def reflect(self, line):
from sympy import atan, Line, Point, Dummy, oo
g = self
l = line
o = Point(0, 0)
if l == Line(o, slope=0):
return g.scale(y=-1)
elif l == Line(o, slope=oo):
return g.scale(-1)
if not hasattr(g, 'reflect') and not all(
isinstance(arg, Point) for arg in g.args):
raise NotImplementedError
a = atan(l.slope)
c = l.coefficients
d = -c[-1] / c[1] # y-intercept
# apply the transform to a single point
x, y = Dummy(), Dummy()
xf = Point(x, y)
xf = xf.translate(y=-d).rotate(-a,
o).scale(y=-1).rotate(a,
o).translate(y=d)
# replace every point using that transform
reps = [(p, xf.xreplace({x: p.x, y: p.y})) for p in g.atoms(Point)]
return g.xreplace(dict(reps))
def get_intersection_points2D_with_img(intersection_points: list,
plane_range: np.ndarray) -> tuple:
x, y = intersection_points
p1 = Point(x[0], y[0])
p2 = Point(x[1], y[1])
intersection_line = Line(p1, p2)
points1 = Point(plane_range[0, 1],
plane_range[0, 0]), Point(plane_range[0, 1],
plane_range[1, 0])
points2 = Point(plane_range[0, 1],
plane_range[1, 0]), Point(plane_range[1, 1],
plane_range[1, 0])
points3 = Point(plane_range[1, 1],
plane_range[1, 0]), Point(plane_range[1, 1],
plane_range[0, 0])
points4 = Point(plane_range[1, 1],
plane_range[0, 0]), Point(plane_range[0, 1],
plane_range[0, 0])
line1 = Segment(*points1)
line2 = Segment(*points2)
line3 = Segment(*points3)
line4 = Segment(*points4)
result = tuple(
filter(
lambda x: x != [],
intersection_line.intersection(line1) +
intersection_line.intersection(line2) +
intersection_line.intersection(line3) +
intersection_line.intersection(line4)))
return (float(result[0].x), float(result[0].y)), (float(result[1].x),
float(result[1].y))
def find_valid_corners(mat_size, corners):
popped = False
top_edge_line = Line(Point(0, 0), Point(100, 0))
while corners and corners[0][1] < 0:
pt = corners.popleft()
left_line = Line(pt, corners[0])
temp_pt = left_line.intersection(top_edge_line)
popped = True
if popped:
first_pt = corners[0]
if first_pt[1] != temp_pt[0].y:
new_point = (int(temp_pt[0].x), int(temp_pt[0].y))
if new_point[0] != corners[0][0] and new_point[1] != corners[0[1]]:
corners.appendleft(new_point)
popped = False
bottom_edge_line = Line(Point(0, mat_size[1] - 1), Point(100, mat_size[1] - 1))
while corners[-1][1] >= mat_size[1] and len(corners) > 0:
pt = corners.pop()
left_line = Line(pt, corners[-1])
temp_pt = left_line.intersection(bottom_edge_line)
popped = True
if popped:
first_pt = corners[0]
if first_pt[1] != temp_pt[0].y:
new_point = (int(temp_pt[0].x), int(temp_pt[0].y))
if new_point[0] != corners[-1][0] and new_point[1] != corners[-1][1]:
corners.append(new_point)
return corners
class wire:
def __init__(self, left0, left1, right0, right1, planeNo, wireNo,
trueWireNo):
self.leftBound = Line(left0, left1)
self.rightBound = Line(right0, right1)
self.planeNo = planeNo
self.wireNo = wireNo
self.trueWireNo = trueWireNo
def rotate(self, angle):
self.leftBound = self.leftBound.rotate(angle)
self.rightBound = self.rightBound.rotate(angle)
def translate(self, x, y):
self.leftBound = self.leftBound.translate(x, y)
self.rightBound = self.rightBound.translate(x, y)
def doesIntersect(self, wire):
ll = intersect(self.leftBound.points[0], self.leftBound.points[1],
wire.leftBound.points[0], wire.leftBound.points[1])
lr = intersect(self.leftBound.points[0], self.leftBound.points[1],
wire.rightBound.points[0], wire.rightBound.points[1])
rl = intersect(self.rightBound.points[0], self.rightBound.points[1],
wire.leftBound.points[0], wire.leftBound.points[1])
rr = intersect(self.rightBound.points[0], self.rightBound.points[1],
wire.rightBound.points[0], wire.rightBound.points[1])
# print(ll,lr,rl,rr)
return ll and lr and rl and rr
def __repr__(self):
# return str([self.planeNo,self.wireNo,self.trueWireNo])
return str([self.leftBound, self.rightBound])
def Dubins_msg(UAV, target, R0):
v = UAV.v
phi0 = UAV.phi
UAV_p = Point(UAV.site)
target_p = Point(target[0:2])
c1 = Point(UAV_p.x + R0 * np.sin(phi0), UAV_p.y - R0 * np.cos(phi0))
c2 = Point(UAV_p.x - R0 * np.sin(phi0), UAV_p.y + R0 * np.cos(phi0))
len1 = c1.distance(target_p)
len2 = c2.distance(target_p)
center = c1
if len2 > len1:
center = c2
center = Point(round(center.x.evalf(), 4), round(center.y.evalf(), 4))
circle = Circle(center, R0)
tangent_lines = Tangent_lines(circle, target_p)
tangent_line1 = tangent_lines[0]
tangent_line1 = Line(tangent_line1.p2, tangent_line1.p1)
tangent_point1 = tangent_line1.p1
y = float((target_p.y - tangent_point1.y).evalf())
x = float((target_p.x - tangent_point1.x).evalf())
tangent_angle1 = np.arctan2(y, x)
tangent_line2 = tangent_lines[1]
tangent_line2 = Line(tangent_line2.p2, tangent_line2.p1)
tangent_point2 = tangent_line2.p1
y = float((target_p.y - tangent_point2.y).evalf())
x = float((target_p.x - tangent_point2.x).evalf())
tangent_angle2 = np.arctan2(y, x)
vec1 = [UAV_p.x - center.x, UAV_p.y - center.y]
vec2 = [np.cos(phi0), np.sin(phi0)]
direction = np.sign(vec1[0] * vec2[1] - vec1[1] * vec2[0])
sin1 = float(tangent_point1.distance(UAV_p).evalf()) / (2 * R0)
angle1 = 2 * np.arcsin(sin1)
sin2 = float(tangent_point2.distance(UAV_p).evalf()) / (2 * R0)
angle2 = 2 * np.arcsin(sin2)
tangent_point = []
radian = 0
if abs(modf(abs(direction * angle1 + phi0 - tangent_angle1) / (2 * np.pi))[0] - 0.5) > 0.5 - deviation:
tangent_point = tangent_point1
radian = angle1
elif abs(modf(abs(direction * (2 * np.pi - angle1) + phi0 - tangent_angle1) / (2 * np.pi))[
0] - 0.5) > 0.5 - deviation:
tangent_point = tangent_point1
radian = 2 * np.pi - angle1
elif abs(modf(abs(direction * angle2 + phi0 - tangent_angle2) / (2 * np.pi))[0] - 0.5) > 0.5 - deviation:
tangent_point = tangent_point2
radian = angle2
elif abs(modf(abs(direction * (2 * np.pi - angle2) + phi0 - tangent_angle2) / (2 * np.pi))[
0] - 0.5) > 0.5 - deviation:
tangent_point = tangent_point2
radian = 2 * np.pi - angle2
return direction, radian, (float(tangent_point.x.evalf()), float(tangent_point.y.evalf())), (
float(center.x.evalf()), float(center.y.evalf()))
def __init__(self, left0, left1, right0, right1, planeNo, wireNo,
trueWireNo):
self.leftBound = Line(left0, left1)
self.rightBound = Line(right0, right1)
self.planeNo = planeNo
self.wireNo = wireNo
self.trueWireNo = trueWireNo
def Tangent_lines(circle_C, point_P):
# 圆外一点到圆的切线，
# 返回从point到切点的line
R = float(circle_C.radius.evalf())
circle = [
float(circle_C.center.x.evalf()),
float(circle_C.center.y.evalf())
]
point = [float(point_P.x.evalf()), float(point_P.y.evalf())]
circle_point_angle = np.arctan2(point[1] - circle[1], point[0] - circle[0])
cos = R / np.sqrt(np.sum((np.array(circle) - np.array(point))**2))
hudu_half = np.arccos(cos)
tangent_angle1 = circle_point_angle + hudu_half
tangent_point1 = Point(circle[0] + R * np.cos(tangent_angle1),
circle[1] + R * np.sin(tangent_angle1))
tangent_angle2 = circle_point_angle - hudu_half
tangent_point2 = Point(circle[0] + R * np.cos(tangent_angle2),
circle[1] + R * np.sin(tangent_angle2))
return [
Line(Point(point), Point(tangent_point1)),
Line(Point(point), Point(tangent_point2))
]
def test(f, col=30, n=200):
for i in range(0, n):
points = []
while True:
points = generate_test(col)
if points[0] is points[1] or points[0][0] is points[0][
1] or points[1][0] is points[1][1]:
continue
l = Line(P(points[0][0], points[0][1]),
P(points[1][0], points[1][1]))
if len(l.intersection(P(points[2][0], points[2][1]))) != 0:
continue
break
if i % 50 == 0 and i != 0:
print('passed {} tests'.format(i))
for j in range(0, 2 * len(points)):
point = np.random.randint(0, 25, size=(2))
answer = check(points, point)
for k in range(0, len(points) - 1):
points.insert(len(points), points[0])
points.remove(points[0])
result = f(points, point)
if result is answer:
continue
print("Test â„–{} failed".format(i + 1))
print("Expected {}, result {}".format(answer, result))
print("points={}".format(points))
print("point={}".format(point))
draw(points, point)
return
print("All tests passed")
def compute_distances_between_two_points_set(points1, points2, check = None) :
index = 0
distances = []
i = 0
li = []
while i < len(points1):
p1 = points1[i]
if index >= len(points2) - 1: break
if check:
if i < len(points1) - 1:
if check(points2[index], points2[index+1], points1[i], points1[i+1]):
logging.warn("crossing~")
line = Line(points2[index], points2[index + 1])
pro = line.projection(p1)
if is_projection_between_two_points(pro, points2[index], points2[index + 1]):
distances.append(p1.distance(pro))
li.append([p1, pro])
index += 1
else:
if pro.distance(points2[index + 1]) < pro.distance(points2[index]):
i -= 1
index += 1
i += 1
return distances, li
def slice_file(image_position_patient_array,
image_orientation_patient,
output_path=None,
input_path=None):
print("Status: Loading File.")
model = STLModel(input_path)
stats = model.stats()
print(stats)
print("Status: Calculating Slices")
v1 = Point3D(image_orientation_patient[0][0],
image_orientation_patient[0][1],
image_orientation_patient[0][2])
v2 = Point3D(image_orientation_patient[1][0],
image_orientation_patient[1][1],
image_orientation_patient[1][2])
org = Point3D(0, 0, 0)
for i, slice_loc in enumerate(image_position_patient_array):
slice_loc = Point3D(slice_loc[0], slice_loc[1], slice_loc[2])
dwg = Drawing(output_path + str(i) + '.svg', profile='tiny')
plane = Plane(v1 + slice_loc, v2 + slice_loc, org + slice_loc)
x_axis = Line(org + slice_loc, v1 + slice_loc)
y_axis = Line(org + slice_loc, v2 + slice_loc)
pairs = model.slice_at_plane(plane, x_axis, y_axis)
for pair in pairs:
dwg.add(dwg.line(pair[0], pair[1], stroke=rgb(0, 0, 0, "%")))
dwg.save()
print("Status: Finished Outputting Slices")
def locate_puzzle(img, debug=False):
# Blurr image to reduce noise in edges
thresh = cv.GaussianBlur(img, (3,3), cv.BORDER_REFLECT)
param1, param2 = 15, 20
while True:
# Canny edge detection
edges = cv.Canny(thresh, param1, param2, None, 3)
# Dilate and erode edges (from https://stackoverflow.com/questions/48954246/find-sudoku-grid-using-opencv-and-python)
edges = cv.dilate(edges, np.ones((3,3),np.uint8), iterations=1)
edges = cv.erode(edges, np.ones((5,5),np.uint8), iterations=1)
lines = cv.HoughLines(edges, 1, np.pi / 180, 150, None, 0, 0)
param1, param2 = param1+5, param2+30
if lines is None: continue
if len(lines) <= 35: break
# Copy edges to the images that will display the results in BGR
cdst = cv.cvtColor(edges, cv.COLOR_GRAY2BGR)
# Find four corners of sudoku board
poss_corners = []
for i in range(len(lines)):
rho = lines[i][0][0]
theta = lines[i][0][1]
pt1, pt2 = polar_to_points(rho, theta)
cv.line(cdst, pt1, pt2, (0,0,255), 3, cv.LINE_AA)
p1, p2 = Point(pt1), Point(pt2)
l1 = Line(p1, p2)
for j in range(len(lines)):
if i == j: continue
rho = lines[j][0][0]
theta = lines[j][0][1]
p3, p4 = polar_to_points(rho, theta, return_class=True)
l2 = Line(p3, p4)
p = l1.intersection(l2)
if len(p) == 0: continue
p = np.array([int(p[0][1]), int(p[0][0])])
if 0 <= p[0] < len(img) and 0 <= p[1] < len(img[1]):
poss_corners.append(p)
tl = poss_corners[np.argmin(np.array(list(map(euclidean, poss_corners, [[0,0]]*len(poss_corners)))))]
tr = poss_corners[np.argmin(np.array(list(map(euclidean, poss_corners, [[0,len(img[0])]]*len(poss_corners)))))]
bl = poss_corners[np.argmin(np.array(list(map(euclidean, poss_corners, [[len(img),0]]*len(poss_corners)))))]
br = poss_corners[np.argmin(np.array(list(map(euclidean, poss_corners, [[len(img),len(img[0])]]*len(poss_corners)))))]
# Idea for warping using imutils: https://www.pyimagesearch.com/2020/08/10/opencv-sudoku-solver-and-ocr/
img = four_point_transform(img, np.array([
[tl[1],tl[0]],
[tr[1],tr[0]],
[bl[1],bl[0]],
[br[1],br[0]]]))
if debug:
cv.imshow("Lines", cdst)
cv.imshow("Cropped", img)
cv.waitKey()
return img
def on_track(self, line): """Are we still on track (that is, is our distance to the given line small enough? If not, better re-navigate""" if line is None: return False else: line = Line(*line) return line.distance(self.tracker.getPosition()) < THRESHOLD
def __init__(self, p0, p1, center):
self.p0 = p0
self.p1 = p1
self.center = center
self.radius = self.center.distance(self.p0)
line1 = Line(self.center, self.p1)
line2 = Line(self.center, self.p0)
self.central_angle = line1.angle_between(line2)
def eval_end_pt_tang(self, first):
trgt_pt = self.p0 if first else self.p1
res_norm = Line(self.center, trgt_pt).direction.unit
res_tang = res_norm.rotate(np.pi / 2.)
halfpl = get_halfplane(self.p0, self.p1, self.center)
if -1 == halfpl:
res_tang = -res_tang
return res_tang
def extendExWall(P0, P1, l1, msp):
l0 = Line(p0, p1)
intersectedPoint = l0.intersection(l1)
xE, yE = intersectedPoint
xS, yS = p1
msp.add_line(((xS, yS, 0), (xE, yE, 0)))
l0 = Line(p1, intersectedPoint)
return l0
def crossing(p1: Point, p2: Point, p3: Point, p4: Point):
line1, seg1 = Line(p1, p2), Segment(p1, p2)
line2, seg2 = Line(p3, p4), Segment(p3, p4)
intersect = line1.intersection(line2)
if intersect:
seg1 = Segment(p1, p2)
seg2 = Segment(p3, p4)
pi = intersect[0]
return seg1.contains(pi) and seg2.contains(pi)
def calculateFaceTilt(leftEye, rightEye):
zeroLine = Line(Point(1, 0), Point(0, 0))
eyeMiddlePoint = Point((leftEye + rightEye) / 2)
eyeLine = Line(leftEye, rightEye)
angle = mpmath.degrees(eyeLine.angle_between(zeroLine))
if (leftEye.y > rightEye.y):
return int(angle) - 180
else:
return 180 - int(angle)
def __compute_1st_vanishing_points(self):
road_l1 = Line(Point(self.p1), Point(self.p2))
road_l2 = Line(Point(self.p3), Point(self.p4))
road_intersection = intersection(road_l1, road_l2)
u0 = float(road_intersection[0][0])
v0 = float(road_intersection[0][1])
return u0, v0
def path_of_white_ball(p1, p2, r):
pathBallW[:] = []
middle_ray = Line(p1, p2)
cue_circle = Circle(p1, r)
normal_line = middle_ray.perpendicular_line(p1)
points = intersection(cue_circle, normal_line)
pathBallW.append(middle_ray.parallel_line(points[0]))
pathBallW.append(middle_ray)
pathBallW.append(middle_ray.parallel_line(points[1]))
def projection(self, eye1, eye2):
target = self.estimate(eye1, eye2)
horizontal, = Line(target, self.abscissa_hinge).intersection(abscissa)
vertical, = Line(target, self.ordinate_hinge).intersection(ordinate)
x = self.to_width(horizontal.x)
y = self.to_height(vertical.y)
return float(x), float(y)
def _calculate_angle(line: Line) -> float:
angle = line.angle_between(Line((0, 0), (1, 0))).evalf()
if line.p2.x <= line.p1.x:
if line.p2.y <= line.p1.y:
angle = math.pi - angle + math.pi
else:
if line.p2.y <= line.p1.y:
angle = 2 * math.pi - angle
return angle
def __compute_2nd_vanishing_points(self):
# perp_l1 = Line(Point(self.p2), Point(self.p3))
perp_l1 = Line(Point(self.p1), Point(self.p4))
# horizon_l = Line(Point(0, self.v0), (1, self.v0))
horizon_l = Line(Point(self.p2), Point(self.p3))
perp_intersection = intersection(perp_l1, horizon_l)
u1 = float(perp_intersection[0][0])
return u1
def formperpenicularlines(xpos):
xpos = xpos.reshape(len(cutpos), 1)
xpts = np.insert(xpos, 1, [0], axis=1)
xpts = map(Point, xpts)
xaxis = Line((0, 0), (1, 0))
cutlines = []
for pt in xpts:
cutline = xaxis.perpendicular_line(pt)
cutlines.append(cutline)
return cutlines
def calculateFaceTilt(faceEyesIrisPoints, regionOfInterestColorObjects):
zeroLine = Line (Point (1,0), Point (0,0));
leftEye = Point (faceEyesIrisPoints.pop());
rightEye = Point (faceEyesIrisPoints.pop());
eyeMiddlePoint = Point ((leftEye + rightEye)/2);
eyeLine = Line (leftEye, rightEye);
faceSymmetryLine = eyeLine.perpendicular_line(eyeMiddlePoint);
angle = mpmath.degrees(eyeLine.angle_between(zeroLine));
if (int(angle) > 90):
return {'angle':int(angle) - 180, 'tiltline':faceSymmetryLine};
else:
return {'angle':int(angle), 'tiltline':faceSymmetryLine};
def get_polygon(left, right, top, bottom):
# convert rays to lines
left = Line(left.p1, left.p2)
right = Line(right.p1, right.p2)
top = Line(top.p1, top.p2)
bottom = Line(bottom.p1, bottom.p2)
top_left = left.intersection(top)[0]
top_right = right.intersection(top)[0]
bottom_left = left.intersection(bottom)[0]
bottom_right = right.intersection(bottom)[0]
return Polygon(top_left, top_right, bottom_right, bottom_left)
def get_osculating_center(pt, tang, radius, jnc_cntr):
init_line = Line(pt, pt + tang)
tang_perp = init_line.perpendicular_line(pt).direction.unit
cand_cntr1 = pt + tang_perp * radius
cand_cntr2 = pt - tang_perp * radius
dist_cand1 = jnc_cntr.distance(cand_cntr1)
dist_cand2 = jnc_cntr.distance(cand_cntr2)
if (dist_cand1 < dist_cand2):
res_cntr = cand_cntr1
else:
res_cntr = cand_cntr2
return res_cntr
def find_circle(circle,A,C,D,i):
AD = Line(A,D)
svg.append(AD,"AD",i)
K = intersection(circle, AD)[0]
svg.append(K,"K",i)
tangentK = Line(A,D).perpendicular_line(K)
svg.append(tangentK,"tangK",i)
P1 = intersection(tangentK, Line(A,C))[0]
svg.append(P1,"P1",i)
P2 = intersection(tangentK, xaxis)[0]
svg.append(P2,"P2",i)
T = Triangle(P1,A,P2)
svg.append(T,"T",i)
return T.incircle
def test_project_on_line_parallel(self):
"""
Simple test, building line and points near it, which can form parallel line.
"""
line = Line(Point2D(0, 0), Point2D(4, 4))
not_line_points = set()
start_point = Point2D(0, -2)
points_reference = []
not_line_point = start_point
for i in range(0, 5):
not_line_points.add(Point2D(not_line_point.x, not_line_point.y))
projected_point = SegmentsInLineFinder.ProjectedPoint(not_line_point, Point2D(not_line_point.x - 1,
not_line_point.y + 1),
(i - 1) * sqrt(2))
points_reference.append(projected_point)
not_line_point = Point2D(not_line_point.x + 1, not_line_point.y + 1)
points_test = SegmentsInLineFinder.project_on_line(line, not_line_points)
self.assertListEqual(points_test, points_reference)
def calc_prompt_perpendicular_line(p_1: QPointF, p_2: QPointF,
p_mouse: QPointF):
if p_1 == p_2:
return None, None
mouse = Point(p_mouse.x(), p_mouse.y())
p_1 = Point(p_1.x(), p_1.y())
p_2 = Point(p_2.x(), p_2.y())
line = Line(p_1, p_2)
para_line = line.parallel_line(mouse)
perp_line_1 = line.perpendicular_line(p_1)
perp_line_2 = line.perpendicular_line(p_2)
conj_p1 = para_line.intersection(perp_line_1)
conj_p2 = para_line.intersection(perp_line_2)
qp1 = QPointF(conj_p1[0].x, conj_p1[0].y)
qp2 = QPointF(conj_p2[0].x, conj_p2[0].y)
return qp1, qp2
def plotline(ax, rwaypoints, width):
pointx, pointy = pointtolist(rwaypoints)
ax.plot(pointx, pointy)
for i in range(len(rwaypoints) - 1):
x = []
y = []
if (rwaypoints[i].x == rwaypoints[i + 1].x
and rwaypoints[i].y == rwaypoints[i + 1].y):
continue
else:
line = Line(rwaypoints[i], rwaypoints[i + 1])
diracp = line.direction.unit
diracn = diracp.rotate(math.pi / 2)
rectpt1 = rwaypoints[i].translate(
(diracn.x - diracp.x) * width / 2,
(diracn.y - diracp.y) * width / 2)
rectpt2 = rwaypoints[i + 1].translate(
(diracn.x + diracp.x) * width / 2,
(diracn.y + diracp.y) * width / 2)
rectpt3 = rwaypoints[i + 1].translate(
(diracp.x - diracn.x) * width / 2,
(diracp.y - diracn.y) * width / 2)
rectpt4 = rwaypoints[i].translate(
(-diracp.x - diracn.x) * width / 2,
(-diracp.y - diracn.y) * width / 2)
x.extend([rectpt1.x, rectpt2.x, rectpt3.x, rectpt4.x])
y.extend([rectpt1.y, rectpt2.y, rectpt3.y, rectpt4.y])
ax.fill(x, y, 'b', alpha=0.2)
def during_collision(cue_point, radius, stick_point, ball_coord):
future_point = cue_point
collision_ball_info = cue_point
min_distance = 1e9
temp_ray = Ray(cue_point, stick_point)
temp_Line = Line(cue_point, stick_point)
temp_circle = Circle(cue_point, radius)
temp_collision_points = intersection(temp_Line, temp_circle)
if temp_ray.contains(temp_collision_points[0]):
white_ray = Ray(cue_point, temp_collision_points[1])
else:
white_ray = Ray(cue_point, temp_collision_points[0])
for coord in ball_coord:
enlarged_ball = Circle(Point(coord[0], coord[1]), coord[2] + radius)
intersect_point = intersection(white_ray, enlarged_ball)
if len(intersect_point) == 2 and cue_point.distance(
intersect_point[0]) >= cue_point.distance(intersect_point[1]):
temp_point = intersect_point[1]
elif len(intersect_point) == 2 or len(intersect_point) == 1:
temp_point = intersect_point[0]
else:
continue
dist = cue_point.distance(temp_point)
if min_distance > dist:
min_distance = dist
future_point = temp_point
collision_ball_info = coord
return future_point, collision_ball_info
def find_direction_split(self, template, x, nn, pre_nn):
samples = polytope.sample(10000, template, np.array(x))
preprocessed = pre_nn(torch.tensor(samples).float())
preprocessed_np = preprocessed.detach().numpy()
samples_ontput = torch.softmax(nn(preprocessed), 1)
predicted_label = samples_ontput.detach().numpy()[:, 0]
y = np.clip(predicted_label, 1e-7, 1 - 1e-7)
inv_sig_y = np.log(y / (1 - y)) # transform to log-odds-ratio space
from sklearn.linear_model import LinearRegression
lr = LinearRegression()
lr.fit(samples, inv_sig_y)
template_2d: np.ndarray = np.array([Experiment.e(3, 2), Experiment.e(3, 0) - Experiment.e(3, 1)])
def sigmoid(x):
ex = np.exp(x)
return ex / (1 + ex)
preds = sigmoid(lr.predict(samples))
plot_points_and_prediction(samples @ template_2d.T, preds)
plot_points_and_prediction(samples @ template_2d.T, predicted_label)
coeff = lr.coef_
intercept = lr.intercept_
a = sympy.symbols('x')
b = sympy.symbols('y')
classif_line1 = Line(coeff[0].item() * a + coeff[1].item() * b + intercept)
new_coeff = -coeff[0].item() / coeff[1].item()
def get_anchor_pt(p0, p1, t0, t1, r0, r1):
jnc_cntr, jnc_radius = get_junction_circle(p0, p1, t0, t1)
if -1 == jnc_radius:
# Straight line - "infinite" circle
anchor_pt = (p0 + p1) / 2.
else:
aux_start = get_auxiliary_pt(p0, t0, r0, jnc_cntr, jnc_radius, p1)
aux_end = get_auxiliary_pt(p1, t1, r1, jnc_cntr, jnc_radius, p0)
aux_mid_pt = (aux_start + aux_end) / 2.
if aux_mid_pt.distance(jnc_cntr) < 0.0001:
# half a circle. Give the preference to p0
assert abs(aux_mid_pt.distance(aux_start) - jnc_radius) < 0.0001
diameter_line = Line(aux_start, aux_end)
bisec_radius_vec = diameter_line.perpendicular_line(
jnc_cntr).direction.unit
anch_pt_1 = jnc_cntr + bisec_radius_vec * jnc_radius
anch_pt_2 = jnc_cntr - bisec_radius_vec * jnc_radius
test_pt = p0 + t0
closest_cand = get_closest_pt(anch_pt_1, anch_pt_2, test_pt)
if closest_cand == anch_pt_2:
bisec_radius_vec = -bisec_radius_vec
else:
bisec_radius_vec = Line(jnc_cntr, aux_mid_pt).direction.unit
anchor_pt = jnc_cntr + bisec_radius_vec * jnc_radius
DEBUG = 'IN_DEBUG' in globals()
if DEBUG and IN_DEBUG:
crc = mpt.Circle(
[float(aux_start.x), float(aux_start.y)],
radius=float(0.1),
color="#D4AC0D",
fill=True)
plt.gca().add_patch(crc)
crc = mpt.Circle(
[float(aux_end.x), float(aux_end.y)],
radius=float(0.1),
color="#D4AC0D",
fill=True)
plt.gca().add_patch(crc)
crc = mpt.Circle(
[float(anchor_pt.x), float(anchor_pt.y)],
radius=float(0.1),
color="#85929E",
fill=True)
plt.gca().add_patch(crc)
return anchor_pt
def _select_optimal_threshold(self, thresholds: np.ndarray,
spot_counts: List[int]) -> float:
# calculate the gradient of the number of spots
grad = np.gradient(spot_counts)
self._grad = grad
optimal_threshold_index = np.argmin(grad)
# only consider thresholds > than optimal threshold
thresholds = thresholds[optimal_threshold_index:]
grad = grad[optimal_threshold_index:]
# if all else fails, return 0.
selected_thr = 0
if len(thresholds) > 1:
distances = []
# create a line whose end points are the threshold and and corresponding gradient value
# for spot_counts corresponding to the threshold
start_point = Point(thresholds[0], grad[0])
end_point = Point(thresholds[-1], grad[-1])
line = Line(start_point, end_point)
# calculate the distance between all points and the line
for k in range(len(thresholds)):
p = Point(thresholds[k], grad[k])
dst = line.distance(p)
distances.append(dst.evalf())
# remove the end points
thresholds = thresholds[1:-1]
distances = distances[1:-1]
# select the threshold that has the maximum distance from the line
# if stringency is passed, select a threshold that is n steps higher, where n is the
# value of stringency
if distances:
thr_idx = np.argmax(np.array(distances))
if thr_idx + self.stringency < len(thresholds):
selected_thr = thresholds[thr_idx + self.stringency]
else:
selected_thr = thresholds[thr_idx]
return selected_thr
def compute_distances_between_two_points_set(points1, points2) :
index = 0
distances = []
i = 0
li = []
while i < len(points1):
p1 = points1[i]
if index >= len(points2) - 1: break
line = Line(points2[index], points2[index + 1])
pro = line.projection(p1)
if is_projection_between_two_points(pro, points2[index], points2[index + 1]):
distances.append(p1.distance(pro))
li.append([p1, pro])
index += 1
else:
if pro.distance(points2[index + 1]) < pro.distance(points2[index]):
i -= 1
index += 1
i += 1
return distances, li
def demonstrate_circle_power(circle):
"""Demonstrate power-of-a-point theorem."""
A, B, C, D = (circle.random_point() for i in range(4))
P = Line.intersection(Line(A, B), Line(C, D))
assert len(P) == 1
P = P[0]
PAPB = P.distance(A) * P.distance(B)
PCPD = P.distance(C) * P.distance(D)
print("PA * PB =", PAPB.evalf())
print("PC * PD =", PCPD.evalf())
def triangulate(self, vertex):
others = [0, 1, 2, 0, 1]
others = others[(vertex + 1):(vertex + 3)]
segment = Segment(self.triangle[others[0]], self.triangle[others[1]])
vertex_str = 'h' + str(vertex)
segment_heights_str = ['h' + str(other) for other in others]
new_points = []
counter = 2
for line in self.polygon_lines:
perp = line.perpendicular_line(Point2D(self.triangle[vertex][0],
self.triangle[vertex][1]))
intersections = perp.intersection(segment)
if len(intersections) > 0:
counter = counter + 1
new_points.append(Point3D(intersections[0].x,
intersections[0].y,
'h' + str(counter)))
no_vars = counter + 1
all_side_points = [Point3D(segment.points[0][0],
segment.points[0][1],
segment_heights_str[0])] + new_points + \
[Point3D(segment.points[1][0],
segment.points[1][1],
segment_heights_str[1])]
all_pairs = zip(all_side_points, all_side_points[1:])
h_coefs = matrix(0.0, (len(all_pairs) * len(self.polygon), no_vars))
rhs_coefs = []
for (idx1, pair) in enumerate(all_pairs):
# Compute gradient for each triangulation.
gradient = compute_plane_gradient(
Point3D(self.triangle[vertex][0], self.triangle[vertex][1], vertex_str),
pair[0],
pair[1])
heights_str = [str(pair[0][2]), str(pair[1][2])]
hs = [int(heights_str[0][1:]), int(heights_str[1][1:])]
# Ensure that each gradient is with the convex polygon.
for (idx2, (prev_point, curr_point, next_point)) in enumerate(self.adj_polygon_points):
line = Line(Point2D(next_point), Point2D(curr_point))
line_equation_poly = poly(str(line.equation()), gens=sp.symbols(['x', 'y']))
# Flip equation if necessary.
if line_equation_poly.eval(prev_point) > 0:
line_equation_poly = -line_equation_poly
gradient_poly = poly(str(line_equation_poly.eval(gradient)),
gens=sp.symbols([vertex_str, heights_str[0], heights_str[1]]))
row = idx1 * len(self.polygon) + idx2
h_coefs[row, 0] = float(gradient_poly.diff(vertex_str).eval((0, 0, 0)))
h_coefs[row, hs[0]] = float(gradient_poly.diff(heights_str[0]).eval((0, 0, 0)))
h_coefs[row, hs[1]] = float(gradient_poly.diff(heights_str[1]).eval((0, 0, 0)))
rhs_coefs.append(-float(gradient_poly.eval((0, 0, 0))))
ones = [1.0] * no_vars
# Final LP Problem.
# Objective function.
objective_function_vector = matrix(ones)
# Coefficient matrix.
ones_matrix = spmatrix(ones, range(no_vars), range(no_vars))
heights_coef_matrix = h_coefs
bounds_coef_matrix = matrix([ones_matrix, -ones_matrix])
coef_matrix = sparse([heights_coef_matrix, bounds_coef_matrix])
# Column vector of right hand sides.
column_vector = matrix(rhs_coefs + \
[self.bounds[1]] * no_vars + [-self.bounds[0]] * no_vars)
min_sol = solvers.lp(objective_function_vector, coef_matrix, column_vector)
is_consistent = min_sol['x'] is not None
if is_consistent:
self.min_heights = np.array(min_sol['x'])
print np.around(self.min_heights, decimals=2)
max_sol = solvers.lp(-objective_function_vector, coef_matrix, column_vector)
self.max_heights = np.array(max_sol['x'])
print np.around(self.max_heights, decimals=2)
return is_consistent
def solveLP(self):
# Check simple case when gradient of plane is contained within the convex polygon.
gradient = compute_plane_gradient(Point3D(self.triangle[0][0], self.triangle[0][1], 'h0'),
Point3D(self.triangle[1][0], self.triangle[1][1], 'h1'),
Point3D(self.triangle[2][0], self.triangle[2][1], 'h2'))
# Get all adjacent pairs of points that make up all sides of the polygon.
self.adj_polygon_points = zip(*[[self.polygon[-1]] + self.polygon[:-1],
self.polygon,
self.polygon[1:] + [self.polygon[0]]])
# Vectors of coefficients.
(h1_coefs, h2_coefs, h3_coefs, rhs_coefs) = ([], [], [], [])
for (prev_point, curr_point, next_point) in self.adj_polygon_points:
# Choose clockwise order when constructing line of eq. a x + b y + c = 0 from 2 given
# points. Then the semi-plane containing the convex polygon will be given by:
# a x + b y + c <= 0.
line = Line(Point2D(next_point), Point2D(curr_point))
self.polygon_lines.append(line)
line_equation_poly = poly(str(line.equation()), gens=sp.symbols(['x', 'y']))
# Check if a x + b y + c <= 0 holds; if not, flip the line equation -- critical step!
if line_equation_poly.eval(prev_point) > 0:
line_equation_poly = -line_equation_poly
gradient_poly = poly(str(line_equation_poly.eval(gradient)),
gens=sp.symbols(['h0', 'h1', 'h2']))
h1_coefs.append(float(gradient_poly.diff('h0').eval((0, 0, 0))))
h2_coefs.append(float(gradient_poly.diff('h1').eval((0, 0, 0))))
h3_coefs.append(float(gradient_poly.diff('h2').eval((0, 0, 0))))
rhs_coefs.append(-float(gradient_poly.eval((0, 0, 0))))
# Construct LP problem.
# Objective function: Minimise/Maximise h1 + h2 + h3
objective_function_vector = matrix([1.0, 1.0, 1.0])
# Coefficient matrix.
ones_matrix = spmatrix([1.0, 1.0, 1.0], range(3), range(3))
heights_coef_matrix = matrix([h1_coefs, h2_coefs, h3_coefs])
bounds_coef_matrix = matrix([ones_matrix, -ones_matrix])
coef_matrix = sparse([heights_coef_matrix, bounds_coef_matrix])
# Column vector of right hand sides.
column_vector = matrix(rhs_coefs + [self.bounds[1]] * 3 + [-self.bounds[0]] * 3)
min_sol = solvers.lp(objective_function_vector, coef_matrix, column_vector)
is_consistent = min_sol['x'] is not None
if is_consistent:
self.min_heights = np.array(min_sol['x'])
print np.around(self.min_heights, decimals=2)
max_sol = solvers.lp(-objective_function_vector, coef_matrix, column_vector)
self.max_heights = np.array(max_sol['x'])
print np.around(self.max_heights, decimals=2)
else:
# Try to determine triangulation of the given triangle.
print "Triangulating..."
# Perform triangulation w.r.t to a fixed vertex.
return self.triangulate(0) or self.triangulate(1) or self.triangulate(2)
from sympy import Point, Line, Segment p1, p2, p3 = Point(0, 0), Point(1, 1), Point(1, 2) l1 = Line(p1, p2) print l1.contains(Point(-1,-1)) print l1.contains(Point(1,1)) print l1.contains(Point(0.1,0.1))
def find_left_and_right_points_on_lines_from_corners(corners, mat_size):
corners_tmp = deque(list(map(lambda x: list(map(lambda y: int(y), x)), corners)))
assert (len(corners_tmp) == 4)
left_top_c_id = 0
for c_id, c in enumerate(corners_tmp):
if c[1] < corners_tmp[left_top_c_id][1]:
left_top_c_id = c_id
elif c[1] == corners_tmp[left_top_c_id][1] and c[0] < corners[left_top_c_id][0]:
left_top_c_id = c_id
corners = deque([])
for i in list(range(left_top_c_id, len(corners_tmp))) + list(range(0, left_top_c_id)):
corners.append(corners_tmp[i])
left_corners, right_corners = deque([]), deque([])
if corners[0][1] == corners[1][1]:
left_corners.append(corners[0])
right_corners.append(corners[1])
elif corners[0][1] < corners[1][1]:
left_corners.append(corners[0])
right_corners.append(corners[0])
right_corners.append(corners[1])
else:
left_corners.append(corners[1])
left_corners.append(corners[0])
right_corners.append(corners[1])
if corners[2][1] == corners[3][1]:
right_corners.append(corners[2])
left_corners.append(corners[3])
elif corners[2][1] < corners[3][1]:
left_corners.append(corners[3])
right_corners.append(corners[2])
right_corners.append(corners[3])
else:
left_corners.append(corners[3])
left_corners.append(corners[2])
right_corners.append(corners[2])
left_corners = find_valid_corners(mat_size, left_corners)
right_corners = find_valid_corners(mat_size, right_corners)
if not (left_corners and right_corners):
return []
assert (left_corners[0][1] == right_corners[0][1])
left1 = left_corners.popleft()
left2 = left_corners.popleft()
left_line = Line(left1, left2)
right1 = right_corners.popleft()
right2 = right_corners.popleft()
right_line = Line(right1, right2)
pts_on_lines = [] # y, left_x, right_x
curr_y = left1[1]
while True:
if curr_y > left2[1]:
if not left_corners:
break
else:
left1 = left2
left2 = left_corners.popleft()
left_line = Line(left1, left2)
if curr_y > right2[1]:
if not right_corners:
break
else:
right1 = right2
right2 = right_corners.popleft()
right_line = Line(right1, right2)
hor_line_with_curr_y = Line(Point(0, curr_y), Point(100, curr_y))
temp_pt = left_line.intersection(hor_line_with_curr_y)
left_cross = temp_pt[0]
left_x = 0 if left_cross.x < 0 else (left_cross.x if left_cross.x < mat_size[0] else (mat_size[0] - 1))
temp_pt = right_line.intersection(hor_line_with_curr_y)
right_cross = temp_pt[0]
right_x = 0 if right_cross.x < 0 else (right_cross.x if right_cross.x < mat_size[0] else (mat_size[0] - 1))
pts_on_lines.append((curr_y, int(left_x), int(right_x)))
curr_y += 1
return pts_on_lines
from sympy import Line, Point
f=open('D:\UVA\Python\Q378.txt','r')
while f:
a=f.readline().strip().split(' ')
if a ==['']:
break
p1,p2,p3,p4=Point(int(a[0]),int(a[1])),Point(int(a[2]),int(a[3])),Point(int(a[4]),int(a[5])),Point(int(a[6]),int(a[7]))
l1=Line(p1,p2)
l2=Line(p3,p4)
if l1.is_similar(l2):
print("LINE")
elif Line.is_parallel(l1,l2):
print("NONE")
elif Line.are_concurrent(l1,l2):
smaepoint= l1.intersection(l2)
print("POINT %.2f %.2f " %(smaepoint[0].x,smaepoint[0].y))
print("END OF OUTPUT")