Linear transformation and matrix multiplication fails with JS

I’m learning linear algebra and trying to make a little program with basic linear transformations (rotating, scaling, translating).

Here is the fully working example:

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

I wrote functions for generating each matrix for each transformation and functions to calculate them (multiplying matrix with a point, multiplying matrices).

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;
};

For showing the transformations I used CSS’s matrix3d

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

And here are the executing part of the code

  ...
  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]);
  ...

Firstly I thought it’s because I didn’t transpose the matrix, I tried to transpose it, it helped a little but didn’t fix all bugs. Also, I tried to collect all transformations and apply them at once, but it was a very bad solution and didn’t work well.

I need to have a separate rotation, scaling and transition, but rotation and transition are didn’t work well because they are using the same segments of matrix. Also, I can’t achieve normal rotation against Z-axis.