根据数学公式实现代码编写

来个人帮忙！
根据下面题目描述实现一个计算函数。（编程语言是python或java）
根据题目描述，已知四边形abcd的坐标和经过平移+旋转后的c’和d’的坐标，要推算出a’和b’的坐标，可以按照以下步骤进行计算：

计算平移向量：平移向量是c到c'的位移，即(c'.x - c.x, c'.y - c.y)。然后将这个平移向量分别应用到a和b的坐标上，得到a’和b’的临时坐标。

计算旋转角度：使用向量法计算，先将向量c'd'和向量cd单位化，然后计算它们之间的夹角。假设这个夹角为θ。

利用旋转矩阵：通过旋转角度θ可以构造一个逆时针旋转矩阵R，形式为：
R = [[cos(θ), -sin(θ)],
[sin(θ), cos(θ)]]

将旋转矩阵应用到临时坐标点(a’, b’)上，得到最终的坐标点。

综上所述，最终的计算公式如下：
a'.x = (c'.x - c.x) * cos(θ) - (c'.y - c.y) * sin(θ) + c.x
a'.y = (c'.x - c.x) * sin(θ) + (c'.y - c.y) * cos(θ) + c.y

b'.x = (d'.x - d.x) * cos(θ) - (d'.y - d.y) * sin(θ) + d.x
b'.y = (d'.x - d.x) * sin(θ) + (d'.y - d.y) * cos(θ) + d.y

其中，θ是旋转角度。计算旋转角度可以使用向量之间的夹角公式：
θ = arccos((cd·c'd') / (||cd|| x ||c'd'||))

注意，在使用以上公式时，要确保旋转角度在弧度制下，并确保坐标点的顺序正确。应根据具体问题和数学要求进行适当调整。

python实现代码：

import math

def calculate_coordinates(a, b, c, c_prime, d, d_prime):
    # 计算平移向量
    translation_vector = (c_prime[0] - c[0], c_prime[1] - c[1])

    # 计算旋转角度
    cd = (d[0] - c[0], d[1] - c[1])
    cd_prime = (d_prime[0] - c_prime[0], d_prime[1] - c_prime[1])
    norm_cd = math.sqrt(cd[0] ** 2 + cd[1] ** 2)
    norm_cd_prime = math.sqrt(cd_prime[0] ** 2 + cd_prime[1] ** 2)
    dot_product = cd[0] * cd_prime[0] + cd[1] * cd_prime[1]
    theta = math.acos(dot_product / (norm_cd * norm_cd_prime))

    # 应用旋转矩阵到临时坐标点a'和b'
    a_prime_x = (c_prime[0] - c[0]) * math.cos(theta) - (c_prime[1] - c[1]) * math.sin(theta) + c[0]
    a_prime_y = (c_prime[0] - c[0]) * math.sin(theta) + (c_prime[1] - c[1]) * math.cos(theta) + c[1]
    b_prime_x = (d_prime[0] - d[0]) * math.cos(theta) - (d_prime[1] - d[1]) * math.sin(theta) + d[0]
    b_prime_y = (d_prime[0] - d[0]) * math.sin(theta) + (d_prime[1] - d[1]) * math.cos(theta) + d[1]

    return (a_prime_x, a_prime_y), (b_prime_x, b_prime_y)

# 示例数据
a = (1, 2)
b = (3, 4)
c = (5, 6)
c_prime = (7, 8)
d = (9, 10)
d_prime = (11, 12)

a_prime, b_prime = calculate_coordinates(a, b, c, c_prime, d, d_prime)
print("a' coordinates:", a_prime)
print("b' coordinates:", b_prime)

如果以上回答对您有所帮助，点击一下采纳该答案～谢谢

import java.awt.geom.Point2D;

public class QuadrilateralCoordinate {
    public static void main(String[] args) {
        // 已知的坐标
        Point2D.Double a = new Point2D.Double(1, 1);
        Point2D.Double b = new Point2D.Double(2, 2);
        Point2D.Double c = new Point2D.Double(3, 3);
        Point2D.Double d = new Point2D.Double(4, 4);

        // 经过平移+旋转后的坐标
        Point2D.Double cPrime = new Point2D.Double(5, 5);
        Point2D.Double dPrime = new Point2D.Double(6, 6);

        // 计算平移向量
        double translateX = cPrime.getX() - c.getX();
        double translateY = cPrime.getY() - c.getY();

        // 应用平移向量到临时坐标点得到a'和b'的临时坐标
        Point2D.Double aTemp = new Point2D.Double(a.getX() + translateX, a.getY() + translateY);
        Point2D.Double bTemp = new Point2D.Double(b.getX() + translateX, b.getY() + translateY);

        // 计算旋转角度
        Point2D.Double cd = new Point2D.Double(d.getX() - c.getX(), d.getY() - c.getY());
        Point2D.Double cdPrime = new Point2D.Double(dPrime.getX() - cPrime.getX(), dPrime.getY() - cPrime.getY());

        // 检查除数是否为0
        if (cd.distance(0, 0) == 0 || cdPrime.distance(0, 0) == 0) {
            System.out.println("Cannot compute rotation angle. Divide by zero error.");
            return;
        }

        double dotProduct = cd.getX() * cdPrime.getX() + cd.getY() * cdPrime.getY();
        double magnitudeProduct = cd.distance(0, 0) * cdPrime.distance(0, 0);
        double theta = Math.acos(dotProduct / magnitudeProduct);

        // 应用旋转矩阵到临时坐标点得到最终的坐标点
        double cosTheta = Math.cos(theta);
        double sinTheta = Math.sin(theta);

        // 应用旋转矩阵前，先将aTemp和bTemp移到原点
        aTemp.setLocation(aTemp.getX() - c.getX(), aTemp.getY() - c.getY());
        bTemp.setLocation(bTemp.getX() - d.getX(), bTemp.getY() - d.getY());

        // 应用旋转矩阵，再将aPrime和bPrime平移回原位置
        Point2D.Double aPrime = new Point2D.Double(
                aTemp.getX() * cosTheta - aTemp.getY() * sinTheta + c.getX(),
                aTemp.getX() * sinTheta + aTemp.getY() * cosTheta + c.getY()
        );
        Point2D.Double bPrime = new Point2D.Double(
                bTemp.getX() * cosTheta - bTemp.getY() * sinTheta + d.getX(),
                bTemp.getX() * sinTheta + bTemp.getY() * cosTheta + d.getY()
        );

        // 输出最终的坐标点
        System.out.println("a' coordinates: (" + aPrime.getX() + ", " + aPrime.getY() + ")");
        System.out.println("b' coordinates: (" + bPrime.getX() + ", " + bPrime.getY() + ")");
    }
}

import math


def calculate(a, b, c, d, c_prime, d_prime):

    delta_x = c_prime[0] - c[0]
    delta_y = c_prime[1] - c[1]


    a_temp = (a[0] + delta_x, a[1] + delta_y)
    b_temp = (b[0] + delta_x, b[1] + delta_y)


    cd = (d[0] - c[0], d[1] - c[1])
    cd_prime = (d_prime[0] - c_prime[0], d_prime[1] - c_prime[1])
    cd_norm = math.sqrt(cd[0]**2 + cd[1]**2)
    cd_prime_norm = math.sqrt(cd_prime[0]**2 + cd_prime[1]**2)
    theta = math.acos((cd[0]*cd_prime[0] + cd[1]*cd_prime[1]) / (cd_norm * cd_prime_norm))


    R = [[math.cos(theta), -math.sin(theta)], [math.sin(theta), math.cos(theta)]]


    a_prime = (R[0][0]*(a_temp[0]-c[0]) + R[0][1]*(a_temp[1]-c[1]) + c[0], R[1][0]*(a_temp[0]-c[0]) + R[1][1]*(a_temp[1]-c[1]) + c[1])
    b_prime = (R[0][0]*(b_temp[0]-d[0]) + R[0][1]*(b_temp[1]-d[1]) + d[0], R[1][0]*(b_temp[0]-d[0]) + R[1][1]*(b_temp[1]-d[1]) + d[1])


    return a_prime, b_prime

#输入你正常的坐标即可
a = (1.4544155877, 2.1558772843)
b = (3.4544155877, 4.1558772843)
c = (5.4544155877, 6.1558772843)
d = (7.4544155877, 8.1558772843)

#输入你正常的坐标即可
c_prime = (6.4544155877, 7.450304571)
d_prime = (9.4544155877, 11.450304571)


print(calculate(a, b, c, d, c_prime, d_prime))

这只是个简单的表达式转代码的问题吧

定义一个坐标点类
class Point: def init(self, x, y): self.x = x self.y = y

def __sub__(self, other):
    # 重载减法运算符，返回两个点之间的向量
    return Point(self.x - other.x, self.y - other.y)

def __add__(self, other):
    # 重载加法运算符，返回两个点的和
    return Point(self.x + other.x, self.y + other.y)

def __mul__(self, other):
    # 重载乘法运算符，返回两个向量的点积
    return self.x * other.x + self.y * other.y

def __str__(self):
    # 重载字符串表示方法，返回坐标点的字符串形式
    return f"({self.x}, {self.y})"

def length(self):
    # 返回向量的长度
    return (self.x ** 2 + self.y ** 2) ** 0.5

def rotate(self, theta):
    # 返回向量逆时针旋转theta角度后的新向量
    return Point(self.x * math.cos(theta) - self.y * math.sin(theta),
                 self.x * math.sin(theta) + self.y * math.cos(theta))

导入数学模块
import math

定义一个计算函数，输入四边形abcd的坐标和c’和d’的坐标，输出a’和b’的坐标
def calculate(a, b, c, d, c_prime, d_prime): # 计算平移向量 translation = c_prime - c

# 计算旋转角度
cd = d - c
c_d_prime = d_prime - c_prime
theta = math.acos((cd * c_d_prime) / (cd.length() * c_d_prime.length()))

# 计算a'和b'的临时坐标
a_temp = a + translation
b_temp = b + translation

# 计算a'和b'的最终坐标
a_prime = a_temp.rotate(theta) + c - c.rotate(theta)
b_prime = b_temp.rotate(theta) + d - d.rotate(theta)

# 返回a'和b'的坐标
return a_prime, b_prime


测试计算函数，假设abcd为正方形，c’和d’为旋转90度后的坐标
a = Point(0, 0) b = Point(0, 1) c = Point(1, 1) d = Point(1, 0) c_prime = Point(0.5, 1.5) d_prime = Point(-0.5, 1.5)

调用计算函数，打印结果
a_prime, b_prime = calculate(a, b, c, d, c_prime, d_prime) print(f"a’ = {a_prime}“) print(f"b’ = {b_prime}”)

python
将实际的坐标值填入下面代码中，它将计算并打印出a'和b'的新坐标。请确保在使用时提供正确的坐标值，并根据需要进行必要的数值调整。

import math

def calculate_rotation_angle(v1, v2):
    dot_product = v1[0] * v2[0] + v1[1] * v2[1]
    norm_v1 = math.sqrt(v1[0] ** 2 + v1[1] ** 2)
    norm_v2 = math.sqrt(v2[0] ** 2 + v2[1] ** 2)
    cos_theta = dot_product / (norm_v1 * norm_v2)
    return math.acos(cos_theta)

def calculate_new_coordinates(a, b, c, d, c_prime, d_prime):
    translation_vector_c = (c_prime[0] - c[0], c_prime[1] - c[1])
    translation_vector_d = (d_prime[0] - d[0], d_prime[1] - d[1])

    v_cd = ((d[0] - c[0]), (d[1] - c[1]))
    v_c_prime_d_prime = ((d_prime[0] - c_prime[0]), (d_prime[1] - c_prime[1]))

    rotation_angle = calculate_rotation_angle(v_cd, v_c_prime_d_prime)

    cos_theta = math.cos(rotation_angle)
    sin_theta = math.sin(rotation_angle)

    a_prime = (
        (c_prime[0] - c[0]) * cos_theta - (c_prime[1] - c[1]) * sin_theta + c[0],
        (c_prime[0] - c[0]) * sin_theta + (c_prime[1] - c[1]) * cos_theta + c[1]
    )

    b_prime = (
        (d_prime[0] - d[0]) * cos_theta - (d_prime[1] - d[1]) * sin_theta + d[0],
        (d_prime[0] - d[0]) * sin_theta + (d_prime[1] - d[1]) * cos_theta + d[1]
    )

    return a_prime, b_prime

# Example coordinates
a = (x1, y1)
b = (x2, y2)
c = (x3, y3)
d = (x4, y4)
c_prime = (x5, y5)
d_prime = (x6, y6)

a_prime, b_prime = calculate_new_coordinates(a, b, c, d, c_prime, d_prime)
print("a' coordinates:", a_prime)
print("b' coordinates:", b_prime)

java
在这个示例中，我使用了Point2D.Double类来表示坐标点，calculatePoint方法接受c、cPrime、d和dPrime坐标点作为参数，并计算出对应的a'坐标点。你可以将这个示例程序根据实际需求进行扩展和修改。

import java.awt.geom.Point2D;

public class QuadrilateralCalculation {

    public static Point2D.Double calculatePoint(Point2D.Double c, Point2D.Double cPrime,
                                                Point2D.Double d, Point2D.Double dPrime) {
        // Calculate translation vector
        double tx = cPrime.getX() - c.getX();
        double ty = cPrime.getY() - c.getY();

        // Calculate normalized vectors
        Point2D.Double cd = new Point2D.Double(d.getX() - c.getX(), d.getY() - c.getY());
        Point2D.Double cdPrime = new Point2D.Double(dPrime.getX() - cPrime.getX(),
                                                    dPrime.getY() - cPrime.getY());
        double normCd = Math.sqrt(cd.getX() * cd.getX() + cd.getY() * cd.getY());
        double normCdPrime = Math.sqrt(cdPrime.getX() * cdPrime.getX() +
                                       cdPrime.getY() * cdPrime.getY());

        // Calculate rotation angle
        double dotProduct = cd.getX() * cdPrime.getX() + cd.getY() * cdPrime.getY();
        double theta = Math.acos(dotProduct / (normCd * normCdPrime));

        // Apply rotation matrix
        double cosTheta = Math.cos(theta);
        double sinTheta = Math.sin(theta);
        double aPrimeX = (cPrime.getX() - c.getX()) * cosTheta -
                         (cPrime.getY() - c.getY()) * sinTheta + c.getX();
        double aPrimeY = (cPrime.getX() - c.getX()) * sinTheta +
                         (cPrime.getY() - c.getY()) * cosTheta + c.getY();

        return new Point2D.Double(aPrimeX, aPrimeY);
    }

    public static void main(String[] args) {
        Point2D.Double c = new Point2D.Double(1.0, 1.0);
        Point2D.Double cPrime = new Point2D.Double(3.0, 1.0);
        Point2D.Double d = new Point2D.Double(1.0, 3.0);
        Point2D.Double dPrime = new Point2D.Double(2.0, 4.0);

        Point2D.Double aPrime = calculatePoint(c, cPrime, d, dPrime);
        System.out.println("a' coordinates: (" + aPrime.getX() + ", " + aPrime.getY() + ")");
    }
}