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@@ -1323,27 +1323,31 @@ var BABYLON;
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return this;
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};
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Quaternion.prototype.toRotationMatrix = function (result) {
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- var x = this.x, y = this.y, z = this.z, w = this.w;
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- var x2 = x + x, y2 = y + y, z2 = z + z;
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- var xx = x * x2, xy = x * y2, xz = x * z2;
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- var yy = y * y2, yz = y * z2, zz = z * z2;
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- var wx = w * x2, wy = w * y2, wz = w * z2;
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- result.m[0] = 1 - (yy + zz);
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- result.m[4] = xy - wz;
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- result.m[8] = xz + wy;
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- result.m[1] = xy + wz;
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- result.m[5] = 1 - (xx + zz);
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- result.m[9] = yz - wx;
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- result.m[2] = xz - wy;
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- result.m[6] = yz + wx;
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- result.m[10] = 1 - (xx + yy);
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+ var xx = this.x * this.x;
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+ var yy = this.y * this.y;
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+ var zz = this.z * this.z;
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+ var xy = this.x * this.y;
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+ var zw = this.z * this.w;
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+ var zx = this.z * this.x;
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+ var yw = this.y * this.w;
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+ var yz = this.y * this.z;
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+ var xw = this.x * this.w;
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+ result.m[0] = 1.0 - (2.0 * (yy + zz));
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+ result.m[1] = 2.0 * (xy + zw);
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+ result.m[2] = 2.0 * (zx - yw);
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result.m[3] = 0;
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+ result.m[4] = 2.0 * (xy - zw);
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+ result.m[5] = 1.0 - (2.0 * (zz + xx));
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+ result.m[6] = 2.0 * (yz + xw);
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result.m[7] = 0;
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+ result.m[8] = 2.0 * (zx + yw);
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+ result.m[9] = 2.0 * (yz - xw);
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+ result.m[10] = 1.0 - (2.0 * (yy + xx));
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result.m[11] = 0;
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result.m[12] = 0;
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result.m[13] = 0;
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result.m[14] = 0;
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- result.m[15] = 1;
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+ result.m[15] = 1.0;
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return this;
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};
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Quaternion.prototype.fromRotationMatrix = function (matrix) {
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@@ -1357,46 +1361,40 @@ var BABYLON;
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return result;
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};
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Quaternion.FromRotationMatrixToRef = function (matrix, result) {
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- var absQ = Math.pow(matrix.determinant(), 1.0 / 3.0);
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- result.w = Math.sqrt(Math.max(0, absQ + matrix.m[0] + matrix.m[5] + matrix.m[10])) / 2;
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- result.x = Math.sqrt(Math.max(0, absQ + matrix.m[0] - matrix.m[5] - matrix.m[10])) / 2;
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- result.y = Math.sqrt(Math.max(0, absQ - matrix.m[0] + matrix.m[5] - matrix.m[10])) / 2;
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- result.z = Math.sqrt(Math.max(0, absQ - matrix.m[0] - matrix.m[5] + matrix.m[10])) / 2;
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- result.x = (matrix.m[6] - matrix.m[9]) < 0 ? -Math.abs(result.x) : Math.abs(result.x);
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- result.y = (matrix.m[8] - matrix.m[2]) < 0 ? -Math.abs(result.y) : Math.abs(result.y);
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- result.z = (matrix.m[1] - matrix.m[4]) < 0 ? -Math.abs(result.z) : Math.abs(result.z);
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- result.normalize();
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- //var data = matrix.m;
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- //var m11 = data[0], m12 = data[4], m13 = data[8];
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- //var m21 = data[1], m22 = data[5], m23 = data[9];
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- //var m31 = data[2], m32 = data[6], m33 = data[10];
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- //var trace = m11 + m22 + m33;
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- //var s;
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- //if (trace > 0) {
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- // s = 0.5 / Math.sqrt(trace + 1.0);
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- // result.w = 0.25 / s;
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- // result.x = (m32 - m23) * s;
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- // result.y = (m13 - m31) * s;
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- // result.z = (m21 - m12) * s;
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- //} else if (m11 > m22 && m11 > m33) {
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- // s = 2.0 * Math.sqrt(1.0 + m11 - m22 - m33);
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- // result.w = (m32 - m23) / s;
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- // result.x = 0.25 * s;
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- // result.y = (m12 + m21) / s;
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- // result.z = (m13 + m31) / s;
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- //} else if (m22 > m33) {
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- // s = 2.0 * Math.sqrt(1.0 + m22 - m11 - m33);
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- // result.w = (m13 - m31) / s;
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- // result.x = (m12 + m21) / s;
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- // result.y = 0.25 * s;
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- // result.z = (m23 + m32) / s;
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- //} else {
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- // s = 2.0 * Math.sqrt(1.0 + m33 - m11 - m22);
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- // result.w = (m21 - m12) / s;
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- // result.x = (m13 + m31) / s;
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- // result.y = (m23 + m32) / s;
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- // result.z = 0.25 * s;
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- //}
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+ var data = matrix.m;
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+ var m11 = data[0], m12 = data[4], m13 = data[8];
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+ var m21 = data[1], m22 = data[5], m23 = data[9];
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+ var m31 = data[2], m32 = data[6], m33 = data[10];
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+ var trace = m11 + m22 + m33;
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+ var s;
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+ if (trace > 0) {
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+ s = 0.5 / Math.sqrt(trace + 1.0);
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+ result.w = 0.25 / s;
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+ result.x = (m32 - m23) * s;
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+ result.y = (m13 - m31) * s;
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+ result.z = (m21 - m12) * s;
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+ }
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+ else if (m11 > m22 && m11 > m33) {
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+ s = 2.0 * Math.sqrt(1.0 + m11 - m22 - m33);
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+ result.w = (m32 - m23) / s;
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+ result.x = 0.25 * s;
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+ result.y = (m12 + m21) / s;
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+ result.z = (m13 + m31) / s;
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+ }
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+ else if (m22 > m33) {
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+ s = 2.0 * Math.sqrt(1.0 + m22 - m11 - m33);
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+ result.w = (m13 - m31) / s;
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+ result.x = (m12 + m21) / s;
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+ result.y = 0.25 * s;
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+ result.z = (m23 + m32) / s;
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+ }
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+ else {
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+ s = 2.0 * Math.sqrt(1.0 + m33 - m11 - m22);
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+ result.w = (m21 - m12) / s;
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+ result.x = (m13 + m31) / s;
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+ result.y = (m23 + m32) / s;
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+ result.z = 0.25 * s;
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+ }
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};
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Quaternion.Inverse = function (q) {
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return new Quaternion(-q.x, -q.y, -q.z, q.w);
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@@ -1456,63 +1454,27 @@ var BABYLON;
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result.z = Math.sin(halfGammaPlusAlpha) * Math.cos(halfBeta);
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result.w = Math.cos(halfGammaPlusAlpha) * Math.cos(halfBeta);
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};
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- // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/
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Quaternion.Slerp = function (left, right, amount) {
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- var cosHalfTheta = left.w * right.w + left.x * right.x + left.y * right.y + left.z * right.z;
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- var result = new Quaternion();
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- if (cosHalfTheta < 0) {
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- result.w = -right.w;
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- result.x = -right.x;
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- result.y = -right.y;
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- result.z = -right.z;
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- cosHalfTheta = -cosHalfTheta;
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+ var num2;
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+ var num3;
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+ var num = amount;
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+ var num4 = (((left.x * right.x) + (left.y * right.y)) + (left.z * right.z)) + (left.w * right.w);
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+ var flag = false;
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+ if (num4 < 0) {
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+ flag = true;
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+ num4 = -num4;
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+ }
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+ if (num4 > 0.999999) {
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+ num3 = 1 - num;
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+ num2 = flag ? -num : num;
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}
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else {
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- result.copyFrom(right);
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- }
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- if (Math.abs(cosHalfTheta) >= 1.0) {
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- result.w = left.w;
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- result.x = left.x;
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- result.y = left.y;
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- result.z = left.z;
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- return result;
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- }
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- var halfTheta = Math.acos(cosHalfTheta);
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- var sinHalfTheta = Math.sqrt(1.0 - cosHalfTheta * cosHalfTheta);
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- if (Math.abs(sinHalfTheta) < 0.001) {
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- result.w = 0.5 * (left.w + result.w);
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- result.x = 0.5 * (left.x + result.x);
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- result.y = 0.5 * (left.y + result.y);
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- result.z = 0.5 * (left.z + result.z);
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- return result;
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- }
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- var ratioA = Math.sin((1 - amount) * halfTheta) / sinHalfTheta;
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- var ratioB = Math.sin(amount * halfTheta) / sinHalfTheta;
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- result.w = (left.w * ratioA + result.w * ratioB);
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- result.x = (left.x * ratioA + result.x * ratioB);
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- result.y = (left.y * ratioA + result.y * ratioB);
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- result.z = (left.z * ratioA + result.z * ratioB);
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- return result;
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- //var num2;
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- //var num3;
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- //var num = amount;
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- //var num4 = (((left.x * right.x) + (left.y * right.y)) + (left.z * right.z)) + (left.w * right.w);
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- //var flag = false;
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- //if (num4 < 0) {
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- // flag = true;
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- // num4 = -num4;
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- //}
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- //if (num4 > 0.999999) {
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- // num3 = 1 - num;
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- // num2 = flag ? -num : num;
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- //}
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- //else {
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- // var num5 = Math.acos(num4);
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- // var num6 = (1.0 / Math.sin(num5));
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- // num3 = (Math.sin((1.0 - num) * num5)) * num6;
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- // num2 = flag ? ((-Math.sin(num * num5)) * num6) : ((Math.sin(num * num5)) * num6);
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- //}
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- //return new Quaternion((num3 * left.x) + (num2 * right.x), (num3 * left.y) + (num2 * right.y), (num3 * left.z) + (num2 * right.z), (num3 * left.w) + (num2 * right.w));
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+ var num5 = Math.acos(num4);
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+ var num6 = (1.0 / Math.sin(num5));
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+ num3 = (Math.sin((1.0 - num) * num5)) * num6;
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+ num2 = flag ? ((-Math.sin(num * num5)) * num6) : ((Math.sin(num * num5)) * num6);
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+ }
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+ return new Quaternion((num3 * left.x) + (num2 * right.x), (num3 * left.y) + (num2 * right.y), (num3 * left.z) + (num2 * right.z), (num3 * left.w) + (num2 * right.w));
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};
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return Quaternion;
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})();
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@@ -1963,6 +1925,20 @@ var BABYLON;
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Matrix.TranslationToRef = function (x, y, z, result) {
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Matrix.FromValuesToRef(1.0, 0, 0, 0, 0, 1.0, 0, 0, 0, 0, 1.0, 0, x, y, z, 1.0, result);
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};
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+ Matrix.Lerp = function (startValue, endValue, gradient) {
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+ var startScale = new Vector3(0, 0, 0);
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+ var startRotation = new Quaternion();
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+ var startTranslation = new Vector3(0, 0, 0);
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+ startValue.decompose(startScale, startRotation, startTranslation);
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+ var endScale = new Vector3(0, 0, 0);
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+ var endRotation = new Quaternion();
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+ var endTranslation = new Vector3(0, 0, 0);
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+ endValue.decompose(endScale, endRotation, endTranslation);
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+ var resultScale = Vector3.Lerp(startScale, endScale, gradient);
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+ var resultRotation = Quaternion.Slerp(startRotation, endRotation, gradient);
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+ var resultTranslation = Vector3.Lerp(startTranslation, endTranslation, gradient);
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+ return Matrix.Compose(resultScale, resultRotation, resultTranslation);
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+ };
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Matrix.LookAtLH = function (eye, target, up) {
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var result = Matrix.Zero();
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Matrix.LookAtLHToRef(eye, target, up, result);
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@@ -2131,20 +2107,6 @@ var BABYLON;
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result.m[14] = temp3 * plane.d;
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result.m[15] = 1.0;
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};
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- Matrix.Lerp = function (startValue, endValue, gradient) {
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- var startScale = new Vector3(0, 0, 0);
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- var startRotation = new Quaternion();
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- var startTranslation = new Vector3(0, 0, 0);
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- startValue.decompose(startScale, startRotation, startTranslation);
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- var endScale = new Vector3(0, 0, 0);
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- var endRotation = new Quaternion();
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- var endTranslation = new Vector3(0, 0, 0);
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- endValue.decompose(endScale, endRotation, endTranslation);
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- var resultScale = Vector3.Lerp(startScale, endScale, gradient);
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- var resultRotation = Quaternion.Slerp(startRotation, endRotation, gradient);
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- var resultTranslation = Vector3.Lerp(startTranslation, endTranslation, gradient);
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- return Matrix.Compose(resultScale, resultRotation, resultTranslation);
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- };
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Matrix._tempQuaternion = new Quaternion();
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Matrix._xAxis = Vector3.Zero();
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Matrix._yAxis = Vector3.Zero();
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David Catuhe