Midpoint circle and circle intersection
This commit is contained in:
NichiHachi
@@ -1,5 +1,5 @@
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from Metro_Line import *
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from math import pi, cos, sin
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from math import pi, cos, sin, sqrt, atan2, inf
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from pygame import Surface
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import pygame
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@@ -83,7 +83,7 @@ def bezier_curve(control_points, num_points) -> tuple[list[Position], list[Posit
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def osculating_circle(points: list[Position], derivative: list[Position], second_derivative: list[Position]) \
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-> list[tuple[float, Position]]:
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-> list[tuple[int, Position]]:
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"""
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Calculate the osculating circle at each point of a curve
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An osculating circle is the circle that best approximates the curve at a given point
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@@ -107,12 +107,12 @@ def osculating_circle(points: list[Position], derivative: list[Position], second
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center = points[i] + Position(-derivative[i].y * radius / normal, derivative[i].x * radius / normal)
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else:
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center = points[i] + Position(derivative[i].y * radius / normal, -derivative[i].x * radius / normal)
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circle.append((radius, center))
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circle.append((int(radius), center))
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return circle
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def merge_similar_circles(circles: list[tuple[float, Position]], radius_threshold: float, center_threshold: float) \
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-> list[tuple[float, Position]]:
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def merge_similar_circles(circles: list[tuple[int, Position]], radius_threshold: float, center_threshold: float) \
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-> list[tuple[int, Position]]:
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"""
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Merge similar osculating circles
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@@ -127,7 +127,7 @@ def merge_similar_circles(circles: list[tuple[float, Position]], radius_threshol
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radius1, center1 = circles[i]
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radius2, center2 = circles[i + 1]
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if abs(radius1 - radius2) <= radius_threshold and center1.distance_to(center2) <= center_threshold:
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merged_radius = (radius1 + radius2) / 2
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merged_radius = (radius1 + radius2) // 2
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merged_center = Position((center1.x + center2.x) // 2, (center1.y + center2.y) // 2)
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merged_circles.append((merged_radius, merged_center))
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i += 2
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@@ -143,6 +143,81 @@ def merge_similar_circles(circles: list[tuple[float, Position]], radius_threshol
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return merge_similar_circles(merged_circles, radius_threshold, center_threshold)
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def circle_intersection(circle1: tuple[int, Position], circle2: tuple[int, Position]) -> list[Position]:
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distance = circle1[1].distance_to(circle2[1])
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if (distance > circle1[0] + circle2[0] or distance < abs(circle1[0] - circle2[0])
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or (distance == 0 and circle1[0] == circle2[0])):
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return []
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distance_line_circle = (circle1[0] ** 2 - circle2[0] ** 2 + distance ** 2) / (2 * distance)
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distance_line_intersec_point = sqrt(circle1[0] ** 2 - distance_line_circle ** 2)
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p = circle1[1] + (circle2[1] - circle1[1]) * distance_line_circle / distance
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return [Position(int(p.x + distance_line_intersec_point * (circle2[1].y - circle1[1].y) / distance),
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int(p.y - distance_line_intersec_point * (circle2[1].x - circle1[1].x) / distance)),
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Position(int(p.x - distance_line_intersec_point * (circle2[1].y - circle1[1].y) / distance),
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int(p.y + distance_line_intersec_point * (circle2[1].x - circle1[1].x) / distance))]
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def closest_to_curve(points: list[Position], curve_points: list[Position]) -> Position:
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closest_point = Position()
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distance = inf
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for point in points:
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for curve_point in curve_points:
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distance_point_curve = point.distance_to(curve_point)
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if distance_point_curve < distance:
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distance = distance_point_curve
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closest_point = point
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return closest_point
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def midpoint_circle_segment(circle: tuple[int, Position], start_point: Position, end_point: Position, curve_points: list[Position]) -> list[
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Position]:
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points = []
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start_angle = circle[1].angle_to(start_point)
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end_angle = circle[1].angle_to(end_point)
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if start_angle < 0:
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start_angle += 2 * pi
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if end_angle < 0:
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end_angle += 2 * pi
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if start_angle > end_angle:
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start_angle, end_angle = end_angle, start_angle
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middle_angle = (start_angle+end_angle)/2
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middle_point = circle[1] + Position(int(circle[0]*cos(middle_angle)), -int(circle[0]*sin(middle_angle)))
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is_outside_point = closest_to_curve([middle_point, circle[1]], curve_points) == middle_point
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x0, y0 = circle[1].x, circle[1].y
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x = circle[0]
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y = 0
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err = 0
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while x >= y:
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for (x1, y1) in [(x0 + x, y0 + y), (x0 + y, y0 + x), (x0 - y, y0 + x), (x0 - x, y0 + y),
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(x0 - x, y0 - y), (x0 - y, y0 - x), (x0 + y, y0 - x), (x0 + x, y0 - y)]:
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angle = atan2(y0 - y1, x1 - x0)
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if angle < 0:
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angle += 2*pi
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if is_outside_point:
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if start_angle <= angle <= end_angle:
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points.append(Position(int(x1), int(y1)))
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else:
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if angle <= start_angle or end_angle <= angle:
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points.append(Position(int(x1), int(y1)))
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if err <= 0:
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y += 1
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err += 2 * y + 1
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if err > 0:
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x -= 1
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err -= 2 * x + 1
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return points
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def calculate_control_points(station, next_station, curve_factor) -> tuple[Position, Position]:
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"""
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Calculate the control points for a Bézier curve between two stations
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@@ -164,8 +239,8 @@ def calculate_control_points(station, next_station, curve_factor) -> tuple[Posit
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return control_point_pos, control_point_next_pos
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def metro_line_osculating_circles(metro: Metro_Line, curve_factor: float = 0.5, num_points_factor: float = 1/20) -> (
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tuple)[list[tuple[float, Position]], list[list[Position]]]:
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def metro_line_osculating_circles(metro: Metro_Line, curve_factor: float = 0.5, num_points_factor: float = 1 / 20) -> (
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tuple)[list[tuple[int, Position]], list[Position]]:
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"""
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Calculate the osculating circles of a metro line
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@@ -191,17 +266,18 @@ def metro_line_osculating_circles(metro: Metro_Line, curve_factor: float = 0.5,
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int(distance * num_points_factor))
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osculating_circles = osculating_circle(points, derivatives, second_derivatives)
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merged_circles = merge_similar_circles(osculating_circles, 100, 100)
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print(f"[METRO LINE] {len(osculating_circles) - len(merged_circles)} out of {len(osculating_circles)} circles deleted !")
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merged_circles = merge_similar_circles(osculating_circles, 50, 50)
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print(
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f"[METRO LINE] {len(osculating_circles) - len(merged_circles)} out of {len(osculating_circles)} circles deleted !")
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circles.extend(merged_circles)
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points_list.append(points)
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points_list.extend(points)
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print(f"[METRO LINE] Osculating circles done")
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return circles, points_list
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# --- DRAW PART ---
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def draw_osculating_circle(circle: list[tuple[float, Position]], surface: Surface):
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def draw_osculating_circle(circle: list[tuple[int, Position]], surface: Surface):
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"""
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:param circle: The osculating circles to draw
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:param surface: The surface on which to draw the circles
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@@ -228,6 +304,15 @@ def draw_points(points: list[Position], surface):
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pygame.draw.circle(surface, (40, 255, 40), (point.x, point.y), 5)
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def draw_point(point: Position, surface):
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pygame.draw.circle(surface, (40, 255, 40), (point.x, point.y), 5)
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def draw_pixels(points: list[Position], surface):
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for point in points:
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surface.set_at((point.x, point.y), (0, 255, 255))
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def draw_metro_line(metro: Metro_Line, surface: Surface, show_points: bool = True):
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"""
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:param metro: The metro line to draw
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@@ -241,9 +326,37 @@ def draw_metro_line(metro: Metro_Line, surface: Surface, show_points: bool = Tru
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circles, points = metro_line_osculating_circles(metro)
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draw_osculating_circle(circles, surface)
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if show_points:
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for points in points:
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draw_points(points, surface)
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for i in range(1, len(circles) - 1):
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intersect_point_circle_before = closest_to_curve(circle_intersection(circles[i - 1], circles[i]), points)
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intersect_point_circle_after = closest_to_curve(circle_intersection(circles[i], circles[i + 1]), points)
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if intersect_point_circle_before == Position():
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continue
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intersect_point_circle_before = circles[i - 1][1]
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else:
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draw_point(intersect_point_circle_before, surface)
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if intersect_point_circle_after == Position():
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continue
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intersect_point_circle_after = circles[i + 1][1]
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else:
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draw_point(intersect_point_circle_after, surface)
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points_midpoint = midpoint_circle_segment(circles[i], intersect_point_circle_before,
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intersect_point_circle_after, points)
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draw_pixels(points_midpoint, surface)
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if len(points) != 0:
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intersect_point_circle_before = points[0]
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intersect_point_circle_after = closest_to_curve(circle_intersection(circles[0], circles[1]), points)
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points_midpoint = midpoint_circle_segment(circles[0], intersect_point_circle_before,
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intersect_point_circle_after, points)
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draw_pixels(points_midpoint, surface)
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intersect_point_circle_before = points[-1]
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intersect_point_circle_after = closest_to_curve(circle_intersection(circles[-1], circles[-2]), points)
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points_midpoint = midpoint_circle_segment(circles[-1], intersect_point_circle_before,
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intersect_point_circle_after, points)
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draw_pixels(points_midpoint, surface)
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def interface():
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