我正在学习线性代数，并试图用基本的线性变换（旋转、缩放、平移）制作一个小程序。

这是完整的工作示例：

https://codesandbox.io/embed/determined-diffie-t2iy5?fontsize=14&hidenavigation=1&theme=dark

我编写了用于为每个变换生成每个矩阵的函数和计算它们的函数（将矩阵与一个点相乘，将矩阵相乘）。

export const multiplyMatrixWithPoint = (matrix, point) => {
  return point.map((dimension, index) => {
    let result = 0;

    for (let i = 0; i < 4; i++) {
      const matrixIndex = index * 4 + i;
      result += dimension * matrix[matrixIndex];
    }

    return +result.toFixed(2);
  })
};

// Just creating 2D array to make it easy to calculate the matrix
export const matrixToPoints = matrix => {
  const result = [];

  for (let i = 0; i < 4; i++) {
    const onePoint = [];

    for (let j = 0; j < 4; j++) {
      onePoint.push(matrix[4 * i + j]);
    }
    
    result.push(onePoint);
  }

  return result;
};

// Just making 2D array to 1D
export const pointsToMatrix = points => points.reduce((acc, points) => [...acc, ...points], []);

// Transpose function to make the matrix multiplication correct
export const transposeCSSMatrixToTransform = matrix => matrix[0].map((column, index) => matrix.map(row => row[index]));

export const multiplyMatrices = (matrixA, matrixB) => {
  const separatePoints = transposeCSSMatrixToTransform(matrixToPoints(matrixB));

  return pointsToMatrix(transposeCSSMatrixToTransform(separatePoints.map(point => multiplyMatrixWithPoint(matrixA, point))));
};

export const rotationMatrixGenerator = (matrix, angle) => {
  const radians = degreeToRadian(angle);

  matrix[0] = Math.cos(radians);
  matrix[1] = -Math.sin(radians);
  matrix[4] = Math.sin(radians);
  matrix[5] = Math.cos(radians);

  return matrix; 
};

export const scaleMatrixGenerator = (matrix, { x, y }) => {
  matrix[0] = x;
  matrix[5] = y;

  return matrix;
};

export const translateMatrixGenerator = (matrix, { x, y }) => {
  matrix[12] = x;
  matrix[13] = y;

  return matrix;
};

为了显示转换，我使用了 CSS 的matrix3d

export const matrixToCSSMatrix = matrix => `matrix3d(${matrix.join(',')})`;

这是代码的执行部分

  ...
  const [matrix, setMatrix] = useState(DEFAULT_MATRIX);
  const [rotationAngle, setRotationAngle] = useState(0);
  const [scale, setScale] = useState(DEFAULT_XY);
  const [translate, setTranslate] = useState(DEFAULT_XY);

  const classes = useStyles();
  const { app } = classes;

  // ---------------------- Rotate --------------------- //
  const rotate = useCallback(e => {
    const { value: angle } = e.target;

    const rotationMatrix = rotationMatrixGenerator(matrix, +angle);
    const updatedMatrix = multiplyMatrices(matrix, rotationMatrix);

    setMatrix(updatedMatrix);
    setRotationAngle(angle);
  }, [matrix]);

  // ---------------------- Scale --------------------- //
  const changeScale = useCallback((e, dimension) => {
    const { value } = e.target;
    const updatedScale = {
      ...scale,
      [dimension]: +value
    };

    const scaleMatrix = scaleMatrixGenerator(matrix, updatedScale);
    const updatedMatrix = multiplyMatrices(matrix, scaleMatrix);

    setMatrix(scaleMatrix);
    setScale(updatedScale);
  }, [matrix, scale]);

  // ------------------ Translate --------------------- //
  const changeTranslation = useCallback((e, position) => {
    const { value } = e.target;
    const updatedTranslation = {
      ...translate,
      [position]: +value
    };

    const translateMatrix = translateMatrixGenerator(matrix, updatedTranslation);
    const updatedMatrix = multiplyMatrices(matrix, translateMatrix);

    setMatrix(translateMatrix);
    setTranslate(updatedTranslation);
  }, [matrix, translate]);
  ...

首先我认为这是因为我没有转置矩阵，我尝试转置它，它有一点帮助但没有修复所有错误。此外，我尝试收集所有转换并立即应用它们，但这是一个非常糟糕的解决方案并且效果不佳。

我需要单独的旋转、缩放和过渡，但旋转和过渡效果不佳，因为它们使用相同的矩阵段。此外，我无法实现对 Z 轴的正常旋转。