Quelle test_DOMMatrix.html Sprache: HTML

products/Sources/formale Sprachen/C/Firefox/dom/tests/mochitest/general/test_DOMMatrix.html

<!DOCTYPE HTML>
<html>
<head>
  <title>Test DOMMatrix behavior</title>
  <script src="/tests/SimpleTest/SimpleTest.js"></script>
  <link rel="stylesheet" type="text/css" href="/tests/SimpleTest/test.css">
</head>
<script>
function createMatrix(a, b, c, d, e, f)
{
  var m = new DOMMatrix();
  m.a = a;
  m.b = b;
  m.c = c;
  m.d = d;
  m.e = e;
  m.f = f;
  return m;
}

function create3DMatrix(a, b, c, d, e, f)
{
  var m = new DOMMatrix();
  m.a = a;
  m.b = b;
  m.c = c;
  m.d = d;
  m.e = e;
  m.f = f;
  m.m13 = 0;
  return m;
}

function cmpMatrix(a, b, msg)
{
  if (Array.isArray(a))
    a = new DOMMatrix(a);
  if (Array.isArray(b))
    b = new DOMMatrix(b);

  ok(CompareDOMMatrix(a, b),
     msg + " - got " + formatMatrix(a)
         + ", expected " + formatMatrix(b));
}

function roughCmpMatrix(a, b, msg)
{
  if (Array.isArray(a))
    a = new DOMMatrix(a);
  if (Array.isArray(b))
    b = new DOMMatrix(b);

  ok(RoughCompareDOMMatrix(a, b),
     msg + " - got " + formatMatrix(a)
         + ", expected " + formatMatrix(b));
}

function formatMatrix(m)
{
  m = new DOMMatrix(m);

  if (m.is2D)
    return "(" + [m.a, m.b, m.c, m.d, m.e, m.f].join(', ') + ")";
  else
    return "(" + [m.m11, m.m12, m.m13, m.m14,
                  m.m21, m.m22, m.m23, m.m24,
                  m.m31, m.m32, m.m33, m.m34,
                  m.m41, m.m42, m.m43, m.m44,].join(', ') + ")";
}

function CompareMatrix(dm, m)
{
  var ma = m.toFloat32Array();
  for (var x = 0; x < ma.length; x++) {
    if (Math.abs(ma[x] - dm.m[x]) > 0.000001)
      return false;
  }

  return true;
}

function CompareDOMMatrix(dm1, dm2)
{
  var m1 = dm1.toFloat32Array();
  var m2 = dm2.toFloat32Array();

  if (m1.length !=  m2.length)
    return false;

  for (var x = 0; x < m1.length; x++) {
    if (Math.abs(m1[x] - m2[x]) > 0.000001)
      return false;
  }

  return true;
}

function RoughCompareDOMMatrix(dm1, dm2)
{
  var m1 = dm1.toFloat32Array();
  var m2 = dm2.toFloat32Array();

  if (m1.length != m2.length)
    return false;

  const tolerance = 1 / 65535;
  for (var x = 0; x < m1.length; x++) {
    if (Math.abs(m1[x] - m2[x]) > tolerance)
      return false;
  }

  return true;
}

SimpleTest.waitForExplicitFinish();

function main()
{
  var tests = [
      testCreateMatrix,
      testMultiply,
      testInverse,
      testTranslate,
      testScale,
      testScaleNonUniform,
      testRotate,
      testRotateFromVector,
      testFlipX,
      testFlipY,
      testSkewX,
      testSkewY,
      testMultiplyInPlace,
      testInverseInPlace,
      testTranslateInPlace,
      testScaleInPlace,
      testRotateInPlace,
      testRotateFromVectorInPlace,
      testSkewXInPlace,
      testSkewYInPlace,
      testCreateMatrix3D,
      testMultiply3D,
      testInverse3D,
      testTranslate3D,
      testScale3D,
      test3D,
      testParsing,
      testStringify
    ];
  for (var i = 0; i < tests.length; i++) {
    try{
      tests[i]();
    } catch (e) {
      ok(false, "uncaught exception in test " + i + ": " + e.name);
    }
  }
  SimpleTest.finish();
}

function testCreateMatrix()
{
  var m = new DOMMatrix();

  // Should be initialised to identity
  cmpMatrix(m, [1, 0, 0, 1, 0, 0],
            "DOMMatrix should produce identity matrix");

  m = new DOMMatrix([1,2,3,4,5,6]);
  cmpMatrix(m, [1,2,3,4,5,6],
            "DOMMatrix should produce the same matrix");
  ok(m.is2D, "Failed to mark matrix as 2D.");

  m = new DOMMatrix([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]);
  cmpMatrix(m, [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],
            "DOMMatrix should produce the same matrix");
  ok(!m.is2D, "Failed to mark matrix as 3D.");

  var n = new DOMMatrix(m.toFloat32Array());
  cmpMatrix(n, [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],
            "DOMMatrix should produce the same matrix with float32array constructor");
  ok(!n.is2D, "Failed to mark matrix as 3D.");

  var n = new DOMMatrix(m.toFloat64Array());
  cmpMatrix(n, [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],
            "DOMMatrix should produce the same matrix with float64array constructor");
  ok(!n.is2D, "Failed to mark matrix as 3D.");

  var exn = null;
  try {
    m = new DOMMatrix([0]);
  } catch (e) {
    exn = e;
  }
  ok(exn, "did throw exception with bad DOMMatrix constructor with 1 parameter");

  exn = null;
  try {
    m = new DOMMatrix([1,2,3,4,5,6,7,8,9]);
  } catch (e) {
    exn = e;
  }
  ok(exn, "did throw exception with bad DOMMatrix constructor with 9 parameters");

  exn = null;
  try {
    m = new DOMMatrix([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]);
  } catch (e) {
    exn = e;
  }
  ok(exn, "did throw exception with bad DOMMatrix constructor with 17 parameters");
}

// DOMMatrix multiply(in DOMMatrix secondMatrix);
function testMultiply()
{
  var m1 = createMatrix(1, 0, 0, 1, 50, 90);
  var m2 = createMatrix(Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 0, 0);
  var m3 = createMatrix(1, 0, 0, 1, 130, 160);
  var result = m1.multiply(m2).multiply(m3);
  roughCmpMatrix(result, [Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 255.060974, 111.213203],
    "Unexpected result after multiplying matrices");

  // Check orig matrices are unchanged
  cmpMatrix(m1, [1, 0, 0, 1, 50, 90], "Matrix changed after multiplication");
  roughCmpMatrix(m2, [Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 0, 0],
                 "Matrix changed after multiplication");
  cmpMatrix(m3, [1, 0, 0, 1, 130, 160], "Matrix changed after multiplication");
}

// DOMMatrix inverse() raises(SVGException);
function testInverse()
{
  // Test inversion
  var m = createMatrix(2, 0, 0, 4, 110, -50);
  roughCmpMatrix(m.inverse(), [0.5, 0, 0, 0.25, -55, 12.5],
    "Unexpected result after inverting matrix");

  // Test non-invertable
  m = createMatrix(0, 0, 1, 0, 0, 0);
  m = m.inverse();
  ok(isNaN(m.a), "Failed to invalidate inverted singular matrix, got " + m.a);
  ok(!m.is2D, "Failed to mark invalidated inverted singular matrix as 3D.");
}

// DOMMatrix translate(in float x, in float y);
function testTranslate()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  roughCmpMatrix(m.translate(100, -50), [2, 0, 0, 1, 320, 50],
    "Unexpected result after translate");
}

// DOMMatrix scale(in float scaleFactor);
function testScale()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  roughCmpMatrix(m.scale(0.5), [1, 0, 0, 0.5, 120, 100],
    "Unexpected result after scale");
}

// DOMMatrix scaleNonUniform(in float scaleFactorX, in float scaleFactorY);
function testScaleNonUniform()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  roughCmpMatrix(m.scaleNonUniform(0.5, -3), [1, 0, 0, -3, 120, 100],
    "Unexpected result after scaleNonUniform");
}

// DOMMatrix rotate(in float angle);
function testRotate()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  roughCmpMatrix(m.rotate(45),
                 [2*Math.cos(Math.PI/4), Math.sin(Math.PI/4),
                  2*-Math.sin(Math.PI/4), Math.cos(Math.PI/4),
                  120, 100],
                 "Unexpected result after rotate");
}

// DOMMatrix rotateFromVector(in float x, in float y) raises(SVGException);
function testRotateFromVector()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  // Make a 150 degree angle
  var result = m.rotateFromVector(-2, 1.1547);
  roughCmpMatrix(result,
                 [2*Math.cos(5*Math.PI/6), Math.sin(5*Math.PI/6),
                  2*-Math.sin(5*Math.PI/6), Math.cos(5*Math.PI/6),
                  120, 100],
                 "Unexpected result after rotateFromVector");

  // Test bad input (1)
  var exn = null;
  try {
    m.rotateFromVector(1, 0);
  } catch (e) {
    exn = e;
  }
  is(exn, null, "did not throw exception with zero coord for rotateFromVector");

  // Test bad input (2)
  exn = null;
  try {
    m.rotateFromVector(0, 1);
  } catch (e) {
    exn = e;
  }
  is(exn, null, "did not throw exception with zero coord for rotateFromVector");
}

// DOMMatrix flipX();
function testFlipX()
{
  var m = createMatrix(1, 2, 3, 4, 5, 6);
  cmpMatrix(m.flipX(), [-1, -2, 3, 4, 5, 6], "Unexpected result after flipX");
}

// DOMMatrix flipY();
function testFlipY()
{
  var m = createMatrix(1, 2, 3, 4, 5, 6);
  cmpMatrix(m.flipY(), [1, 2, -3, -4, 5, 6], "Unexpected result after flipY");
}

// DOMMatrix skewX(in float angle);
function testSkewX()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  roughCmpMatrix(m.skewX(30), [2, 0, 2*Math.tan(Math.PI/6), 1, 120, 100],
                 "Unexpected result after skewX");
}

// DOMMatrix skewY(in float angle);
function testSkewY()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  roughCmpMatrix(m.skewY(30), [2, Math.tan(Math.PI/6), 0, 1, 120, 100],
                 "Unexpected result after skewY");
}

// DOMMatrix multiply(in DOMMatrix secondMatrix);
function testMultiplyInPlace()
{
  var m1 = createMatrix(1, 0, 0, 1, 50, 90);
  var m2 = createMatrix(Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 0, 0);
  var m3 = createMatrix(1, 0, 0, 1, 130, 160);
  m1.multiplySelf(m2).multiplySelf(m3);
  roughCmpMatrix(m1, [Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 255.060974, 111.213203],
    "Unexpected result after multiplying matrices");

  // Check orig matrices are unchanged
  roughCmpMatrix(m2, [Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 0, 0],
                 "Matrix changed after multiplication");
  cmpMatrix(m3, [1, 0, 0, 1, 130, 160], "Matrix changed after multiplication");
}

// DOMMatrix inverse() raises(SVGException);
function testInverseInPlace()
{
  // Test inversion
  var m = createMatrix(2, 0, 0, 4, 110, -50);
  m.invertSelf();
  roughCmpMatrix(m, [0.5, 0, 0, 0.25, -55, 12.5],
    "Unexpected result after inverting matrix");

  // Test non-invertable
  m = createMatrix(0, 0, 1, 0, 0, 0);
  m.invertSelf();
  ok(isNaN(m.a), "Failed to invalidate inverted singular matrix, got " + m.a);
  ok(!m.is2D, "Failed to mark invalidated inverted singular matrix as 3D.");
}

// DOMMatrix translate(in float x, in float y);
function testTranslateInPlace()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  m.translateSelf(100, -50)
  roughCmpMatrix(m, [2, 0, 0, 1, 320, 50],
    "Unexpected result after translate");
}

// DOMMatrix scale(in float scaleFactor);
function testScaleInPlace()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  m.scaleSelf(0.5);
  roughCmpMatrix(m, [1, 0, 0, 0.5, 120, 100],
    "Unexpected result after scale");
}

// DOMMatrix rotate(in float angle);
function testRotateInPlace()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  m.rotateSelf(45);
  roughCmpMatrix(m,
                 [2*Math.cos(Math.PI/4), Math.sin(Math.PI/4),
                  2*-Math.sin(Math.PI/4), Math.cos(Math.PI/4),
                  120, 100],
                 "Unexpected result after rotate");
}

// DOMMatrix rotateFromVector(in float x, in float y) raises(SVGException);
function testRotateFromVectorInPlace()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  // Make a 150 degree angle
  m.rotateFromVectorSelf(-2, 1.1547);
  roughCmpMatrix(m,
                 [2*Math.cos(5*Math.PI/6), Math.sin(5*Math.PI/6),
                  2*-Math.sin(5*Math.PI/6), Math.cos(5*Math.PI/6),
                  120, 100],
                 "Unexpected result after rotateFromVector");

  // Test bad input (1)
  try {
    m.rotateFromVectorSelf(1, 0);
    ok(true, "did not throw exception with zero coord for rotateFromVector");
  } catch (e) {
    ok(false,
      "Got unexpected exception " + e + ", expected NotSupportedError");
  }

  // Test bad input (2)
  try {
    m.rotateFromVectorSelf(0, 1);
    ok(true, "did not throw exception with zero coord for rotateFromVector");
  } catch (e) { }
}

// DOMMatrix skewX(in float angle);
function testSkewXInPlace()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  m.skewXSelf(30);
  roughCmpMatrix(m, [2, 0, 2*Math.tan(Math.PI/6), 1, 120, 100],
                 "Unexpected result after skewX");
}

// DOMMatrix skewY(in float angle);
function testSkewYInPlace()
{
  var m = createMatrix(2, 0, 0, 1, 120, 100);
  m.skewYSelf(30);
  roughCmpMatrix(m, [2, Math.tan(Math.PI/6), 0, 1, 120, 100],
                 "Unexpected result after skewY");
}

function testCreateMatrix3D()
{
  var m = new DOMMatrix([1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]);

  // Should be initialised to identity
  cmpMatrix(m, [1, 0, 0, 1, 0, 0],
            "DOMMatrix should produce identity matrix");
  is(m.is2D, false, "should produce 3d matrix");

  m = new DOMMatrix([1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]);

  // Should be initialised to identity
  cmpMatrix(m, [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
            "DOMMatrix should produce identity matrix");
  is(m.is2D, false, "should produce 3d matrix");
}

// DOMMatrix multiply(in DOMMatrix secondMatrix);
function testMultiply3D()
{
  var m1 = createMatrix(1, 0, 0, 1, 50, 90);
  var m2 = create3DMatrix(Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 0, 0);
  var m3 = create3DMatrix(1, 0, 0, 1, 130, 160);
  var result = m1.multiply(m2).multiply(m3);
  ok(m1.is2D == true, "should produce 3d matrix");
  roughCmpMatrix(result, [Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 255.060974, 111.213203],
    "Unexpected result after multiplying matrices");

  // Check orig matrices are unchanged
  cmpMatrix(m1, [1, 0, 0, 1, 50, 90], "Matrix changed after multiplication");
  roughCmpMatrix(m2, [Math.SQRT1_2, -Math.SQRT1_2, Math.SQRT1_2, Math.SQRT1_2, 0, 0],
                 "Matrix changed after multiplication");
  cmpMatrix(m3, [1, 0, 0, 1, 130, 160], "Matrix changed after multiplication");
}

// DOMMatrix inverse() raises(SVGException);
function testInverse3D()
{
  // Test inversion
  var m = create3DMatrix(2, 0, 0, 4, 110, -50);
  roughCmpMatrix(m.inverse(), [0.5, 0, 0, 0.25, -55, 12.5],
    "Unexpected result after inverting matrix");

  // Test non-invertable
  m = createMatrix(0, 0, 1, 0, 0, 0);
  m = m.inverse();
  ok(isNaN(m.a), "Failed to invalidate inverted singular matrix, got " + m.a);
  ok(!m.is2D, "Failed to mark invalidated inverted singular matrix as 3D.");
}

// DOMMatrix translate(in float x, in float y);
function testTranslate3D()
{
  var m = create3DMatrix(2, 0, 0, 1, 120, 100);
  roughCmpMatrix(m.translate(100, -50), [2, 0, 0, 1, 320, 50],
    "Unexpected result after translate");
}

// DOMMatrix scale(in float scaleFactor);
function testScale3D()
{
  var m = create3DMatrix(2, 0, 0, 1, 120, 100);
  roughCmpMatrix(m.scale(0.5), [1, 0, 0, 0.5, 120, 100],
    "Unexpected result after scale");
}

function Matrix3D() {
  this.m = new Float32Array([
      1, 0, 0, 0,
      0, 1, 0, 0,
      0, 0, 1, 0,
      0, 0, 0, 1
    ]);
}

Matrix3D.prototype = {
  translate(x, y, z, result) {
    result = result || new Matrix3D();
    var m = result.m;

    m[0] = 1;
    m[1] = 0;
    m[2] = 0;
    m[3] = x;

    m[4] = 0;
    m[5] = 1;
    m[6] = 0;
    m[7] = y;

    m[8] = 0;
    m[9] = 0;
    m[10] = 1;
    m[11] = z;

    m[12] = 0;
    m[13] = 0;
    m[14] = 0;
    m[15] = 1;

    return result;
  },
  inverse(matrix, result) {
    result = result || new Matrix3D();
    var m = matrix.m, r = result.m;

    r[0] = m[5]*m[10]*m[15] - m[5]*m[14]*m[11] - m[6]*m[9]*m[15] + m[6]*m[13]*m[11] + m[7]*m[9]*m[14] - m[7]*m[13]*m[10];
    r[1] = -m[1]*m[10]*m[15] + m[1]*m[14]*m[11] + m[2]*m[9]*m[15] - m[2]*m[13]*m[11] - m[3]*m[9]*m[14] + m[3]*m[13]*m[10];
    r[2] = m[1]*m[6]*m[15] - m[1]*m[14]*m[7] - m[2]*m[5]*m[15] + m[2]*m[13]*m[7] + m[3]*m[5]*m[14] - m[3]*m[13]*m[6];
    r[3] = -m[1]*m[6]*m[11] + m[1]*m[10]*m[7] + m[2]*m[5]*m[11] - m[2]*m[9]*m[7] - m[3]*m[5]*m[10] + m[3]*m[9]*m[6];

    r[4] = -m[4]*m[10]*m[15] + m[4]*m[14]*m[11] + m[6]*m[8]*m[15] - m[6]*m[12]*m[11] - m[7]*m[8]*m[14] + m[7]*m[12]*m[10];
    r[5] = m[0]*m[10]*m[15] - m[0]*m[14]*m[11] - m[2]*m[8]*m[15] + m[2]*m[12]*m[11] + m[3]*m[8]*m[14] - m[3]*m[12]*m[10];
    r[6] = -m[0]*m[6]*m[15] + m[0]*m[14]*m[7] + m[2]*m[4]*m[15] - m[2]*m[12]*m[7] - m[3]*m[4]*m[14] + m[3]*m[12]*m[6];
    r[7] = m[0]*m[6]*m[11] - m[0]*m[10]*m[7] - m[2]*m[4]*m[11] + m[2]*m[8]*m[7] + m[3]*m[4]*m[10] - m[3]*m[8]*m[6];

    r[8] = m[4]*m[9]*m[15] - m[4]*m[13]*m[11] - m[5]*m[8]*m[15] + m[5]*m[12]*m[11] + m[7]*m[8]*m[13] - m[7]*m[12]*m[9];
    r[9] = -m[0]*m[9]*m[15] + m[0]*m[13]*m[11] + m[1]*m[8]*m[15] - m[1]*m[12]*m[11] - m[3]*m[8]*m[13] + m[3]*m[12]*m[9];
    r[10] = m[0]*m[5]*m[15] - m[0]*m[13]*m[7] - m[1]*m[4]*m[15] + m[1]*m[12]*m[7] + m[3]*m[4]*m[13] - m[3]*m[12]*m[5];
    r[11] = -m[0]*m[5]*m[11] + m[0]*m[9]*m[7] + m[1]*m[4]*m[11] - m[1]*m[8]*m[7] - m[3]*m[4]*m[9] + m[3]*m[8]*m[5];

    r[12] = -m[4]*m[9]*m[14] + m[4]*m[13]*m[10] + m[5]*m[8]*m[14] - m[5]*m[12]*m[10] - m[6]*m[8]*m[13] + m[6]*m[12]*m[9];
    r[13] = m[0]*m[9]*m[14] - m[0]*m[13]*m[10] - m[1]*m[8]*m[14] + m[1]*m[12]*m[10] + m[2]*m[8]*m[13] - m[2]*m[12]*m[9];
    r[14] = -m[0]*m[5]*m[14] + m[0]*m[13]*m[6] + m[1]*m[4]*m[14] - m[1]*m[12]*m[6] - m[2]*m[4]*m[13] + m[2]*m[12]*m[5];
    r[15] = m[0]*m[5]*m[10] - m[0]*m[9]*m[6] - m[1]*m[4]*m[10] + m[1]*m[8]*m[6] + m[2]*m[4]*m[9] - m[2]*m[8]*m[5];

    var det = m[0]*r[0] + m[1]*r[4] + m[2]*r[8] + m[3]*r[12];
    for (var i = 0; i < 16; i++) r[i] /= det;
    return result;
  },
  multiply(left, result) {
    result = result || new Matrix3D();
    var a = this.m, b = left.m, r = result.m;

    r[0] = a[0] * b[0] + a[1] * b[4] + a[2] * b[8] + a[3] * b[12];
    r[1] = a[0] * b[1] + a[1] * b[5] + a[2] * b[9] + a[3] * b[13];
    r[2] = a[0] * b[2] + a[1] * b[6] + a[2] * b[10] + a[3] * b[14];
    r[3] = a[0] * b[3] + a[1] * b[7] + a[2] * b[11] + a[3] * b[15];

    r[4] = a[4] * b[0] + a[5] * b[4] + a[6] * b[8] + a[7] * b[12];
    r[5] = a[4] * b[1] + a[5] * b[5] + a[6] * b[9] + a[7] * b[13];
    r[6] = a[4] * b[2] + a[5] * b[6] + a[6] * b[10] + a[7] * b[14];
    r[7] = a[4] * b[3] + a[5] * b[7] + a[6] * b[11] + a[7] * b[15];

    r[8] = a[8] * b[0] + a[9] * b[4] + a[10] * b[8] + a[11] * b[12];
    r[9] = a[8] * b[1] + a[9] * b[5] + a[10] * b[9] + a[11] * b[13];
    r[10] = a[8] * b[2] + a[9] * b[6] + a[10] * b[10] + a[11] * b[14];
    r[11] = a[8] * b[3] + a[9] * b[7] + a[10] * b[11] + a[11] * b[15];

    r[12] = a[12] * b[0] + a[13] * b[4] + a[14] * b[8] + a[15] * b[12];
    r[13] = a[12] * b[1] + a[13] * b[5] + a[14] * b[9] + a[15] * b[13];
    r[14] = a[12] * b[2] + a[13] * b[6] + a[14] * b[10] + a[15] * b[14];
    r[15] = a[12] * b[3] + a[13] * b[7] + a[14] * b[11] + a[15] * b[15];

    return result;
  },
  scale(x, y, z, result) {
    result = result || new Matrix3D();
    var m = result.m;

    m[0] = x;
    m[1] = 0;
    m[2] = 0;
    m[3] = 0;

    m[4] = 0;
    m[5] = y;
    m[6] = 0;
    m[7] = 0;

    m[8] = 0;
    m[9] = 0;
    m[10] = z;
    m[11] = 0;

    m[12] = 0;
    m[13] = 0;
    m[14] = 0;
    m[15] = 1;

    return result;
  },
  rotate(a, x, y, z, result) {
    result = result || new Matrix3D();
    var m = result.m;

    var d = Math.sqrt(x*x + y*y + z*z);
    a *= Math.PI / 180; x /= d; y /= d; z /= d;
    var c = Math.cos(a), s = Math.sin(a), t = 1 - c;

    m[0] = x * x * t + c;
    m[1] = x * y * t - z * s;
    m[2] = x * z * t + y * s;
    m[3] = 0;

    m[4] = y * x * t + z * s;
    m[5] = y * y * t + c;
    m[6] = y * z * t - x * s;
    m[7] = 0;

    m[8] = z * x * t - y * s;
    m[9] = z * y * t + x * s;
    m[10] = z * z * t + c;
    m[11] = 0;

    m[12] = 0;
    m[13] = 0;
    m[14] = 0;
    m[15] = 1;

    return result;
  },
  swap(result) {
    result = result || new Matrix3D();
    for (var x = 0; x < 16; x++)
      result.m[x] = this.m[Math.floor(x/4) + (x%4)*4];

    return result;
  }
};

function test3D()
{
  var m = new DOMMatrix()
  var m2 = new Matrix3D();

  m.translateSelf(2,3,4).scaleSelf(1.2, 2.3, 3.4, 0, 0, 0);
  m2 = m2.multiply(m2.translate(2,3,4)).multiply(m2.scale(1.2, 2.3, 3.4)).swap();

  ok(CompareMatrix(m2, m), "translate + scale in 3d didn't match, expected: " + formatMatrix(m2.m) + ", got: " + formatMatrix(m));

  m.invertSelf();
  m2 = new Matrix3D();
  m2 = m2.multiply(m2.translate(2,3,4)).multiply(m2.scale(1.2, 2.3, 3.4));
  m2 = m2.inverse(m2).swap();
  ok(CompareMatrix(m2, m), "translate + scale in inverted 3d didn't match, expected: " + formatMatrix(m2.m) + ", got: " + formatMatrix(m));
}

function testParsing()
{
  var m = new DOMMatrix("translate(10px, 20px) scale(.5, 2) rotate(45deg)");
  var m2 = new DOMMatrix();
  m2.translateSelf(10, 20).scaleSelf(.5,2).rotateSelf(45);
  ok(CompareDOMMatrix(m2, m), "string parsing didn't match");

  m = new DOMMatrix();
  m.setMatrixValue("translate(10px, 20px) scale(.5, 2) rotate(45deg)");
  ok(CompareDOMMatrix(m2, m), "string parsing didn't match");
}

function testStringify() {
    var m = new DOMMatrix();
    var s = "" + m;
    ok(s == "matrix" + formatMatrix(m), "stringifier 1 produced wrong result: " + s);
    m.a = 100;
    s = "" + m;
    ok(s == "matrix" + formatMatrix(m), "stringifier 2 produced wrong result: " + s);
    m.m43 = 200;
    s = "" + m;
    ok(s == "matrix3d" + formatMatrix(m), "stringifier 3 produced wrong result:" + s);
}

window.addEventListener("load", main);

</script>
</pre>
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Messung V0.5

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Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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