ShadowEditor/THREE/Math/Matrix4.cs
2018-12-08 07:56:02 +08:00

1001 lines
26 KiB
C#

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace THREE
{
/// <summary>
/// @author mrdoob / http://mrdoob.com/
/// @author supereggbert / http://www.paulbrunt.co.uk/
/// @author philogb / http://blog.thejit.org/
/// @author jordi_ros / http://plattsoft.com
/// @author D1plo1d / http://github.com/D1plo1d
/// @author alteredq / http://alteredqualia.com/
/// @author mikael emtinger / http://gomo.se/
/// @author timknip / http://www.floorplanner.com/
/// @author bhouston / http://clara.io
/// @author WestLangley / http://github.com/WestLangley
/// </summary>
public class Matrix4
{
public double[] elements;
public Matrix4()
{
this.elements = new double[] {
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
};
}
isMatrix4: true,
set: function(n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 )
{
var te = this.elements;
te[0] = n11; te[4] = n12; te[8] = n13; te[12] = n14;
te[1] = n21; te[5] = n22; te[9] = n23; te[13] = n24;
te[2] = n31; te[6] = n32; te[10] = n33; te[14] = n34;
te[3] = n41; te[7] = n42; te[11] = n43; te[15] = n44;
return this;
},
identity: function()
{
this.set(
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
);
return this;
},
clone: function()
{
return new Matrix4().fromArray(this.elements);
},
copy: function(m )
{
var te = this.elements;
var me = m.elements;
te[0] = me[0]; te[1] = me[1]; te[2] = me[2]; te[3] = me[3];
te[4] = me[4]; te[5] = me[5]; te[6] = me[6]; te[7] = me[7];
te[8] = me[8]; te[9] = me[9]; te[10] = me[10]; te[11] = me[11];
te[12] = me[12]; te[13] = me[13]; te[14] = me[14]; te[15] = me[15];
return this;
},
copyPosition: function(m )
{
var te = this.elements, me = m.elements;
te[12] = me[12];
te[13] = me[13];
te[14] = me[14];
return this;
},
extractBasis: function(xAxis, yAxis, zAxis )
{
xAxis.setFromMatrixColumn(this, 0);
yAxis.setFromMatrixColumn(this, 1);
zAxis.setFromMatrixColumn(this, 2);
return this;
},
makeBasis: function(xAxis, yAxis, zAxis )
{
this.set(
xAxis.x, yAxis.x, zAxis.x, 0,
xAxis.y, yAxis.y, zAxis.y, 0,
xAxis.z, yAxis.z, zAxis.z, 0,
0, 0, 0, 1
);
return this;
},
extractRotation: function()
{
var v1 = new Vector3();
return function extractRotation(m) {
// this method does not support reflection matrices
var te = this.elements;
var me = m.elements;
var scaleX = 1 / v1.setFromMatrixColumn(m, 0).length();
var scaleY = 1 / v1.setFromMatrixColumn(m, 1).length();
var scaleZ = 1 / v1.setFromMatrixColumn(m, 2).length();
te[0] = me[0] * scaleX;
te[1] = me[1] * scaleX;
te[2] = me[2] * scaleX;
te[3] = 0;
te[4] = me[4] * scaleY;
te[5] = me[5] * scaleY;
te[6] = me[6] * scaleY;
te[7] = 0;
te[8] = me[8] * scaleZ;
te[9] = me[9] * scaleZ;
te[10] = me[10] * scaleZ;
te[11] = 0;
te[12] = 0;
te[13] = 0;
te[14] = 0;
te[15] = 1;
return this;
};
}
(),
makeRotationFromEuler: function(euler )
{
if (!(euler && euler.isEuler))
{
console.error('THREE.Matrix4: .makeRotationFromEuler() now expects a Euler rotation rather than a Vector3 and order.');
}
var te = this.elements;
var x = euler.x, y = euler.y, z = euler.z;
var a = Math.cos(x), b = Math.sin(x);
var c = Math.cos(y), d = Math.sin(y);
var e = Math.cos(z), f = Math.sin(z);
if (euler.order === 'XYZ')
{
var ae = a * e, af = a * f, be = b * e, bf = b * f;
te[0] = c * e;
te[4] = -c * f;
te[8] = d;
te[1] = af + be * d;
te[5] = ae - bf * d;
te[9] = -b * c;
te[2] = bf - ae * d;
te[6] = be + af * d;
te[10] = a * c;
}
else if (euler.order === 'YXZ')
{
var ce = c * e, cf = c * f, de = d * e, df = d * f;
te[0] = ce + df * b;
te[4] = de * b - cf;
te[8] = a * d;
te[1] = a * f;
te[5] = a * e;
te[9] = -b;
te[2] = cf * b - de;
te[6] = df + ce * b;
te[10] = a * c;
}
else if (euler.order === 'ZXY')
{
var ce = c * e, cf = c * f, de = d * e, df = d * f;
te[0] = ce - df * b;
te[4] = -a * f;
te[8] = de + cf * b;
te[1] = cf + de * b;
te[5] = a * e;
te[9] = df - ce * b;
te[2] = -a * d;
te[6] = b;
te[10] = a * c;
}
else if (euler.order === 'ZYX')
{
var ae = a * e, af = a * f, be = b * e, bf = b * f;
te[0] = c * e;
te[4] = be * d - af;
te[8] = ae * d + bf;
te[1] = c * f;
te[5] = bf * d + ae;
te[9] = af * d - be;
te[2] = -d;
te[6] = b * c;
te[10] = a * c;
}
else if (euler.order === 'YZX')
{
var ac = a * c, ad = a * d, bc = b * c, bd = b * d;
te[0] = c * e;
te[4] = bd - ac * f;
te[8] = bc * f + ad;
te[1] = f;
te[5] = a * e;
te[9] = -b * e;
te[2] = -d * e;
te[6] = ad * f + bc;
te[10] = ac - bd * f;
}
else if (euler.order === 'XZY')
{
var ac = a * c, ad = a * d, bc = b * c, bd = b * d;
te[0] = c * e;
te[4] = -f;
te[8] = d * e;
te[1] = ac * f + bd;
te[5] = a * e;
te[9] = ad * f - bc;
te[2] = bc * f - ad;
te[6] = b * e;
te[10] = bd * f + ac;
}
// bottom row
te[3] = 0;
te[7] = 0;
te[11] = 0;
// last column
te[12] = 0;
te[13] = 0;
te[14] = 0;
te[15] = 1;
return this;
},
makeRotationFromQuaternion: function()
{
var zero = new Vector3(0, 0, 0);
var one = new Vector3(1, 1, 1);
return function makeRotationFromQuaternion(q) {
return this.compose(zero, q, one);
};
}
(),
lookAt: function()
{
var x = new Vector3();
var y = new Vector3();
var z = new Vector3();
return function lookAt(eye, target, up) {
var te = this.elements;
z.subVectors(eye, target);
if (z.lengthSq() === 0)
{
// eye and target are in the same position
z.z = 1;
}
z.normalize();
x.crossVectors(up, z);
if (x.lengthSq() === 0)
{
// up and z are parallel
if (Math.abs(up.z) === 1)
{
z.x += 0.0001;
}
else
{
z.z += 0.0001;
}
z.normalize();
x.crossVectors(up, z);
}
x.normalize();
y.crossVectors(z, x);
te[0] = x.x; te[4] = y.x; te[8] = z.x;
te[1] = x.y; te[5] = y.y; te[9] = z.y;
te[2] = x.z; te[6] = y.z; te[10] = z.z;
return this;
};
}
(),
multiply: function(m, n )
{
if (n !== undefined)
{
console.warn('THREE.Matrix4: .multiply() now only accepts one argument. Use .multiplyMatrices( a, b ) instead.');
return this.multiplyMatrices(m, n);
}
return this.multiplyMatrices(this, m);
},
premultiply: function(m )
{
return this.multiplyMatrices(m, this);
},
multiplyMatrices: function(a, b )
{
var ae = a.elements;
var be = b.elements;
var te = this.elements;
var a11 = ae[0], a12 = ae[4], a13 = ae[8], a14 = ae[12];
var a21 = ae[1], a22 = ae[5], a23 = ae[9], a24 = ae[13];
var a31 = ae[2], a32 = ae[6], a33 = ae[10], a34 = ae[14];
var a41 = ae[3], a42 = ae[7], a43 = ae[11], a44 = ae[15];
var b11 = be[0], b12 = be[4], b13 = be[8], b14 = be[12];
var b21 = be[1], b22 = be[5], b23 = be[9], b24 = be[13];
var b31 = be[2], b32 = be[6], b33 = be[10], b34 = be[14];
var b41 = be[3], b42 = be[7], b43 = be[11], b44 = be[15];
te[0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
te[4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
te[8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
te[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
te[1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
te[5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
te[9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
te[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
te[2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
te[6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
te[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
te[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
te[3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
te[7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
te[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
te[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
return this;
},
multiplyScalar: function(s )
{
var te = this.elements;
te[0] *= s; te[4] *= s; te[8] *= s; te[12] *= s;
te[1] *= s; te[5] *= s; te[9] *= s; te[13] *= s;
te[2] *= s; te[6] *= s; te[10] *= s; te[14] *= s;
te[3] *= s; te[7] *= s; te[11] *= s; te[15] *= s;
return this;
},
applyToBufferAttribute: function()
{
var v1 = new Vector3();
return function applyToBufferAttribute(attribute) {
for (var i = 0, l = attribute.count; i < l; i++)
{
v1.x = attribute.getX(i);
v1.y = attribute.getY(i);
v1.z = attribute.getZ(i);
v1.applyMatrix4(this);
attribute.setXYZ(i, v1.x, v1.y, v1.z);
}
return attribute;
};
}
(),
determinant: function()
{
var te = this.elements;
var n11 = te[0], n12 = te[4], n13 = te[8], n14 = te[12];
var n21 = te[1], n22 = te[5], n23 = te[9], n24 = te[13];
var n31 = te[2], n32 = te[6], n33 = te[10], n34 = te[14];
var n41 = te[3], n42 = te[7], n43 = te[11], n44 = te[15];
//TODO: make this more efficient
//( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )
return (
n41 * (
+n14 * n23 * n32
- n13 * n24 * n32
- n14 * n22 * n33
+ n12 * n24 * n33
+ n13 * n22 * n34
- n12 * n23 * n34
) +
n42 * (
+n11 * n23 * n34
- n11 * n24 * n33
+ n14 * n21 * n33
- n13 * n21 * n34
+ n13 * n24 * n31
- n14 * n23 * n31
) +
n43 * (
+n11 * n24 * n32
- n11 * n22 * n34
- n14 * n21 * n32
+ n12 * n21 * n34
+ n14 * n22 * n31
- n12 * n24 * n31
) +
n44 * (
-n13 * n22 * n31
- n11 * n23 * n32
+ n11 * n22 * n33
+ n13 * n21 * n32
- n12 * n21 * n33
+ n12 * n23 * n31
)
);
},
transpose: function()
{
var te = this.elements;
var tmp;
tmp = te[1]; te[1] = te[4]; te[4] = tmp;
tmp = te[2]; te[2] = te[8]; te[8] = tmp;
tmp = te[6]; te[6] = te[9]; te[9] = tmp;
tmp = te[3]; te[3] = te[12]; te[12] = tmp;
tmp = te[7]; te[7] = te[13]; te[13] = tmp;
tmp = te[11]; te[11] = te[14]; te[14] = tmp;
return this;
},
setPosition: function(v )
{
var te = this.elements;
te[12] = v.x;
te[13] = v.y;
te[14] = v.z;
return this;
},
getInverse: function(m, throwOnDegenerate )
{
// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
var te = this.elements,
me = m.elements,
n11 = me[0], n21 = me[1], n31 = me[2], n41 = me[3],
n12 = me[4], n22 = me[5], n32 = me[6], n42 = me[7],
n13 = me[8], n23 = me[9], n33 = me[10], n43 = me[11],
n14 = me[12], n24 = me[13], n34 = me[14], n44 = me[15],
t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44,
t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44,
t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44,
t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;
var det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;
if (det === 0)
{
var msg = "THREE.Matrix4: .getInverse() can't invert matrix, determinant is 0";
if (throwOnDegenerate === true)
{
throw new Error(msg);
}
else
{
console.warn(msg);
}
return this.identity();
}
var detInv = 1 / det;
te[0] = t11 * detInv;
te[1] = (n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44) * detInv;
te[2] = (n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44) * detInv;
te[3] = (n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43) * detInv;
te[4] = t12 * detInv;
te[5] = (n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44) * detInv;
te[6] = (n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44) * detInv;
te[7] = (n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43) * detInv;
te[8] = t13 * detInv;
te[9] = (n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44) * detInv;
te[10] = (n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44) * detInv;
te[11] = (n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43) * detInv;
te[12] = t14 * detInv;
te[13] = (n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34) * detInv;
te[14] = (n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34) * detInv;
te[15] = (n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33) * detInv;
return this;
},
scale: function(v )
{
var te = this.elements;
var x = v.x, y = v.y, z = v.z;
te[0] *= x; te[4] *= y; te[8] *= z;
te[1] *= x; te[5] *= y; te[9] *= z;
te[2] *= x; te[6] *= y; te[10] *= z;
te[3] *= x; te[7] *= y; te[11] *= z;
return this;
},
getMaxScaleOnAxis: function()
{
var te = this.elements;
var scaleXSq = te[0] * te[0] + te[1] * te[1] + te[2] * te[2];
var scaleYSq = te[4] * te[4] + te[5] * te[5] + te[6] * te[6];
var scaleZSq = te[8] * te[8] + te[9] * te[9] + te[10] * te[10];
return Math.sqrt(Math.max(scaleXSq, scaleYSq, scaleZSq));
},
makeTranslation: function(x, y, z )
{
this.set(
1, 0, 0, x,
0, 1, 0, y,
0, 0, 1, z,
0, 0, 0, 1
);
return this;
},
makeRotationX: function(theta )
{
var c = Math.cos(theta), s = Math.sin(theta);
this.set(
1, 0, 0, 0,
0, c, -s, 0,
0, s, c, 0,
0, 0, 0, 1
);
return this;
},
makeRotationY: function(theta )
{
var c = Math.cos(theta), s = Math.sin(theta);
this.set(
c, 0, s, 0,
0, 1, 0, 0,
-s, 0, c, 0,
0, 0, 0, 1
);
return this;
},
makeRotationZ: function(theta )
{
var c = Math.cos(theta), s = Math.sin(theta);
this.set(
c, -s, 0, 0,
s, c, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
);
return this;
},
makeRotationAxis: function(axis, angle )
{
// Based on http://www.gamedev.net/reference/articles/article1199.asp
var c = Math.cos(angle);
var s = Math.sin(angle);
var t = 1 - c;
var x = axis.x, y = axis.y, z = axis.z;
var tx = t * x, ty = t * y;
this.set(
tx * x + c, tx * y - s * z, tx * z + s * y, 0,
tx * y + s * z, ty * y + c, ty * z - s * x, 0,
tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
0, 0, 0, 1
);
return this;
},
makeScale: function(x, y, z )
{
this.set(
x, 0, 0, 0,
0, y, 0, 0,
0, 0, z, 0,
0, 0, 0, 1
);
return this;
},
makeShear: function(x, y, z )
{
this.set(
1, y, z, 0,
x, 1, z, 0,
x, y, 1, 0,
0, 0, 0, 1
);
return this;
},
compose: function(position, quaternion, scale )
{
var te = this.elements;
var x = quaternion._x, y = quaternion._y, z = quaternion._z, w = quaternion._w;
var x2 = x + x, y2 = y + y, z2 = z + z;
var xx = x * x2, xy = x * y2, xz = x * z2;
var yy = y * y2, yz = y * z2, zz = z * z2;
var wx = w * x2, wy = w * y2, wz = w * z2;
var sx = scale.x, sy = scale.y, sz = scale.z;
te[0] = (1 - (yy + zz)) * sx;
te[1] = (xy + wz) * sx;
te[2] = (xz - wy) * sx;
te[3] = 0;
te[4] = (xy - wz) * sy;
te[5] = (1 - (xx + zz)) * sy;
te[6] = (yz + wx) * sy;
te[7] = 0;
te[8] = (xz + wy) * sz;
te[9] = (yz - wx) * sz;
te[10] = (1 - (xx + yy)) * sz;
te[11] = 0;
te[12] = position.x;
te[13] = position.y;
te[14] = position.z;
te[15] = 1;
return this;
},
decompose: function()
{
var vector = new Vector3();
var matrix = new Matrix4();
return function decompose(position, quaternion, scale) {
var te = this.elements;
var sx = vector.set(te[0], te[1], te[2]).length();
var sy = vector.set(te[4], te[5], te[6]).length();
var sz = vector.set(te[8], te[9], te[10]).length();
// if determine is negative, we need to invert one scale
var det = this.determinant();
if (det < 0) sx = -sx;
position.x = te[12];
position.y = te[13];
position.z = te[14];
// scale the rotation part
matrix.copy(this);
var invSX = 1 / sx;
var invSY = 1 / sy;
var invSZ = 1 / sz;
matrix.elements[0] *= invSX;
matrix.elements[1] *= invSX;
matrix.elements[2] *= invSX;
matrix.elements[4] *= invSY;
matrix.elements[5] *= invSY;
matrix.elements[6] *= invSY;
matrix.elements[8] *= invSZ;
matrix.elements[9] *= invSZ;
matrix.elements[10] *= invSZ;
quaternion.setFromRotationMatrix(matrix);
scale.x = sx;
scale.y = sy;
scale.z = sz;
return this;
};
}
(),
makePerspective: function(left, right, top, bottom, near, far )
{
if (far === undefined)
{
console.warn('THREE.Matrix4: .makePerspective() has been redefined and has a new signature. Please check the docs.');
}
var te = this.elements;
var x = 2 * near / (right - left);
var y = 2 * near / (top - bottom);
var a = (right + left) / (right - left);
var b = (top + bottom) / (top - bottom);
var c = -(far + near) / (far - near);
var d = -2 * far * near / (far - near);
te[0] = x; te[4] = 0; te[8] = a; te[12] = 0;
te[1] = 0; te[5] = y; te[9] = b; te[13] = 0;
te[2] = 0; te[6] = 0; te[10] = c; te[14] = d;
te[3] = 0; te[7] = 0; te[11] = -1; te[15] = 0;
return this;
},
makeOrthographic: function(left, right, top, bottom, near, far )
{
var te = this.elements;
var w = 1.0 / (right - left);
var h = 1.0 / (top - bottom);
var p = 1.0 / (far - near);
var x = (right + left) * w;
var y = (top + bottom) * h;
var z = (far + near) * p;
te[0] = 2 * w; te[4] = 0; te[8] = 0; te[12] = -x;
te[1] = 0; te[5] = 2 * h; te[9] = 0; te[13] = -y;
te[2] = 0; te[6] = 0; te[10] = -2 * p; te[14] = -z;
te[3] = 0; te[7] = 0; te[11] = 0; te[15] = 1;
return this;
},
equals: function(matrix )
{
var te = this.elements;
var me = matrix.elements;
for (var i = 0; i < 16; i++)
{
if (te[i] !== me[i]) return false;
}
return true;
},
fromArray: function(array, offset )
{
if (offset === undefined) offset = 0;
for (var i = 0; i < 16; i++)
{
this.elements[i] = array[i + offset];
}
return this;
},
toArray: function(array, offset )
{
if (array === undefined) array = [];
if (offset === undefined) offset = 0;
var te = this.elements;
array[offset] = te[0];
array[offset + 1] = te[1];
array[offset + 2] = te[2];
array[offset + 3] = te[3];
array[offset + 4] = te[4];
array[offset + 5] = te[5];
array[offset + 6] = te[6];
array[offset + 7] = te[7];
array[offset + 8] = te[8];
array[offset + 9] = te[9];
array[offset + 10] = te[10];
array[offset + 11] = te[11];
array[offset + 12] = te[12];
array[offset + 13] = te[13];
array[offset + 14] = te[14];
array[offset + 15] = te[15];
return array;
}
}
}