def test_cubic_cubic(self):
# q1 = Bezier(10,100, 90,30, 40,140, 220,220)
# q2 = Bezier(5,150, 180,20, 80,250, 210,190)
# console.log(q1.intersects(q2))
q1 = CubicBezier(Point(10, 100), Point(90, 30), Point(40, 140),
Point(220, 220))
q2 = CubicBezier(Point(5, 150), Point(180, 20), Point(80, 250),
Point(210, 190))
i = q1.intersections(q2)
# self.assertEqual(len(i),3)
# self.assertAlmostEqual(i[0].point.x,81.7904225873)
# self.assertAlmostEqual(i[0].point.y,109.899396337)
# self.assertAlmostEqual(i[1].point.x,133.186831292)
# self.assertAlmostEqual(i[1].point.y,167.148173322)
# self.assertAlmostEqual(i[2].point.x,179.869157678)
# self.assertAlmostEqual(i[2].point.y,199.661989162)
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, [q1])
path.plot(ax)
path.activeRepresentation = SegmentRepresentation(path, [q2])
path.plot(ax)
for n in i:
circle = plt.Circle((n.point.x, n.point.y),
2,
fill=True,
color="red")
ax.add_artist(circle)
def test_loop(self):
q = CubicBezier(
Point(171,272), Point(388,249), Point(167,444), Point(388,176)
)
self.assertTrue(not q.hasLoop)
q = CubicBezier(
Point(171,272), Point(595,249), Point(167,444), Point(388,176)
)
roots = q.hasLoop
p1 = q.pointAtTime(roots[0])
p2 = q.pointAtTime(roots[1])
self.assertTrue(q.hasLoop)
self.assertEqual(p1,p2)
def cubic_beziers_from_arc(r, phi, flagA, flagS, p1, p2):
#========================================================
r_abs = tuple2(abs(r.x), abs(r.y))
d = tuple2((p1.x - p2.x), (p1.y - p2.y))
p = tuple2(
math.cos(phi) * d.x / 2 + math.sin(phi) * d.y / 2,
-math.sin(phi) * d.x / 2 + math.cos(phi) * d.y / 2)
p_sq = tuple2(p.x**2, p.y**2)
r_sq = tuple2(r_abs.x**2, r_abs.y**2)
ratio = p_sq.x / r_sq.x + p_sq.y / r_sq.y
if ratio > 1:
scale = math.sqrt(ratio)
r_abs = tuple2(scale * r_abs.x, scale * r_abs.y)
r_sq = tuple2(r_abs.x**2, r_abs.y**2)
dq = r_sq.x * p_sq.y + r_sq.y * p_sq.x
pq = (r_sq.x * r_sq.y - dq) / dq
q = math.sqrt(max(0, pq))
if flagA == flagS:
q = -q
cp = tuple2(q * r_abs.x * p.y / r_abs.y, -q * r_abs.y * p.x / r_abs.x)
c = tuple2(
cp.x * math.cos(phi) - cp.y * math.sin(phi) + (p1.x + p2.x) / 2.0,
cp.x * math.sin(phi) + cp.y * math.cos(phi) + (p1.y + p2.y) / 2.0)
lambda1 = svg_angle(tuple2(1, 0),
tuple2((p.x - cp.x) / r_abs.x, (p.y - cp.y) / r_abs.y))
delta = svg_angle(tuple2((p.x - cp.x) / r_abs.x, (p.y - cp.y) / r_abs.y),
tuple2((-p.x - cp.x) / r_abs.x, (-p.y - cp.y) / r_abs.y))
delta = delta - 2 * math.pi * math.floor(delta / (2 * math.pi))
if not flagS:
delta -= 2 * math.pi
lambda2 = lambda1 + delta
t = lambda1
dt = math.pi / 4
curves = []
while (t + dt) < lambda2:
control_points = (BezierPoint(
*cp) for cp in cubic_bezier_control_points(c, r_abs, phi, t, t +
dt))
curves.append(CubicBezier(*control_points))
t += dt
control_points = (BezierPoint(
*cp) for cp in cubic_bezier_control_points(c, r_abs, phi, t, lambda2))
curves.append(CubicBezier(*(tuple(control_points)[:3]), BezierPoint(*p2)))
return curves
def test_cubic_cubic(self):
# q1 = Bezier(10,100, 90,30, 40,140, 220,220)
# q2 = Bezier(5,150, 180,20, 80,250, 210,190)
# console.log(q1.intersects(q2))
q1 = CubicBezier(Point(10, 100), Point(90, 30), Point(40, 140),
Point(220, 220))
q2 = CubicBezier(Point(5, 150), Point(180, 20), Point(80, 250),
Point(210, 190))
i = q1.intersections(q2)
self.assertEqual(len(i), 3)
self.assertAlmostEqual(i[0].point.x, 81.7904225873)
self.assertAlmostEqual(i[0].point.y, 109.899396337)
self.assertAlmostEqual(i[1].point.x, 133.186831292)
self.assertAlmostEqual(i[1].point.y, 167.148173322)
self.assertAlmostEqual(i[2].point.x, 179.869157678)
self.assertAlmostEqual(i[2].point.y, 199.661989162)
def join_beziers_in_region(last_bezier, join_region, next_bezier):
#=================================================================
last_bezier = trim_bezier_to_region_edge(last_bezier.asSegments()[-1],
join_region,
start=False)
next_bezier = trim_bezier_to_region_edge(next_bezier.asSegments()[0],
join_region,
start=True)
# now want intersection of derivative lines
intersection = line_intersection(last_bezier.points[2:4],
next_bezier.points[0:2])
intersection = BezierPoint(*intersection)
#join_bezier = CubicBezier(last_bezier.points[3], intersection, intersection, next_bezier.points[0])
## What if intersection is outside of join_region? Or even not near the region's centre??
region_centre = BezierPoint(*join_region.centroid.coords[0])
join_bezier = CubicBezier(last_bezier.points[3], region_centre,
region_centre, next_bezier.points[0])
## Adjust derivatives at end/start of last/next bezier to have same magnitudes
## as join_bezier's start/end derivative (slope will already match so simply set as
## last_bezier.points[2] = (last_bezier.points[3] - (intersection - last_bezier.points[3]))
## etc...
return (last_bezier, join_bezier, next_bezier)
def appendSegment(self, seg):
seg = [Point(n[0], n[1]) for n in seg]
if len(seg) == 2:
self.segments.append(Line(*seg))
elif len(seg) == 3:
self.segments.append(QuadraticBezier(*seg))
elif len(seg) == 4:
self.segments.append(CubicBezier(*seg))
else:
raise ValueError("Unknown segment type")
def Ellipse(x_radius, y_radius, origin=None, superness=CIRCULAR_SUPERNESS):
"""Returns a path representing an ellipse of given x and y radii.
You can specify the `origin` as a Point and the `superness` of the ellipse."""
if not origin:
origin = Point(0, 0)
w = origin + west * x_radius
e = origin + east * x_radius
n = origin + north * y_radius
s = origin + south * y_radius
w_n = CubicBezier(w, w + north * y_radius * superness,
n + west * x_radius * superness, n)
n_e = CubicBezier(n, n + east * x_radius * superness,
e + north * y_radius * superness, e)
e_s = CubicBezier(e, e + south * y_radius * superness,
s + east * x_radius * superness, s)
s_w = CubicBezier(s, s + west * x_radius * superness,
w + south * y_radius * superness, w)
return BezierPath.fromSegments([w_n, n_e, e_s, s_w])
def test_cubic_line(self):
q = CubicBezier(Point(100, 240), Point(30, 60), Point(210, 230),
Point(160, 30))
l = Line(Point(25, 260), Point(230, 20))
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, [q])
i = q.intersections(l)
self.assertEqual(len(i), 3)
self.assertEqual(i[0].point, q.pointAtTime(0.117517031451))
self.assertEqual(i[1].point, q.pointAtTime(0.518591792307))
self.assertEqual(i[2].point, q.pointAtTime(0.867886610031))
def test_addextremes(self):
q = CubicBezier(Point(42, 135), Point(129, 242), Point(167, 77),
Point(65, 59))
ex = q.findExtremes()
self.assertEqual(len(ex), 2)
path = BezierPath()
path.closed = False
path.activeRepresentation = SegmentRepresentation(path, [q])
path.addExtremes()
path.balance()
segs = path.asSegments()
self.assertEqual(len(segs), 3)
def test_extremes(self):
q = CubicBezier(
Point(65,59), Point(194,90), Point(220,260), Point(70,261)
)
# console.log(Bezier(65,59, 194,90, 220,260, 70,261).extrema())
r = q.findExtremes()
self.assertEqual(len(r), 1)
self.assertAlmostEqual(r[0], 0.5275787707261016)
r = q.findExtremes(inflections = True)
self.assertEqual(len(r), 2)
self.assertAlmostEqual(r[0], 0.4512987012987013)
self.assertAlmostEqual(r[1], 0.5275787707261016)
def bezier_paths_from_arc_endpoints(r, phi, flagA, flagS, p1, p2, T):
#====================================================================
arc = arc_endpoints_to_centre(r, phi, flagA, flagS, p1, p2)
end_theta = arc.theta + arc.delta_theta
t = arc.theta
dt = math.pi / 4
segments = []
while (t + dt) < end_theta:
control_points = (BezierPoint(*T.transform_point(cp))
for cp in cubic_bezier_control_points(
arc.centre, arc.radii, phi, t, t + dt))
segments.append(CubicBezier(*control_points))
t += dt
control_points = (BezierPoint(*T.transform_point(cp))
for cp in cubic_bezier_control_points(
arc.centre, arc.radii, phi, t, end_theta))
segments.append(
CubicBezier(*(tuple(control_points)[:3]),
BezierPoint(*T.transform_point(p2))))
path = BezierPath.fromSegments(segments)
path.closed = False
return path
def test_align(self):
q = CubicBezier(
Point(120,160), Point(35,200), Point(220,260), Point(220,40)
)
s = q.aligned()
self.assertAlmostEqual(s[0].x,0.0)
self.assertAlmostEqual(s[0].y,0.0)
self.assertAlmostEqual(s[1].x,-85.14452515537582)
self.assertAlmostEqual(s[1].y,-39.69143277919774)
self.assertAlmostEqual(s[2].x,-12.803687993289572)
self.assertAlmostEqual(s[2].y,140.84056792618557)
self.assertAlmostEqual(s[3].x,156.2049935181331)
self.assertAlmostEqual(s[3].y,0.0)
def fitLine(self, data, tHat1, tHat2):
p0, p3 = data[0], data[-1]
dist = p0.distanceFrom(p3) / 3.0
if tHat1:
p1 = p0 + tHat1 * dist
else:
p1 = ((p0 * 2.0) + p3) / 3.0
if tHat2:
p2 = p3 + tHat2 * dist
else:
p2 = ((p3 * 2.0) + p0) / 3.0
return CubicBezier(p0, p1, p2, p3)
def estimateLengths(self, data, u, tHat1, tHat2):
C = [ [ 0.0, 0.0], [ 0.0, 0.0 ]]
X = [ 0.0, 0.0 ]
# bez = SCBezier()
for (coeff,datum) in zip(u, data):
(b0,b1,b2,b3) = (B0(coeff), B1(coeff), B2(coeff), B3(coeff))
(a1, a2) = (tHat1 * b1, tHat2 * b2)
C[0][0] += a1.__matmul__(a1)
C[0][1] += a1.__matmul__(a2)
C[1][0] = C[0][1]
C[1][1] += a2.__matmul__(a2)
s1 = data[0] * (b0+b1)
shortfall = datum - s1
shortfall = shortfall - (data[-1] * (b2+b3))
X[0] += a1.__matmul__(shortfall)
X[1] += a2.__matmul__(shortfall)
det_C0_C1 = C[0][0] * C[1][1] - C[1][0] * C[0][1]
if det_C0_C1 != 0.0:
det_C0_X = C[0][0] * X[1] - C[0][1] * X[0]
det_X_C1 = X[0] * C[1][1] - X[1] * C[0][1]
alpha_l = det_X_C1 / det_C0_C1
alpha_r = det_C0_X / det_C0_C1
else:
c0 = C[0][0] + C[0][1]
if c0 != 0:
alpha_l = X[0] / c0
alpha_r = X[0] / c0
else:
alpha_l = 0.0
alpha_r = 0.0
if alpha_l < 1.0e-6 or alpha_r < 1.0e-6:
alpha_l = data[-1].distanceFrom(data[0]) / 3.0
alpha_r = alpha_l
return CubicBezier(data[0],
tHat1 * alpha_l + data[0],
tHat2 * alpha_r + data[-1],
data[-1])
def process_shape(self, shape, transform):
feature = {'type': 'Feature', 'id': shape.shape_id, 'properties': {}}
if shape.name_id != '':
feature['properties']['id'] = '{}/{}'.format(
self.layer_id, shape.name_id)
feature['properties']['selectable'] = True
if len(shape.name_attributes):
feature['properties']['type'] = shape.name_attributes[0]
geometry = {}
coordinates = []
pptx_geometry = Geometry(shape)
for path in pptx_geometry.path_list:
bbox = (shape.width, shape.height) if path.w is None else (path.w,
path.h)
T = transform * Transform(shape, bbox).matrix()
moved = False
first_point = None
current_point = None
closed = False
for c in path.getchildren():
if c.tag == DML('arcTo'):
wR = pptx_geometry.attrib_value(c, 'wR')
hR = pptx_geometry.attrib_value(c, 'hR')
stAng = radians(pptx_geometry.attrib_value(c, 'stAng'))
swAng = radians(pptx_geometry.attrib_value(c, 'swAng'))
p1 = ellipse_point(wR, hR, stAng)
p2 = ellipse_point(wR, hR, stAng + swAng)
pt = (current_point[0] - p1[0] + p2[0],
current_point[1] - p1[1] + p2[1])
large_arc_flag = 1 if swAng >= math.pi else 0
beziers = cubic_beziers_from_arc(tuple2(wR, hR), 0,
large_arc_flag, 1,
tuple2(*current_point),
tuple2(*pt))
for bz in beziers:
coordinates.extend(transform_bezier_samples(T, bz))
current_point = pt
elif c.tag == DML('close'):
if first_point is not None and current_point != first_point:
coordinates.append(transform_point(T, first_point))
closed = True
first_point = None
# Close current pptx_geometry and start a new one...
elif c.tag == DML('cubicBezTo'):
coords = [BezierPoint(*current_point)]
for p in c.getchildren():
pt = pptx_geometry.point(p)
coords.append(BezierPoint(*pt))
current_point = pt
bz = CubicBezier(*coords)
coordinates.extend(transform_bezier_samples(T, bz))
elif c.tag == DML('lnTo'):
pt = pptx_geometry.point(c.pt)
if moved:
coordinates.append(transform_point(T, current_point))
moved = False
coordinates.append(transform_point(T, pt))
current_point = pt
elif c.tag == DML('moveTo'):
pt = pptx_geometry.point(c.pt)
if first_point is None:
first_point = pt
current_point = pt
moved = True
elif c.tag == DML('quadBezTo'):
coords = [BezierPoint(*current_point)]
for p in c.getchildren():
pt = pptx_geometry.point(p)
coords.append(BezierPoint(*pt))
current_point = pt
bz = QuadraticBezier(*coords)
coordinates.extend(transform_bezier_samples(T, bz))
else:
print('Unknown path element: {}'.format(c.tag))
lat_lon = points_to_lon_lat(coordinates)
if closed:
geometry['type'] = 'Polygon'
geometry['coordinates'] = [lat_lon]
else:
geometry['type'] = 'LineString'
geometry['coordinates'] = lat_lon
feature['geometry'] = geometry
self._features.append(feature)
def __get_geometry(self, element, properties, transform):
#=======================================================
##
## Returns path element as a `shapely` object.
##
coordinates = []
bezier_segments = []
moved = False
first_point = None
current_point = None
closed = False
path_tokens = []
T = transform@SVGTransform(element.attrib.get('transform'))
if element.tag == SVG_NS('path'):
path_tokens = list(parse_svg_path(element.attrib.get('d', '')))
elif element.tag == SVG_NS('rect'):
x = length_as_pixels(element.attrib.get('x', 0))
y = length_as_pixels(element.attrib.get('y', 0))
width = length_as_pixels(element.attrib.get('width', 0))
height = length_as_pixels(element.attrib.get('height', 0))
rx = length_as_pixels(element.attrib.get('rx'))
ry = length_as_pixels(element.attrib.get('ry'))
if width == 0 or height == 0: return None
if rx is None and ry is None:
rx = ry = 0
elif ry is None:
ry = rx
elif rx is None:
rx = ry
rx = min(rx, width/2)
ry = min(ry, height/2)
if rx == 0 and ry == 0:
path_tokens = ['M', x, y,
'H', x+width,
'V', y+height,
'H', x,
'V', y,
'Z']
else:
path_tokens = ['M', x+rx, y,
'H', x+width-rx,
'A', rx, ry, 0, 0, 1, x+width, y+ry,
'V', y+height-ry,
'A', rx, ry, 0, 0, 1, x+width-rx, y+height,
'H', x+rx,
'A', rx, ry, 0, 0, 1, x, y+height-ry,
'V', y+ry,
'A', rx, ry, 0, 0, 1, x+rx, y,
'Z']
elif element.tag == SVG_NS('line'):
x1 = length_as_pixels(element.attrib.get('x1', 0))
y1 = length_as_pixels(element.attrib.get('y1', 0))
x2 = length_as_pixels(element.attrib.get('x2', 0))
y2 = length_as_pixels(element.attrib.get('y2', 0))
path_tokens = ['M', x1, y1, x2, y2]
elif element.tag == SVG_NS('polyline'):
points = element.attrib.get('points', '').replace(',', ' ').split()
path_tokens = ['M'] + points
elif element.tag == SVG_NS('polygon'):
points = element.attrib.get('points', '').replace(',', ' ').split()
path_tokens = ['M'] + points + ['Z']
elif element.tag == SVG_NS('circle'):
cx = length_as_pixels(element.attrib.get('cx', 0))
cy = length_as_pixels(element.attrib.get('cy', 0))
r = length_as_pixels(element.attrib.get('r', 0))
if r == 0: return None
path_tokens = ['M', cx+r, cy,
'A', r, r, 0, 0, 0, cx, cy-r,
'A', r, r, 0, 0, 0, cx-r, cy,
'A', r, r, 0, 0, 0, cx, cy+r,
'A', r, r, 0, 0, 0, cx+r, cy,
'Z']
elif element.tag == SVG_NS('ellipse'):
cx = length_as_pixels(element.attrib.get('cx', 0))
cy = length_as_pixels(element.attrib.get('cy', 0))
rx = length_as_pixels(element.attrib.get('rx', 0))
ry = length_as_pixels(element.attrib.get('ry', 0))
if rx == 0 or ry == 0: return None
path_tokens = ['M', cx+rx, cy,
'A', rx, ry, 0, 0, 0, cx, cy-ry,
'A', rx, ry, 0, 0, 0, cx-rx, cy,
'A', rx, ry, 0, 0, 0, cx, cy+ry,
'A', rx, ry, 0, 0, 0, cx+rx, cy,
'Z']
elif element.tag == SVG_NS('image'):
if 'id' in properties or 'class' in properties:
width = length_as_pixels(element.attrib.get('width', 0))
height = length_as_pixels(element.attrib.get('height', 0))
path_tokens = ['M', 0, 0,
'H', width,
'V', height,
'H', 0,
'V', 0,
'Z']
pos = 0
while pos < len(path_tokens):
if isinstance(path_tokens[pos], str) and path_tokens[pos].isalpha():
cmd = path_tokens[pos]
pos += 1
# Else repeat previous command with new coordinates
# with `moveTo` becoming `lineTo`
elif cmd == 'M':
cmd = 'L'
elif cmd == 'm':
cmd = 'l'
if cmd not in ['s', 'S']:
second_cubic_control = None
if cmd not in ['t', 'T']:
second_quad_control = None
if cmd in ['a', 'A']:
params = [float(x) for x in path_tokens[pos:pos+7]]
pos += 7
pt = params[5:7]
if cmd == 'a':
pt[0] += current_point[0]
pt[1] += current_point[1]
phi = radians(params[2])
path = bezier_path_from_arc_endpoints(tuple2(*params[0:2]), phi, *params[3:5],
tuple2(*current_point), tuple2(*pt), T)
bezier_segments.extend(path.asSegments())
coordinates.extend(bezier_sample(path))
current_point = pt
elif cmd in ['c', 'C', 's', 'S']:
coords = [BezierPoint(*T.transform_point(current_point))]
if cmd in ['c', 'C']:
n_params = 6
else:
n_params = 4
if second_cubic_control is None:
coords.append(BezierPoint(*T.transform_point(current_point)))
else:
coords.append(BezierPoint(*T.transform_point(
reflect_point(second_cubic_control, current_point))))
params = [float(x) for x in path_tokens[pos:pos+n_params]]
pos += n_params
for n in range(0, n_params, 2):
pt = params[n:n+2]
if cmd.islower():
pt[0] += current_point[0]
pt[1] += current_point[1]
if n == (n_params - 4):
second_cubic_control = pt
coords.append(BezierPoint(*T.transform_point(pt)))
bz = CubicBezier(*coords)
bezier_segments.append(bz)
coordinates.extend(bezier_sample(bz))
current_point = pt
elif cmd in ['l', 'L', 'h', 'H', 'v', 'V']:
if cmd in ['l', 'L']:
params = [float(x) for x in path_tokens[pos:pos+2]]
pos += 2
pt = params[0:2]
if cmd == 'l':
pt[0] += current_point[0]
pt[1] += current_point[1]
else:
param = float(path_tokens[pos])
pos += 1
if cmd == 'h':
param += current_point[0]
elif cmd == 'v':
param += current_point[1]
if cmd in ['h', 'H']:
pt = [param, current_point[1]]
else:
pt = [current_point[0], param]
if moved:
coordinates.append(T.transform_point(current_point))
moved = False
coordinates.append(T.transform_point(pt))
current_point = pt
elif cmd in ['m', 'M']:
params = [float(x) for x in path_tokens[pos:pos+2]]
pos += 2
pt = params[0:2]
if first_point is None:
# First `m` in a path is treated as `M`
first_point = pt
else:
if cmd == 'm':
pt[0] += current_point[0]
pt[1] += current_point[1]
current_point = pt
moved = True
elif cmd in ['q', 'Q', 't', 'T']:
coords = [BezierPoint(*T.transform_point(current_point))]
if cmd in ['q', 'Q']:
n_params = 4
else:
n_params = 2
if second_quad_control is None:
coords.append(BezierPoint(*T.transform_point(current_point)))
else:
coords.append(BezierPoint(*T.transform_point(
reflect_point(second_quad_control, current_point))))
params = [float(x) for x in path_tokens[pos:pos+n_params]]
pos += n_params
for n in range(0, n_params, 2):
pt = params[n:n+2]
if cmd.islower():
pt[0] += current_point[0]
pt[1] += current_point[1]
if n == (n_params - 4):
second_quad_control = pt
coords.append(BezierPoint(*T.transform_point(pt)))
bz = QuadraticBezier(*coords)
bezier_segments.append(bz)
coordinates.extend(bezier_sample(bz))
current_point = pt
elif cmd in ['z', 'Z']:
if first_point is not None and current_point != first_point:
coordinates.append(T.transform_point(first_point))
closed = True
first_point = None
else:
log.warn('Unknown path command: {}'.format(cmd))
if len(bezier_segments) > 0:
properties['bezier-path'] = BezierPath.fromSegments(bezier_segments)
if closed and len(coordinates) >= 3:
geometry = shapely.geometry.Polygon(coordinates)
elif properties.get('closed', False) and len(coordinates) >= 3:
# Return a polygon if flagged as `closed`
coordinates.append(coordinates[0])
geometry = shapely.geometry.Polygon(coordinates)
elif len(coordinates) >= 2:
geometry = shapely.geometry.LineString(coordinates)
else:
geometry = None
return geometry
# Subdivision
r1 = self.minDist(uinterval=(umin, newuMid), vinterval=(vmin, newvMid))
r2 = self.minDist(uinterval=(umin, newuMid), vinterval=(newvMid, vmax))
r3 = self.minDist(uinterval=(newuMid, umax), vinterval=(vmin, newvMid))
r4 = self.minDist(uinterval=(newuMid, umax), vinterval=(newvMid, vmax))
results = min([r1, r2, r3, r4], key=lambda x: x[0])
return results
def curveDistance(bez1, bez2):
"""Find the distance between two curves."""
c = MinimumCurveDistanceFinder(bez1, bez2)
dist, t1, t2 = c.minDist()
return math.sqrt(dist), t1, t2
if __name__ == "__main__":
bez1 = CubicBezier(Point(129, 139), Point(190, 139), Point(201, 364),
Point(90, 364))
bez2 = CubicBezier(Point(309, 159), Point(178, 159), Point(215, 408),
Point(309, 408))
bez3 = Line(Point(309, 159), Point(309, 408))
c = MinimumCurveDistanceFinder(bez1, bez3)
dist, t1, t2 = c.minDist()
print(bez1.pointAtTime(t1))
print(bez3.pointAtTime(t2))
print(math.sqrt(dist))
print(c.iterations)
def process_shape(self, shape, properties, transform):
#=====================================================
##
## Returns shape's geometry as `shapely` object.
##
coordinates = []
pptx_geometry = Geometry(shape)
for path in pptx_geometry.path_list:
bbox = (shape.width,
shape.height) if path.w is None or path.h is None else (
path.w, path.h)
T = transform @ Transform(shape, bbox).matrix()
moved = False
first_point = None
current_point = None
closed = False
for c in path.getchildren():
if c.tag == DML('arcTo'):
wR = pptx_geometry.attrib_value(c, 'wR')
hR = pptx_geometry.attrib_value(c, 'hR')
stAng = radians(pptx_geometry.attrib_value(c, 'stAng'))
swAng = radians(pptx_geometry.attrib_value(c, 'swAng'))
p1 = ellipse_point(wR, hR, stAng)
p2 = ellipse_point(wR, hR, stAng + swAng)
pt = (current_point[0] - p1[0] + p2[0],
current_point[1] - p1[1] + p2[1])
large_arc_flag = 1 if swAng >= math.pi else 0
beziers = cubic_beziers_from_arc(tuple2(wR, hR), 0,
large_arc_flag, 1,
tuple2(*current_point),
tuple2(*pt))
for bz in beziers:
coordinates.extend(transform_bezier_samples(T, bz))
current_point = pt
elif c.tag == DML('close'):
if first_point is not None and current_point != first_point:
coordinates.append(transform_point(T, first_point))
closed = True
first_point = None
# Close current pptx_geometry and start a new one...
elif c.tag == DML('cubicBezTo'):
coords = [BezierPoint(*current_point)]
for p in c.getchildren():
pt = pptx_geometry.point(p)
coords.append(BezierPoint(*pt))
current_point = pt
bz = CubicBezier(*coords)
coordinates.extend(transform_bezier_samples(T, bz))
elif c.tag == DML('lnTo'):
pt = pptx_geometry.point(c.pt)
if moved:
coordinates.append(transform_point(T, current_point))
moved = False
coordinates.append(transform_point(T, pt))
current_point = pt
elif c.tag == DML('moveTo'):
pt = pptx_geometry.point(c.pt)
if first_point is None:
first_point = pt
current_point = pt
moved = True
elif c.tag == DML('quadBezTo'):
coords = [BezierPoint(*current_point)]
for p in c.getchildren():
pt = pptx_geometry.point(p)
coords.append(BezierPoint(*pt))
current_point = pt
bz = QuadraticBezier(*coords)
coordinates.extend(transform_bezier_samples(T, bz))
else:
print('Unknown path element: {}'.format(c.tag))
if closed:
geometry = shapely.geometry.Polygon(coordinates)
else:
geometry = shapely.geometry.LineString(coordinates)
if properties.get('closed', False):
# Return a polygon if flagged as `closed`
coordinates.append(coordinates[0])
return shapely.geometry.Polygon(coordinates)
return geometry
def test_curvature(self):
q = CubicBezier(
Point(122,102), Point(35,200), Point(228,145), Point(190,46)
)
self.assertAlmostEqual(q.curvatureAtTime(0.5),-103450.5)
def test_cubicLength(self):
b1 = CubicBezier(Point(100, 25), Point(10, 90), Point(110, 100),
Point(132, 192))
self.assertAlmostEqual(b1.length, 202.20118972656385)
def __get_geometry(self, shape, properties, transform):
#======================================================
##
## Returns shape's geometry as `shapely` object.
##
coordinates = []
bezier_segments = []
pptx_geometry = Geometry(shape)
for path in pptx_geometry.path_list:
bbox = (shape.width,
shape.height) if path.w is None or path.h is None else (
path.w, path.h)
T = transform @ DrawMLTransform(shape, bbox)
moved = False
first_point = None
current_point = None
closed = False
for c in path.getchildren():
if c.tag == DML('arcTo'):
(wR, hR) = ((pptx_geometry.attrib_value(c, 'wR'),
pptx_geometry.attrib_value(c, 'hR')))
stAng = radians(pptx_geometry.attrib_value(c, 'stAng'))
swAng = radians(pptx_geometry.attrib_value(c, 'swAng'))
p1 = ellipse_point(wR, hR, stAng)
p2 = ellipse_point(wR, hR, stAng + swAng)
pt = (current_point[0] - p1[0] + p2[0],
current_point[1] - p1[1] + p2[1])
large_arc_flag = 1 if swAng >= math.pi else 0
paths = bezier_paths_from_arc_endpoints(
tuple2(wR, hR), 0, large_arc_flag, 1,
tuple2(*current_point), tuple2(*pt), T)
bezier_segments.extend(paths.asSegments())
coordinates.extend(bezier_sample(paths))
current_point = pt
elif c.tag == DML('close'):
if first_point is not None and current_point != first_point:
coordinates.append(T.transform_point(first_point))
closed = True
first_point = None
# Close current pptx_geometry and start a new one...
elif c.tag == DML('cubicBezTo'):
coords = [BezierPoint(*T.transform_point(current_point))]
for p in c.getchildren():
pt = pptx_geometry.point(p)
coords.append(BezierPoint(*T.transform_point(pt)))
current_point = pt
bz = CubicBezier(*coords)
bezier_segments.append(bz)
coordinates.extend(bezier_sample(bz))
elif c.tag == DML('lnTo'):
pt = pptx_geometry.point(c.pt)
if moved:
coordinates.append(T.transform_point(current_point))
moved = False
coordinates.append(T.transform_point(pt))
current_point = pt
elif c.tag == DML('moveTo'):
pt = pptx_geometry.point(c.pt)
if first_point is None:
first_point = pt
current_point = pt
moved = True
elif c.tag == DML('quadBezTo'):
coords = [BezierPoint(*T.transform_point(current_point))]
for p in c.getchildren():
pt = pptx_geometry.point(p)
coords.append(BezierPoint(*T.transform_point(pt)))
current_point = pt
bz = QuadraticBezier(*coords)
bezier_segments.append(bz)
coordinates.extend(bezier_sample(bz))
else:
print('Unknown path element: {}'.format(c.tag))
if settings.get('saveBeziers', False) and len(bezier_segments) > 0:
properties['bezier-segments'] = [
repr(bz) for bz in bezier_segments
]
if closed:
geometry = shapely.geometry.Polygon(coordinates)
else:
geometry = shapely.geometry.LineString(coordinates)
if properties.get('closed', False):
# Return a polygon if flagged as `closed`
coordinates.append(coordinates[0])
return shapely.geometry.Polygon(coordinates)
return geometry
def toCubicBezier(self):
"""Converts the quadratic bezier to a CubicBezier"""
from beziers.cubicbezier import CubicBezier
return CubicBezier(self[0], self[0] * (1 / 3.) + self[1] * (2 / 3.),
self[1] * (2 / 3.) + self[2] * (1 / 3.), self[2])
def test_length(self):
q = CubicBezier(
Point(120,160), Point(35,200), Point(220,260), Point(220,40)
)
self.assertAlmostEqual(q.length,272.87003168)