def split_by_plane(self, node):
plane = node.get_plane_line()
inter = skgeom.intersection(plane, skgeom.Segment2(skgeom.Point2(self.x1, self.y1),
skgeom.Point2(self.x2, self.y2)))
#print(inter)
px1 = node.partition_x_coord
px2 = px1 + node.dx
py1 = node.partition_y_coord
py2 = py1 + node.dy
(ix, iy) = intersect_portal_by_plane(self.x1, self.y1, self.x2, self.y2,
px1, py1, px2, py2)
#plane.x1, plane.y1, plane.x2, plane.y2)
p1 = Point(self.x1, self.y1)
p2 = Point(self.x2, self.y2)
p1_class = p1.classify_against_plane(node)
p2_class = p2.classify_against_plane(node)
p1_to_intersection = Line(self.x1, self.y1, ix, iy)
intersection_to_p2 = Line(ix, iy, self.x2, self.y2)
if p1_class == IN_FRONT and p2_class == BEHIND:
return (p1_to_intersection, intersection_to_p2)
elif p1_class == BEHIND and p2_class == IN_FRONT:
return (intersection_to_p2, p1_to_intersection)
else:
raise Exception("This shouldnt happen")
def draw_rv():
segments = []
for i in range(10):
segments.append(sg.Segment2(sg.Point2(r(), r()),
sg.Point2(r(), r())))
intersections = []
for s1, s2 in itertools.permutations(segments, 2):
isect = sg.intersection(s1, s2)
if isect:
intersections.append(isect)
for s in segments:
draw(s)
for i in intersections:
draw(i)
HEIGHT = 10
THETA_H = 45
THETA_V = 60
pt_h_r = sg.Point2(HEIGHT * math.tan(THETA_H * math.pi / 180), 0)
pt_v_r = sg.Point2(HEIGHT * math.tan(THETA_V * math.pi / 180), 0)
print(dir(sg.Transformation2))
pt_v_r = pt_v_r.transform(sg.Transformation2.Rotation(3, math.pi/2))
pt_r = sg.Segment2(pt_h_r, pt_v_r)
draw(pt_h_r)
draw(pt_v_r)
draw(pt_r)
plt.show()
def pts2Edges(self, pts):
edges = []
for i in range(1, len(pts)):
e = sg.Segment2(sg.Point2(pts[i - 1][0], pts[i - 1][1]),
sg.Point2(pts[i][0], pts[i][1]))
edges.append(e)
e = sg.Segment2(sg.Point2(pts[len(pts) - 1][0], pts[len(pts) - 1][1]),
sg.Point2(pts[0][0], pts[0][1]))
edges.append(e)
return edges
def intersect_portal_by_plane(portal_x1, portal_y1, portal_x2, portal_y2, plane_x1, plane_y1, plane_x2, plane_y2):
""" returns a (x, y) tuple or None if there is no intersection """
portal_seg = skgeom.Segment2(skgeom.Point2(portal_x1, portal_y1), skgeom.Point2(portal_x2, portal_y2))
plane_line = skgeom.Segment2(skgeom.Point2(plane_x1, plane_y1), skgeom.Point2(plane_x2, plane_y2)).supporting_line()
inter = skgeom.intersection(plane_line, portal_seg)
#print(inter)
if inter:
return (inter.x(), inter.y())
"""
def compute_graph_margins(G):
# (1) pick the graph M component that contains the corner nodes.
# (2) in M, compute an arrangement to find unbounded faces.
# (3) from these faces' edges, computer an outer graph.
# (4) on this outer graph, compute margins by shortest paths.
assert not nx.is_directed(G)
components = list(nx.connected_components(G))
assert len(components) == 1
node00 = sorted(list(G.nodes), key=lambda node: (node[0], node[1]))[0]
node10 = sorted(list(G.nodes), key=lambda node: (-node[0], node[1]))[0]
node11 = sorted(list(G.nodes), key=lambda node: (-node[0], -node[1]))[0]
node01 = sorted(list(G.nodes), key=lambda node: (node[0], -node[1]))[0]
corners = (node00, node10, node11, node01)
main_graph = G.subgraph([nodes for nodes in components
if node00 in nodes][0])
if not all(c in main_graph for c in corners):
#print("corners", corners)
#print("G", list(G.edges))
raise ValueError()
arr = sg.arrangement.Arrangement()
for a, b in main_graph.edges:
arr.insert(sg.Segment2(sg.Point2(*a), sg.Point2(*b)))
boundary = set()
for h in arr.halfedges:
if h.face().is_unbounded():
c = h.curve()
boundary.add(_tuple(c.source()))
boundary.add(_tuple(c.target()))
outer_graph = main_graph.subgraph(boundary)
assert all(c in outer_graph for c in corners)
set_euclidean_weights(outer_graph)
return dict(
((Margin.LEFT,
nx.shortest_path(outer_graph, node00, node01, "euclidean")),
(Margin.RIGHT,
nx.shortest_path(outer_graph, node10, node11, "euclidean")),
(Margin.TOP, nx.shortest_path(outer_graph, node00, node10,
"euclidean")),
(Margin.BOTTOM,
nx.shortest_path(outer_graph, node01, node11, "euclidean"))))
def qh_wrapper(points):
array = points_to_np(points)
np_vert = qh.calc(array)
#print(np_vert)
segments = []
for vert_idx in range(np_vert.shape[0] - 1):
segments.append(
sg.Segment2(
sg.Point2(np_vert[vert_idx, 0], np_vert[vert_idx, 1]),
sg.Point2(np_vert[vert_idx + 1, 0], np_vert[vert_idx + 1, 1])))
segments.append(
sg.Segment2(sg.Point2(np_vert[-1, 0], np_vert[-1, 1]),
sg.Point2(np_vert[0, 0], np_vert[0, 1])))
return segments
def test_voronoi(self):
npoints = np.random.rand(100, 2) * 20 - 10
points = []
for r in npoints:
print(r)
points.append(skgeom.Point2(*r))
vdiag = voronoi.VoronoiDiagram()
for p in points:
vdiag.insert(p)
xx = vdiag.finite_edges
for el in xx:
print(el)
for he in vdiag.edges:
source, target = he.source(), he.target()
if source and target:
plt.plot([source.point().x(), target.point().x()], [source.point().y(), target.point().y()])
plt.scatter(npoints[:, 0], npoints[:, 1])
plt.axis('equal')
plt.gca().set_adjustable("box")
plt.gca().set_xlim([-10, 10])
plt.gca().set_ylim([-10, 10])
plt.show()
def on_button_press(event):
if 65 <= event.x <= 450 and 350 >= event.y >= 42:
click_point = sg.Point2((float(event.x - 65) / (450 - 65)) * 2 - 1,
(float(event.y - 42) / (350 - 42)) * 2 - 1)
points.append(click_point)
_draw()
button_press_handler(event, canvas)
def classify_against_plane(self, node):
plane_line = node.get_plane_line()
self_seg = skgeom.Segment2(skgeom.Point2(self.x1, self.y1),
skgeom.Point2(self.x2, self.y2))
inter = skgeom.intersection(plane_line, self_seg)
if inter:
if isinstance(inter, skgeom.Segment2):
return COINCIDENT
else:
return SPANNING
else:
num_positive = 0
num_negative = 0
#print("-- classifying point --")
for point in [Point(self.x1,self.y1), Point(self.x2, self.y2)]:
#proj = plane_line.projection(skgeom.Point2(point.x, point.y))
#print("projection: {}".format(proj))
val = point.classify_against_plane(node)
if val == IN_FRONT:
#print("one point in front")
num_positive += 1
elif val == BEHIND:
#print("one point behind")
num_negative += 1
#print("-- done --\n")
if num_positive == 0 and num_negative > 0:
return BEHIND
if num_positive > 0 and num_negative > 0:
return SPANNING
#print(self)
#print(node)
#raise Exception("This should not happen")
# return SPANNING
if num_positive == 2:
return IN_FRONT
elif num_negative == 2:
return BEHIND
return COINCIDENT
def getVisibilityPolygon(self, fromPt):
vs = sg.RotationalSweepVisibility(self.boundary_obs)
q = sg.Point2(fromPt[0], fromPt[1])
face = self.boundary_obs.find(q)
vx = vs.compute_visibility(q, face)
visibilityPolygon = self.getSgPolyFromArr(vx)
self.visbilityPolygon = visibilityPolygon
return visibilityPolygon
def isPtinPoly(self, pt, polygon):
# pt as a list
position = polygon.oriented_side(sg.Point2(pt[0], pt[1]))
if position == sg.Sign.POSITIVE:
return 1
elif position == sg.Sign.NEGATIVE:
return -1
elif position == sg.Sign.ZERO:
return 0
def _extract_simple_polygons_skgeom(coords, orientation=None):
coords = _without_closing_point(coords)
assert coords[0] != coords[-1]
arr = sg.arrangement.Arrangement()
for a, b in zip(coords, coords[1:] + [coords[0]]):
arr.insert(sg.Segment2(sg.Point2(*a), sg.Point2(*b)))
polygons = []
for _, boundary in geometry.face_boundaries(arr):
polygons.append(
sg.Polygon(list(reversed(_without_closing_point(boundary)))))
if len(polygons) > 1 and orientation is not None:
polygons = sorted(polygons,
key=lambda p: np.dot(p.coords[0], orientation))
return polygons
def assign_region_mask(img, poly, pixel):
for i0 in range(0, pixel):
for j0 in range(0, pixel):
d_list = []
for e0 in poly.edges:
d = distance(e0.point(0), e0.point(1), sg.Point2(i0, j0))
d_list.append(d)
# on one of the edges
if abs(min(d_list)) < 0.5 * np.sqrt(2):
img[j0, i0, :] = 999
# not on the edges
else:
if poly.oriented_side(sg.Point2(i0, j0)) == sg.Sign.NEGATIVE:
img[j0, i0, :] = -1.0
else:
img[j0, i0, :] = 1.0
# assign value to the inner and outer region of the domain
img_c = img[:, :, 0:1]
img_h = img[:, :, 1:3]
img_c = np.where(img_c != 1, img_c, -2)
img_h = np.where(img_h != 1, img_h, 0)
img = np.concatenate((img_c, img_h), axis=2)
return img
def create_polygon(points, pixel, shape_id=0, use_convex_hull=True):
sgPoints = []
for p0 in points:
sgPoints.append(sg.Point2(p0[0], p0[1]))
if use_convex_hull:
# the following make sure the inside has +1, and outside has -1
# but not work for L-shape, I guess.
chull_points = sg.convex_hull.graham_andrew(sgPoints)
poly = sg.Polygon(chull_points)
else:
# for L-shape, please define points counter-clock-wise
print(
"Please define the points counter-clock-wise to make sure inner has flag of +1 and outer has -1"
)
poly = sg.Polygon(sgPoints)
draw(sgPoints)
return poly
def apply_bcs_one_edge(img, list_of_edges, pixel, e0, _val, one_bc_value,
bc_order_type):
"""
apply bcs on one edge
"""
if _val == 'c':
channel = 0
elif _val == 'h':
channel = 1
else:
print("bc val type = ", _val,
". Not sure what it is! In apply_bcs_one_edge()")
exit(0)
for i0 in range(0, pixel):
for j0 in range(0, pixel):
# only distance of pixels on the boundary will be calculated to save computational time
if img[j0, i0, channel] == 999:
d = distance(e0.point(0), e0.point(1), sg.Point2(i0, j0))
if abs(d) < 0.5 * np.sqrt(2):
# if d < 0.5 and d >= 0.0: # inside the domain
# if d > -0.5 and d <= 0.0: # outside the domain
# print(d)
if channel == 0:
img[j0, i0, channel] = compute_bc_value(one_bc_value,
bc_order_type,
e0,
i0,
j0,
bc_type=_val)
if channel == 1:
# bc_x = compute_bc_value(one_bc_value, bc_order_type, e0, i0, j0, bc_type=_val)
[bc_x, bc_y] = compute_bc_value(one_bc_value,
bc_order_type,
e0,
i0,
j0,
bc_type=_val)
img[j0, i0, channel] = bc_x
img[j0, i0, channel + 1] = bc_y
def _generate():
n_points = int(v.get())
for i in range(n_points):
points.append(sg.Point2(2 * r() - 1, 2 * r() - 1))
_draw()
def compute_margins_from_boundary(boundary_pts, phi=-math.pi / 2, cache=None):
k_gon = sg.maximum_area_inscribed_k_gon(
[sg.Point2(*p) for p in boundary_pts], 4)
corners = [(float(v.x()), float(v.y())) for v in k_gon.vertices]
def _sort_by(a, axis):
return sorted(a, key=lambda p: p[axis])
by_y = _sort_by(corners, 1)
top_left, top_right = _sort_by(by_y[:2], 0)
bottom_left, bottom_right = _sort_by(by_y[2:], 0)
top_left, top_right, bottom_right, bottom_left = _maximize_margins_area(
boundary_pts, [top_left, top_right, bottom_right, bottom_left])
pts = [tuple(x) for x in boundary_pts]
G = nx.Graph()
G.add_nodes_from(pts)
G.add_edges_from(list(closed_boundary(pts)))
set_euclidean_weights(G)
m = dict()
m[Margin.TOP] = nx.shortest_path(G,
top_left,
top_right,
weight='euclidean')
m[Margin.RIGHT] = nx.shortest_path(G,
top_right,
bottom_right,
weight='euclidean')
m[Margin.BOTTOM] = nx.shortest_path(G,
bottom_right,
bottom_left,
weight='euclidean')
m[Margin.LEFT] = nx.shortest_path(G,
bottom_left,
top_left,
weight='euclidean')
return m
if False:
annotated = [[] for _ in range(len(boundary_pts))]
pts = np.array(boundary_pts)
xmin = np.min(pts[:, 0])
xmax = np.max(pts[:, 0])
ymin = np.min(pts[:, 1])
ymax = np.max(pts[:, 1])
largest = sg.LargestEmptyIsoRectangle(sg.Point2(xmin, ymin),
sg.Point2(xmax, ymax))
largest.insert([sg.Point2(*p) for p in convex_boundary_pts])
rectangle = largest.largest_empty_iso_rectangle
r_xmin = rectangle.xmin()
r_xmax = rectangle.xmax()
r_ymin = rectangle.ymin()
r_ymax = rectangle.ymax()
eps = 0.5
for m, p in zip(annotated, boundary_pts):
if p[0] >= r_xmax - eps:
m.append(Margin.RIGHT)
if p[0] <= r_xmin + eps:
m.append(Margin.LEFT)
if p[1] >= r_ymax - eps:
m.append(Margin.BOTTOM)
if p[1] <= r_ymin + eps:
m.append(Margin.TOP)
return _extract_margins(boundary_pts, annotated)
def get_plane_line(self):
px = self.partition_x_coord
py = self.partition_y_coord
return skgeom.Segment2(skgeom.Point2(px, px + self.dx),
skgeom.Point2(py, py + self.dy)).supporting_line()
