[5897] | 1 | #!/usr/bin/env python |
---|
| 2 | |
---|
[7276] | 3 | """Polygon manipulations""" |
---|
[5897] | 4 | |
---|
[7276] | 5 | import numpy as num |
---|
| 6 | |
---|
[5897] | 7 | from anuga.utilities.numerical_tools import ensure_numeric |
---|
[7778] | 8 | from anuga.geospatial_data.geospatial_data import ensure_absolute, \ |
---|
| 9 | Geospatial_data |
---|
[7317] | 10 | import anuga.utilities.log as log |
---|
[5897] | 11 | |
---|
[7858] | 12 | from aabb import AABB |
---|
[5897] | 13 | |
---|
[7276] | 14 | ## |
---|
| 15 | # @brief Determine whether a point is on a line segment. |
---|
| 16 | # @param point (x, y) of point in question (tuple, list or array). |
---|
| 17 | # @param line ((x1,y1), (x2,y2)) for line (tuple, list or array). |
---|
| 18 | # @param rtol Relative error for 'close'. |
---|
| 19 | # @param atol Absolute error for 'close'. |
---|
| 20 | # @return True or False. |
---|
[5932] | 21 | def point_on_line(point, line, rtol=1.0e-5, atol=1.0e-8): |
---|
[5897] | 22 | """Determine whether a point is on a line segment |
---|
| 23 | |
---|
[7276] | 24 | Input: |
---|
[5897] | 25 | point is given by [x, y] |
---|
[7276] | 26 | line is given by [x0, y0], [x1, y1]] or |
---|
| 27 | the equivalent 2x2 numeric array with each row corresponding to a point. |
---|
[5897] | 28 | |
---|
| 29 | Output: |
---|
| 30 | |
---|
[7276] | 31 | Note: Line can be degenerate and function still works to discern coinciding |
---|
| 32 | points from non-coinciding. |
---|
[5897] | 33 | """ |
---|
| 34 | |
---|
| 35 | point = ensure_numeric(point) |
---|
| 36 | line = ensure_numeric(line) |
---|
| 37 | |
---|
| 38 | res = _point_on_line(point[0], point[1], |
---|
[7858] | 39 | line[0, 0], line[0, 1], |
---|
| 40 | line[1, 0], line[1, 1], |
---|
[5897] | 41 | rtol, atol) |
---|
[7276] | 42 | |
---|
[5897] | 43 | return bool(res) |
---|
| 44 | |
---|
| 45 | |
---|
[5942] | 46 | ###### |
---|
| 47 | # Result functions used in intersection() below for collinear lines. |
---|
| 48 | # (p0,p1) defines line 0, (p2,p3) defines line 1. |
---|
| 49 | ###### |
---|
[5897] | 50 | |
---|
[5942] | 51 | # result functions for possible states |
---|
[7858] | 52 | def lines_dont_coincide(p0, p1, p2, p3): |
---|
| 53 | return (3, None) |
---|
| 54 | |
---|
| 55 | def lines_0_fully_included_in_1(p0, p1, p2, p3): |
---|
| 56 | return (2, num.array([p0, p1])) |
---|
| 57 | |
---|
| 58 | def lines_1_fully_included_in_0(p0, p1, p2, p3): |
---|
| 59 | return (2, num.array([p2, p3])) |
---|
| 60 | |
---|
| 61 | def lines_overlap_same_direction(p0, p1, p2, p3): |
---|
| 62 | return (2, num.array([p0, p3])) |
---|
| 63 | |
---|
| 64 | def lines_overlap_same_direction2(p0, p1, p2, p3): |
---|
| 65 | return (2, num.array([p2, p1])) |
---|
| 66 | |
---|
| 67 | def lines_overlap_opposite_direction(p0, p1, p2, p3): |
---|
| 68 | return (2, num.array([p0, p2])) |
---|
| 69 | |
---|
| 70 | def lines_overlap_opposite_direction2(p0, p1, p2, p3): |
---|
| 71 | return (2, num.array([p3, p1])) |
---|
[5897] | 72 | |
---|
[5942] | 73 | # this function called when an impossible state is found |
---|
[7276] | 74 | def lines_error(p1, p2, p3, p4): |
---|
| 75 | raise RuntimeError, ('INTERNAL ERROR: p1=%s, p2=%s, p3=%s, p4=%s' |
---|
| 76 | % (str(p1), str(p2), str(p3), str(p4))) |
---|
[5897] | 77 | |
---|
[7778] | 78 | collinear_result = { |
---|
| 79 | # line 0 starts on 1, 0 ends 1, 1 starts 0, 1 ends 0 |
---|
| 80 | # 0s1 0e1 1s0 1e0 |
---|
| 81 | (False, False, False, False): lines_dont_coincide, |
---|
| 82 | (False, False, False, True ): lines_error, |
---|
| 83 | (False, False, True, False): lines_error, |
---|
| 84 | (False, False, True, True ): lines_1_fully_included_in_0, |
---|
| 85 | (False, True, False, False): lines_error, |
---|
| 86 | (False, True, False, True ): lines_overlap_opposite_direction2, |
---|
| 87 | (False, True, True, False): lines_overlap_same_direction2, |
---|
| 88 | (False, True, True, True ): lines_1_fully_included_in_0, |
---|
| 89 | (True, False, False, False): lines_error, |
---|
| 90 | (True, False, False, True ): lines_overlap_same_direction, |
---|
| 91 | (True, False, True, False): lines_overlap_opposite_direction, |
---|
| 92 | (True, False, True, True ): lines_1_fully_included_in_0, |
---|
| 93 | (True, True, False, False): lines_0_fully_included_in_1, |
---|
| 94 | (True, True, False, True ): lines_0_fully_included_in_1, |
---|
| 95 | (True, True, True, False): lines_0_fully_included_in_1, |
---|
| 96 | (True, True, True, True ): lines_0_fully_included_in_1 |
---|
| 97 | } |
---|
[5942] | 98 | |
---|
[7276] | 99 | ## |
---|
| 100 | # @brief Finds intersection point of two line segments. |
---|
| 101 | # @param line0 First line ((x1,y1), (x2,y2)). |
---|
| 102 | # @param line1 Second line ((x1,y1), (x2,y2)). |
---|
| 103 | # @param rtol Relative error for 'close'. |
---|
| 104 | # @param atol Absolute error for 'close'. |
---|
| 105 | # @return (status, value) where: |
---|
| 106 | # status = 0 - no intersection, value set to None |
---|
| 107 | # 1 - intersection found, value=(x,y) |
---|
| 108 | # 2 - lines collienar, overlap, value=overlap segment |
---|
| 109 | # 3 - lines collinear, no overlap, value is None |
---|
| 110 | # 4 - lines parallel, value is None |
---|
[5932] | 111 | def intersection(line0, line1, rtol=1.0e-5, atol=1.0e-8): |
---|
[7276] | 112 | """Returns intersecting point between two line segments. |
---|
[5897] | 113 | |
---|
[7276] | 114 | However, if parallel lines coincide partly (i.e. share a common segment), |
---|
[5897] | 115 | the line segment where lines coincide is returned |
---|
| 116 | |
---|
| 117 | Inputs: |
---|
| 118 | line0, line1: Each defined by two end points as in: [[x0, y0], [x1, y1]] |
---|
[5942] | 119 | A line can also be a 2x2 numpy array with each row |
---|
[5897] | 120 | corresponding to a point. |
---|
| 121 | |
---|
| 122 | Output: |
---|
[7276] | 123 | status, value - where status and value is interpreted as follows: |
---|
[5942] | 124 | status == 0: no intersection, value set to None. |
---|
| 125 | status == 1: intersection point found and returned in value as [x,y]. |
---|
[7276] | 126 | status == 2: Collinear overlapping lines found. |
---|
| 127 | Value takes the form [[x0,y0], [x1,y1]]. |
---|
[5942] | 128 | status == 3: Collinear non-overlapping lines. Value set to None. |
---|
[7276] | 129 | status == 4: Lines are parallel. Value set to None. |
---|
[5897] | 130 | """ |
---|
| 131 | |
---|
| 132 | # FIXME (Ole): Write this in C |
---|
| 133 | |
---|
[7276] | 134 | line0 = ensure_numeric(line0, num.float) |
---|
| 135 | line1 = ensure_numeric(line1, num.float) |
---|
[5897] | 136 | |
---|
[7841] | 137 | x0 = line0[0, 0]; y0 = line0[0, 1] |
---|
| 138 | x1 = line0[1, 0]; y1 = line0[1, 1] |
---|
[5897] | 139 | |
---|
[7841] | 140 | x2 = line1[0, 0]; y2 = line1[0, 1] |
---|
| 141 | x3 = line1[1, 0]; y3 = line1[1, 1] |
---|
[5897] | 142 | |
---|
| 143 | denom = (y3-y2)*(x1-x0) - (x3-x2)*(y1-y0) |
---|
| 144 | u0 = (x3-x2)*(y0-y2) - (y3-y2)*(x0-x2) |
---|
| 145 | u1 = (x2-x0)*(y1-y0) - (y2-y0)*(x1-x0) |
---|
[7276] | 146 | |
---|
[6158] | 147 | if num.allclose(denom, 0.0, rtol=rtol, atol=atol): |
---|
[5942] | 148 | # Lines are parallel - check if they are collinear |
---|
[6158] | 149 | if num.allclose([u0, u1], 0.0, rtol=rtol, atol=atol): |
---|
[5942] | 150 | # We now know that the lines are collinear |
---|
| 151 | state_tuple = (point_on_line([x0, y0], line1, rtol=rtol, atol=atol), |
---|
| 152 | point_on_line([x1, y1], line1, rtol=rtol, atol=atol), |
---|
| 153 | point_on_line([x2, y2], line0, rtol=rtol, atol=atol), |
---|
| 154 | point_on_line([x3, y3], line0, rtol=rtol, atol=atol)) |
---|
[5897] | 155 | |
---|
[7858] | 156 | return collinear_result[state_tuple]([x0, y0], [x1, y1], |
---|
| 157 | [x2, y2], [x3, y3]) |
---|
[5897] | 158 | else: |
---|
[5942] | 159 | # Lines are parallel but aren't collinear |
---|
[7276] | 160 | return 4, None #FIXME (Ole): Add distance here instead of None |
---|
[5897] | 161 | else: |
---|
[5942] | 162 | # Lines are not parallel, check if they intersect |
---|
[5897] | 163 | u0 = u0/denom |
---|
[7276] | 164 | u1 = u1/denom |
---|
[5897] | 165 | |
---|
| 166 | x = x0 + u0*(x1-x0) |
---|
| 167 | y = y0 + u0*(y1-y0) |
---|
| 168 | |
---|
| 169 | # Sanity check - can be removed to speed up if needed |
---|
[6158] | 170 | assert num.allclose(x, x2 + u1*(x3-x2), rtol=rtol, atol=atol) |
---|
[7276] | 171 | assert num.allclose(y, y2 + u1*(y3-y2), rtol=rtol, atol=atol) |
---|
[5897] | 172 | |
---|
| 173 | # Check if point found lies within given line segments |
---|
[7276] | 174 | if 0.0 <= u0 <= 1.0 and 0.0 <= u1 <= 1.0: |
---|
[5897] | 175 | # We have intersection |
---|
[6158] | 176 | return 1, num.array([x, y]) |
---|
[5897] | 177 | else: |
---|
| 178 | # No intersection |
---|
| 179 | return 0, None |
---|
| 180 | |
---|
[7276] | 181 | ## |
---|
| 182 | # @brief Finds intersection point of two line segments. |
---|
| 183 | # @param line0 First line ((x1,y1), (x2,y2)). |
---|
| 184 | # @param line1 Second line ((x1,y1), (x2,y2)). |
---|
| 185 | # @return (status, value) where: |
---|
| 186 | # status = 0 - no intersection, value set to None |
---|
| 187 | # 1 - intersection found, value=(x,y) |
---|
| 188 | # 2 - lines collienar, overlap, value=overlap segment |
---|
| 189 | # 3 - lines collinear, no overlap, value is None |
---|
| 190 | # 4 - lines parallel, value is None |
---|
| 191 | # @note Wrapper for C function. |
---|
[5897] | 192 | def NEW_C_intersection(line0, line1): |
---|
[7276] | 193 | """Returns intersecting point between two line segments. |
---|
[5897] | 194 | |
---|
[7276] | 195 | However, if parallel lines coincide partly (i.e. share a common segment), |
---|
[5897] | 196 | the line segment where lines coincide is returned |
---|
| 197 | |
---|
| 198 | Inputs: |
---|
| 199 | line0, line1: Each defined by two end points as in: [[x0, y0], [x1, y1]] |
---|
[7276] | 200 | A line can also be a 2x2 numpy array with each row |
---|
[5897] | 201 | corresponding to a point. |
---|
| 202 | |
---|
| 203 | Output: |
---|
[7276] | 204 | status, value - where status and value is interpreted as follows: |
---|
| 205 | status == 0: no intersection, value set to None. |
---|
| 206 | status == 1: intersection point found and returned in value as [x,y]. |
---|
| 207 | status == 2: Collinear overlapping lines found. |
---|
| 208 | Value takes the form [[x0,y0], [x1,y1]]. |
---|
| 209 | status == 3: Collinear non-overlapping lines. Value set to None. |
---|
| 210 | status == 4: Lines are parallel. Value set to None. |
---|
[5897] | 211 | """ |
---|
| 212 | |
---|
[7276] | 213 | line0 = ensure_numeric(line0, num.float) |
---|
| 214 | line1 = ensure_numeric(line1, num.float) |
---|
[5897] | 215 | |
---|
[7841] | 216 | status, value = _intersection(line0[0, 0], line0[0, 1], |
---|
| 217 | line0[1, 0], line0[1, 1], |
---|
| 218 | line1[0, 0], line1[0, 1], |
---|
| 219 | line1[1, 0], line1[1, 1]) |
---|
[5897] | 220 | |
---|
| 221 | return status, value |
---|
| 222 | |
---|
[8031] | 223 | def polygon_overlap(triangles, polygon, verbose=False): |
---|
| 224 | """Determine if a polygon and triangle overlap |
---|
| 225 | |
---|
| 226 | """ |
---|
| 227 | polygon = ensure_numeric(polygon) |
---|
| 228 | triangles = ensure_numeric(triangles) |
---|
| 229 | |
---|
| 230 | M = triangles.shape[0]/3 # Number of triangles |
---|
| 231 | |
---|
| 232 | indices = num.zeros(M, num.int) |
---|
| 233 | |
---|
| 234 | count = _polygon_overlap(polygon, triangles, indices) |
---|
| 235 | |
---|
| 236 | if verbose: |
---|
| 237 | log.critical('Found %d triangles (out of %d) that polygon' % (count, M)) |
---|
| 238 | |
---|
| 239 | return indices[:count] |
---|
| 240 | |
---|
| 241 | def not_polygon_overlap(triangles, polygon, verbose=False): |
---|
| 242 | """Determine if a polygon and triangle overlap |
---|
| 243 | |
---|
| 244 | """ |
---|
| 245 | polygon = ensure_numeric(polygon) |
---|
| 246 | triangles = ensure_numeric(triangles) |
---|
| 247 | |
---|
| 248 | M = triangles.shape[0]/3 # Number of triangles |
---|
| 249 | |
---|
| 250 | indices = num.zeros(M, num.int) |
---|
| 251 | |
---|
| 252 | count = _polygon_overlap(polygon, triangles, indices) |
---|
| 253 | |
---|
| 254 | if verbose: |
---|
| 255 | log.critical('Found %d triangles (out of %d) that polygon' % (count, M)) |
---|
| 256 | |
---|
| 257 | return indices[count:] |
---|
| 258 | |
---|
[8053] | 259 | def line_intersect(triangles, line, verbose=False): |
---|
[8037] | 260 | """Determine if a polygon and triangle overlap |
---|
| 261 | |
---|
| 262 | """ |
---|
[8053] | 263 | line = ensure_numeric(line) |
---|
[8037] | 264 | triangles = ensure_numeric(triangles) |
---|
| 265 | |
---|
| 266 | M = triangles.shape[0]/3 # Number of triangles |
---|
| 267 | |
---|
| 268 | indices = num.zeros(M, num.int) |
---|
| 269 | |
---|
[8053] | 270 | count = _line_intersect(line, triangles, indices) |
---|
[8037] | 271 | |
---|
| 272 | if verbose: |
---|
[8053] | 273 | log.critical('Found %d triangles (out of %d) that overlap the polygon' % (count, M)) |
---|
[8037] | 274 | |
---|
| 275 | return indices[:count] |
---|
| 276 | |
---|
[8053] | 277 | def not_line_intersect(triangles, line, verbose=False): |
---|
[8037] | 278 | """Determine if a polyline and triangle overlap |
---|
| 279 | |
---|
| 280 | """ |
---|
[8053] | 281 | line = ensure_numeric(line) |
---|
[8037] | 282 | triangles = ensure_numeric(triangles) |
---|
| 283 | |
---|
| 284 | M = triangles.shape[0]/3 # Number of triangles |
---|
| 285 | |
---|
| 286 | indices = num.zeros(M, num.int) |
---|
| 287 | |
---|
[8053] | 288 | count = _line_intersect(line, triangles, indices) |
---|
[8037] | 289 | |
---|
| 290 | if verbose: |
---|
[8053] | 291 | log.critical('Found %d triangles (out of %d) that intersect the line' % (count, M)) |
---|
[8037] | 292 | |
---|
| 293 | return indices[count:] |
---|
| 294 | |
---|
| 295 | |
---|
[6534] | 296 | def is_inside_triangle(point, triangle, |
---|
| 297 | closed=True, |
---|
[6535] | 298 | rtol=1.0e-12, |
---|
| 299 | atol=1.0e-12, |
---|
[7841] | 300 | check_inputs=True): |
---|
[6534] | 301 | """Determine if one point is inside a triangle |
---|
| 302 | |
---|
| 303 | This uses the barycentric method: |
---|
| 304 | |
---|
| 305 | Triangle is A, B, C |
---|
| 306 | Point P can then be written as |
---|
| 307 | |
---|
| 308 | P = A + alpha * (C-A) + beta * (B-A) |
---|
| 309 | or if we let |
---|
| 310 | v=P-A, v0=C-A, v1=B-A |
---|
| 311 | |
---|
| 312 | v = alpha*v0 + beta*v1 |
---|
[5897] | 313 | |
---|
[6534] | 314 | Dot this equation by v0 and v1 to get two: |
---|
| 315 | |
---|
| 316 | dot(v0, v) = alpha*dot(v0, v0) + beta*dot(v0, v1) |
---|
| 317 | dot(v1, v) = alpha*dot(v1, v0) + beta*dot(v1, v1) |
---|
| 318 | |
---|
| 319 | or if a_ij = dot(v_i, v_j) and b_i = dot(v_i, v) |
---|
| 320 | the matrix equation: |
---|
| 321 | |
---|
| 322 | a_00 a_01 alpha b_0 |
---|
| 323 | = |
---|
| 324 | a_10 a_11 beta b_1 |
---|
| 325 | |
---|
| 326 | Solving for alpha and beta yields: |
---|
| 327 | |
---|
| 328 | alpha = (b_0*a_11 - b_1*a_01)/denom |
---|
| 329 | beta = (b_1*a_00 - b_0*a_10)/denom |
---|
| 330 | |
---|
| 331 | with denom = a_11*a_00 - a_10*a_01 |
---|
| 332 | |
---|
| 333 | The point is in the triangle whenever |
---|
| 334 | alpha and beta and their sums are in the unit interval. |
---|
| 335 | |
---|
| 336 | rtol and atol will determine how close the point has to be to the edge |
---|
[6535] | 337 | before it is deemed to be on the edge. |
---|
[6534] | 338 | |
---|
| 339 | """ |
---|
[5897] | 340 | |
---|
[6544] | 341 | triangle = ensure_numeric(triangle) |
---|
[7276] | 342 | point = ensure_numeric(point, num.float) |
---|
[6544] | 343 | |
---|
[6534] | 344 | if check_inputs is True: |
---|
| 345 | msg = 'is_inside_triangle must be invoked with one point only' |
---|
| 346 | assert num.allclose(point.shape, [2]), msg |
---|
| 347 | |
---|
[6544] | 348 | |
---|
[6541] | 349 | # Use C-implementation |
---|
[6535] | 350 | return bool(_is_inside_triangle(point, triangle, int(closed), rtol, atol)) |
---|
[6534] | 351 | |
---|
[8057] | 352 | def is_complex(polygon, closed=True, verbose=False): |
---|
[7690] | 353 | """Check if a polygon is complex (self-intersecting). |
---|
| 354 | Uses a sweep algorithm that is O(n^2) in the worst case, but |
---|
| 355 | for most normal looking polygons it'll be O(n log n). |
---|
| 356 | |
---|
| 357 | polygon is a list of points that define a closed polygon. |
---|
| 358 | verbose will print a list of the intersection points if true |
---|
| 359 | |
---|
| 360 | Return True if polygon is complex. |
---|
| 361 | """ |
---|
| 362 | |
---|
| 363 | def key_xpos(item): |
---|
[7858] | 364 | """ Return the x coord out of the passed point for sorting key. """ |
---|
[7690] | 365 | return (item[0][0]) |
---|
[7686] | 366 | |
---|
[7690] | 367 | def segments_joined(seg0, seg1): |
---|
[7841] | 368 | """ See if there are identical segments in the 2 lists. """ |
---|
[7690] | 369 | for i in seg0: |
---|
| 370 | for j in seg1: |
---|
| 371 | if i == j: return True |
---|
| 372 | return False |
---|
| 373 | |
---|
[7686] | 374 | polygon = ensure_numeric(polygon, num.float) |
---|
| 375 | |
---|
[7690] | 376 | # build a list of discrete segments from the polygon |
---|
| 377 | unsorted_segs = [] |
---|
[7686] | 378 | for i in range(0, len(polygon)-1): |
---|
[7690] | 379 | unsorted_segs.append([list(polygon[i]), list(polygon[i+1])]) |
---|
[8057] | 380 | |
---|
| 381 | if closed: |
---|
| 382 | unsorted_segs.append([list(polygon[0]), list(polygon[-1])]) |
---|
[7690] | 383 | |
---|
| 384 | # all segments must point in same direction |
---|
| 385 | for val in unsorted_segs: |
---|
| 386 | if val[0][0] > val[1][0]: |
---|
| 387 | val[0], val[1] = val[1], val[0] |
---|
| 388 | |
---|
| 389 | l_x = sorted(unsorted_segs, key=key_xpos) |
---|
[7686] | 390 | |
---|
[7690] | 391 | comparisons = 0 |
---|
| 392 | |
---|
| 393 | # loop through, only comparing lines that partially overlap in x |
---|
| 394 | for index, leftmost in enumerate(l_x): |
---|
| 395 | cmp = index+1 |
---|
| 396 | while cmp < len(l_x) and leftmost[1][0] > l_x[cmp][0][0]: |
---|
| 397 | if not segments_joined(leftmost, l_x[cmp]): |
---|
| 398 | (type, point) = intersection(leftmost, l_x[cmp]) |
---|
| 399 | comparisons += 1 |
---|
[7778] | 400 | if type != 0 and type != 4 or (type == 2 and list(point[0]) !=\ |
---|
| 401 | list(point[1])): |
---|
[7687] | 402 | if verbose: |
---|
[7778] | 403 | print 'Self-intersecting polygon found, type ', type |
---|
| 404 | print 'point', point, |
---|
[7858] | 405 | print 'vertices: ', leftmost, ' - ', l_x[cmp] |
---|
[7690] | 406 | return True |
---|
| 407 | cmp += 1 |
---|
[7686] | 408 | |
---|
| 409 | return False |
---|
| 410 | |
---|
[6534] | 411 | |
---|
[5897] | 412 | def is_inside_polygon(point, polygon, closed=True, verbose=False): |
---|
| 413 | """Determine if one point is inside a polygon |
---|
| 414 | |
---|
| 415 | See inside_polygon for more details |
---|
| 416 | """ |
---|
| 417 | |
---|
| 418 | indices = inside_polygon(point, polygon, closed, verbose) |
---|
| 419 | |
---|
| 420 | if indices.shape[0] == 1: |
---|
| 421 | return True |
---|
| 422 | elif indices.shape[0] == 0: |
---|
| 423 | return False |
---|
| 424 | else: |
---|
| 425 | msg = 'is_inside_polygon must be invoked with one point only' |
---|
[7841] | 426 | raise Exception(msg) |
---|
[5897] | 427 | |
---|
[7276] | 428 | ## |
---|
| 429 | # @brief Determine which of a set of points are inside a polygon. |
---|
| 430 | # @param points A set of points (tuple, list or array). |
---|
| 431 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
| 432 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 433 | # @param verbose True if this function is to be verbose. |
---|
| 434 | # @return A list of indices of points inside the polygon. |
---|
[5897] | 435 | def inside_polygon(points, polygon, closed=True, verbose=False): |
---|
| 436 | """Determine points inside a polygon |
---|
| 437 | |
---|
| 438 | Functions inside_polygon and outside_polygon have been defined in |
---|
[7276] | 439 | terms of separate_by_polygon which will put all inside indices in |
---|
[5897] | 440 | the first part of the indices array and outside indices in the last |
---|
| 441 | |
---|
| 442 | See separate_points_by_polygon for documentation |
---|
| 443 | |
---|
| 444 | points and polygon can be a geospatial instance, |
---|
| 445 | a list or a numeric array |
---|
| 446 | """ |
---|
| 447 | |
---|
| 448 | try: |
---|
| 449 | points = ensure_absolute(points) |
---|
[7858] | 450 | except NameError, err: |
---|
| 451 | raise NameError, err |
---|
[5897] | 452 | except: |
---|
| 453 | # If this fails it is going to be because the points can't be |
---|
| 454 | # converted to a numeric array. |
---|
[7276] | 455 | msg = 'Points could not be converted to numeric array' |
---|
| 456 | raise Exception, msg |
---|
[5897] | 457 | |
---|
[6534] | 458 | polygon = ensure_absolute(polygon) |
---|
[5897] | 459 | try: |
---|
| 460 | polygon = ensure_absolute(polygon) |
---|
| 461 | except NameError, e: |
---|
| 462 | raise NameError, e |
---|
| 463 | except: |
---|
| 464 | # If this fails it is going to be because the points can't be |
---|
| 465 | # converted to a numeric array. |
---|
[7276] | 466 | msg = ('Polygon %s could not be converted to numeric array' |
---|
| 467 | % (str(polygon))) |
---|
| 468 | raise Exception, msg |
---|
[5897] | 469 | |
---|
| 470 | if len(points.shape) == 1: |
---|
| 471 | # Only one point was passed in. Convert to array of points |
---|
[7276] | 472 | points = num.reshape(points, (1,2)) |
---|
[5897] | 473 | |
---|
| 474 | indices, count = separate_points_by_polygon(points, polygon, |
---|
| 475 | closed=closed, |
---|
| 476 | verbose=verbose) |
---|
| 477 | |
---|
| 478 | # Return indices of points inside polygon |
---|
| 479 | return indices[:count] |
---|
| 480 | |
---|
[7276] | 481 | ## |
---|
| 482 | # @brief Determine if one point is outside a polygon. |
---|
| 483 | # @param point The point of interest. |
---|
| 484 | # @param polygon The polygon to test inclusion in. |
---|
| 485 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 486 | # @param verbose True if this function is to be verbose. |
---|
| 487 | # @return True if point is outside the polygon. |
---|
| 488 | # @note Uses inside_polygon() to do the work. |
---|
[5897] | 489 | def is_outside_polygon(point, polygon, closed=True, verbose=False, |
---|
| 490 | points_geo_ref=None, polygon_geo_ref=None): |
---|
| 491 | """Determine if one point is outside a polygon |
---|
| 492 | |
---|
| 493 | See outside_polygon for more details |
---|
| 494 | """ |
---|
| 495 | |
---|
| 496 | indices = outside_polygon(point, polygon, closed, verbose) |
---|
| 497 | |
---|
| 498 | if indices.shape[0] == 1: |
---|
| 499 | return True |
---|
| 500 | elif indices.shape[0] == 0: |
---|
| 501 | return False |
---|
| 502 | else: |
---|
| 503 | msg = 'is_outside_polygon must be invoked with one point only' |
---|
[7276] | 504 | raise Exception, msg |
---|
[5897] | 505 | |
---|
[7276] | 506 | ## |
---|
| 507 | # @brief Determine which of a set of points are outside a polygon. |
---|
| 508 | # @param points A set of points (tuple, list or array). |
---|
| 509 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
| 510 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 511 | # @param verbose True if this function is to be verbose. |
---|
| 512 | # @return A list of indices of points outside the polygon. |
---|
[5897] | 513 | def outside_polygon(points, polygon, closed = True, verbose = False): |
---|
| 514 | """Determine points outside a polygon |
---|
| 515 | |
---|
| 516 | Functions inside_polygon and outside_polygon have been defined in |
---|
[7276] | 517 | terms of separate_by_polygon which will put all inside indices in |
---|
[5897] | 518 | the first part of the indices array and outside indices in the last |
---|
| 519 | |
---|
| 520 | See separate_points_by_polygon for documentation |
---|
| 521 | """ |
---|
| 522 | |
---|
| 523 | try: |
---|
[7276] | 524 | points = ensure_numeric(points, num.float) |
---|
[5897] | 525 | except NameError, e: |
---|
| 526 | raise NameError, e |
---|
| 527 | except: |
---|
[7276] | 528 | msg = 'Points could not be converted to numeric array' |
---|
| 529 | raise Exception, msg |
---|
[5897] | 530 | |
---|
| 531 | try: |
---|
[7276] | 532 | polygon = ensure_numeric(polygon, num.float) |
---|
[5897] | 533 | except NameError, e: |
---|
| 534 | raise NameError, e |
---|
| 535 | except: |
---|
[7276] | 536 | msg = 'Polygon could not be converted to numeric array' |
---|
| 537 | raise Exception, msg |
---|
[5897] | 538 | |
---|
| 539 | if len(points.shape) == 1: |
---|
| 540 | # Only one point was passed in. Convert to array of points |
---|
[7858] | 541 | points = num.reshape(points, (1, 2)) |
---|
[5897] | 542 | |
---|
| 543 | indices, count = separate_points_by_polygon(points, polygon, |
---|
| 544 | closed=closed, |
---|
| 545 | verbose=verbose) |
---|
| 546 | |
---|
| 547 | # Return indices of points outside polygon |
---|
| 548 | if count == len(indices): |
---|
| 549 | # No points are outside |
---|
[6158] | 550 | return num.array([]) |
---|
[5897] | 551 | else: |
---|
| 552 | return indices[count:][::-1] #return reversed |
---|
| 553 | |
---|
[7276] | 554 | ## |
---|
| 555 | # @brief Separate a list of points into two sets inside+outside a polygon. |
---|
| 556 | # @param points A set of points (tuple, list or array). |
---|
| 557 | # @param polygon A set of points defining a polygon (tuple, list or array). |
---|
| 558 | # @param closed True if points on boundary are considered 'inside' polygon. |
---|
| 559 | # @param verbose True if this function is to be verbose. |
---|
| 560 | # @return A tuple (in, out) of point indices for poinst inside amd outside. |
---|
[6534] | 561 | def in_and_outside_polygon(points, polygon, closed=True, verbose=False): |
---|
[5897] | 562 | """Determine points inside and outside a polygon |
---|
| 563 | |
---|
| 564 | See separate_points_by_polygon for documentation |
---|
| 565 | |
---|
[7276] | 566 | Returns an array of points inside and array of points outside the polygon |
---|
[5897] | 567 | """ |
---|
| 568 | |
---|
| 569 | try: |
---|
[7276] | 570 | points = ensure_numeric(points, num.float) |
---|
[5897] | 571 | except NameError, e: |
---|
| 572 | raise NameError, e |
---|
| 573 | except: |
---|
[7276] | 574 | msg = 'Points could not be converted to numeric array' |
---|
| 575 | raise Exception, msg |
---|
[5897] | 576 | |
---|
| 577 | try: |
---|
[7276] | 578 | polygon = ensure_numeric(polygon, num.float) |
---|
[5897] | 579 | except NameError, e: |
---|
| 580 | raise NameError, e |
---|
| 581 | except: |
---|
[7276] | 582 | msg = 'Polygon could not be converted to numeric array' |
---|
| 583 | raise Exception, msg |
---|
[5897] | 584 | |
---|
| 585 | if len(points.shape) == 1: |
---|
| 586 | # Only one point was passed in. Convert to array of points |
---|
[7858] | 587 | points = num.reshape(points, (1, 2)) |
---|
[5897] | 588 | |
---|
| 589 | indices, count = separate_points_by_polygon(points, polygon, |
---|
| 590 | closed=closed, |
---|
| 591 | verbose=verbose) |
---|
[7276] | 592 | |
---|
[5897] | 593 | # Returns indices of points inside and indices of points outside |
---|
| 594 | # the polygon |
---|
| 595 | if count == len(indices): |
---|
| 596 | # No points are outside |
---|
[7778] | 597 | return indices[:count], [] |
---|
[5897] | 598 | else: |
---|
| 599 | return indices[:count], indices[count:][::-1] #return reversed |
---|
| 600 | |
---|
[7778] | 601 | |
---|
| 602 | |
---|
[5897] | 603 | def separate_points_by_polygon(points, polygon, |
---|
[6534] | 604 | closed=True, |
---|
| 605 | check_input=True, |
---|
| 606 | verbose=False): |
---|
[5897] | 607 | """Determine whether points are inside or outside a polygon |
---|
| 608 | |
---|
| 609 | Input: |
---|
| 610 | points - Tuple of (x, y) coordinates, or list of tuples |
---|
| 611 | polygon - list of vertices of polygon |
---|
| 612 | closed - (optional) determine whether points on boundary should be |
---|
| 613 | regarded as belonging to the polygon (closed = True) |
---|
| 614 | or not (closed = False) |
---|
[6534] | 615 | check_input: Allows faster execution if set to False |
---|
[5897] | 616 | |
---|
| 617 | Outputs: |
---|
| 618 | indices: array of same length as points with indices of points falling |
---|
| 619 | inside the polygon listed from the beginning and indices of points |
---|
| 620 | falling outside listed from the end. |
---|
| 621 | |
---|
| 622 | count: count of points falling inside the polygon |
---|
| 623 | |
---|
| 624 | The indices of points inside are obtained as indices[:count] |
---|
| 625 | The indices of points outside are obtained as indices[count:] |
---|
| 626 | |
---|
| 627 | Examples: |
---|
| 628 | U = [[0,0], [1,0], [1,1], [0,1]] #Unit square |
---|
| 629 | |
---|
| 630 | separate_points_by_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]], U) |
---|
| 631 | will return the indices [0, 2, 1] and count == 2 as only the first |
---|
| 632 | and the last point are inside the unit square |
---|
| 633 | |
---|
| 634 | Remarks: |
---|
| 635 | The vertices may be listed clockwise or counterclockwise and |
---|
| 636 | the first point may optionally be repeated. |
---|
| 637 | Polygons do not need to be convex. |
---|
| 638 | Polygons can have holes in them and points inside a hole is |
---|
| 639 | regarded as being outside the polygon. |
---|
| 640 | |
---|
| 641 | Algorithm is based on work by Darel Finley, |
---|
| 642 | http://www.alienryderflex.com/polygon/ |
---|
| 643 | |
---|
| 644 | Uses underlying C-implementation in polygon_ext.c |
---|
| 645 | """ |
---|
| 646 | |
---|
[6534] | 647 | if check_input: |
---|
| 648 | #Input checks |
---|
[7778] | 649 | assert isinstance(closed, bool), \ |
---|
| 650 | 'Keyword argument "closed" must be boolean' |
---|
| 651 | assert isinstance(verbose, bool), \ |
---|
| 652 | 'Keyword argument "verbose" must be boolean' |
---|
[5897] | 653 | |
---|
[6534] | 654 | try: |
---|
[7276] | 655 | points = ensure_numeric(points, num.float) |
---|
[6534] | 656 | except NameError, e: |
---|
| 657 | raise NameError, e |
---|
| 658 | except: |
---|
[7276] | 659 | msg = 'Points could not be converted to numeric array' |
---|
[7858] | 660 | raise Exception(msg) |
---|
[5897] | 661 | |
---|
[6534] | 662 | try: |
---|
[7276] | 663 | polygon = ensure_numeric(polygon, num.float) |
---|
[6534] | 664 | except NameError, e: |
---|
[7858] | 665 | raise NameError(e) |
---|
[6534] | 666 | except: |
---|
[7276] | 667 | msg = 'Polygon could not be converted to numeric array' |
---|
[7858] | 668 | raise Exception(msg) |
---|
[5897] | 669 | |
---|
[6534] | 670 | msg = 'Polygon array must be a 2d array of vertices' |
---|
| 671 | assert len(polygon.shape) == 2, msg |
---|
[5897] | 672 | |
---|
[6534] | 673 | msg = 'Polygon array must have two columns' |
---|
[7858] | 674 | assert polygon.shape[1] == 2, msg |
---|
[5897] | 675 | |
---|
[8009] | 676 | |
---|
[7276] | 677 | msg = ('Points array must be 1 or 2 dimensional. ' |
---|
| 678 | 'I got %d dimensions' % len(points.shape)) |
---|
[6534] | 679 | assert 0 < len(points.shape) < 3, msg |
---|
[5897] | 680 | |
---|
[6534] | 681 | if len(points.shape) == 1: |
---|
[7276] | 682 | # Only one point was passed in. Convert to array of points. |
---|
[7858] | 683 | points = num.reshape(points, (1, 2)) |
---|
[5897] | 684 | |
---|
[7276] | 685 | msg = ('Point array must have two columns (x,y), ' |
---|
| 686 | 'I got points.shape[1]=%d' % points.shape[0]) |
---|
| 687 | assert points.shape[1]==2, msg |
---|
[5897] | 688 | |
---|
| 689 | |
---|
[7276] | 690 | msg = ('Points array must be a 2d array. I got %s.' |
---|
| 691 | % str(points[:30])) |
---|
[7858] | 692 | assert len(points.shape) == 2, msg |
---|
[5897] | 693 | |
---|
[6534] | 694 | msg = 'Points array must have two columns' |
---|
[7858] | 695 | assert points.shape[1] == 2, msg |
---|
[5897] | 696 | |
---|
[6534] | 697 | N = polygon.shape[0] # Number of vertices in polygon |
---|
| 698 | M = points.shape[0] # Number of points |
---|
[5897] | 699 | |
---|
[7276] | 700 | indices = num.zeros(M, num.int) |
---|
[5897] | 701 | |
---|
| 702 | count = _separate_points_by_polygon(points, polygon, indices, |
---|
| 703 | int(closed), int(verbose)) |
---|
| 704 | |
---|
[7276] | 705 | if verbose: |
---|
[7317] | 706 | log.critical('Found %d points (out of %d) inside polygon' % (count, M)) |
---|
[7276] | 707 | |
---|
[5897] | 708 | return indices, count |
---|
| 709 | |
---|
[7858] | 710 | |
---|
[7276] | 711 | def polygon_area(input_polygon): |
---|
| 712 | """ Determine area of arbitrary polygon. |
---|
[5897] | 713 | |
---|
[7858] | 714 | input_polygon The polygon to get area of. |
---|
| 715 | |
---|
| 716 | return A scalar value for the polygon area. |
---|
| 717 | |
---|
| 718 | Reference: http://mathworld.wolfram.com/PolygonArea.html |
---|
[5897] | 719 | """ |
---|
[6000] | 720 | # Move polygon to origin (0,0) to avoid rounding errors |
---|
[6001] | 721 | # This makes a copy of the polygon to avoid destroying it |
---|
| 722 | input_polygon = ensure_numeric(input_polygon) |
---|
[7858] | 723 | min_x = min(input_polygon[:, 0]) |
---|
| 724 | min_y = min(input_polygon[:, 1]) |
---|
[6001] | 725 | polygon = input_polygon - [min_x, min_y] |
---|
[6000] | 726 | |
---|
[7276] | 727 | # Compute area |
---|
[5897] | 728 | n = len(polygon) |
---|
| 729 | poly_area = 0.0 |
---|
| 730 | |
---|
| 731 | for i in range(n): |
---|
| 732 | pti = polygon[i] |
---|
| 733 | if i == n-1: |
---|
| 734 | pt1 = polygon[0] |
---|
| 735 | else: |
---|
| 736 | pt1 = polygon[i+1] |
---|
| 737 | xi = pti[0] |
---|
| 738 | yi1 = pt1[1] |
---|
| 739 | xi1 = pt1[0] |
---|
| 740 | yi = pti[1] |
---|
| 741 | poly_area += xi*yi1 - xi1*yi |
---|
[7276] | 742 | |
---|
[5897] | 743 | return abs(poly_area/2) |
---|
| 744 | |
---|
[7778] | 745 | |
---|
[7276] | 746 | def plot_polygons(polygons_points, |
---|
| 747 | style=None, |
---|
| 748 | figname=None, |
---|
| 749 | label=None, |
---|
[7841] | 750 | alpha=None): |
---|
[5897] | 751 | """ Take list of polygons and plot. |
---|
| 752 | |
---|
| 753 | Inputs: |
---|
| 754 | |
---|
| 755 | polygons - list of polygons |
---|
| 756 | |
---|
| 757 | style - style list corresponding to each polygon |
---|
| 758 | - for a polygon, use 'line' |
---|
| 759 | - for points falling outside a polygon, use 'outside' |
---|
[7511] | 760 | - style can also be user defined as in normal pylab plot. |
---|
[7276] | 761 | |
---|
[5897] | 762 | figname - name to save figure to |
---|
| 763 | |
---|
[7516] | 764 | label - title for plotA |
---|
[5897] | 765 | |
---|
[7516] | 766 | alpha - transparency of polygon fill, 0.0=none, 1.0=solid |
---|
| 767 | if not supplied, no fill. |
---|
| 768 | |
---|
[5897] | 769 | Outputs: |
---|
| 770 | |
---|
| 771 | - plot of polygons |
---|
[7276] | 772 | """ |
---|
[5897] | 773 | |
---|
[7841] | 774 | from pylab import ion, hold, plot, savefig, xlabel, \ |
---|
[7516] | 775 | ylabel, title, close, title, fill |
---|
[5897] | 776 | |
---|
[7276] | 777 | assert type(polygons_points) == list, \ |
---|
| 778 | 'input must be a list of polygons and/or points' |
---|
| 779 | |
---|
[5897] | 780 | ion() |
---|
| 781 | hold(True) |
---|
| 782 | |
---|
[7276] | 783 | if label is None: |
---|
| 784 | label = '' |
---|
[5897] | 785 | |
---|
[7516] | 786 | # clamp alpha to sensible range |
---|
| 787 | if alpha: |
---|
| 788 | try: |
---|
| 789 | alpha = float(alpha) |
---|
| 790 | except ValueError: |
---|
| 791 | alpha = None |
---|
| 792 | else: |
---|
[7841] | 793 | alpha = max(0.0, min(1.0, alpha)) |
---|
[7516] | 794 | |
---|
[7858] | 795 | num_points = len(polygons_points) |
---|
[5897] | 796 | colour = [] |
---|
| 797 | if style is None: |
---|
[7276] | 798 | style_type = 'line' |
---|
[5897] | 799 | style = [] |
---|
[7858] | 800 | for i in range(num_points): |
---|
[5897] | 801 | style.append(style_type) |
---|
| 802 | colour.append('b-') |
---|
| 803 | else: |
---|
[7858] | 804 | for style_name in style: |
---|
| 805 | if style_name == 'line': |
---|
| 806 | colour.append('b-') |
---|
| 807 | if style_name == 'outside': |
---|
| 808 | colour.append('r.') |
---|
| 809 | if style_name == 'point': |
---|
| 810 | colour.append('g.') |
---|
| 811 | if style_name not in ['line', 'outside', 'point']: |
---|
| 812 | colour.append(style_name) |
---|
[7276] | 813 | |
---|
[5897] | 814 | for i, item in enumerate(polygons_points): |
---|
[7858] | 815 | pt_x, pt_y = _poly_xy(item) |
---|
| 816 | plot(pt_x, pt_y, colour[i]) |
---|
[7516] | 817 | if alpha: |
---|
[7858] | 818 | fill(pt_x, pt_y, colour[i], alpha=alpha) |
---|
[5897] | 819 | xlabel('x') |
---|
| 820 | ylabel('y') |
---|
| 821 | title(label) |
---|
| 822 | |
---|
| 823 | if figname is not None: |
---|
| 824 | savefig(figname) |
---|
| 825 | else: |
---|
| 826 | savefig('test_image') |
---|
| 827 | |
---|
| 828 | close('all') |
---|
| 829 | |
---|
| 830 | |
---|
[7858] | 831 | def _poly_xy(polygon): |
---|
[5897] | 832 | """ this is used within plot_polygons so need to duplicate |
---|
| 833 | the first point so can have closed polygon in plot |
---|
[7778] | 834 | # @param polygon A set of points defining a polygon. |
---|
| 835 | # @param verbose True if this function is to be verbose. |
---|
| 836 | # @return A tuple (x, y) of X and Y coordinates of the polygon. |
---|
| 837 | # @note We duplicate the first point so can have closed polygon in plot. |
---|
[5897] | 838 | """ |
---|
| 839 | |
---|
| 840 | try: |
---|
[7276] | 841 | polygon = ensure_numeric(polygon, num.float) |
---|
[7858] | 842 | except NameError, err: |
---|
| 843 | raise NameError, err |
---|
[5897] | 844 | except: |
---|
[7276] | 845 | msg = ('Polygon %s could not be converted to numeric array' |
---|
| 846 | % (str(polygon))) |
---|
| 847 | raise Exception, msg |
---|
[5897] | 848 | |
---|
[7858] | 849 | pts_x = num.concatenate((polygon[:, 0], [polygon[0, 0]]), axis = 0) |
---|
| 850 | pts_y = num.concatenate((polygon[:, 1], [polygon[0, 1]]), axis = 0) |
---|
[7276] | 851 | |
---|
[7858] | 852 | return pts_x, pts_y |
---|
[5897] | 853 | |
---|
| 854 | |
---|
[7276] | 855 | ################################################################################ |
---|
| 856 | # Functions to read and write polygon information |
---|
| 857 | ################################################################################ |
---|
[5897] | 858 | |
---|
[8057] | 859 | def read_polygon(filename, delimiter=',', closed='True'): |
---|
| 860 | """ Read points assumed to form a (closed) polygon. |
---|
| 861 | Can also be used toread in a polyline (closed = 'False') |
---|
[7778] | 862 | |
---|
[8057] | 863 | Also checks to make sure polygon (polyline) |
---|
| 864 | is not complex (self-intersecting). |
---|
[7276] | 865 | |
---|
[7858] | 866 | filename Path to file containing polygon data. |
---|
| 867 | delimiter Delimiter to split polygon data with. |
---|
| 868 | A list of point data from the polygon file. |
---|
[7778] | 869 | |
---|
[7858] | 870 | There must be exactly two numbers in each line separated by the delimiter. |
---|
| 871 | No header. |
---|
[5897] | 872 | """ |
---|
| 873 | |
---|
| 874 | fid = open(filename) |
---|
| 875 | lines = fid.readlines() |
---|
| 876 | fid.close() |
---|
| 877 | polygon = [] |
---|
| 878 | for line in lines: |
---|
[7276] | 879 | fields = line.split(delimiter) |
---|
| 880 | polygon.append([float(fields[0]), float(fields[1])]) |
---|
[7686] | 881 | |
---|
[8057] | 882 | # check this is a valid polygon (polyline). |
---|
| 883 | if is_complex(polygon, closed, verbose=True): |
---|
[7778] | 884 | msg = 'ERROR: Self-intersecting polygon detected in file ' |
---|
| 885 | msg += filename +'. A complex polygon will not ' |
---|
| 886 | msg += 'necessarily break the algorithms within ANUGA, but it' |
---|
| 887 | msg += 'usually signifies pathological data. Please fix this file.' |
---|
[7690] | 888 | raise Exception, msg |
---|
[7686] | 889 | |
---|
[5897] | 890 | return polygon |
---|
| 891 | |
---|
[7858] | 892 | |
---|
[5897] | 893 | def write_polygon(polygon, filename=None): |
---|
| 894 | """Write polygon to csv file. |
---|
[7276] | 895 | |
---|
| 896 | There will be exactly two numbers, easting and northing, in each line |
---|
| 897 | separated by a comma. |
---|
| 898 | |
---|
| 899 | No header. |
---|
[5897] | 900 | """ |
---|
| 901 | |
---|
| 902 | fid = open(filename, 'w') |
---|
| 903 | for point in polygon: |
---|
[7276] | 904 | fid.write('%f, %f\n' % point) |
---|
[5897] | 905 | fid.close() |
---|
| 906 | |
---|
[7276] | 907 | |
---|
[5897] | 908 | def populate_polygon(polygon, number_of_points, seed=None, exclude=None): |
---|
| 909 | """Populate given polygon with uniformly distributed points. |
---|
| 910 | |
---|
| 911 | Input: |
---|
| 912 | polygon - list of vertices of polygon |
---|
| 913 | number_of_points - (optional) number of points |
---|
| 914 | seed - seed for random number generator (default=None) |
---|
[7276] | 915 | exclude - list of polygons (inside main polygon) from where points |
---|
| 916 | should be excluded |
---|
[5897] | 917 | |
---|
| 918 | Output: |
---|
| 919 | points - list of points inside polygon |
---|
| 920 | |
---|
| 921 | Examples: |
---|
| 922 | populate_polygon( [[0,0], [1,0], [1,1], [0,1]], 5 ) |
---|
| 923 | will return five randomly selected points inside the unit square |
---|
| 924 | """ |
---|
| 925 | |
---|
| 926 | from random import uniform, seed as seed_function |
---|
| 927 | |
---|
| 928 | seed_function(seed) |
---|
| 929 | |
---|
| 930 | points = [] |
---|
| 931 | |
---|
| 932 | # Find outer extent of polygon |
---|
[7858] | 933 | extents = AABB(polygon) |
---|
| 934 | |
---|
[5897] | 935 | while len(points) < number_of_points: |
---|
[7858] | 936 | rand_x = uniform(extents.xmin, extents.xmax) |
---|
| 937 | rand_y = uniform(extents.ymin, extents.ymax) |
---|
[5897] | 938 | |
---|
| 939 | append = False |
---|
[7858] | 940 | if is_inside_polygon([rand_x, rand_y], polygon): |
---|
[5897] | 941 | append = True |
---|
| 942 | |
---|
| 943 | #Check exclusions |
---|
| 944 | if exclude is not None: |
---|
| 945 | for ex_poly in exclude: |
---|
[7858] | 946 | if is_inside_polygon([rand_x, rand_y], ex_poly): |
---|
[5897] | 947 | append = False |
---|
| 948 | |
---|
| 949 | if append is True: |
---|
[7858] | 950 | points.append([rand_x, rand_y]) |
---|
[5897] | 951 | |
---|
| 952 | return points |
---|
| 953 | |
---|
[7778] | 954 | |
---|
[5897] | 955 | def point_in_polygon(polygon, delta=1e-8): |
---|
| 956 | """Return a point inside a given polygon which will be close to the |
---|
| 957 | polygon edge. |
---|
| 958 | |
---|
| 959 | Input: |
---|
| 960 | polygon - list of vertices of polygon |
---|
| 961 | delta - the square root of 2 * delta is the maximum distance from the |
---|
| 962 | polygon points and the returned point. |
---|
| 963 | Output: |
---|
| 964 | points - a point inside polygon |
---|
| 965 | |
---|
[7276] | 966 | searches in all diagonals and up and down (not left and right). |
---|
[5897] | 967 | """ |
---|
[7276] | 968 | |
---|
[6534] | 969 | polygon = ensure_numeric(polygon) |
---|
| 970 | |
---|
[7858] | 971 | while True: |
---|
| 972 | for poly_point in polygon: |
---|
| 973 | for x_mult in range(-1, 2): |
---|
| 974 | for y_mult in range(-1, 2): |
---|
| 975 | pt_x, pt_y = poly_point |
---|
[7276] | 976 | |
---|
[7858] | 977 | if pt_x == 0: |
---|
| 978 | x_delta = x_mult * delta |
---|
| 979 | else: |
---|
| 980 | x_delta = pt_x + x_mult*pt_x*delta |
---|
[5897] | 981 | |
---|
[7858] | 982 | if pt_y == 0: |
---|
| 983 | y_delta = y_mult * delta |
---|
| 984 | else: |
---|
| 985 | y_delta = pt_y + y_mult*pt_y*delta |
---|
[5897] | 986 | |
---|
[7858] | 987 | point = [x_delta, y_delta] |
---|
[7276] | 988 | |
---|
[7858] | 989 | if is_inside_polygon(point, polygon, closed=False): |
---|
| 990 | return point |
---|
| 991 | delta = delta * 0.1 |
---|
[7276] | 992 | |
---|
[5897] | 993 | |
---|
| 994 | def number_mesh_triangles(interior_regions, bounding_poly, remainder_res): |
---|
| 995 | """Calculate the approximate number of triangles inside the |
---|
| 996 | bounding polygon and the other interior regions |
---|
| 997 | |
---|
[7276] | 998 | Polygon areas are converted to square Kms |
---|
[5897] | 999 | |
---|
| 1000 | FIXME: Add tests for this function |
---|
| 1001 | """ |
---|
[7276] | 1002 | |
---|
[5897] | 1003 | # TO DO check if any of the regions fall inside one another |
---|
| 1004 | |
---|
[7317] | 1005 | log.critical('-' * 80) |
---|
| 1006 | log.critical('Polygon Max triangle area (m^2) Total area (km^2) ' |
---|
| 1007 | 'Estimated #triangles') |
---|
| 1008 | log.critical('-' * 80) |
---|
[5897] | 1009 | |
---|
| 1010 | no_triangles = 0.0 |
---|
| 1011 | area = polygon_area(bounding_poly) |
---|
[7276] | 1012 | |
---|
[5897] | 1013 | for poly, resolution in interior_regions: |
---|
| 1014 | this_area = polygon_area(poly) |
---|
| 1015 | this_triangles = this_area/resolution |
---|
| 1016 | no_triangles += this_triangles |
---|
| 1017 | area -= this_area |
---|
[7276] | 1018 | |
---|
[7317] | 1019 | log.critical('Interior %s%s%d' |
---|
| 1020 | % (('%.0f' % resolution).ljust(25), |
---|
| 1021 | ('%.2f' % (this_area/1000000)).ljust(19), |
---|
| 1022 | this_triangles)) |
---|
| 1023 | #print 'Interior ', |
---|
| 1024 | #print ('%.0f' % resolution).ljust(25), |
---|
| 1025 | #print ('%.2f' % (this_area/1000000)).ljust(19), |
---|
| 1026 | #print '%d' % (this_triangles) |
---|
[7276] | 1027 | |
---|
[5897] | 1028 | bound_triangles = area/remainder_res |
---|
| 1029 | no_triangles += bound_triangles |
---|
| 1030 | |
---|
[7317] | 1031 | log.critical('Bounding %s%s%d' |
---|
| 1032 | % (('%.0f' % remainder_res).ljust(25), |
---|
| 1033 | ('%.2f' % (area/1000000)).ljust(19), |
---|
| 1034 | bound_triangles)) |
---|
| 1035 | #print 'Bounding ', |
---|
| 1036 | #print ('%.0f' % remainder_res).ljust(25), |
---|
| 1037 | #print ('%.2f' % (area/1000000)).ljust(19), |
---|
| 1038 | #print '%d' % (bound_triangles) |
---|
[5897] | 1039 | |
---|
| 1040 | total_number_of_triangles = no_triangles/0.7 |
---|
| 1041 | |
---|
[7317] | 1042 | log.critical('Estimated total number of triangles: %d' |
---|
| 1043 | % total_number_of_triangles) |
---|
| 1044 | log.critical('Note: This is generally about 20%% ' |
---|
| 1045 | 'less than the final amount') |
---|
[5897] | 1046 | |
---|
| 1047 | return int(total_number_of_triangles) |
---|
| 1048 | |
---|
[7778] | 1049 | |
---|
| 1050 | def decimate_polygon(polygon, factor=10): |
---|
| 1051 | """Reduce number of points in polygon by the specified |
---|
| 1052 | factor (default=10, hence the name of the function) such that |
---|
| 1053 | the extrema in both axes are preserved. |
---|
| 1054 | |
---|
[7276] | 1055 | ## |
---|
| 1056 | # @brief Reduce number of points in polygon by the specified factor. |
---|
| 1057 | # @param polygon The polygon to reduce. |
---|
| 1058 | # @param factor The factor to reduce polygon points by (default 10). |
---|
| 1059 | # @note The extrema of both axes are preserved. |
---|
[5897] | 1060 | |
---|
| 1061 | Return reduced polygon |
---|
| 1062 | """ |
---|
| 1063 | |
---|
| 1064 | # FIXME(Ole): This doesn't work at present, |
---|
| 1065 | # but it isn't critical either |
---|
| 1066 | |
---|
| 1067 | # Find outer extent of polygon |
---|
| 1068 | num_polygon = ensure_numeric(polygon) |
---|
[7841] | 1069 | max_x = max(num_polygon[:, 0]) |
---|
| 1070 | max_y = max(num_polygon[:, 1]) |
---|
| 1071 | min_x = min(num_polygon[:, 0]) |
---|
| 1072 | min_y = min(num_polygon[:, 1]) |
---|
[5897] | 1073 | |
---|
| 1074 | # Keep only some points making sure extrema are kept |
---|
[7276] | 1075 | reduced_polygon = [] |
---|
[5897] | 1076 | for i, point in enumerate(polygon): |
---|
[7858] | 1077 | if point[0] in [min_x, max_x] and point[1] in [min_y, max_y]: |
---|
[5897] | 1078 | # Keep |
---|
| 1079 | reduced_polygon.append(point) |
---|
| 1080 | else: |
---|
| 1081 | if len(reduced_polygon)*factor < i: |
---|
[7276] | 1082 | reduced_polygon.append(point) |
---|
[5897] | 1083 | |
---|
| 1084 | return reduced_polygon |
---|
| 1085 | |
---|
[7778] | 1086 | |
---|
[6189] | 1087 | def interpolate_polyline(data, |
---|
| 1088 | polyline_nodes, |
---|
| 1089 | gauge_neighbour_id, |
---|
| 1090 | interpolation_points=None, |
---|
| 1091 | rtol=1.0e-6, |
---|
[7841] | 1092 | atol=1.0e-8): |
---|
[6189] | 1093 | """Interpolate linearly between values data on polyline nodes |
---|
[7276] | 1094 | of a polyline to list of interpolation points. |
---|
[6189] | 1095 | |
---|
| 1096 | data is the data on the polyline nodes. |
---|
| 1097 | |
---|
| 1098 | Inputs: |
---|
| 1099 | data: Vector or array of data at the polyline nodes. |
---|
[7276] | 1100 | polyline_nodes: Location of nodes where data is available. |
---|
[6189] | 1101 | gauge_neighbour_id: ? |
---|
| 1102 | interpolation_points: Interpolate polyline data to these positions. |
---|
| 1103 | List of coordinate pairs [x, y] of |
---|
[7276] | 1104 | data points or an nx2 numeric array or a Geospatial_data object |
---|
| 1105 | rtol, atol: Used to determine whether a point is on the polyline or not. |
---|
| 1106 | See point_on_line. |
---|
[6189] | 1107 | |
---|
| 1108 | Output: |
---|
| 1109 | Interpolated values at interpolation points |
---|
| 1110 | """ |
---|
[7276] | 1111 | |
---|
[6189] | 1112 | if isinstance(interpolation_points, Geospatial_data): |
---|
[7276] | 1113 | interpolation_points = interpolation_points.\ |
---|
| 1114 | get_data_points(absolute=True) |
---|
[6189] | 1115 | |
---|
[7276] | 1116 | interpolated_values = num.zeros(len(interpolation_points), num.float) |
---|
[6189] | 1117 | |
---|
[7276] | 1118 | data = ensure_numeric(data, num.float) |
---|
| 1119 | polyline_nodes = ensure_numeric(polyline_nodes, num.float) |
---|
| 1120 | interpolation_points = ensure_numeric(interpolation_points, num.float) |
---|
| 1121 | gauge_neighbour_id = ensure_numeric(gauge_neighbour_id, num.int) |
---|
[6189] | 1122 | |
---|
[7841] | 1123 | num_nodes = polyline_nodes.shape[0] # Number of nodes in polyline |
---|
[7276] | 1124 | |
---|
[6189] | 1125 | # Input sanity check |
---|
[7841] | 1126 | assert_msg = 'interpolation_points are not given (interpolate.py)' |
---|
| 1127 | assert interpolation_points is not None, assert_msg |
---|
[7276] | 1128 | |
---|
[7841] | 1129 | assert_msg = 'function value must be specified at every interpolation node' |
---|
| 1130 | assert data.shape[0] == polyline_nodes.shape[0], assert_msg |
---|
[7276] | 1131 | |
---|
[7841] | 1132 | assert_msg = 'Must define function value at one or more nodes' |
---|
| 1133 | assert data.shape[0] > 0, assert_msg |
---|
[6189] | 1134 | |
---|
[7841] | 1135 | if num_nodes == 1: |
---|
| 1136 | assert_msg = 'Polyline contained only one point. I need more. ' |
---|
| 1137 | assert_msg += str(data) |
---|
| 1138 | raise Exception, assert_msg |
---|
| 1139 | elif num_nodes > 1: |
---|
[6189] | 1140 | _interpolate_polyline(data, |
---|
| 1141 | polyline_nodes, |
---|
| 1142 | gauge_neighbour_id, |
---|
[7276] | 1143 | interpolation_points, |
---|
[6189] | 1144 | interpolated_values, |
---|
| 1145 | rtol, |
---|
| 1146 | atol) |
---|
[7276] | 1147 | |
---|
[7699] | 1148 | |
---|
[6189] | 1149 | return interpolated_values |
---|
| 1150 | |
---|
[7699] | 1151 | |
---|
| 1152 | def polylist2points_verts(polylist): |
---|
| 1153 | """ Convert a list of polygons to discrete points and vertices. |
---|
| 1154 | """ |
---|
| 1155 | |
---|
| 1156 | offset = 0 |
---|
| 1157 | points = [] |
---|
| 1158 | vertices = [] |
---|
| 1159 | for poly in polylist: |
---|
| 1160 | points.extend(poly) |
---|
| 1161 | vertices.extend([[i, i+1] for i in range(offset, offset+len(poly)-1)]) |
---|
| 1162 | offset += len(poly) |
---|
| 1163 | |
---|
| 1164 | return points, vertices |
---|
[7276] | 1165 | |
---|
| 1166 | |
---|
| 1167 | ################################################################################ |
---|
| 1168 | # Initialise module |
---|
| 1169 | ################################################################################ |
---|
[5897] | 1170 | |
---|
[6119] | 1171 | from anuga.utilities import compile |
---|
| 1172 | if compile.can_use_C_extension('polygon_ext.c'): |
---|
[5897] | 1173 | # Underlying C implementations can be accessed |
---|
| 1174 | from polygon_ext import _point_on_line |
---|
| 1175 | from polygon_ext import _separate_points_by_polygon |
---|
[6189] | 1176 | from polygon_ext import _interpolate_polyline |
---|
[8031] | 1177 | from polygon_ext import _polygon_overlap |
---|
[8053] | 1178 | from polygon_ext import _line_intersect |
---|
[6535] | 1179 | from polygon_ext import _is_inside_triangle |
---|
[5897] | 1180 | #from polygon_ext import _intersection |
---|
| 1181 | |
---|
| 1182 | else: |
---|
[7858] | 1183 | ERROR_MSG = 'C implementations could not be accessed by %s.\n ' % __file__ |
---|
| 1184 | ERROR_MSG += 'Make sure compile_all.py has been run as described in ' |
---|
| 1185 | ERROR_MSG += 'the ANUGA installation guide.' |
---|
| 1186 | raise Exception(ERROR_MSG) |
---|
[5897] | 1187 | |
---|
| 1188 | |
---|
| 1189 | if __name__ == "__main__": |
---|
| 1190 | pass |
---|