# marching_squares

## `marching_squares(S, GV, nx, ny)`

Marching squares algorithm for extracting isocontours from a scalar field. Output is given as a list of (unordered) vertices and edge indices into the vertex list.

Parameters:

Name Type Description Default
`S` `(nx`

Scalar field

required
`GV` `(nx`

Grid vertex positions

required
`nx` `int`

Number of grid vertices in x direction

required
`ny` `int`

Number of grid vertices in y direction

required

Returns:

Name Type Description
`V` `(nv,2) numpy double array`

Vertex positions

`E` `(ne,2) numpy int array`

Edge indices into V

marching_cubes

Examples:

``````import numpy as np
import matplotlib.pyplot as plt
import gpytoolbox as gpt
# Create a scalar field
nx = 100
ny = 100
x = np.linspace(-1,1,nx)
y = np.linspace(-1,1,ny)
X,Y = np.meshgrid(x,y)
S = np.exp(-X**2-Y**2)
# Extract isocontours
V,E = gpt.marching_squares(S,np.c_[X.flatten(),Y.flatten()],nx,ny)
# Plot
plt.figure()
plt.imshow(S.reshape((nx,ny),order='F'),extent=[-1,1,-1,1])
for i in range(E.shape[0]):
plt.plot([V[E[i,0],0],V[E[i,1],0]],
[V[E[i,0],1],V[E[i,1],1]],
'k-')
plt.show()
plt.axis('equal')
plt.show()
``````
Source code in `src/gpytoolbox/marching_squares.py`
 ``` 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197``` ``````def marching_squares(S,GV,nx,ny): """ Marching squares algorithm for extracting isocontours from a scalar field. Output is given as a list of (unordered) vertices and edge indices into the vertex list. Parameters ---------- S : (nx*ny,) numpy double array Scalar field GV : (nx*ny,2) numpy double array Grid vertex positions nx : int Number of grid vertices in x direction ny : int Number of grid vertices in y direction Returns ------- V : (nv,2) numpy double array Vertex positions E : (ne,2) numpy int array Edge indices into V See Also -------- marching_cubes Examples -------- ```python import numpy as np import matplotlib.pyplot as plt import gpytoolbox as gpt # Create a scalar field nx = 100 ny = 100 x = np.linspace(-1,1,nx) y = np.linspace(-1,1,ny) X,Y = np.meshgrid(x,y) S = np.exp(-X**2-Y**2) # Extract isocontours V,E = gpt.marching_squares(S,np.c_[X.flatten(),Y.flatten()],nx,ny) # Plot plt.figure() plt.imshow(S.reshape((nx,ny),order='F'),extent=[-1,1,-1,1]) for i in range(E.shape[0]): plt.plot([V[E[i,0],0],V[E[i,1],0]], [V[E[i,0],1],V[E[i,1],1]], 'k-') plt.show() plt.axis('equal') plt.show() ``` """ S = np.reshape(S,(nx,ny),order='F') # Create empty list for verts = [] edge_list = [] # index of edge vertices # Loop over all grid points for i in range(nx-1): for j in range(ny-1): # Get the scalar values at the corners of the grid cell a = S[i,j] b = S[i+1,j] c = S[i+1,j+1] d = S[i,j+1] # Get the contour index k = 0 if a > 0: k += 1 if b > 0: k += 2 if c > 0: k += 4 if d > 0: k += 8 # Use symmetry flip = False if k > 7: flip = True k = 15 - k # Get the contour line segments if k == 1: # x = i x = i - a/(b-a) y = j verts.append([x,y]) x = i y = j - a/(d-a) # y = j verts.append([x,y]) if flip: edge_list.append([len(verts)-2,len(verts)-1]) else: edge_list.append([len(verts)-1,len(verts)-2]) elif k == 2: x = i - a/(b-a) # x = i y = j verts.append([x,y]) x = i + 1 y = j - b/(c-b) verts.append([x,y]) if flip: edge_list.append([len(verts)-1,len(verts)-2]) else: edge_list.append([len(verts)-2,len(verts)-1]) elif k == 3: x = i y = j - a/(d-a) verts.append([x,y]) x = i + 1 y = j - b/(c-b) verts.append([x,y]) if flip: edge_list.append([len(verts)-1,len(verts)-2]) else: edge_list.append([len(verts)-2,len(verts)-1]) elif k == 4: x = i + 1 y = j- b/(c-b) verts.append([x,y]) x = i - d/(c-d) y = j + 1 verts.append([x,y]) if flip: edge_list.append([len(verts)-1,len(verts)-2]) else: edge_list.append([len(verts)-2,len(verts)-1]) elif k == 5: x = i - a/(b-a) y = j verts.append([x,y]) x = i y = j - a/(d-a) # y = j verts.append([x,y]) x = i + 1 y = j- b/(c-b) verts.append([x,y]) x = i - d/(c-d) y = j + 1 verts.append([x,y]) if flip: edge_list.append([len(verts)-4,len(verts)-3]) else: edge_list.append([len(verts)-3,len(verts)-4]) if flip: edge_list.append([len(verts)-1,len(verts)-2]) else: edge_list.append([len(verts)-2,len(verts)-1]) elif k == 6: x = i - a/(b-a) y = j verts.append([x,y]) x = i - d/(c-d) y = j + 1 verts.append([x,y]) if flip: edge_list.append([len(verts)-1,len(verts)-2]) else: edge_list.append([len(verts)-2,len(verts)-1]) elif k == 7: x = i - d/(c-d) y = j + 1 verts.append([x,y]) x = i y = j - a/(d-a) verts.append([x,y]) if flip: edge_list.append([len(verts)-2,len(verts)-1]) else: edge_list.append([len(verts)-1,len(verts)-2]) else: pass # Convert list to numpy array verts = np.array(verts) edges = np.array(edge_list) verts, SVI, SVJ, edges = remove_duplicate_vertices(verts,faces=edges, epsilon=np.sqrt(np.finfo(verts.dtype).eps)) # Remove trivial edges edges = edges[np.not_equal(edges[:,0], edges[:,1]), :] # # Remove duplicate edges # edges = np.unique(edges, axis=0) # Rescale to original grid verts[:,0] = verts[:,0]/(nx-1) verts[:,1] = verts[:,1]/(ny-1) verts = verts*(GV.max(axis=0)-GV.min(axis=0)) + GV.min(axis=0) return verts, edges ``````