我知道如何检测与圆形和矩形的碰撞，但是我不确定如何找到两者之间的最小平移向量。我知道如何使用SAT碰撞检测算法来做到这一点，但是对于我现在的简单实现而言，这太复杂了。
我真的不知道该怎么做，除非适当地更改x坐标。
这里是代码。当您按下向下按钮时，我想要的是当不断按下向下按钮时，圆自动“推”到左侧（因为它已经定位在中心了一点点），即它向下移动但滑动向左转。
import pygame
if __name__ == "__main__":
pygame.init()
display = pygame.display.set_mode((500, 500))
display.fill((255, 255, 255))
circle_x = 240
circle_y = 50
pygame.draw.circle(display, (0, 0, 255), (circle_x, circle_y), 50)
pygame.draw.rect(display, (0, 255, 255), (240, 250, 20, 250))
pygame.display.update()
vel = 1
is_down_held = False
clock = pygame.time.Clock()
while True:
pressed_keys = pygame.key.get_pressed()
if pressed_keys[pygame.K_DOWN]:
circle_y += vel
display.fill((255, 255, 255))
pygame.draw.circle(display, (0, 0, 255), (circle_x, circle_y), 50)
pygame.draw.rect(display, (0, 255, 255), (240, 250, 20, 250))
pygame.display.update()
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
quit()
dt = clock.tick(60)
dt /= 1000
我尝试用某个常数移动x坐标，但是，它看起来不切实际，有时实际上正在穿过矩形（因为它实际上未检测到矩形）。
好吧，看来我还是必须在最后实现SAT碰撞检测。要计算矩形和圆形之间的最小平移矢量，您需要经过形状的必要轴（有关其说明，请参见https://jcharry.com/blog/physengine10和https://www.sevenson.com.au/actionscript/sat/），然后在发生碰撞时采用最小的重叠轴。下面是使用pygame GUI库的代码：
import math
import pygame
class Vector:
def __init__(self, x, y):
self.x = x
self.y = y
self.magnitude = math.sqrt(x ** 2 + y ** 2)
if self.magnitude != 0:
self.direction_x = -x / self.magnitude
self.direction_y = -y / self.magnitude
else:
self.direction_x = 0
self.direction_y = 0
def normalize(self):
if self.magnitude != 0:
self.x /= self.magnitude
self.y /= self.magnitude
self.magnitude = 1
def project_vector(vector1, vector2):
return get_dot_product(vector1, get_unit_vector(vector2))
def get_dot_product(vector1, vector2):
return (vector1.x * vector2.x) + (vector1.y * vector2.y)
def get_normal(vector):
return Vector(vector.y, -vector.x)
def get_vector(point):
return Vector(point[0], point[1])
def scale_vector(vector, magnitude):
return Vector(vector.x*magnitude, vector.y*magnitude)
def get_unit_vector(vector):
if vector.magnitude != 0:
return scale_vector(vector, 1 / vector.magnitude)
else:
return scale_vector(vector, 0)
def get_closest_point(circle_centre, rectangle_points):
closest_distance = float('inf')
closest_point = None
for point in rectangle_points:
distance = (circle_centre[0] - point[0])**2 + (circle_centre[1] - point[1])**2
if distance <= closest_distance:
closest_distance = distance
closest_point = point
return closest_point
def is_collision(circle_centre, rectangle_points):
closest_point = get_closest_point(circle_centre, rectangle_points)
rectangle_edge_vectors = []
for point in rectangle_points:
rectangle_edge_vectors += [get_vector(point)]
rectangle_edge_normals = []
for i in range(len(rectangle_points) - 1):
rectangle_edge_normals += [get_normal(get_vector((rectangle_points[i + 1][0] - rectangle_points[i][0], rectangle_points[i + 1][1] - rectangle_points[i][1])))]
rectangle_edge_normals += [get_normal(get_vector((rectangle_points[0][0] - rectangle_points[len(rectangle_points) - 1][0], rectangle_points[0][1] - rectangle_points[len(rectangle_points) - 1][1])))]
rectangle_edge_normals += [get_vector((circle_centre[0] - closest_point[0], circle_centre[1] - closest_point[1]))]
axes = rectangle_edge_normals
vectors = rectangle_edge_vectors
for axis in axes:
current_rect_max_x = float('-inf')
current_rect_min_x = float('inf')
for vector in vectors:
current_rect_projection = project_vector(vector, axis)
if current_rect_projection >= current_rect_max_x:
current_rect_max_x = current_rect_projection
if current_rect_projection <= current_rect_min_x:
current_rect_min_x = current_rect_projection
current_circle_projection = project_vector(get_vector(circle_centre), axis)
current_circle_max_x = current_circle_projection + 25
current_circle_min_x = current_circle_projection - 25
if current_rect_min_x > current_circle_max_x or current_circle_min_x > current_rect_max_x:
return False
return True
def get_minimum_translation_vector(circle_centre, rectangle_points):
closest_point = get_closest_point(circle_centre, rectangle_points)
rectangle_edge_vectors = []
for point in rectangle_points:
rectangle_edge_vectors += [get_vector(point)]
rectangle_edge_normals = []
for i in range(len(rectangle_points) - 1):
rectangle_edge_normals += [get_normal(get_vector((rectangle_points[i + 1][0] - rectangle_points[i][0], rectangle_points[i + 1][1] - rectangle_points[i][1])))]
rectangle_edge_normals += [get_normal(get_vector((rectangle_points[0][0] - rectangle_points[len(rectangle_points) - 1][0], rectangle_points[0][1] - rectangle_points[len(rectangle_points) - 1][1])))]
rectangle_edge_normals += [get_vector((circle_centre[0] - closest_point[0], circle_centre[1] - closest_point[1]))]
axes = rectangle_edge_normals
for axis in axes:
axis.normalize()
vectors = rectangle_edge_vectors
minimum_translation_vector = Vector(axes[0].x, axes[0].y)
minimum_translation_vector.magnitude = float('inf')
current_minimum_translation_vector = Vector(axes[0].x, axes[0].y)
current_minimum_translation_vector.magnitude = float('inf')
for axis in axes:
current_rect_max_x = float('-inf')
current_rect_min_x = float('inf')
for vector in vectors:
current_rect_projection = project_vector(vector, axis)
if current_rect_projection >= current_rect_max_x:
current_rect_max_x = current_rect_projection
if current_rect_projection <= current_rect_min_x:
current_rect_min_x = current_rect_projection
current_circle_projection = project_vector(get_vector(circle_centre), axis)
current_circle_max_x = current_circle_projection + 25
current_circle_min_x = current_circle_projection - 25
current_minimum_translation_vector = axis
current_minimum_translation_vector.magnitude = abs(current_circle_min_x - current_rect_max_x)
if current_minimum_translation_vector.magnitude <= minimum_translation_vector.magnitude:
minimum_translation_vector = axis
minimum_translation_vector.magnitude = current_minimum_translation_vector.magnitude
return minimum_translation_vector
if __name__ == "__main__":
pygame.init()
display = pygame.display.set_mode((500, 500))
rectangle_points_main = [(250, 250), (300, 250), (300, 300), (250, 300)]
circle_centre_main = (0, 0)
clock = pygame.time.Clock()
while True:
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
quit()
circle_centre_main = (pygame.mouse.get_pos()[0], pygame.mouse.get_pos()[1])
display.fill((255, 255, 255))
if is_collision(circle_centre_main, rectangle_points_main):
pygame.draw.circle(display, (255, 0, 0), circle_centre_main, 25)
minimum_translation_vector_main = get_minimum_translation_vector(circle_centre_main, rectangle_points_main)
dx = minimum_translation_vector_main.magnitude * minimum_translation_vector_main.direction_x
dy = minimum_translation_vector_main.magnitude * minimum_translation_vector_main.direction_y
rectangle_points_main = [(rectangle_points_main[0][0] + dx, rectangle_points_main[0][1] + dy),
(rectangle_points_main[1][0] + dx, rectangle_points_main[1][1] + dy),
(rectangle_points_main[2][0] + dx, rectangle_points_main[2][1] + dy),
(rectangle_points_main[3][0] + dx, rectangle_points_main[3][1] + dy)]
else:
pygame.draw.circle(display, (0, 0, 255), circle_centre_main, 25)
pygame.draw.rect(display, (0, 255, 0), (rectangle_points_main[0][0], rectangle_points_main[0][1], 50, 50))
dt = clock.tick(60)
dt /= 1000
pygame.display.update()