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- goog.provide('goog.vec.Quaternion');
- goog.provide('goog.vec.Quaternion.AnyType');
- goog.require('goog.vec');
- goog.require('goog.vec.Vec3');
- goog.require('goog.vec.Vec4');
- goog.vec.Quaternion.Float32;
- goog.vec.Quaternion.Float64;
- goog.vec.Quaternion.Number;
- goog.vec.Quaternion.AnyType;
- goog.vec.Quaternion.createFloat32 = goog.vec.Vec4.createFloat32;
- goog.vec.Quaternion.createFloat64 = goog.vec.Vec4.createFloat64;
- goog.vec.Quaternion.createNumber = goog.vec.Vec4.createNumber;
- goog.vec.Quaternion.createFloat32FromArray =
- goog.vec.Vec4.createFloat32FromArray;
- goog.vec.Quaternion.createFloat64FromArray =
- goog.vec.Vec4.createFloat64FromArray;
- goog.vec.Quaternion.createFloat32FromValues =
- goog.vec.Vec4.createFloat32FromValues;
- goog.vec.Quaternion.createFloat64FromValues =
- goog.vec.Vec4.createFloat64FromValues;
- goog.vec.Quaternion.cloneFloat32 = goog.vec.Vec4.cloneFloat32;
- goog.vec.Quaternion.cloneFloat64 = goog.vec.Vec4.cloneFloat64;
- goog.vec.Quaternion.createIdentityFloat32 = function() {
- var quat = goog.vec.Quaternion.createFloat32();
- goog.vec.Quaternion.makeIdentity(quat);
- return quat;
- };
- goog.vec.Quaternion.createIdentityFloat64 = function() {
- var quat = goog.vec.Quaternion.createFloat64();
- goog.vec.Quaternion.makeIdentity(quat);
- return quat;
- };
- goog.vec.Quaternion.setFromValues = goog.vec.Vec4.setFromValues;
- goog.vec.Quaternion.setFromArray = goog.vec.Vec4.setFromArray;
- goog.vec.Quaternion.add = goog.vec.Vec4.add;
- goog.vec.Quaternion.negate = goog.vec.Vec4.negate;
- goog.vec.Quaternion.scale = goog.vec.Vec4.scale;
- goog.vec.Quaternion.magnitudeSquared = goog.vec.Vec4.magnitudeSquared;
- goog.vec.Quaternion.magnitude = goog.vec.Vec4.magnitude;
- goog.vec.Quaternion.normalize = goog.vec.Vec4.normalize;
- goog.vec.Quaternion.dot = goog.vec.Vec4.dot;
- goog.vec.Quaternion.invert = function(quat, resultQuat) {
- var a0 = quat[0], a1 = quat[1], a2 = quat[2], a3 = quat[3];
- var dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;
- var invDot = dot ? 1.0 / dot : 0;
- resultQuat[0] = -a0 * invDot;
- resultQuat[1] = -a1 * invDot;
- resultQuat[2] = -a2 * invDot;
- resultQuat[3] = a3 * invDot;
- return resultQuat;
- };
- goog.vec.Quaternion.conjugate = function(quat, resultQuat) {
- resultQuat[0] = -quat[0];
- resultQuat[1] = -quat[1];
- resultQuat[2] = -quat[2];
- resultQuat[3] = quat[3];
- return resultQuat;
- };
- goog.vec.Quaternion.concat = function(quat0, quat1, resultQuat) {
- var x0 = quat0[0], y0 = quat0[1], z0 = quat0[2], w0 = quat0[3];
- var x1 = quat1[0], y1 = quat1[1], z1 = quat1[2], w1 = quat1[3];
- resultQuat[0] = w0 * x1 + x0 * w1 + y0 * z1 - z0 * y1;
- resultQuat[1] = w0 * y1 - x0 * z1 + y0 * w1 + z0 * x1;
- resultQuat[2] = w0 * z1 + x0 * y1 - y0 * x1 + z0 * w1;
- resultQuat[3] = w0 * w1 - x0 * x1 - y0 * y1 - z0 * z1;
- return resultQuat;
- };
- goog.vec.Quaternion.makeIdentity = function(quat) {
- quat[0] = 0;
- quat[1] = 0;
- quat[2] = 0;
- quat[3] = 1;
- return quat;
- };
- goog.vec.Quaternion.fromAngleAxis = function(angle, axis, quat) {
-
- goog.vec.Vec3.normalize(axis, axis);
- var halfAngle = 0.5 * angle;
- var sin = Math.sin(halfAngle);
- goog.vec.Quaternion.setFromValues(
- quat, sin * axis[0], sin * axis[1], sin * axis[2], Math.cos(halfAngle));
-
- goog.vec.Quaternion.normalize(quat, quat);
- return quat;
- };
- goog.vec.Quaternion.toAngleAxis = function(quat, axis) {
- var angle = 2 * Math.acos(quat[3]);
- var magnitude = Math.min(Math.max(1 - quat[3] * quat[3], 0), 1);
- if (magnitude < goog.vec.EPSILON) {
-
- goog.vec.Vec3.setFromValues(axis, 1, 0, 0);
- } else {
-
- goog.vec.Vec3.setFromValues(axis, quat[0], quat[1], quat[2]);
-
- goog.vec.Vec3.normalize(axis, axis);
- }
-
- if (angle > Math.PI) {
- angle -= 2 * Math.PI;
- }
- return angle;
- };
- goog.vec.Quaternion.fromRotationMatrix3 = function(matrix, quat) {
-
-
- var fTrace = matrix[0] + matrix[4] + matrix[8];
- var fRoot;
- if (fTrace > 0.0) {
-
- fRoot = Math.sqrt(fTrace + 1.0);
- quat[3] = 0.5 * fRoot;
- fRoot = 0.5 / fRoot;
- quat[0] = (matrix[5] - matrix[7]) * fRoot;
- quat[1] = (matrix[6] - matrix[2]) * fRoot;
- quat[2] = (matrix[1] - matrix[3]) * fRoot;
- } else {
-
- var i = 0;
- if (matrix[4] > matrix[0]) i = 1;
- if (matrix[8] > matrix[i * 3 + i]) i = 2;
- var j = (i + 1) % 3;
- var k = (i + 2) % 3;
- fRoot = Math.sqrt(
- matrix[i * 3 + i] - matrix[j * 3 + j] - matrix[k * 3 + k] + 1.0);
- quat[i] = 0.5 * fRoot;
- fRoot = 0.5 / fRoot;
- quat[3] = (matrix[j * 3 + k] - matrix[k * 3 + j]) * fRoot;
- quat[j] = (matrix[j * 3 + i] + matrix[i * 3 + j]) * fRoot;
- quat[k] = (matrix[k * 3 + i] + matrix[i * 3 + k]) * fRoot;
-
- if (quat[3] < 0) {
- quat[0] = -quat[0];
- quat[1] = -quat[1];
- quat[2] = -quat[2];
- quat[3] = -quat[3];
- }
- }
- return quat;
- };
- goog.vec.Quaternion.fromRotationMatrix4 = function(matrix, quat) {
- var fTrace = matrix[0] + matrix[5] + matrix[10];
- var fRoot;
- if (fTrace > 0.0) {
-
- fRoot = Math.sqrt(fTrace + 1.0);
- quat[3] = 0.5 * fRoot;
- fRoot = 0.5 / fRoot;
- quat[0] = (matrix[6] - matrix[9]) * fRoot;
- quat[1] = (matrix[8] - matrix[2]) * fRoot;
- quat[2] = (matrix[1] - matrix[4]) * fRoot;
- } else {
-
- var i = 0;
- if (matrix[5] > matrix[0]) i = 1;
- if (matrix[10] > matrix[i * 4 + i]) i = 2;
- var j = (i + 1) % 3;
- var k = (i + 2) % 3;
- fRoot = Math.sqrt(
- matrix[i * 4 + i] - matrix[j * 4 + j] - matrix[k * 4 + k] + 1.0);
- quat[i] = 0.5 * fRoot;
- fRoot = 0.5 / fRoot;
- quat[3] = (matrix[j * 4 + k] - matrix[k * 4 + j]) * fRoot;
- quat[j] = (matrix[j * 4 + i] + matrix[i * 4 + j]) * fRoot;
- quat[k] = (matrix[k * 4 + i] + matrix[i * 4 + k]) * fRoot;
-
- if (quat[3] < 0) {
- quat[0] = -quat[0];
- quat[1] = -quat[1];
- quat[2] = -quat[2];
- quat[3] = -quat[3];
- }
- }
- return quat;
- };
- goog.vec.Quaternion.toRotationMatrix3 = function(quat, matrix) {
- var x = quat[0], y = quat[1], z = quat[2], w = quat[3];
- var x2 = 2 * x, y2 = 2 * y, z2 = 2 * z;
- var wx = x2 * w;
- var wy = y2 * w;
- var wz = z2 * w;
- var xx = x2 * x;
- var xy = y2 * x;
- var xz = z2 * x;
- var yy = y2 * y;
- var yz = z2 * y;
- var zz = z2 * z;
- matrix[0] = 1 - (yy + zz);
- matrix[1] = xy + wz;
- matrix[2] = xz - wy;
- matrix[3] = xy - wz;
- matrix[4] = 1 - (xx + zz);
- matrix[5] = yz + wx;
- matrix[6] = xz + wy;
- matrix[7] = yz - wx;
- matrix[8] = 1 - (xx + yy);
- return matrix;
- };
- goog.vec.Quaternion.toRotationMatrix4 = function(quat, matrix) {
- var x = quat[0], y = quat[1], z = quat[2], w = quat[3];
- var x2 = 2 * x, y2 = 2 * y, z2 = 2 * z;
- var wx = x2 * w;
- var wy = y2 * w;
- var wz = z2 * w;
- var xx = x2 * x;
- var xy = y2 * x;
- var xz = z2 * x;
- var yy = y2 * y;
- var yz = z2 * y;
- var zz = z2 * z;
- matrix[0] = 1 - (yy + zz);
- matrix[1] = xy + wz;
- matrix[2] = xz - wy;
- matrix[3] = 0;
- matrix[4] = xy - wz;
- matrix[5] = 1 - (xx + zz);
- matrix[6] = yz + wx;
- matrix[7] = 0;
- matrix[8] = xz + wy;
- matrix[9] = yz - wx;
- matrix[10] = 1 - (xx + yy);
- matrix[11] = 0;
- matrix[12] = 0;
- matrix[13] = 0;
- matrix[14] = 0;
- matrix[15] = 1;
- return matrix;
- };
- goog.vec.Quaternion.rotateX = function(quat, angle, resultQuat) {
- angle *= 0.5;
- var ax = quat[0], ay = quat[1], az = quat[2], aw = quat[3];
- var bx = Math.sin(angle), bw = Math.cos(angle);
- resultQuat[0] = ax * bw + aw * bx;
- resultQuat[1] = ay * bw + az * bx;
- resultQuat[2] = az * bw - ay * bx;
- resultQuat[3] = aw * bw - ax * bx;
- return resultQuat;
- };
- goog.vec.Quaternion.rotateY = function(quat, angle, resultQuat) {
- angle *= 0.5;
- var ax = quat[0], ay = quat[1], az = quat[2], aw = quat[3];
- var by = Math.sin(angle), bw = Math.cos(angle);
- resultQuat[0] = ax * bw - az * by;
- resultQuat[1] = ay * bw + aw * by;
- resultQuat[2] = az * bw + ax * by;
- resultQuat[3] = aw * bw - ay * by;
- return resultQuat;
- };
- goog.vec.Quaternion.rotateZ = function(quat, angle, resultQuat) {
- angle *= 0.5;
- var ax = quat[0], ay = quat[1], az = quat[2], aw = quat[3];
- var bz = Math.sin(angle), bw = Math.cos(angle);
- resultQuat[0] = ax * bw + ay * bz;
- resultQuat[1] = ay * bw - ax * bz;
- resultQuat[2] = az * bw + aw * bz;
- resultQuat[3] = aw * bw - az * bz;
- return resultQuat;
- };
- goog.vec.Quaternion.transformVec = function(vec, quat, resultVec) {
- var x = vec[0], y = vec[1], z = vec[2];
- var qx = quat[0], qy = quat[1], qz = quat[2], qw = quat[3];
-
- var ix = qw * x + qy * z - qz * y;
- var iy = qw * y + qz * x - qx * z;
- var iz = qw * z + qx * y - qy * x;
- var iw = -qx * x - qy * y - qz * z;
-
- resultVec[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
- resultVec[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
- resultVec[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
- return resultVec;
- };
- goog.vec.Quaternion.slerp = function(q0, q1, t, resultQuat) {
-
-
-
-
- var cosVal = goog.vec.Quaternion.dot(q0, q1);
- if (cosVal > 1 || cosVal < -1) {
- goog.vec.Vec4.setFromArray(resultQuat, q1);
- return resultQuat;
- }
-
-
-
-
- var factor = 1;
- if (cosVal < 0) {
- factor = -1;
- cosVal = -cosVal;
- }
-
-
- var angle = Math.acos(cosVal);
- if (angle <= goog.vec.EPSILON) {
- goog.vec.Vec4.setFromArray(resultQuat, q1);
- return resultQuat;
- }
-
- var invSinVal = 1 / Math.sin(angle);
- var c0 = Math.sin((1 - t) * angle) * invSinVal;
- var c1 = factor * Math.sin(t * angle) * invSinVal;
- resultQuat[0] = q0[0] * c0 + q1[0] * c1;
- resultQuat[1] = q0[1] * c0 + q1[1] * c1;
- resultQuat[2] = q0[2] * c0 + q1[2] * c1;
- resultQuat[3] = q0[3] * c0 + q1[3] * c1;
- return resultQuat;
- };
- goog.vec.Quaternion.nlerp = goog.vec.Vec4.lerp;
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