from __future__ import annotations from math import floor import numpy as np from toolz import memoize from datashader.glyphs.points import _PointLike from datashader.utils import isreal, ngjit class _PolygonLike(_PointLike): """_PointLike class, with methods overridden for vertex-delimited shapes. Key differences from _PointLike: - added self.z as a list, representing vertex weights - constructor accepts additional kwargs: * weight_type (bool): Whether the weights are on vertices (True) or on the shapes (False) * interp (bool): Whether to interpolate (True), or to have one color per shape (False) """ def __init__(self, x, y, z=None, weight_type=True, interp=True): super(_PolygonLike, self).__init__(x, y) if z is None: self.z = [] else: self.z = z self.interpolate = interp self.weight_type = weight_type @property def ndims(self): return None @property def inputs(self): return (tuple([self.x, self.y] + list(self.z)) + (self.weight_type, self.interpolate)) def validate(self, in_dshape): for col in [self.x, self.y] + list(self.z): if not isreal(in_dshape.measure[str(col)]): raise ValueError('{} must be real'.format(col)) def required_columns(self): return [self.x, self.y] + list(self.z) def compute_x_bounds(self, df): xs = df[self.x].values bounds = self._compute_bounds(xs.reshape(np.prod(xs.shape))) return self.maybe_expand_bounds(bounds) def compute_y_bounds(self, df): ys = df[self.y].values bounds = self._compute_bounds(ys.reshape(np.prod(ys.shape))) return self.maybe_expand_bounds(bounds) class Triangles(_PolygonLike): """An unstructured mesh of triangles, with vertices defined by ``xs`` and ``ys``. Parameters ---------- xs, ys, zs : list of str Column names of x, y, and (optional) z coordinates of each vertex. """ @memoize def _build_extend(self, x_mapper, y_mapper, info, append, _antialias_stage_2, _antialias_stage_2_funcs): draw_triangle, draw_triangle_interp = _build_draw_triangle(append) map_onto_pixel = _build_map_onto_pixel_for_triangle(x_mapper, y_mapper) extend_triangles = _build_extend_triangles(draw_triangle, draw_triangle_interp, map_onto_pixel) weight_type = self.weight_type interpolate = self.interpolate def extend(aggs, df, vt, bounds, plot_start=True): cols = info(df, aggs[0].shape[:2]) assert cols, 'There must be at least one column on which to aggregate' # mapped to pixels, then may be clipped extend_triangles(vt, bounds, df.values, weight_type, interpolate, aggs, cols) return extend def _build_draw_triangle(append): """Specialize a triangle plotting kernel for a given append/axis combination""" @ngjit def edge_func(ax, ay, bx, by, cx, cy): return (cx - ax) * (by - ay) - (cy - ay) * (bx - ax) @ngjit def draw_triangle_interp(verts, bbox, biases, aggs, weights): """Same as `draw_triangle()`, but with weights interpolated from vertex values. """ minx, maxx, miny, maxy = bbox w0, w1, w2 = weights if minx == maxx and miny == maxy: # Subpixel case; area == 0 append(minx, miny, *(aggs + ((w0 + w1 + w2) / 3,))) else: (ax, ay), (bx, by), (cx, cy) = verts bias0, bias1, bias2 = biases area = edge_func(ax, ay, bx, by, cx, cy) for j in range(miny, maxy+1): for i in range(minx, maxx+1): g2 = edge_func(ax, ay, bx, by, i, j) g0 = edge_func(bx, by, cx, cy, i, j) g1 = edge_func(cx, cy, ax, ay, i, j) if ((g2 > 0 or (bias0 < 0 and g2 == 0)) and (g0 > 0 or (bias1 < 0 and g0 == 0)) and (g1 > 0 or (bias2 < 0 and g1 == 0))): interp_res = (g0 * w0 + g1 * w1 + g2 * w2) / area append(i, j, *(aggs + (interp_res,))) @ngjit def draw_triangle(verts, bbox, biases, aggs, val): """Draw a triangle on a grid. Plots a triangle with integer coordinates onto a pixel grid, clipping to the bounds. The vertices are assumed to have already been scaled and transformed. """ minx, maxx, miny, maxy = bbox if minx == maxx and miny == maxy: # Subpixel case; area == 0 append(minx, miny, *(aggs + (val,))) else: (ax, ay), (bx, by), (cx, cy) = verts bias0, bias1, bias2 = biases for j in range(miny, maxy+1): for i in range(minx, maxx+1): g2 = edge_func(ax, ay, bx, by, i, j) g0 = edge_func(bx, by, cx, cy, i, j) g1 = edge_func(cx, cy, ax, ay, i, j) if ((g2 > 0 or (bias0 < 0 and g2 == 0)) and (g0 > 0 or (bias1 < 0 and g0 == 0)) and (g1 > 0 or (bias2 < 0 and g1 == 0))): append(i, j, *(aggs + (val,))) return draw_triangle, draw_triangle_interp def _build_extend_triangles(draw_triangle, draw_triangle_interp, map_onto_pixel): @ngjit def extend_triangles(vt, bounds, verts, weight_type, interpolate, aggs, cols): """Aggregate along an array of triangles formed by arrays of CW vertices. Each row corresponds to a single triangle definition. `weight_type == True` means "weights are on vertices" """ xmin, xmax, ymin, ymax = bounds cmax_x, cmax_y = max(xmin, xmax), max(ymin, ymax) cmin_x, cmin_y = min(xmin, xmax), min(ymin, ymax) vmax_x, vmax_y = map_onto_pixel(vt, bounds, cmax_x, cmax_y) vmin_x, vmin_y = map_onto_pixel(vt, bounds, cmin_x, cmin_y) max_x_pixels = round((bounds[1] - bounds[0])*vt[0]) - 1 max_y_pixels = round((bounds[3] - bounds[2])*vt[2]) - 1 col = cols[0] # Only aggregate over one column, for now n_tris = verts.shape[0] for n in range(0, n_tris, 3): a = verts[n] b = verts[n+1] c = verts[n+2] axn, ayn = a[0], a[1] bxn, byn = b[0], b[1] cxn, cyn = c[0], c[1] col0, col1, col2 = col[n], col[n+1], col[n+2] # Map triangle vertices onto pixels ax, ay = map_onto_pixel(vt, bounds, axn, ayn) bx, by = map_onto_pixel(vt, bounds, bxn, byn) cx, cy = map_onto_pixel(vt, bounds, cxn, cyn) # Get bounding box minx = min(ax, bx, cx) maxx = max(ax, bx, cx) miny = min(ay, by, cy) maxy = max(ay, by, cy) # Skip any further processing of triangles outside of viewing area if (minx >= vmax_x or maxx < vmin_x or miny >= vmax_y or maxy < vmin_y): continue # Clip bbox to viewing area minx = max(minx, vmin_x) maxx = min(maxx, vmax_x) miny = max(miny, vmin_y) maxy = min(maxy, vmax_y) # Convert bbox to integer pixels minx = max(floor(minx+0.5), 0) miny = max(floor(miny+0.5), 0) maxx = min(floor(maxx+0.5), max_x_pixels) maxy = min(floor(maxy+0.5), max_y_pixels) # Prevent double-drawing edges. # https://msdn.microsoft.com/en-us/library/windows/desktop/bb147314(v=vs.85).aspx bias0, bias1, bias2 = -1, -1, -1 if ay < by or (by == ay and ax < bx): bias0 = 0 if by < cy or (cy == by and bx < cx): bias1 = 0 if cy < ay or (ay == cy and cx < ax): bias2 = 0 bbox = minx, maxx, miny, maxy biases = bias0, bias1, bias2 mapped_verts = (ax, ay), (bx, by), (cx, cy) # draw triangles (will be clipped where outside bounds) if interpolate: weights = col0, col1, col2 draw_triangle_interp(mapped_verts, bbox, biases, aggs, weights) else: val = (col[n] + col[n+1] + col[n+2]) / 3 draw_triangle(mapped_verts, bbox, biases, aggs, val) return extend_triangles def _build_map_onto_pixel_for_triangle(x_mapper, y_mapper): @ngjit def map_onto_pixel(vt, bounds, x, y): """Map points onto pixel grid. """ # Do not snap to pixel centers sx, tx, sy, ty = vt xx = x_mapper(x)*sx + tx - 0.5 yy = y_mapper(y)*sy + ty - 0.5 return xx, yy return map_onto_pixel