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)
[docs]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
