes the optional third argument boundary which is a |
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| 54 | dictionary mapping from (element_id, edge_id) to boundary tag. |
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| 55 | The default value is None which will assign the default_boundary_tag |
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| 56 | as specified in config.py to all boundary edges. |
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| 57 | """ |
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| 58 | |
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| 59 | #FIXME: Maybe rename coordinates to points (as in a poly file) |
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| 60 | #But keep 'vertex_coordinates' |
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| 61 | |
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| 62 | #FIXME: Put in check for angles less than a set minimum |
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| 63 | |
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| 64 | |
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| 65 | def __init__(self, coordinates, triangles, |
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| 66 | boundary=None, |
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| 67 | tagged_elements=None, |
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| 68 | geo_reference=None, |
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| 69 | use_inscribed_circle=False, |
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| 70 | verbose=False): |
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| 71 | """ |
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| 72 | Build triangles from x,y coordinates (sequence of 2-tuples or |
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| 73 | Mx2 Numeric array of floats) and triangles (sequence of 3-tuples |
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| 74 | or Nx3 Numeric array of non-negative integers). |
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| 75 | """ |
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| 76 | |
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| 77 | |
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| 78 | |
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| 79 | from Numeric import array, zeros, Int, Float, maximum, sqrt, sum |
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| 80 | |
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| 81 | General_mesh.__init__(self, coordinates, triangles, |
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| 82 | geo_reference, verbose=verbose) |
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| 83 | |
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| 84 | if verbose: print 'Initialising mesh' |
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| 85 | |
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| 86 | N = self.number_of_elements |
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| 87 | |
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| 88 | self.use_inscribed_circle = use_inscribed_circle |
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| 89 | |
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| 90 | #Allocate space for geometric quantities |
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| 91 | self.centroid_coordinates = zeros((N, 2), Float) |
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| 92 | |
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| 93 | self.radii = zeros(N, Float) |
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| 94 | |
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| 95 | self.neighbours = zeros((N, 3), Int) |
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| 96 | self.neighbour_edges = zeros((N, 3), Int) |
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| 97 | self.number_of_boundaries = zeros(N, Int) |
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| 98 | self.surrogate_neighbours = zeros((N, 3), Int) |
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| 99 | |
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| 100 | #Get x,y coordinates for all triangles and store |
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| 101 | V = self.vertex_coordinates # Relative coordinates |
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| 102 | |
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| 103 | #Initialise each triangle |
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| 104 | if verbose: print 'Mesh: Computing centroids and radii' |
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| 105 | for i in range(N): |
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| 106 | if verbose and i % ((N+10)/10) == 0: print '(%d/%d)' %(i, N) |
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| 107 | |
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| 108 | x0 = V[i, 0]; y0 = V[i, 1] |
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| 109 | x1 = V[i, 2]; y1 = V[i, 3] |
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| 110 | x2 = V[i, 4]; y2 = V[i, 5] |
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| 111 | |
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| 112 | #Compute centroid |
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| 113 | centroid = array([(x0 + x1 + x2)/3, (y0 + y1 + y2)/3]) |
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| 114 | self.centroid_coordinates[i] = centroid |
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| 115 | |
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| 116 | |
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| 117 | if self.use_inscribed_circle == False: |
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| 118 | #OLD code. Computed radii may exceed that of an |
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| 119 | #inscribed circle |
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| 120 | |
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| 121 | #Midpoints |
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| 122 | m0 = array([(x1 + x2)/2, (y1 + y2)/2]) |
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| 123 | m1 = array([(x0 + x2)/2, (y0 + y2)/2]) |
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| 124 | m2 = array([(x1 + x0)/2, (y1 + y0)/2]) |
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| 125 | |
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| 126 | #The radius is the distance from the centroid of |
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| 127 | #a triangle to the midpoint of the side of the triangle |
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| 128 | #closest to the centroid |
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| 129 | d0 = sqrt(sum( (centroid-m0)**2 )) |
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| 130 | d1 = sqrt(sum( (centroid-m1)**2 )) |
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| 131 | d2 = sqrt(sum( (centroid-m2)**2 )) |
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| 132 | |
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| 133 | self.radii[i] = min(d0, d1, d2) |
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| 134 | |
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| 135 | else: |
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| 136 | #NEW code added by Peter Row. True radius |
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| 137 | #of inscribed circle is computed |
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| 138 | |
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| 139 | a = sqrt((x0-x1)**2+(y0-y1)**2) |
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| 140 | b = sqrt((x1-x2)**2+(y1-y2)**2) |
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| 141 | c = sqrt((x2-x0)**2+(y2-y0)**2) |
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| 142 | |
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| 143 | self.radii[i]=2.0*self.areas[i]/(a+b+c) |
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| 144 | |
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| 145 | |
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| 146 | #Initialise Neighbours (-1 means that it is a boundary neighbour) |
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| 147 | self.neighbours[i, :] = [-1, -1, -1] |
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| 148 | |
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| 149 | #Initialise edge ids of neighbours |
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| 150 | #In case of boundaries this slot is not used |
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| 151 | self.neighbour_edges[i, :] = [-1, -1, -1] |
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| 152 | |
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| 153 | |
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| 154 | #Build neighbour structure |
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| 155 | if verbose: print 'Mesh: Building neigbour structure' |
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| 156 | self.build_neighbour_structure() |
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| 157 | |
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| 158 | #Build surrogate neighbour structure |
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| 159 | if verbose: print 'Mesh: Building surrogate neigbour structure' |
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| 160 | self.build_surrogate_neighbour_structure() |
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| 161 | |
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| 162 | #Build boundary dictionary mapping (id, edge) to symbolic tags |
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| 163 | if verbose: print 'Mesh: Building boundary dictionary' |
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| 164 | self.build_boundary_dictionary(boundary) |
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| 165 | |
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| 166 | #Build tagged element dictionary mapping (tag) to array of elements |
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| 167 | if verbose: print 'Mesh: Building tagged elements dictionary' |
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| 168 | self.build_tagged_elements_dictionary(tagged_elements) |
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| 169 | |
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| 170 | #Update boundary indices FIXME: OBSOLETE |
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| 171 | #self.build_boundary_structure() |
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| 172 | |
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| 173 | #FIXME check integrity? |
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| 174 | if verbose: print 'Mesh: Done' |
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| 175 | |
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| 176 | def __repr__(self): |
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| 177 | return 'Mesh: %d triangles, %d elements, %d boundary segments'\ |
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| 178 | %(self.coordinates.shape[0], len(self), len(self.boundary)) |
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| 179 | |
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| 180 | |
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| 181 | def set_to_inscribed_circle(self,safety_factor = 1): |
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| 182 | #FIXME phase out eventually |
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| 183 | N = self.number_of_elements |
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| 184 | V = self.vertex_coordinates |
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| 185 | |
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| 186 | #initialising min and max ratio |
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| 187 | i=0 |
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| 188 | old_rad = self.radii[i] |
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| 189 | x0 = V[i, 0]; y0 = V[i, 1] |
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| 190 | x1 = V[i, 2]; y1 = V[i, 3] |
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| 191 | x2 = V[i, 4]; y2 = V[i, 5] |
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| 192 | a = sqrt((x0-x1)**2+(y0-y1)**2) |
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| 193 | b = sqrt((x1-x2)**2+(y1-y2)**2) |
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| 194 | c = sqrt((x2-x0)**2+(y2-y0)**2) |
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| 195 | ratio = old_rad/self.radii[i] |
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| 196 | max_ratio = ratio |
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| 197 | min_ratio = ratio |
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| 198 | |
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| 199 | for i in range(N): |
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| 200 | old_rad = self.radii[i] |
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| 201 | x0 = V[i, 0]; y0 = V[i, 1] |
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| 202 | x1 = V[i, 2]; y1 = V[i, 3] |
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| 203 | x2 = V[i, 4]; y2 = V[i, 5] |
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| 204 | a = sqrt((x0-x1)**2+(y0-y1)**2) |
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| 205 | b = sqrt((x1-x2)**2+(y1-y2)**2) |
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| 206 | c = sqrt((x2-x0)**2+(y2-y0)**2) |
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| 207 | self.radii[i]=self.areas[i]/(2*(a+b+c))*safety_factor |
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| 208 | ratio = old_rad/self.radii[i] |
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| 209 | if ratio >= max_ratio: max_ratio = ratio |
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| 210 | if ratio <= min_ratio: min_ratio = ratio |
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| 211 | return max_ratio,min_ratio |
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| 212 | |
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| 213 | def build_neighbour_structure(self): |
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| 214 | """Update all registered triangles to point to their neighbours. |
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| 215 | |
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| 216 | Also, keep a tally of the number of boundaries for each triangle |
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| 217 | |
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| 218 | Postconditions: |
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| 219 | neighbours and neighbour_edges is populated |
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| 220 | number_of_boundaries integer array is defined. |
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| 221 | """ |
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| 222 | |
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| 223 | #Step 1: |
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| 224 | #Build dictionary mapping from segments (2-tuple of points) |
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| 225 | #to left hand side edge (facing neighbouring triangle) |
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| 226 | |
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| 227 | N = self.number_of_elements |
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| 228 | neighbourdict = {} |
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| 229 | for i in range(N): |
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| 230 | |
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| 231 | #Register all segments as keys mapping to current triangle |
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| 232 | #and segment id |
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| 233 | a = self.triangles[i, 0] |
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| 234 | b = self.triangles[i, 1] |
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| 235 | c = self.triangles[i, 2] |
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| 236 | if neighbourdict.has_key((a,b)): |
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| 237 | 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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| 238 | raise msg |
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| 239 | if neighbourdict.has_key((b,c)): |
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| 240 | 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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| 241 | raise msg |
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| 242 | if neighbourdict.has_key((c,a)): |
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| 243 | 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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| 244 | raise msg |
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| 245 | |
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| 246 | neighbourdict[a,b] = (i, 2) #(id, edge) |
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| 247 | neighbourdict[b,c] = (i, 0) #(id, edge) |
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| 248 | neighbourdict[c,a] = (i, 1) #(id, edge) |
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| 249 | |
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| 250 | |
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| 251 | #Step 2: |
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| 252 | #Go through triangles again, but this time |
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| 253 | #reverse direction of segments and lookup neighbours. |
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| 254 | for i in range(N): |
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| 255 | a = self.triangles[i, 0] |
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| 256 | b = self.triangles[i, 1] |
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| 257 | c = self.triangles[i, 2] |
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| 258 | |
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| 259 | self.number_of_boundaries[i] = 3 |
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| 260 | if neighbourdict.has_key((b,a)): |
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| 261 | self.neighbours[i, 2] = neighbourdict[b,a][0] |
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| 262 | self.neighbour_edges[i, 2] = neighbourdict[b,a][1] |
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| 263 | self.number_of_boundaries[i] -= 1 |
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| 264 | |
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| 265 | if neighbourdict.has_key((c,b)): |
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| 266 | self.neighbours[i, 0] = neighbourdict[c,b][0] |
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| 267 | self.neighbour_edges[i, 0] = neighbourdict[c,b][1] |
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| 268 | self.number_of_boundaries[i] -= 1 |
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| 269 | |
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| 270 | if neighbourdict.has_key((a,c)): |
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| 271 | self.neighbours[i, 1] = neighbourdict[a,c][0] |
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| 272 | self.neighbour_edges[i, 1] = neighbourdict[a,c][1] |
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| 273 | self.number_of_boundaries[i] -= 1 |
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| 274 | |
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| 275 | |
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| 276 | def build_surrogate_neighbour_structure(self): |
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| 277 | """Build structure where each triangle edge points to its neighbours |
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| 278 | if they exist. Otherwise point to the triangle itself. |
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| 279 | |
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| 280 | The surrogate neighbour structure is useful for computing gradients |
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| 281 | based on centroid values of neighbours. |
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| 282 | |
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| 283 | Precondition: Neighbour structure is defined |
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| 284 | Postcondition: |
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| 285 | Surrogate neighbour structure is defined: |
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| 286 | surrogate_neighbours: i0, i1, i2 where all i_k >= 0 point to |
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| 287 | triangles. |
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| 288 | |
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| 289 | """ |
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| 290 | |
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| 291 | N = self.number_of_elements |
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| 292 | for i in range(N): |
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| 293 | #Find all neighbouring volumes that are not boundaries |
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| 294 | for k in range(3): |
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| 295 | if self.neighbours[i, k] < 0: |
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| 296 | self.surrogate_neighbours[i, k] = i #Point this triangle |
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| 297 | else: |
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| 298 | self.surrogate_neighbours[i, k] = self.neighbours[i, k] |
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| 299 | |
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| 300 | |
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| 301 | |
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| 302 | def build_boundary_dictionary(self, boundary = None): |
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| 303 | """Build or check the dictionary of boundary tags. |
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| 304 | self.boundary is a dictionary of tags, |
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| 305 | keyed by volume id and edge: |
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| 306 | { (id, edge): tag, ... } |
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| 307 | |
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| 308 | Postconditions: |
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| 309 | self.boundary is defined. |
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| 310 | """ |
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| 311 | |
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| 312 | from config import default_boundary_tag |
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| 313 | |
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| 314 | if boundary is None: |
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| 315 | boundary = {} |
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| 316 | for vol_id in range(self.number_of_elements): |
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| 317 | for edge_id in range(0, 3): |
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| 318 | if self.neighbours[vol_id, edge_id] < 0: |
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| 319 | boundary[(vol_id, edge_id)] = default_boundary_tag |
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| 320 | else: |
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| 321 | #Check that all keys in given boundary exist |
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| 322 | for vol_id, edge_id in boundary.keys(): |
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| 323 | msg = 'Segment (%d, %d) does not exist' %(vol_id, edge_id) |
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| 324 | a, b = self.neighbours.shape |
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| 325 | assert vol_id < a and edge_id < b, msg |
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| 326 | |
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| 327 | #FIXME: This assert violates internal boundaries (delete it) |
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| 328 | #msg = 'Segment (%d, %d) is not a boundary' %(vol_id, edge_id) |
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| 329 | #assert self.neighbours[vol_id, edge_id] < 0, msg |
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| 330 | |
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| 331 | #Check that all boundary segments are assigned a tag |
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| 332 | for vol_id in range(self.number_of_elements): |
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| 333 | for edge_id in range(0, 3): |
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| 334 | if self.neighbours[vol_id, edge_id] < 0: |
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| 335 | if not boundary.has_key( (vol_id, edge_id) ): |
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| 336 | msg = 'WARNING: Given boundary does not contain ' |
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| 337 | msg += 'tags for edge (%d, %d). '\ |
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| 338 | %(vol_id, edge_id) |
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| 339 | msg += 'Assigning default tag (%s).'\ |
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| 340 | %default_boundary_tag |
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| 341 | |
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| 342 | #FIXME: Print only as per verbosity |
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| 343 | #print msg |
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| 344 | |
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| 345 | #FIXME: Make this situation an error in the future |
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| 346 | #and make another function which will |
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| 347 | #enable default boundary-tags where |
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| 348 | #tags a not specified |
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| 349 | boundary[ (vol_id, edge_id) ] =\ |
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| 350 | default_boundary_tag |
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| 351 | |
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| 352 | |
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| 353 | |
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| 354 | self.boundary = boundary |
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| 355 | |
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| 356 | |
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| 357 | def build_tagged_elements_dictionary(self, tagged_elements = None): |
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| 358 | """Build the dictionary of element tags. |
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| 359 | self.tagged_elements is a dictionary of element arrays, |
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| 360 | keyed by tag: |
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| 361 | { (tag): [e1, e2, e3..] } |
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| 362 | |
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| 363 | Postconditions: |
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| 364 | self.element_tag is defined |
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| 365 | """ |
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| 366 | from Numeric import array, Int |
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| 367 | |
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| 368 | if tagged_elements is None: |
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| 369 | tagged_elements = {} |
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| 370 | else: |
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| 371 | #Check that all keys in given boundary exist |
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| 372 | for tag in tagged_elements.keys(): |
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| 373 | tagged_elements[tag] = array(tagged_elements[tag]).astype(Int) |
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| 374 | |
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| 375 | msg = 'Not all elements exist. ' |
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| 376 | assert max(tagged_elements[tag]) < self.number_of_elements, msg |
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| 377 | #print "tagged_elements", tagged_elements |
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| 378 | self.tagged_elements = tagged_elements |
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| 379 | |
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| 380 | def build_boundary_structure(self): |
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| 381 | """Traverse boundary and |
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| 382 | enumerate neighbour indices from -1 and |
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| 383 | counting down. |
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| 384 | |
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| 385 | Precondition: |
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| 386 | self.boundary is defined. |
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| 387 | Post condition: |
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| 388 | neighbour array has unique negative indices for boundary |
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| 389 | boundary_segments array imposes an ordering on segments |
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| 390 | (not otherwise available from the dictionary) |
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| 391 | |
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| 392 | Note: If a segment is listed in the boundary dictionary |
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| 393 | it *will* become a boundary - even if there is a neighbouring triangle. |
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| 394 | This would be the case for internal boundaries |
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| 395 | """ |
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| 396 | |
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| 397 | #FIXME: Now Obsolete - maybe use some comments from here in |
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| 398 | #domain.set_boundary |
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| 399 | |
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| 400 | if self.boundary is None: |
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| 401 | msg = 'Boundary dictionary must be defined before ' |
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| 402 | msg += 'building boundary structure' |
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| 403 | raise msg |
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| 404 | |
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| 405 | |
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| 406 | self.boundary_segments = self.boundary.keys() |
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| 407 | self.boundary_segments.sort() |
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| 408 | |
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| 409 | index = -1 |
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| 410 | for id, edge in self.boundary_segments: |
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| 411 | |
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| 412 | #FIXME: One would detect internal boundaries as follows |
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| 413 | #if self.neighbours[id, edge] > -1: |
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| 414 | # print 'Internal boundary' |
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| 415 | |
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| 416 | self.neighbours[id, edge] = index |
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| 417 | index -= 1 |
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| 418 | |
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| 419 | |
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| 420 | def get_boundary_tags(self): |
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| 421 | """Return list of available boundary tags |
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| 422 | """ |
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| 423 | |
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| 424 | tags = {} |
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| 425 | for v in self.boundary.values(): |
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| 426 | tags[v] = 1 |
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| 427 | |
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| 428 | return tags.keys() |
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| 429 | |
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| 430 | |
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| 431 | def get_boundary_polygon(self, verbose=False): |
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| 432 | """Return bounding polygon for mesh (counter clockwise) |
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| 433 | |
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| 434 | Using the mesh boundary, derive a bounding polygon for this mesh. |
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| 435 | If multiple vertex values are present, the algorithm will select the |
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| 436 | path that contains the mesh. |
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| 437 | |
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| 438 | All points are in absolute UTM coordinates |
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| 439 | """ |
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| 440 | |
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| 441 | from Numeric import allclose, sqrt, array, minimum, maximum |
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| 442 | from utilities.numerical_tools import angle, ensure_numeric |
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| 443 | |
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| 444 | |
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| 445 | # Get mesh extent |
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| 446 | xmin, xmax, ymin, ymax = self.get_extent(absolute=True) |
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| 447 | pmin = ensure_numeric([xmin, ymin]) |
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| 448 | pmax = ensure_numeric([xmax, ymax]) |
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| 449 | |
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| 450 | |
|---|
| 451 | # Assemble dictionary of boundary segments and choose starting point |
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| 452 | segments = {} |
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| 453 | inverse_segments = {} |
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| 454 | p0 = None |
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| 455 | mindist = sqrt(sum((pmax-pmin)**2)) #Start value across entire mesh |
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| 456 | for i, edge_id in self.boundary.keys(): |
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| 457 | # Find vertex ids for boundary segment |
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| 458 | if edge_id == 0: a = 1; b = 2 |
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| 459 | if edge_id == 1: a = 2; b = 0 |
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| 460 | if edge_id == 2: a = 0; b = 1 |
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| 461 | |
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| 462 | A = self.get_vertex_coordinate(i, a, absolute=True) # Start |
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| 463 | B = self.get_vertex_coordinate(i, b, absolute=True) # End |
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| 464 | |
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| 465 | |
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| 466 | # Take the point closest to pmin as starting point |
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| 467 | # Note: Could be arbitrary, but nice to have |
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| 468 | # a unique way of selecting |
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| 469 | dist_A = sqrt(sum((A-pmin)**2)) |
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| 470 | dist_B = sqrt(sum((B-pmin)**2)) |
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| 471 | |
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| 472 | #Find lower leftmost point |
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| 473 | if dist_A < mindist: |
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| 474 | mindist = dist_A |
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| 475 | p0 = A |
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| 476 | if dist_B < mindist: |
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| 477 | mindist = dist_B |
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| 478 | p0 = B |
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| 479 | |
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| 480 | |
|---|
| 481 | # Sanity check |
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| 482 | if p0 is None: |
|---|
| 483 | raise Exception('Impossible') |
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| 484 | |
|---|
| 485 | |
|---|
| 486 | # Register potential paths from A to B |
|---|
| 487 | if not segments.has_key(tuple(A)): |
|---|
| 488 | segments[tuple(A)] = [] # Empty list for candidate points |
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| 489 | |
|---|
| 490 | segments[tuple(A)].append(B) |
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| 491 | |
|---|
| 492 | |
|---|
| 493 | |
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| 494 | |
|---|
| 495 | #Start with smallest point and follow boundary (counter clock wise) |
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| 496 | polygon = [p0] # Storage for final boundary polygon |
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| 497 | point_registry = {} # Keep track of storage to avoid multiple runs around |
|---|
| 498 | # boundary. This will only be the case if there are |
|---|
| 499 | # more than one candidate. |
|---|
| 500 | # FIXME (Ole): Perhaps we can do away with polygon |
|---|
| 501 | # and use only point_registry to save space. |
|---|
| 502 | |
|---|
| 503 | point_registry[tuple(p0)] = 0 |
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| 504 | |
|---|
| 505 | #while len(polygon) < len(self.boundary): |
|---|
| 506 | while len(point_registry) < len(self.boundary): |
|---|
| 507 | |
|---|
| 508 | candidate_list = segments[tuple(p0)] |
|---|
| 509 | if len(candidate_list) > 1: |
|---|
| 510 | # Multiple points detected |
|---|
| 511 | # Take the candidate that is furthest to the clockwise direction, |
|---|
| 512 | # as that will follow the boundary. |
|---|
| 513 | |
|---|
| 514 | |
|---|
| 515 | if verbose: |
|---|
| 516 | print 'Point %s has multiple candidates: %s'\ |
|---|
| 517 | %(str(p0), candidate_list) |
|---|
| 518 | |
|---|
| 519 | |
|---|
| 520 | # Choose vector against which all angles will be measured |
|---|
| 521 | if len(polygon) > 1: |
|---|
| 522 | v_prev = p0 - polygon[-2] # Vector that leads to p0 |
|---|
| 523 | else: |
|---|
| 524 | # FIXME (Ole): What do we do if the first point has multiple |
|---|
| 525 | # candidates? |
|---|
| 526 | # Being the lower left corner, perhaps we can use the |
|---|
| 527 | # vector [1, 0], but I really don't know if this is completely |
|---|
| 528 | # watertight. |
|---|
| 529 | # Another option might be v_prev = [1.0, 0.0] |
|---|
| 530 | v_prev = [1.0, 0.0] |
|---|
| 531 | |
|---|
| 532 | |
|---|
| 533 | |
|---|
| 534 | # Choose candidate with minimum angle |
|---|
| 535 | minimum_angle = 2*pi |
|---|
| 536 | for pc in candidate_list: |
|---|
| 537 | vc = pc-p0 # Candidate vector |
|---|
| 538 | |
|---|
| 539 | # Angle between each candidate and the previous vector |
|---|
| 540 | # in [-pi, pi] |
|---|
| 541 | ac = angle(vc, v_prev) |
|---|
| 542 | if ac > pi: ac = pi-ac |
|---|
| 543 | |
|---|
| 544 | # take the minimal angle corresponding to the rightmost vector |
|---|
| 545 | if ac < minimum_angle: |
|---|
| 546 | minimum_angle = ac |
|---|
| 547 | p1 = pc # Best candidate |
|---|
| 548 | |
|---|
| 549 | |
|---|
| 550 | if verbose is True: |
|---|
| 551 | print ' Best candidate %s, angle %f' %(p1, minimum_angle*180/pi) |
|---|
| 552 | |
|---|
| 553 | else: |
|---|
| 554 | p1 = candidate_list[0] |
|---|
| 555 | |
|---|
| 556 | if point_registry.has_key(tuple(p1)): |
|---|
| 557 | # We have completed the boundary polygon - yeehaa |
|---|
| 558 | break |
|---|
| 559 | else: |
|---|
| 560 | point_registry[tuple(p1)] = len(point_registry) |
|---|
| 561 | |
|---|
| 562 | polygon.append(p1) |
|---|
| 563 | p0 = p1 |
|---|
| 564 | |
|---|
| 565 | |
|---|
| 566 | return polygon |
|---|
| 567 | |
|---|
| 568 | |
|---|
| 569 | def check_integrity(self): |
|---|
| 570 | """Check that triangles are internally consistent e.g. |
|---|
| 571 | that area corresponds to edgelengths, that vertices |
|---|
| 572 | are arranged in a counter-clockwise order, etc etc |
|---|
| 573 | Neighbour structure will be checked by class Mesh |
|---|
| 574 | """ |
|---|
| 575 | |
|---|
| 576 | from config import epsilon |
|---|
| 577 | from utilities.numerical_tools import anglediff |
|---|
| 578 | |
|---|
| 579 | N = self.number_of_elements |
|---|
| 580 | #Get x,y coordinates for all vertices for all triangles |
|---|
| 581 | V = self.get_vertex_coordinates() |
|---|
| 582 | #Check each triangle |
|---|
| 583 | for i in range(N): |
|---|
| 584 | |
|---|
| 585 | x0 = V[i, 0]; y0 = V[i, 1] |
|---|
| 586 | x1 = V[i, 2]; y1 = V[i, 3] |
|---|
| 587 | x2 = V[i, 4]; y2 = V[i, 5] |
|---|
| 588 | |
|---|
| 589 | #Check that area hasn't been compromised |
|---|
| 590 | area = self.areas[i] |
|---|
| 591 | ref = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
|---|
| 592 | msg = 'Wrong area for vertex coordinates: %f %f %f %f %f %f'\ |
|---|
| 593 | %(x0,y0,x1,y1,x2,y2) |
|---|
| 594 | assert abs((area - ref)/area) < epsilon, msg |
|---|
| 595 | |
|---|
| 596 | #Check that points are arranged in counter clock-wise order |
|---|
| 597 | v0 = [x1-x0, y1-y0] |
|---|
| 598 | v1 = [x2-x1, y2-y1] |
|---|
| 599 | v2 = [x0-x2, y0-y2] |
|---|
| 600 | |
|---|
| 601 | a0 = anglediff(v1, v0) |
|---|
| 602 | a1 = anglediff(v2, v1) |
|---|
| 603 | a2 = anglediff(v0, v2) |
|---|
| 604 | |
|---|
| 605 | msg = '''Vertices (%s,%s), (%s,%s), (%s,%s) are not arranged |
|---|
| 606 | in counter clockwise order''' %(x0, y0, x1, y1, x2, y2) |
|---|
| 607 | assert a0 < pi and a1 < pi and a2 < pi, msg |
|---|
| 608 | |
|---|
| 609 | #Check that normals are orthogonal to edge vectors |
|---|
| 610 | #Note that normal[k] lies opposite vertex k |
|---|
| 611 | |
|---|
| 612 | normal0 = self.normals[i, 0:2] |
|---|
| 613 | normal1 = self.normals[i, 2:4] |
|---|
| 614 | normal2 = self.normals[i, 4:6] |
|---|
| 615 | |
|---|
| 616 | for u, v in [ (v0, normal2), (v1, normal0), (v2, normal1) ]: |
|---|
| 617 | |
|---|
| 618 | #Normalise |
|---|
| 619 | l_u = sqrt(u[0]*u[0] + u[1]*u[1]) |
|---|
| 620 | l_v = sqrt(v[0]*v[0] + v[1]*v[1]) |
|---|
| 621 | |
|---|
| 622 | x = (u[0]*v[0] + u[1]*v[1])/l_u/l_v #Inner product |
|---|
| 623 | |
|---|
| 624 | msg = 'Normal vector (%f,%f) is not perpendicular to' %tuple(v) |
|---|
| 625 | msg += ' edge (%f,%f) in triangle %d.' %(tuple(u) + (i,)) |
|---|
| 626 | msg += ' Inner product is %e.' %x |
|---|
| 627 | assert x < epsilon, msg |
|---|
| 628 | |
|---|
| 629 | self.lone_vertices = [] |
|---|
| 630 | #Check that all vertices have been registered |
|---|
| 631 | for v_id, v in enumerate(self.vertexlist): |
|---|
| 632 | |
|---|
| 633 | #msg = 'Vertex %s does not belong to an element.' |
|---|
| 634 | #assert v is not None, msg |
|---|
| 635 | if v is None: |
|---|
| 636 | #print msg%v_id |
|---|
| 637 | self.lone_vertices.append(v_id) |
|---|
| 638 | |
|---|
| 639 | #Check integrity of neighbour structure |
|---|
| 640 | for i in range(N): |
|---|
| 641 | # print i |
|---|
| 642 | for v in self.triangles[i, :]: |
|---|
| 643 | #Check that all vertices have been registered |
|---|
| 644 | assert self.vertexlist[v] is not None |
|---|
| 645 | |
|---|
| 646 | #Check that this triangle is listed with at least one vertex |
|---|
| 647 | assert (i, 0) in self.vertexlist[v] or\ |
|---|
| 648 | (i, 1) in self.vertexlist[v] or\ |
|---|
| 649 | (i, 2) in self.vertexlist[v] |
|---|
| 650 | |
|---|
| 651 | |
|---|
| 652 | |
|---|
| 653 | #Check neighbour structure |
|---|
| 654 | for k, neighbour_id in enumerate(self.neighbours[i,:]): |
|---|
| 655 | |
|---|
| 656 | #Assert that my neighbour's neighbour is me |
|---|
| 657 | #Boundaries need not fulfill this |
|---|
| 658 | if neighbour_id >= 0: |
|---|
| 659 | edge = self.neighbour_edges[i, k] |
|---|
| 660 | msg = 'Triangle %d has neighbour %d but it does not point back. \n' %(i,neighbour_id) |
|---|
| 661 | msg += 'Only points to (%s)' %(self.neighbours[neighbour_id,:]) |
|---|
| 662 | assert self.neighbours[neighbour_id, edge] == i ,msg |
|---|
| 663 | |
|---|
| 664 | |
|---|
| 665 | |
|---|
| 666 | #Check that all boundaries have |
|---|
| 667 | # unique, consecutive, negative indices |
|---|
| 668 | |
|---|
| 669 | #L = len(self.boundary) |
|---|
| 670 | #for i in range(L): |
|---|
| 671 | # id, edge = self.boundary_segments[i] |
|---|
| 672 | # assert self.neighbours[id, edge] == -i-1 |
|---|
| 673 | |
|---|
| 674 | |
|---|
| 675 | #NOTE: This assert doesn't hold true if there are internal boundaries |
|---|
| 676 | #FIXME: Look into this further. |
|---|
| 677 | #FIXME (Ole): In pyvolution mark 3 this is OK again |
|---|
| 678 | #NOTE: No longer works because neighbour structure is modified by |
|---|
| 679 | # domain set_boundary. |
|---|
| 680 | #for id, edge in self.boundary: |
|---|
| 681 | # assert self.neighbours[id,edge] < 0 |
|---|
| 682 | # |
|---|
| 683 | #NOTE (Ole): I reckon this was resolved late 2004? |
|---|
| 684 | # |
|---|
| 685 | #See domain.set_boundary |
|---|
| 686 | |
|---|
| 687 | def get_lone_vertices(self): |
|---|
| 688 | """Return a list of vertices that are not connected to any triangles. |
|---|
| 689 | |
|---|
| 690 | Precondition |
|---|
| 691 | FIXME(DSG - DSG) Pull the code out of check integrity that builds this |
|---|
| 692 | structure. |
|---|
| 693 | check_integrity has to have been called. |
|---|
| 694 | """ |
|---|
| 695 | return self.lone_vertices |
|---|
| 696 | |
|---|
| 697 | def get_centroid_coordinates(self): |
|---|
| 698 | """Return all centroid coordinates. |
|---|
| 699 | Return all centroid coordinates for all triangles as an Nx2 array |
|---|
| 700 | (ordered as x0, y0 for each triangle) |
|---|
| 701 | """ |
|---|
| 702 | return self.centroid_coordinates |
|---|
| 703 | |
|---|
| 704 | |
|---|
| 705 | |
|---|
| 706 | |
|---|
| 707 | def statistics(self): |
|---|
| 708 | """Output statistics about mesh |
|---|
| 709 | """ |
|---|
| 710 | |
|---|
| 711 | from Numeric import arange |
|---|
| 712 | from utilities.numerical_tools import histogram, create_bins |
|---|
| 713 | |
|---|
| 714 | vertex_coordinates = self.vertex_coordinates # Relative coordinates |
|---|
| 715 | areas = self.areas |
|---|
| 716 | x = vertex_coordinates[:,0] |
|---|
| 717 | y = vertex_coordinates[:,1] |
|---|
| 718 | |
|---|
| 719 | |
|---|
| 720 | #Setup 10 bins for area histogram |
|---|
| 721 | bins = create_bins(areas, 10) |
|---|
| 722 | #m = max(areas) |
|---|
| 723 | #bins = arange(0., m, m/10) |
|---|
| 724 | hist = histogram(areas, bins) |
|---|
| 725 | |
|---|
| 726 | str = '------------------------------------------------\n' |
|---|
| 727 | str += 'Mesh statistics:\n' |
|---|
| 728 | str += ' Number of triangles = %d\n' %self.number_of_elements |
|---|
| 729 | str += ' Extent:\n' |
|---|
| 730 | str += ' x in [%f, %f]\n' %(min(x), max(x)) |
|---|
| 731 | str += ' y in [%f, %f]\n' %(min(y), max(y)) |
|---|
| 732 | str += ' Areas:\n' |
|---|
| 733 | str += ' A in [%f, %f]\n' %(min(areas), max(areas)) |
|---|
| 734 | str += ' number of distinct areas: %d\n' %(len(areas)) |
|---|
| 735 | str += ' Histogram:\n' |
|---|
| 736 | |
|---|
| 737 | hi = bins[0] |
|---|
| 738 | for i, count in enumerate(hist): |
|---|
| 739 | lo = hi |
|---|
| 740 | if i+1 < len(bins): |
|---|
| 741 | #Open upper interval |
|---|
| 742 | hi = bins[i+1] |
|---|
| 743 | str += ' [%f, %f[: %d\n' %(lo, hi, count) |
|---|
| 744 | else: |
|---|
| 745 | #Closed upper interval |
|---|
| 746 | hi = max(areas) |
|---|
| 747 | str += ' [%f, %f]: %d\n' %(lo, hi, count) |
|---|
| 748 | |
|---|
| 749 | N = len(areas) |
|---|
| 750 | if N > 10: |
|---|
| 751 | str += ' Percentiles (10%):\n' |
|---|
| 752 | areas = areas.tolist() |
|---|
| 753 | areas.sort() |
|---|
| 754 | |
|---|
| 755 | k = 0 |
|---|
| 756 | lower = min(areas) |
|---|
| 757 | for i, a in enumerate(areas): |
|---|
| 758 | if i % (N/10) == 0 and i != 0: #For every 10% of the sorted areas |
|---|
| 759 | str += ' %d triangles in [%f, %f]\n' %(i-k, lower, a) |
|---|
| 760 | lower = a |
|---|
| 761 | k = i |
|---|
| 762 | |
|---|
| 763 | str += ' %d triangles in [%f, %f]\n'\ |
|---|
| 764 | %(N-k, lower, max(areas)) |
|---|
| 765 | |
|---|
| 766 | |
|---|
| 767 | str += 'Boundary:\n' |
|---|
| 768 | str += ' Number of boundary segments == %d\n' %(len(self.boundary)) |
|---|
| 769 | str += ' Boundary tags == %s\n' %self.get_boundary_tags() |
|---|
| 770 | str += '------------------------------------------------\n' |
|---|
| 771 | |
|---|
| 772 | |
|---|
| 773 | return str |
|---|
| 774 | |
|---|
