仿射变换编程实现C语言

这里提供一个简单的仿射变换的C语言代码实现：

#include <stdio.h>

// 定义二维向量结构体
typedef struct {
    float x;
    float y;
} Vector2;

// 定义矩阵结构体
typedef struct {
    float m11, m12, m13;
    float m21, m22, m23;
    float m31, m32, m33;
} Matrix3x3;

// 创建单位矩阵
Matrix3x3 createIdentityMatrix() {
    Matrix3x3 matrix = {
        1, 0, 0,
        0, 1, 0,
        0, 0, 1
    };
    return matrix;
}

// 创建平移矩阵
Matrix3x3 createTranslationMatrix(float tx, float ty) {
    Matrix3x3 matrix = createIdentityMatrix();
    matrix.m13 = tx;
    matrix.m23 = ty;
    return matrix;
}

// 创建缩放矩阵
Matrix3x3 createScaleMatrix(float sx, float sy) {
    Matrix3x3 matrix = createIdentityMatrix();
    matrix.m11 = sx;
    matrix.m22 = sy;
    return matrix;
}

// 创建旋转矩阵
Matrix3x3 createRotationMatrix(float angle) {
    Matrix3x3 matrix = createIdentityMatrix();
    float cosAngle = cos(angle);
    float sinAngle = sin(angle);
    matrix.m11 = cosAngle;
    matrix.m12 = -sinAngle;
    matrix.m21 = sinAngle;
    matrix.m22 = cosAngle;
    return matrix;
}

// 矩阵乘法
Matrix3x3 matrixMultiply(Matrix3x3 a, Matrix3x3 b) {
    Matrix3x3 result;
    result.m11 = a.m11 * b.m11 + a.m12 * b.m21 + a.m13 * b.m31;
    result.m12 = a.m11 * b.m12 + a.m12 * b.m22 + a.m13 * b.m32;
    result.m13 = a.m11 * b.m13 + a.m12 * b.m23 + a.m13 * b.m33;

    result.m21 = a.m21 * b.m11 + a.m22 * b.m21 + a.m23 * b.m31;
    result.m22 = a.m21 * b.m12 + a.m22 * b.m22 + a.m23 * b.m32;
    result.m23 = a.m21 * b.m13 + a.m22 * b.m23 + a.m23 * b.m33;

    result.m31 = a.m31 * b.m11 + a.m32 * b.m21 + a.m33 * b.m31;
    result.m32 = a.m31 * b.m12 + a.m32 * b.m22 + a.m33 * b.m32;
    result.m33 = a.m31 * b.m13 + a.m32 * b.m23 + a.m33 * b.m33;

    return result;
}

// 仿射变换
Vector2 transform(Vector2 point, Matrix3x3 matrix) {
    Vector2 result = {
        point.x * matrix.m11 + point.y * matrix.m12 + matrix.m13,
        point.x * matrix.m21 + point.y * matrix.m22 + matrix.m23
    };
    return result;
}

int main() {
    // 创建一个坐标点
    Vector2 point = {2.0f, 3.0f};
    
    // 创建平移矩阵
    Matrix3x3 translationMatrix = createTranslationMatrix(5.0f, 5.0f);
    
    // 创建缩放矩阵
    Matrix3x3 scaleMatrix = createScaleMatrix(2.0f, 2.0f);
    
    // 创建旋转矩阵
    Matrix3x3 rotationMatrix = createRotationMatrix(M_PI / 4.0f);
    
    // 仿射变换
    Matrix3x3 compositeMatrix = matrixMultiply(scaleMatrix, rotationMatrix);
    compositeMatrix = matrixMultiply(compositeMatrix, translationMatrix);
    Vector2 transformedPoint = transform(point, compositeMatrix);
    
    // 输出变换后的坐标点
    printf("Transformed point: (%.2f, %.2f)\n", transformedPoint.x, transformedPoint.y);
    
    return 0;
}

这个示例代码中，定义了一个二维向量结构体`Vector2`，一个三阶矩阵结构体`Matrix3x3`，以及一些常用的矩阵操作函数，如创建单位矩阵、平移矩阵、缩放矩阵、旋转矩阵等。然后，通过矩阵乘法和仿射变换函数，实现了对一个坐标点的平移、缩放、旋转操作。最后输出变换后的坐标点。