如何在 Tkinter Canvas 上旋转多边形？

在使用 Python 和 Tkinter 创建一个版本的 Asteroids 游戏时，需要实现飞船在左右箭头键按下时旋转。飞船在 Tkinter 画布上是一个三角形。开发者在调整三角形坐标的公式上遇到了困难，他认为这与 sin 和 cos 函数有关，但不确定如何使用。目前，开发者有两个类，一个用于飞船，另一个用于游戏。在飞船类中，开发者有用于按键的回调方法。

2、解决方案

首先，需要围绕三角形的中心进行旋转。三角形的质心可能最适合这样做。我们可以使用公式 C = (1/3*(x0 + x1 + x2), 1/3*(y0 + y1 + y2)) 来求解质心，它是三角形中所有点的平均值。然后，需要以该点为中心应用旋转。所以我们可以做如下操作：

import math

class Ship:
    def centroid(self):
        return 1 / 3 * (self.x0 + self.x1 + self.x2), 1 / 3 * (self.y0 + self.y1 + self.y2)

    def __init__(self, canvas, x, y, width, height, turnspeed, acceleration=1):
        self._d = {'Up':1, 'Down':-1, 'Left':1, 'Right':-1}

        self.canvas = canvas
        self.width = width
        self.height = height
        self.speed = 0
        self.turnspeed = turnspeed
        self.acceleration = acceleration

        self.x0, self.y0 = x, y

        self.bearing = -math.pi / 2

        self.x1 = self.x0 + self.width / 2
        self.y1 = self.y0 - self.height

        self.x2 = self.x0 + self.width
        self.y2 = self.y0

        self.x, self.y = self.centroid()

        self.ship = self.canvas.create_polygon((self.x0, self.y0, self.x1, self.y1, self.x2, self.y2), outline="white", width=3)

    def changeCoords(self):
        self.canvas.coords(self.ship,self.x0, self.y0, self.x1, self.y1, self.x2, self.y2)

    def rotate(self, event=None):
        t = self._d[event.keysym] * self.turnspeed * math.pi / 180 # the trig functions generally take radians as their arguments rather than degrees; pi/180 radians is equal to 1 degree

        self.bearing -= t

        def _rot(x, y):
            #note: the rotation is done in the opposite fashion from for a right-handed coordinate system due to the left-handedness of computer coordinates
            x -= self.x
            y -= self.y
            _x = x * math.cos(t) + y * math.sin(t)
            _y = -x * math.sin(t) + y * math.cos(t)
            return _x + self.x, _y + self.y

        self.x0, self.y0 = _rot(self.x0, self.y0)
        self.x1, self.y1 = _rot(self.x1, self.y1)
        self.x2, self.y2 = _rot(self.x2, self.y2)
        self.x, self.y = self.centroid()

        self.changeCoords()

    def accel(self, event=None):
        mh = int(self.canvas['height'])
        mw = int(self.canvas['width'])
        self.speed += self.acceleration * self._d[event.keysym]

        self.x0 += self.speed * math.cos(self.bearing)
        self.x1 += self.speed * math.cos(self.bearing)
        self.x2 += self.speed * math.cos(self.bearing)

        self.y0 += self.speed * math.sin(self.bearing)
        self.y1 += self.speed * math.sin(self.bearing)
        self.y2 += self.speed * math.sin(self.bearing)

        self.x, self.y = self.centroid()

        if self.y < - self.height / 2:
            self.y0 += mh
            self.y1 += mh
            self.y2 += mh
        elif self.y > mh + self.height / 2:
            self.y0 += mh
            self.y1 += mh
            self.y2 += mh

        if self.x < -self.width / 2:
            self.x0 += mw
            self.x1 += mw
            self.x2 += mw
        elif self.x > mw + self.width / 2:
            self.x0 -= mw
            self.x1 -= mw
            self.x2 -= mw

        self.x, self.y = self.centroid()

        self.changeCoords()

在上面的代码中，我们使用质心作为旋转中心并围绕它应用旋转。我们还处理了飞船的移动并将其限制在画布范围内。

除了上述解决方案，还有另外一种方法可以将三角形旋转任意角度。我们可以使用三角形的顶点和旋转角度来计算出新顶点的位置。这种方法相对简单，但是性能不如第一种方法好。

def rotate_triangle(x0, y0, x1, y1, x2, y2, angle):
    # Calculate the center of the triangle
    cx = (x0 + x1 + x2) / 3
    cy = (y0 + y1 + y2) / 3

    # Translate the triangle so that its center is at the origin
    x0 -= cx
    x1 -= cx
    x2 -= cx
    y0 -= cy
    y1 -= cy
    y2 -= cy

    # Rotate the triangle by the given angle
    s = math.sin(angle)
    c = math.cos(angle)

    x0_new = x0 * c - y0 * s
    y0_new = x0 * s + y0 * c

    x1_new = x1 * c - y1 * s
    y1_new = x1 * s + y1 * c

    x2_new = x2 * c - y2 * s
    y2_new = x2 * s + y2 * c

    # Translate the triangle back to its original position
    x0_new += cx
    x1_new += cx
    x2_new += cx
    y0_new += cy
    y1_new += cy
    y2_new += cy

    return x0_new, y0_new, x1_new, y1_new, x2_new, y2_new