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@ -1,7 +1,16 @@
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from typing import Tuple, Optional
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import numpy # type: ignore
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"""
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Module for rasterizing polygons, with float-precision anti-aliasing on
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a non-uniform rectangular grid.
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See the documentation for raster(...) for details.
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"""
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from typing import Tuple
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import numpy
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from numpy import logical_and, diff, floor, ceil, ones, zeros, hstack, full_like, newaxis
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from scipy import sparse # type: ignore
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from scipy import sparse
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__author__ = 'Jan Petykiewicz'
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def raster(vertices: numpy.ndarray,
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@ -18,14 +27,11 @@ def raster(vertices: numpy.ndarray,
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Polygons are assumed to have clockwise vertex order; reversing the vertex order is equivalent
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to multiplying the result by -1.
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Args:
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vertices: 2xN ndarray containing `x,y` coordinates for each vertex of the polygon
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grid_x: x-coordinates for the edges of each pixel (ie, the leftmost two columns span
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`x=grid_x[0]` to `x=grid_x[1]` and `x=grid_x[1]` to `x=grid_x[2]`)
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grid_y: y-coordinates for the edges of each pixel (see `grid_x`)
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Returns:
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2D ndarray with pixel values in the range [0, 1] containing the anti-aliased polygon
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:param vertices: 2xN ndarray containing x,y coordinates for each vertex of the polygon
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:param grid_x: x-coordinates for the edges of each pixel (ie, the leftmost two columns span
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x=grid_x[0] to x=grid_x[1] and x=grid_x[1] to x=grid_x[2])
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:param grid_y: y-coordinates for the edges of each pixel (see grid_x)
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:return: 2D ndarray with pixel values in the range [0, 1] containing the anti-aliased polygon
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"""
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vertices = numpy.array(vertices)
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grid_x = numpy.array(grid_x)
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@ -52,7 +58,7 @@ def find_intersections(
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vertices: numpy.ndarray,
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grid_x: numpy.ndarray,
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grid_y: numpy.ndarray
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) -> Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]:
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) -> Tuple[numpy.ndarray]:
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"""
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Find intersections between a polygon and grid lines
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"""
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@ -129,7 +135,7 @@ def create_vertices(
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vertices: numpy.ndarray,
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grid_x: numpy.ndarray,
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grid_y: numpy.ndarray,
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new_vertex_data: Optional[Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]] = None
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new_vertex_data: Tuple[numpy.ndarray] = None
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) -> sparse.coo_matrix:
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"""
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Create additional vertices where a polygon crosses gridlines
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@ -174,7 +180,6 @@ def create_vertices(
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return vertices
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def clip_vertices_to_window(
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vertices: numpy.ndarray,
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min_x: float = -numpy.inf,
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@ -205,29 +210,26 @@ def get_raster_parts(
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grid_y: numpy.ndarray
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) -> sparse.coo_matrix:
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"""
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This function performs the same task as `raster(...)`, but instead of returning a dense array
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This function performs the same task as raster(...), but instead of returning a dense array
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of pixel values, it returns a sparse array containing the value
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`(-area + 1j * cover)`
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(-area + 1j * cover)
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for each pixel which contains a line segment, where
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`cover` is the fraction of the pixel's y-length that is traversed by the segment,
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multiplied by the sign of `(y_final - y_initial)`
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`area` is the fraction of the pixel's area covered by the trapezoid formed by
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the line segment's endpoints (clipped to the cell edges) and their projections
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onto the pixel's left (i.e., lowest-x) edge, again multiplied by
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the sign of `(y_final - y_initial)`
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cover is the fraction of the pixel's y-length that is traversed by the segment,
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multiplied by the sign of (y_final - y_initial)
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area is the fraction of the pixel's area covered by the trapezoid formed by
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the line segment's endpoints (clipped to the cell edges) and their projections
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onto the pixel's left (i.e., lowest-x) edge, again multiplied by
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the sign of (y_final - y_initial)
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Note that polygons are assumed to be wound clockwise.
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The result from `raster(...)` can be obtained with
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`raster_result = numpy.real(lines_result) + numpy.imag(lines_result).cumsum(axis=0)`
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The result from raster(...) can be obtained with
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raster_result = numpy.real(lines_result) + numpy.imag(lines_result).cumsum(axis=0)
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Args:
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vertices: 2xN ndarray containing `x, y` coordinates for each point in the polygon
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grid_x: x-coordinates for the edges of each pixel (ie, the leftmost two columns span
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`x=grid_x[0]` to `x=grid_x[1]` and `x=grid_x[1]` to `x=grid_x[2]`)
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grid_y: y-coordinates for the edges of each pixel (see `grid_x`)
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Returns:
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Complex sparse COO matrix containing area and cover information
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:param vertices: 2xN ndarray containing x,y coordinates for each point in the polygon
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:param grid_x: x-coordinates for the edges of each pixel (ie, the leftmost two columns span
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x=grid_x[0] to x=grid_x[1] and x=grid_x[1] to x=grid_x[2])
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:param grid_y: y-coordinates for the edges of each pixel (see grid_x)
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:return: Complex sparse COO matrix containing area and cover information
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"""
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if grid_x.size < 2 or grid_y.size < 2:
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raise Exception('Grid must contain at least one full pixel')
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Jan Petykiewicz