StackGenVis/frontend/node_modules/mat4-decompose/index.js

/*jshint unused:true*/
/*
Input:  matrix      ; a 4x4 matrix
Output: translation ; a 3 component vector
        scale       ; a 3 component vector
        skew        ; skew factors XY,XZ,YZ represented as a 3 component vector
        perspective ; a 4 component vector
        quaternion  ; a 4 component vector
Returns false if the matrix cannot be decomposed, true if it can


References:
https://github.com/kamicane/matrix3d/blob/master/lib/Matrix3d.js
https://github.com/ChromiumWebApps/chromium/blob/master/ui/gfx/transform_util.cc
http://www.w3.org/TR/css3-transforms/#decomposing-a-3d-matrix
*/

var normalize = require('./normalize')

var create = require('gl-mat4/create')
var clone = require('gl-mat4/clone')
var determinant = require('gl-mat4/determinant')
var invert = require('gl-mat4/invert')
var transpose = require('gl-mat4/transpose')
var vec3 = {
    length: require('gl-vec3/length'),
    normalize: require('gl-vec3/normalize'),
    dot: require('gl-vec3/dot'),
    cross: require('gl-vec3/cross')
}

var tmp = create()
var perspectiveMatrix = create()
var tmpVec4 = [0, 0, 0, 0]
var row = [ [0,0,0], [0,0,0], [0,0,0] ]
var pdum3 = [0,0,0]

module.exports = function decomposeMat4(matrix, translation, scale, skew, perspective, quaternion) {
    if (!translation) translation = [0,0,0]
    if (!scale) scale = [0,0,0]
    if (!skew) skew = [0,0,0]
    if (!perspective) perspective = [0,0,0,1]
    if (!quaternion) quaternion = [0,0,0,1]

    //normalize, if not possible then bail out early
    if (!normalize(tmp, matrix))
        return false

    // perspectiveMatrix is used to solve for perspective, but it also provides
    // an easy way to test for singularity of the upper 3x3 component.
    clone(perspectiveMatrix, tmp)

    perspectiveMatrix[3] = 0
    perspectiveMatrix[7] = 0
    perspectiveMatrix[11] = 0
    perspectiveMatrix[15] = 1

    // If the perspectiveMatrix is not invertible, we are also unable to
    // decompose, so we'll bail early. Constant taken from SkMatrix44::invert.
    if (Math.abs(determinant(perspectiveMatrix) < 1e-8))
        return false

    var a03 = tmp[3], a13 = tmp[7], a23 = tmp[11],
            a30 = tmp[12], a31 = tmp[13], a32 = tmp[14], a33 = tmp[15]

    // First, isolate perspective.
    if (a03 !== 0 || a13 !== 0 || a23 !== 0) {
        tmpVec4[0] = a03
        tmpVec4[1] = a13
        tmpVec4[2] = a23
        tmpVec4[3] = a33

        // Solve the equation by inverting perspectiveMatrix and multiplying
        // rightHandSide by the inverse.
        // resuing the perspectiveMatrix here since it's no longer needed
        var ret = invert(perspectiveMatrix, perspectiveMatrix)
        if (!ret) return false
        transpose(perspectiveMatrix, perspectiveMatrix)

        //multiply by transposed inverse perspective matrix, into perspective vec4
        vec4multMat4(perspective, tmpVec4, perspectiveMatrix)
    } else { 
        //no perspective
        perspective[0] = perspective[1] = perspective[2] = 0
        perspective[3] = 1
    }

    // Next take care of translation
    translation[0] = a30
    translation[1] = a31
    translation[2] = a32

    // Now get scale and shear. 'row' is a 3 element array of 3 component vectors
    mat3from4(row, tmp)

    // Compute X scale factor and normalize first row.
    scale[0] = vec3.length(row[0])
    vec3.normalize(row[0], row[0])

    // Compute XY shear factor and make 2nd row orthogonal to 1st.
    skew[0] = vec3.dot(row[0], row[1])
    combine(row[1], row[1], row[0], 1.0, -skew[0])

    // Now, compute Y scale and normalize 2nd row.
    scale[1] = vec3.length(row[1])
    vec3.normalize(row[1], row[1])
    skew[0] /= scale[1]

    // Compute XZ and YZ shears, orthogonalize 3rd row
    skew[1] = vec3.dot(row[0], row[2])
    combine(row[2], row[2], row[0], 1.0, -skew[1])
    skew[2] = vec3.dot(row[1], row[2])
    combine(row[2], row[2], row[1], 1.0, -skew[2])

    // Next, get Z scale and normalize 3rd row.
    scale[2] = vec3.length(row[2])
    vec3.normalize(row[2], row[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.
    vec3.cross(pdum3, row[1], row[2])
    if (vec3.dot(row[0], pdum3) < 0) {
        for (var 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
    quaternion[0] = 0.5 * Math.sqrt(Math.max(1 + row[0][0] - row[1][1] - row[2][2], 0))
    quaternion[1] = 0.5 * Math.sqrt(Math.max(1 - row[0][0] + row[1][1] - row[2][2], 0))
    quaternion[2] = 0.5 * Math.sqrt(Math.max(1 - row[0][0] - row[1][1] + row[2][2], 0))
    quaternion[3] = 0.5 * Math.sqrt(Math.max(1 + row[0][0] + row[1][1] + row[2][2], 0))

    if (row[2][1] > row[1][2])
        quaternion[0] = -quaternion[0]
    if (row[0][2] > row[2][0])
        quaternion[1] = -quaternion[1]
    if (row[1][0] > row[0][1])
        quaternion[2] = -quaternion[2]
    return true
}

//will be replaced by gl-vec4 eventually
function vec4multMat4(out, a, m) {
    var x = a[0], y = a[1], z = a[2], w = a[3];
    out[0] = m[0] * x + m[4] * y + m[8] * z + m[12] * w;
    out[1] = m[1] * x + m[5] * y + m[9] * z + m[13] * w;
    out[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;
    out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;
    return out;
}

//gets upper-left of a 4x4 matrix into a 3x3 of vectors
function mat3from4(out, mat4x4) {
    out[0][0] = mat4x4[0]
    out[0][1] = mat4x4[1]
    out[0][2] = mat4x4[2]
    
    out[1][0] = mat4x4[4]
    out[1][1] = mat4x4[5]
    out[1][2] = mat4x4[6]

    out[2][0] = mat4x4[8]
    out[2][1] = mat4x4[9]
    out[2][2] = mat4x4[10]
}

function combine(out, a, b, scale1, scale2) {
    out[0] = a[0] * scale1 + b[0] * scale2
    out[1] = a[1] * scale1 + b[1] * scale2
    out[2] = a[2] * scale1 + b[2] * scale2
}