矩形/矩形碰撞检测

Question

我正在尝试解决两个矩形相互交叉/重叠的问题。发生这种情况时，我想知道交集是真还是假。我找到了一个解决方案，但是它是用 C 或 C++ 编写的。我想用 Python 编写这些代码。

这里是来源：http://www.jeffreythompson.org/collision-detection/rect-rect.php

Answer 1

这是我写过的第一行 Python 代码（不过我知道 C++）

def rectRect(r1x, r1y, r1w, r1h, r2x, r2y, r2w, r2h):

    # are the sides of one rectangle touching the other?

    return r1x + r1w >= r2x and \   # r1 right edge past r2 left
        r1x <= r2x + r2w and \  # r1 left edge past r2 right
        r1y + r1h >= r2y and \   # r1 top edge past r2 bottom
        r1y <= r2y + r2h    # r1 bottom edge past r2 top

恕我直言 rectRect 是一个非常糟糕的函数名称，但是我将它从链接代码中保留下来。

Answer 2

以下是一个简单的类，可以执行矩形-矩形相交以及点到矩形相交。与早期解决方案的区别在于，跟随 sn-p 甚至可以检测到旋转的矩形。

import numpy as np
import matplotlib.pyplot as plt


class Rectangle:
    def __init__(self, center: np.ndarray, dims: np.ndarray, angle: float):
        self.corners = self.get_rect_points(center, dims, angle)
        self.area = dims[0] * dims[1]

    @staticmethod
    def get_rect_points(center: np.ndarray, dims: np.ndarray, angle: float):
        """
        returns four corners of the rectangle.
        bottom left is the first conrner, from there it goes
        counter clockwise.
        """
        center = np.asarray(center)
        length, breadth = dims
        angle = np.deg2rad(angle)
        corners = np.array([[-length/2, -breadth/2],
                            [length/2, -breadth/2],
                            [length/2, breadth/2],
                            [-length/2, breadth/2]])
        rot = np.array([[np.cos(angle), np.sin(angle)], [-np.sin(angle), np.cos(angle)]])
        corners = rot.dot(corners.T) + center[:, None]
        return corners.T

    def is_point_in_collision(self, p: np.ndarray):
        """
        check if a point is in collision with the rectangle.
        """
        def area_triangle(a, b, c):
            return abs((b[0] * a[1] - a[0] * b[1]) + (c[0] * b[1] - b[0] * c[1]) + (a[0] * c[1] - c[0] * a[1])) / 2

        area = 0
        area += area_triangle(self.corners[0], p, self.corners[3])
        area += area_triangle(self.corners[3], p, self.corners[2])
        area += area_triangle(self.corners[2], p, self.corners[1])
        area += area_triangle(self.corners[1], p, self.corners[0])
        return area > self.area

    def is_intersect(self, rect_2: Rectangle):
        """
        check if any of the four corners of the
        rectangle is in collision
        """
        if not np.all([self.is_point_in_collision(c) for c in rect_2.corners]):
            return True
        return False


def plot_rect(p1, p2, p3, p4, color='r'):
    ax.plot([p1[0], p2[0]], [p1[1], p2[1]], color)
    ax.plot([p2[0], p3[0]], [p2[1], p3[1]], color)
    ax.plot([p3[0], p4[0]], [p3[1], p4[1]], color)
    ax.plot([p4[0], p1[0]], [p4[1], p1[1]], color)
    mid_point = 0.5 * (p1 + p3)
    plt.scatter(mid_point[0], mid_point[1], marker='*')
    plt.xlim([-1, 1])
    plt.ylim([-1, 1])

以下是两个示例：

样本 1：

ax = plt.subplot(111)
st = Rectangle((0.067, 0.476),(0.61, 0.41), 90)
gripper = Rectangle((-0.367, 0.476),(0.21,0.16), 45)
plot_rect(*st.corners)
plot_rect(*gripper.corners)
plt.show()
print(f"gripper and rectangle intersect: {st.is_intersect(gripper)}")

示例 2：

ax = plt.subplot(111)
st = Rectangle((0.067, 0.476),(0.61, 0.41), 90)
gripper = Rectangle((-0.167, 0.476),(0.21,0.16), 45)
plot_rect(*st.corners)
plot_rect(*gripper.corners)
plt.show()
print(f"gripper and rectangle intersect: {st.is_intersect(gripper)}")