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""" 



Module for rasterizing polygons, with floatprecision antialiasing on 



a nonuniform rectangular grid. 







See the documentation for raster(...) for details. 



""" 







import numpy 



from numpy import r_, c_, logical_and, diff, floor, ceil, ones, zeros, vstack, hstack,\ 



full_like, newaxis 







__author__ = 'Jan Petykiewicz' 











def raster(poly_xy: numpy.ndarray, 



grid_x: numpy.ndarray, 



grid_y: numpy.ndarray 



) > numpy.ndarray: 



""" 



Draws a polygon onto a 2D grid of pixels, setting pixel values equal to the fraction of the 



pixel area covered by the polygon. This implementation is written for accuracy and works with 



double precision, in contrast to most other implementations which are written for speed and 



usually only allow for 256 (and often fewer) possible pixel values without performing (very 



slow) supersampling. 







:param poly_xy: 2xN ndarray containing x,y coordinates for each point in the polygon 



:param grid_x: xcoordinates for the edges of each pixel (ie, the leftmost two columns span 



x=grid_x[0] to x=grid_x[1] and x=grid_x[1] to x=grid_x[2]) 



:param grid_y: ycoordinates for the edges of each pixel (see grid_x) 



:return: 2D ndarray with pixel values in the range [0, 1] containing the antialiased polygon 



""" 



poly_xy = numpy.array(poly_xy) 



grid_x = numpy.array(grid_x) 



grid_y = numpy.array(grid_y) 







if poly_xy.shape[0] != 2: 



raise Exception('poly_xy must be 2xN') 



if grid_x.size < 1 or grid_y.size < 1: 



raise Exception('Grid must contain at least one full pixel') 







num_xy_px = numpy.array([grid_x.size, grid_y.size])  1 







min_bounds = floor(poly_xy.min(axis=1)) 



max_bounds = ceil(poly_xy.max(axis=1)) 







keep_x = logical_and(numpy.greater_equal(grid_x, min_bounds[0]), 



numpy.less_equal(grid_x, max_bounds[0])) 



keep_y = logical_and(numpy.greater_equal(grid_y, min_bounds[1]), 



numpy.less_equal(grid_y, max_bounds[1])) 







if not (keep_x.any() and keep_y.any()): # polygon doesn't overlap grid 



return zeros(num_xy_px) 







y_seg_xs = hstack((min_bounds[0], grid_x[keep_x], max_bounds[0])).T 



x_seg_ys = hstack((min_bounds[1], grid_y[keep_y], max_bounds[1])).T 







num_poly_vertices = poly_xy.shape[1] 







# ## Calculate intersections 



xy1b = numpy.roll(poly_xy, 1, axis=1) 







xi1 = poly_xy[0, :, newaxis] 



yi1 = poly_xy[1, :, newaxis] 



xf1 = xy1b[0, :, newaxis] 



yf1 = xy1b[1, :, newaxis] 







xi2 = hstack((full_like(x_seg_ys, min_bounds[0]), y_seg_xs)) 



xf2 = hstack((full_like(x_seg_ys, max_bounds[0]), y_seg_xs)) 



yi2 = hstack((x_seg_ys, full_like(y_seg_xs, min_bounds[0]))) 



yf2 = hstack((x_seg_ys, full_like(y_seg_xs, max_bounds[1]))) 







dxi = xi1  xi2 



dyi = yi1  yi2 



dx1 = xf1  xi1 



dx2 = xf2  xi2 



dy1 = yf1  yi1 



dy2 = yf2  yi2 







numerator_a = dx2 * dyi  dy2 * dxi 



numerator_b = dx1 * dyi  dy1 * dxi 



denominator = dy2 * dx1  dx2 * dy1 







# Avoid warnings since we may multiply eg. NaN*False 



with numpy.errstate(invalid='ignore', divide='ignore'): 



u_a = numerator_a / denominator 



u_b = numerator_b / denominator 







# Find the adjacency matrix A of intersecting lines. 



int_x = xi1 + dx1 * u_a 



int_y = yi1 + dy1 * u_a 



int_b = logical_and.reduce((u_a >= 0, u_a <= 1, u_b >= 0, u_b <= 1)) 







# Arrange output. 



int_adjacency_matrix = int_b 



int_matrix_x = int_x * int_b 



int_matrix_y = int_y * int_b 



int_normalized_distance_1to2 = u_a 







# ## Insert intersection points as vertices 



# If new points fall outside the window, shrink them back onto it 



int_matrix_x = int_matrix_x.clip(grid_x[0], grid_x[1]) 



int_matrix_y = int_matrix_y.clip(grid_y[0], grid_y[1]) 







# sort intersections based on distance from first vertex, to add in order 



sortix = int_normalized_distance_1to2.argsort(axis=1) 



sortix_paired = (numpy.arange(num_poly_vertices)[:, newaxis], sortix) 



assert(int_normalized_distance_1to2.shape[0] == num_poly_vertices) 







# Use sortix to sort adjacency matrix and the intersection (x, y) coordinates, 



# and vstack the original points on top of the top row 



xs = vstack((poly_xy[0, :], int_matrix_x[sortix_paired].T)) 



ys = vstack((poly_xy[1, :], int_matrix_y[sortix_paired].T)) 



has_intersection = r_[ones((1, poly_xy.shape[1]), dtype=bool), 



int_adjacency_matrix[sortix_paired].T] 







# Now use has_intersection to index the intersection coordinates, thus creating a 2column 



# array which holds the [[x, y], ...] for the polygon with added vertices at pixelboundary 



# intersections 



poly_xy_xy = c_[xs.T[has_intersection.T], ys.T[has_intersection.T]] 







# Remove points outside the window (these will only be original points) 



# Since the boundaries of the window are also pixel boundaries, this just 



# makes the polygon boundary proceed along the window edge 



inside_window = logical_and.reduce((poly_xy_xy[:, 1] <= grid_y[1], 



poly_xy_xy[:, 1] >= grid_y[0], 



poly_xy_xy[:, 0] <= grid_x[1], 



poly_xy_xy[:, 0] >= grid_x[0])) 



poly_xy_xy = poly_xy_xy[inside_window, :] 







# Remove consecutive duplicate entries 



consecutive = diff(poly_xy_xy, axis=0).any(axis=1) # use any() as !=0 



poly_xy_xy = poly_xy_xy[r_[True, consecutive], :] 







# If the shape fell completely outside our area, just return a blank grid 



if poly_xy_xy.size == 0: 



# for matlab: 



# rg = array.array('d', numpy.nditer(zeros(num_xy_px), order='F')) 



# return rg 



return zeros(num_xy_px) 







# ## Calculate area, cover 



# Calculate segment cover, area, and corresponding pixel's subscripts 



poly = vstack((poly_xy_xy, 



poly_xy_xy[0, :])) 



endpoint_avg = (poly[:1, :] + poly[1:, :]) / 2 







# Remove segments along the right,top edges 



# (they correspond to outside pixels, but couldn't be removed until now 



# because poly_xy stores points, not segments, and the edge points are needed 



# when creating endpoint_avg) 



non_edge = numpy.logical_and(numpy.less(endpoint_avg[:, 0], grid_x[1]), 



numpy.less(endpoint_avg[:, 1], grid_y[1])) 







x_sub = numpy.digitize(endpoint_avg[non_edge, 0], grid_x)  1 



y_sub = numpy.digitize(endpoint_avg[non_edge, 1], grid_y)  1 







cover = diff(poly[:, 1], axis=0)[non_edge] / diff(grid_y)[y_sub] 



area = (endpoint_avg[non_edge, 0]  grid_x[x_sub]) * cover / diff(grid_x)[x_sub] 







hist_range = [[0, num_xy_px[0]], [0, num_xy_px[1]]] 



poly_grid = numpy.histogram2d(x_sub, y_sub, bins=num_xy_px, range=hist_range, weights=area)[0] 



cover_grid = numpy.histogram2d(x_sub, y_sub, bins=num_xy_px, range=hist_range, weights=cover)[0] 







poly_grid += cover_grid.cumsum(axis=0) 







# do other stuff for dealing with multiple polygons? 







# # deal with the user inputting the vertices in the wrong order 



# if poly_grid.sum() < 0: 



# poly_grid = poly_grid 







return poly_grid 