react-native/ReactAndroid/src/main/java/com/facebook/react/uimanager/MatrixMathHelper.java

package com.facebook.react.uimanager;

import com.facebook.infer.annotation.Assertions;

/**
 * Provides helper methods for converting transform operations into a matrix and then into a list
 * of translate, scale and rotate commands.
 */
public class MatrixMathHelper {

  private static final double EPSILON = .00001d;

  public static class MatrixDecompositionContext {
    double[] perspective = new double[4];
    double[] scale = new double[3];
    double[] skew = new double[3];
    double[] translation = new double[3];
    double[] rotationDegrees = new double[3];
  }

  private static boolean isZero(double d) {
    if (Double.isNaN(d)) {
      return false;
    }
    return Math.abs(d) < EPSILON;
  }

  public static void multiplyInto(double[] out, double[] a, double[] b) {
    double a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
      a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
      a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
      a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];

    double b0  = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
    out[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
    out[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
    out[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
    out[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

    b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
    out[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
    out[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
    out[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
    out[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

    b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
    out[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
    out[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
    out[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
    out[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

    b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
    out[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
    out[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
    out[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
    out[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
  }

  /**
   * @param transformMatrix 16-element array of numbers representing 4x4 transform matrix
   */
  public static void decomposeMatrix(double[] transformMatrix, MatrixDecompositionContext ctx) {
    Assertions.assertCondition(transformMatrix.length == 16);

    // output values
    final double[] perspective = ctx.perspective;
    final double[] scale = ctx.scale;
    final double[] skew = ctx.skew;
    final double[] translation = ctx.translation;
    final double[] rotationDegrees = ctx.rotationDegrees;

    // create normalized, 2d array matrix
    // and normalized 1d array perspectiveMatrix with redefined 4th column
    if (isZero(transformMatrix[15])) {
      return;
    }
    double[][] matrix = new double[4][4];
    double[] perspectiveMatrix = new double[16];
    for (int i = 0; i < 4; i++) {
      for (int j = 0; j < 4; j++) {
        double value = transformMatrix[(i * 4) + j] / transformMatrix[15];
        matrix[i][j] = value;
        perspectiveMatrix[(i * 4) + j] = j == 3 ? 0 : value;
      }
    }
    perspectiveMatrix[15] = 1;

    // test for singularity of upper 3x3 part of the perspective matrix
    if (isZero(determinant(perspectiveMatrix))) {
      return;
    }

    // isolate perspective
    if (!isZero(matrix[0][3]) || !isZero(matrix[1][3]) || !isZero(matrix[2][3])) {
      // rightHandSide is the right hand side of the equation.
      // rightHandSide is a vector, or point in 3d space relative to the origin.
      double[] rightHandSide = { matrix[0][3], matrix[1][3], matrix[2][3], matrix[3][3] };

      // Solve the equation by inverting perspectiveMatrix and multiplying
      // rightHandSide by the inverse.
      double[] inversePerspectiveMatrix = inverse(
        perspectiveMatrix
      );
      double[] transposedInversePerspectiveMatrix = transpose(
        inversePerspectiveMatrix
      );
      multiplyVectorByMatrix(rightHandSide, transposedInversePerspectiveMatrix, perspective);
    } else {
      // no perspective
      perspective[0] = perspective[1] = perspective[2] = 0d;
      perspective[3] = 1d;
    }

    // translation is simple
    for (int i = 0; i < 3; i++) {
      translation[i] = matrix[3][i];
    }

    // Now get scale and shear.
    // 'row' is a 3 element array of 3 component vectors
    double[][] row = new double[3][3];
    for (int i = 0; i < 3; i++) {
      row[i][0] = matrix[i][0];
      row[i][1] = matrix[i][1];
      row[i][2] = matrix[i][2];
    }

    // Compute X scale factor and normalize first row.
    scale[0] = v3Length(row[0]);
    row[0] = v3Normalize(row[0], scale[0]);

    // Compute XY shear factor and make 2nd row orthogonal to 1st.
    skew[0] = v3Dot(row[0], row[1]);
    row[1] = v3Combine(row[1], row[0], 1.0, -skew[0]);

    // Compute XY shear factor and make 2nd row orthogonal to 1st.
    skew[0] = v3Dot(row[0], row[1]);
    row[1] = v3Combine(row[1], row[0], 1.0, -skew[0]);

    // Now, compute Y scale and normalize 2nd row.
    scale[1] = v3Length(row[1]);
    row[1] = v3Normalize(row[1], scale[1]);
    skew[0] /= scale[1];

    // Compute XZ and YZ shears, orthogonalize 3rd row
    skew[1] = v3Dot(row[0], row[2]);
    row[2] = v3Combine(row[2], row[0], 1.0, -skew[1]);
    skew[2] = v3Dot(row[1], row[2]);
    row[2] = v3Combine(row[2], row[1], 1.0, -skew[2]);

    // Next, get Z scale and normalize 3rd row.
    scale[2] = v3Length(row[2]);
    row[2] = v3Normalize(row[2], scale[2]);
    skew[1] /= scale[2];
    skew[2] /= scale[2];

    // At this point, the matrix (in rows) is orthonormal.
    // Check for a coordinate system flip.  If the determinant
    // is -1, then negate the matrix and the scaling factors.
    double[] pdum3 = v3Cross(row[1], row[2]);
    if (v3Dot(row[0], pdum3) < 0) {
      for (int i = 0; i < 3; i++) {
        scale[i] *= -1;
        row[i][0] *= -1;
        row[i][1] *= -1;
        row[i][2] *= -1;
      }
    }

    // Now, get the rotations out
    // Based on: http://nghiaho.com/?page_id=846
    double conv = 180 / Math.PI;
    rotationDegrees[0] = roundTo3Places(-Math.atan2(row[2][1], row[2][2]) * conv);
    rotationDegrees[1] = roundTo3Places(-Math.atan2(-row[2][0], Math.sqrt(row[2][1] * row[2][1] + row[2][2] * row[2][2])) * conv);
    rotationDegrees[2] = roundTo3Places(-Math.atan2(row[1][0], row[0][0]) * conv);
  }

  public static double determinant(double[] matrix) {
    double m00 = matrix[0], m01 = matrix[1], m02 = matrix[2], m03 = matrix[3], m10 = matrix[4],
      m11 = matrix[5], m12 = matrix[6], m13 = matrix[7], m20 = matrix[8], m21 = matrix[9],
      m22 = matrix[10], m23 = matrix[11], m30 = matrix[12], m31 = matrix[13], m32 = matrix[14],
      m33 = matrix[15];
    return (
      m03 * m12 * m21 * m30 - m02 * m13 * m21 * m30 -
        m03 * m11 * m22 * m30 + m01 * m13 * m22 * m30 +
        m02 * m11 * m23 * m30 - m01 * m12 * m23 * m30 -
        m03 * m12 * m20 * m31 + m02 * m13 * m20 * m31 +
        m03 * m10 * m22 * m31 - m00 * m13 * m22 * m31 -
        m02 * m10 * m23 * m31 + m00 * m12 * m23 * m31 +
        m03 * m11 * m20 * m32 - m01 * m13 * m20 * m32 -
        m03 * m10 * m21 * m32 + m00 * m13 * m21 * m32 +
        m01 * m10 * m23 * m32 - m00 * m11 * m23 * m32 -
        m02 * m11 * m20 * m33 + m01 * m12 * m20 * m33 +
        m02 * m10 * m21 * m33 - m00 * m12 * m21 * m33 -
        m01 * m10 * m22 * m33 + m00 * m11 * m22 * m33
    );
  }

  /**
   * Inverse of a matrix. Multiplying by the inverse is used in matrix math
   * instead of division.
   *
   * Formula from:
   * http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
   */
  public static double[] inverse(double[] matrix) {
    double det = determinant(matrix);
    if (isZero(det)) {
      return matrix;
    }
    double m00 = matrix[0], m01 = matrix[1], m02 = matrix[2], m03 = matrix[3], m10 = matrix[4],
      m11 = matrix[5], m12 = matrix[6], m13 = matrix[7], m20 = matrix[8], m21 = matrix[9],
      m22 = matrix[10], m23 = matrix[11], m30 = matrix[12], m31 = matrix[13], m32 = matrix[14],
      m33 = matrix[15];
    return new double[] {
      (m12 * m23 * m31 - m13 * m22 * m31 + m13 * m21 * m32 - m11 * m23 * m32 - m12 * m21 * m33 + m11 * m22 * m33) / det,
      (m03 * m22 * m31 - m02 * m23 * m31 - m03 * m21 * m32 + m01 * m23 * m32 + m02 * m21 * m33 - m01 * m22 * m33) / det,
      (m02 * m13 * m31 - m03 * m12 * m31 + m03 * m11 * m32 - m01 * m13 * m32 - m02 * m11 * m33 + m01 * m12 * m33) / det,
      (m03 * m12 * m21 - m02 * m13 * m21 - m03 * m11 * m22 + m01 * m13 * m22 + m02 * m11 * m23 - m01 * m12 * m23) / det,
      (m13 * m22 * m30 - m12 * m23 * m30 - m13 * m20 * m32 + m10 * m23 * m32 + m12 * m20 * m33 - m10 * m22 * m33) / det,
      (m02 * m23 * m30 - m03 * m22 * m30 + m03 * m20 * m32 - m00 * m23 * m32 - m02 * m20 * m33 + m00 * m22 * m33) / det,
      (m03 * m12 * m30 - m02 * m13 * m30 - m03 * m10 * m32 + m00 * m13 * m32 + m02 * m10 * m33 - m00 * m12 * m33) / det,
      (m02 * m13 * m20 - m03 * m12 * m20 + m03 * m10 * m22 - m00 * m13 * m22 - m02 * m10 * m23 + m00 * m12 * m23) / det,
      (m11 * m23 * m30 - m13 * m21 * m30 + m13 * m20 * m31 - m10 * m23 * m31 - m11 * m20 * m33 + m10 * m21 * m33) / det,
      (m03 * m21 * m30 - m01 * m23 * m30 - m03 * m20 * m31 + m00 * m23 * m31 + m01 * m20 * m33 - m00 * m21 * m33) / det,
      (m01 * m13 * m30 - m03 * m11 * m30 + m03 * m10 * m31 - m00 * m13 * m31 - m01 * m10 * m33 + m00 * m11 * m33) / det,
      (m03 * m11 * m20 - m01 * m13 * m20 - m03 * m10 * m21 + m00 * m13 * m21 + m01 * m10 * m23 - m00 * m11 * m23) / det,
      (m12 * m21 * m30 - m11 * m22 * m30 - m12 * m20 * m31 + m10 * m22 * m31 + m11 * m20 * m32 - m10 * m21 * m32) / det,
      (m01 * m22 * m30 - m02 * m21 * m30 + m02 * m20 * m31 - m00 * m22 * m31 - m01 * m20 * m32 + m00 * m21 * m32) / det,
      (m02 * m11 * m30 - m01 * m12 * m30 - m02 * m10 * m31 + m00 * m12 * m31 + m01 * m10 * m32 - m00 * m11 * m32) / det,
      (m01 * m12 * m20 - m02 * m11 * m20 + m02 * m10 * m21 - m00 * m12 * m21 - m01 * m10 * m22 + m00 * m11 * m22) / det
    };
  }

  /**
   * Turns columns into rows and rows into columns.
   */
  public static double[] transpose(double[] m) {
    return new double[] {
      m[0], m[4], m[8], m[12],
      m[1], m[5], m[9], m[13],
      m[2], m[6], m[10], m[14],
      m[3], m[7], m[11], m[15]
    };
  }

  /**
   * Based on: http://tog.acm.org/resources/GraphicsGems/gemsii/unmatrix.c
   */
  public static void multiplyVectorByMatrix(double[] v, double[] m, double[] result) {
    double vx = v[0], vy = v[1], vz = v[2], vw = v[3];
    result[0] = vx * m[0] + vy * m[4] + vz * m[8] + vw * m[12];
    result[1] = vx * m[1] + vy * m[5] + vz * m[9] + vw * m[13];
    result[2] = vx * m[2] + vy * m[6] + vz * m[10] + vw * m[14];
    result[3] = vx * m[3] + vy * m[7] + vz * m[11] + vw * m[15];
  }

  /**
   * From: https://code.google.com/p/webgl-mjs/source/browse/mjs.js
   */
  public static double v3Length(double[] a) {
    return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
  }

  /**
   * Based on: https://code.google.com/p/webgl-mjs/source/browse/mjs.js
   */
  public static double[] v3Normalize(double[] vector, double norm) {
    double im = 1 / (isZero(norm) ? v3Length(vector) : norm);
    return new double[] {
      vector[0] * im,
      vector[1] * im,
      vector[2] * im
    };
  }

  /**
   * The dot product of a and b, two 3-element vectors.
   * From: https://code.google.com/p/webgl-mjs/source/browse/mjs.js
   */
  public static double v3Dot(double[] a, double[] b) {
    return a[0] * b[0] +
      a[1] * b[1] +
      a[2] * b[2];
  }

  /**
   * From:
   * http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
   */
  public static double[] v3Combine(double[] a, double[] b, double aScale, double bScale) {
    return new double[]{
      aScale * a[0] + bScale * b[0],
      aScale * a[1] + bScale * b[1],
      aScale * a[2] + bScale * b[2]
    };
  }

  /**
   * From:
   * http://www.opensource.apple.com/source/WebCore/WebCore-514/platform/graphics/transforms/TransformationMatrix.cpp
   */
  public static double[] v3Cross(double[] a, double[] b) {
    return new double[]{
      a[1] * b[2] - a[2] * b[1],
      a[2] * b[0] - a[0] * b[2],
      a[0] * b[1] - a[1] * b[0]
    };
  }

  public static double roundTo3Places(double n) {
    return Math.round(n * 1000d) * 0.001;
  }

  public static double[] createIdentityMatrix() {
    double[] res = new double[16];
    resetIdentityMatrix(res);
    return res;
  }

  public static double degreesToRadians(double degrees) {
    return degrees * Math.PI / 180;
  }

  public static void resetIdentityMatrix(double[] matrix) {
    matrix[1] = matrix[2] = matrix[3] = matrix[4] = matrix[6] = matrix[7] = matrix[8] = matrix[9] =
      matrix[11] = matrix[12] = matrix[13] = matrix[14] = 0;
    matrix[0] = matrix[5] = matrix[10] = matrix[15] = 1;
  }

  public static void applyPerspective(double[] m, double perspective) {
    m[11] = -1 / perspective;
  }

  public static void applyScaleX(double[] m, double factor) {
    m[0] = factor;
  }

  public static void applyScaleY(double[] m, double factor) {
    m[5] = factor;
  }

  public static void applyScaleZ(double[] m, double factor) {
    m[10] = factor;
  }

  public static void applyTranslate2D(double[] m, double x, double y) {
    m[12] = x;
    m[13] = y;
  }

  public static void applyTranslate3D(double[] m, double x, double y, double z) {
    m[12] = x;
    m[13] = y;
    m[14] = z;
  }

  public static void applySkewX(double[] m, double radians) {
    m[4] = Math.tan(radians);
  }

  public static void applySkewY(double[] m, double radians) {
    m[1] = Math.tan(radians);
  }

  public static void applyRotateX(double[] m, double radians) {
    m[5] = Math.cos(radians);
    m[6] = Math.sin(radians);
    m[9] = -Math.sin(radians);
    m[10] = Math.cos(radians);
  }

  public static void applyRotateY(double[] m, double radians) {
    m[0] = Math.cos(radians);
    m[2] = -Math.sin(radians);
    m[8] = Math.sin(radians);
    m[10] = Math.cos(radians);
  }

  // http://www.w3.org/TR/css3-transforms/#recomposing-to-a-2d-matrix
  public static void applyRotateZ(double[] m, double radians) {
    m[0] = Math.cos(radians);
    m[1] = Math.sin(radians);
    m[4] = -Math.sin(radians);
    m[5] = Math.cos(radians);
  }
}