/**
* @license
* Copyright The Closure Library Authors.
* SPDX-License-Identifier: Apache-2.0
*/
/**
* @fileoverview Implements quaternions and their conversion functions. In this
* implementation, quaternions are represented as 4 element vectors with the
* first 3 elements holding the imaginary components and the 4th element holding
* the real component.
*/
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');
/** @typedef {!goog.vec.Float32} */ goog.vec.Quaternion.Float32;
/** @typedef {!goog.vec.Float64} */ goog.vec.Quaternion.Float64;
/** @typedef {!goog.vec.Number} */ goog.vec.Quaternion.Number;
/** @typedef {!goog.vec.AnyType} */ goog.vec.Quaternion.AnyType;
/**
* Creates a Float32 quaternion, initialized to zero.
*
* @return {!goog.vec.Quaternion.Float32} The new quaternion.
*/
goog.vec.Quaternion.createFloat32 = goog.vec.Vec4.createFloat32;
/**
* Creates a Float64 quaternion, initialized to zero.
*
* @return {!goog.vec.Quaternion.Float64} The new quaternion.
*/
goog.vec.Quaternion.createFloat64 = goog.vec.Vec4.createFloat64;
/**
* Creates a Number quaternion, initialized to zero.
*
* @return {goog.vec.Quaternion.Number} The new quaternion.
*/
goog.vec.Quaternion.createNumber = goog.vec.Vec4.createNumber;
/**
* Creates a new Float32 quaternion initialized with the values from the
* supplied array.
*
* @param {!goog.vec.AnyType} vec The source 4 element array.
* @return {!goog.vec.Quaternion.Float32} The new quaternion.
*/
goog.vec.Quaternion.createFloat32FromArray =
goog.vec.Vec4.createFloat32FromArray;
/**
* Creates a new Float64 quaternion initialized with the values from the
* supplied array.
*
* @param {!goog.vec.AnyType} vec The source 4 element array.
* @return {!goog.vec.Quaternion.Float64} The new quaternion.
*/
goog.vec.Quaternion.createFloat64FromArray =
goog.vec.Vec4.createFloat64FromArray;
/**
* Creates a new Float32 quaternion initialized with the supplied values.
*
* @param {number} v0 The value for element at index 0.
* @param {number} v1 The value for element at index 1.
* @param {number} v2 The value for element at index 2.
* @param {number} v3 The value for element at index 3.
* @return {!goog.vec.Quaternion.Float32} The new quaternion.
*/
goog.vec.Quaternion.createFloat32FromValues =
goog.vec.Vec4.createFloat32FromValues;
/**
* Creates a new Float64 quaternion initialized with the supplied values.
*
* @param {number} v0 The value for element at index 0.
* @param {number} v1 The value for element at index 1.
* @param {number} v2 The value for element at index 2.
* @param {number} v3 The value for element at index 3.
* @return {!goog.vec.Quaternion.Float64} The new quaternion.
*/
goog.vec.Quaternion.createFloat64FromValues =
goog.vec.Vec4.createFloat64FromValues;
/**
* Creates a clone of the given Float32 quaternion.
*
* @param {!goog.vec.Quaternion.Float32} q The source quaternion.
* @return {!goog.vec.Quaternion.Float32} The new quaternion.
*/
goog.vec.Quaternion.cloneFloat32 = goog.vec.Vec4.cloneFloat32;
/**
* Creates a clone of the given Float64 quaternion.
*
* @param {!goog.vec.Quaternion.Float64} q The source quaternion.
* @return {!goog.vec.Quaternion.Float64} The new quaternion.
*/
goog.vec.Quaternion.cloneFloat64 = goog.vec.Vec4.cloneFloat64;
/**
* Creates a Float32 quaternion, initialized to the identity.
*
* @return {!goog.vec.Quaternion.Float32} The new quaternion.
*/
goog.vec.Quaternion.createIdentityFloat32 = function() {
'use strict';
const quat = goog.vec.Quaternion.createFloat32();
goog.vec.Quaternion.makeIdentity(quat);
return quat;
};
/**
* Creates a Float64 quaternion, initialized to the identity.
*
* @return {!goog.vec.Quaternion.Float64} The new quaternion.
*/
goog.vec.Quaternion.createIdentityFloat64 = function() {
'use strict';
const quat = goog.vec.Quaternion.createFloat64();
goog.vec.Quaternion.makeIdentity(quat);
return quat;
};
/**
* Initializes the quaternion with the given values.
*
* @param {!goog.vec.Quaternion.AnyType} q The quaternion to receive
* the values.
* @param {number} v0 The value for element at index 0.
* @param {number} v1 The value for element at index 1.
* @param {number} v2 The value for element at index 2.
* @param {number} v3 The value for element at index 3.
* @return {!goog.vec.Vec4.AnyType} return q so that operations can be
* chained together.
*/
goog.vec.Quaternion.setFromValues = goog.vec.Vec4.setFromValues;
/**
* Initializes the quaternion with the given array of values.
*
* @param {!goog.vec.Quaternion.AnyType} q The quaternion to receive
* the values.
* @param {!goog.vec.AnyType} values The array of values.
* @return {!goog.vec.Quaternion.AnyType} return q so that operations can be
* chained together.
*/
goog.vec.Quaternion.setFromArray = goog.vec.Vec4.setFromArray;
/**
* Adds the two quaternions.
*
* @param {!goog.vec.Quaternion.AnyType} quat0 The first addend.
* @param {!goog.vec.Quaternion.AnyType} quat1 The second addend.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result. May be quat0 or quat1.
*/
goog.vec.Quaternion.add = goog.vec.Vec4.add;
/**
* Negates a quaternion, storing the result into resultQuat.
*
* @param {!goog.vec.Quaternion.AnyType} quat0 The quaternion to negate.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result. May be quat0.
*/
goog.vec.Quaternion.negate = goog.vec.Vec4.negate;
/**
* Multiplies each component of quat0 with scalar storing the product into
* resultVec.
*
* @param {!goog.vec.Quaternion.AnyType} quat0 The source quaternion.
* @param {number} scalar The value to multiply with each component of quat0.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result. May be quat0.
*/
goog.vec.Quaternion.scale = goog.vec.Vec4.scale;
/**
* Returns the square magnitude of the given quaternion.
*
* @param {!goog.vec.Quaternion.AnyType} quat0 The quaternion.
* @return {number} The magnitude of the quaternion.
*/
goog.vec.Quaternion.magnitudeSquared = goog.vec.Vec4.magnitudeSquared;
/**
* Returns the magnitude of the given quaternion.
*
* @param {!goog.vec.Quaternion.AnyType} quat0 The quaternion.
* @return {number} The magnitude of the quaternion.
*/
goog.vec.Quaternion.magnitude = goog.vec.Vec4.magnitude;
/**
* Normalizes the given quaternion storing the result into resultVec.
*
* @param {!goog.vec.Quaternion.AnyType} quat0 The quaternion to
* normalize.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result. May be quat0.
*/
goog.vec.Quaternion.normalize = goog.vec.Vec4.normalize;
/**
* Computes the dot (scalar) product of two quaternions.
*
* @param {!goog.vec.Quaternion.AnyType} q0 The first quaternion.
* @param {!goog.vec.Quaternion.AnyType} q1 The second quaternion.
* @return {number} The scalar product.
*/
goog.vec.Quaternion.dot = goog.vec.Vec4.dot;
/**
* Computes the inverse of the quaternion in quat, storing the result into
* resultQuat.
*
* If the quaternion is already normalized, goog.vec.Quaternion.conjugate
* is faster than this function and produces the same result.
*
* @param {!goog.vec.Quaternion.AnyType} quat The quaternion to invert.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to receive
* the result.
* @return {!goog.vec.Quaternion.AnyType} Return resultQuat so that
* operations can be chained together.
*/
goog.vec.Quaternion.invert = function(quat, resultQuat) {
'use strict';
const a0 = quat[0];
const a1 = quat[1];
const a2 = quat[2];
const a3 = quat[3];
const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;
const invDot = dot ? 1.0 / dot : 0;
resultQuat[0] = -a0 * invDot;
resultQuat[1] = -a1 * invDot;
resultQuat[2] = -a2 * invDot;
resultQuat[3] = a3 * invDot;
return resultQuat;
};
/**
* Computes the conjugate of the quaternion in quat, storing the result into
* resultQuat.
*
* If the quaternion is normalized already, this function is faster than
* goog.Quaternion.inverse and produces the same result.
*
* @param {!goog.vec.Quaternion.AnyType} quat The source quaternion.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result.
* @return {!goog.vec.Quaternion.AnyType} Return resultQuat so that
* operations can be chained together.
*/
goog.vec.Quaternion.conjugate = function(quat, resultQuat) {
'use strict';
resultQuat[0] = -quat[0];
resultQuat[1] = -quat[1];
resultQuat[2] = -quat[2];
resultQuat[3] = quat[3];
return resultQuat;
};
/**
* Concatenates the two quaternions storing the result into resultQuat.
*
* @param {!goog.vec.Quaternion.AnyType} quat0 The first quaternion.
* @param {!goog.vec.Quaternion.AnyType} quat1 The second quaternion.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result.
* @return {!goog.vec.Quaternion.AnyType} Return resultQuat so that
* operations can be chained together.
*/
goog.vec.Quaternion.concat = function(quat0, quat1, resultQuat) {
'use strict';
const w0 = quat0[3];
const x0 = quat0[0];
const y0 = quat0[1];
const z0 = quat0[2];
const w1 = quat1[3];
const x1 = quat1[0];
const y1 = quat1[1];
const z1 = quat1[2];
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;
};
/**
* Makes the given quaternion the identity quaternion (0, 0, 0, 1).
*
* @param {!goog.vec.Quaternion.AnyType} quat The quaternion.
* @return {!goog.vec.Quaternion.AnyType} Return quat so that
* operations can be chained together.
*/
goog.vec.Quaternion.makeIdentity = function(quat) {
'use strict';
quat[0] = 0;
quat[1] = 0;
quat[2] = 0;
quat[3] = 1;
return quat;
};
/**
* Generates a unit quaternion from the given angle-axis rotation pair.
* The rotation axis is not required to be a unit vector, but should
* have non-zero length. The angle should be specified in radians.
*
* @param {number} angle The angle (in radians) to rotate about the axis.
* @param {!goog.vec.Quaternion.AnyType} axis Unit vector specifying the
* axis of rotation.
* @param {!goog.vec.Quaternion.AnyType} quat Unit quaternion to store the
* result.
* @return {!goog.vec.Quaternion.AnyType} Return quat so that
* operations can be chained together.
*/
goog.vec.Quaternion.fromAngleAxis = function(angle, axis, quat) {
'use strict';
// Normalize the axis of rotation.
goog.vec.Vec3.normalize(axis, axis);
const halfAngle = 0.5 * angle;
const sin = Math.sin(halfAngle);
goog.vec.Quaternion.setFromValues(
quat, sin * axis[0], sin * axis[1], sin * axis[2], Math.cos(halfAngle));
// Normalize the resulting quaternion.
goog.vec.Quaternion.normalize(quat, quat);
return quat;
};
/**
* Generates an angle-axis rotation pair from a unit quaternion.
* The quaternion is assumed to be of unit length. The calculated
* values are returned via the passed 'axis' object and the 'angle'
* number returned by the function itself. The returned rotation axis
* is a non-zero length unit vector, and the returned angle is in
* radians in the range of [-PI, +PI].
*
* @param {!goog.vec.Quaternion.AnyType} quat Unit quaternion to convert.
* @param {!goog.vec.Quaternion.AnyType} axis Vector to store the returned
* rotation axis.
* @return {number} angle Angle (in radians) to rotate about 'axis'.
* The range of the returned angle is [-PI, +PI].
*/
goog.vec.Quaternion.toAngleAxis = function(quat, axis) {
'use strict';
let angle = 2 * Math.acos(quat[3]);
const magnitude = Math.min(Math.max(1 - quat[3] * quat[3], 0), 1);
if (magnitude < goog.vec.EPSILON) {
// This is nearly an identity rotation, so just use a fixed +X axis.
goog.vec.Vec3.setFromValues(axis, 1, 0, 0);
} else {
// Compute the proper rotation axis.
goog.vec.Vec3.setFromValues(axis, quat[0], quat[1], quat[2]);
// Make sure the rotation axis is of unit length.
goog.vec.Vec3.normalize(axis, axis);
}
// Adjust the range of the returned angle to [-PI, +PI].
if (angle > Math.PI) {
angle -= 2 * Math.PI;
}
return angle;
};
/**
* Generates the quaternion from the given 3x3 rotation matrix.
*
* Perf: http://jsperf.com/conversion-of-3x3-matrix-to-quaternion
* http://jsperf.com/goog-vec-fromrotationmatrix3-a
*
* @param {!goog.vec.AnyType} matrix The source matrix.
* @param {!goog.vec.Quaternion.AnyType} quat The resulting quaternion.
* @return {!goog.vec.Quaternion.AnyType} Return quat so that
* operations can be chained together.
*/
goog.vec.Quaternion.fromRotationMatrix3 = function(matrix, quat) {
'use strict';
// Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
// article "Quaternion Calculus and Fast Animation".
const fTrace = matrix[0] + matrix[4] + matrix[8];
let fRoot;
if (fTrace > 0.0) {
// |w| > 1/2, may as well choose w > 1/2
fRoot = Math.sqrt(fTrace + 1.0); // 2w
quat[3] = 0.5 * fRoot;
fRoot = 0.5 / fRoot; // 1 / (4w)
quat[0] = (matrix[5] - matrix[7]) * fRoot;
quat[1] = (matrix[6] - matrix[2]) * fRoot;
quat[2] = (matrix[1] - matrix[3]) * fRoot;
} else {
// |w| <= 1/2
let i = 0;
if (matrix[4] > matrix[0]) i = 1;
if (matrix[8] > matrix[i * 3 + i]) i = 2;
const j = (i + 1) % 3;
const 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;
// Flip all signs if w is negative.
if (quat[3] < 0) {
quat[0] = -quat[0];
quat[1] = -quat[1];
quat[2] = -quat[2];
quat[3] = -quat[3];
}
}
return quat;
};
/**
* Generates the quaternion from the given 4x4 rotation matrix.
*
* Perf: http://jsperf.com/goog-vec-fromrotationmatrix4
*
* Implementation is the same as fromRotationMatrix3 but using indices from
* the top left 3x3 in a 4x4 matrix.
*
* @param {!goog.vec.AnyType} matrix The source matrix.
* @param {!goog.vec.Quaternion.AnyType} quat The resulting quaternion.
* @return {!goog.vec.Quaternion.AnyType} Return quat so that
* operations can be chained together.
*/
goog.vec.Quaternion.fromRotationMatrix4 = function(matrix, quat) {
'use strict';
const fTrace = matrix[0] + matrix[5] + matrix[10];
let fRoot;
if (fTrace > 0.0) {
// |w| > 1/2, may as well choose w > 1/2
fRoot = Math.sqrt(fTrace + 1.0); // 2w
quat[3] = 0.5 * fRoot;
fRoot = 0.5 / fRoot; // 1 / (4w)
quat[0] = (matrix[6] - matrix[9]) * fRoot;
quat[1] = (matrix[8] - matrix[2]) * fRoot;
quat[2] = (matrix[1] - matrix[4]) * fRoot;
} else {
// |w| <= 1/2
let i = 0;
if (matrix[5] > matrix[0]) i = 1;
if (matrix[10] > matrix[i * 4 + i]) i = 2;
const j = (i + 1) % 3;
const 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;
// Flip all signs if w is negative.
if (quat[3] < 0) {
quat[0] = -quat[0];
quat[1] = -quat[1];
quat[2] = -quat[2];
quat[3] = -quat[3];
}
}
return quat;
};
/**
* Generates the 3x3 rotation matrix from the given quaternion.
*
* @param {!goog.vec.Quaternion.AnyType} quat The source quaternion.
* @param {!goog.vec.AnyType} matrix The resulting matrix.
* @return {!goog.vec.AnyType} Return resulting matrix so that
* operations can be chained together.
*/
goog.vec.Quaternion.toRotationMatrix3 = function(quat, matrix) {
'use strict';
const w = quat[3];
const x = quat[0];
const y = quat[1];
const z = quat[2];
const x2 = 2 * x;
const y2 = 2 * y;
const z2 = 2 * z;
const wx = x2 * w;
const wy = y2 * w;
const wz = z2 * w;
const xx = x2 * x;
const xy = y2 * x;
const xz = z2 * x;
const yy = y2 * y;
const yz = z2 * y;
const 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;
};
/**
* Generates the 4x4 rotation matrix from the given quaternion.
*
* @param {!goog.vec.Quaternion.AnyType} quat The source quaternion.
* @param {!goog.vec.AnyType} matrix The resulting matrix.
* @return {!goog.vec.AnyType} Return resulting matrix so that
* operations can be chained together.
*/
goog.vec.Quaternion.toRotationMatrix4 = function(quat, matrix) {
'use strict';
const w = quat[3];
const x = quat[0];
const y = quat[1];
const z = quat[2];
const x2 = 2 * x;
const y2 = 2 * y;
const z2 = 2 * z;
const wx = x2 * w;
const wy = y2 * w;
const wz = z2 * w;
const xx = x2 * x;
const xy = y2 * x;
const xz = z2 * x;
const yy = y2 * y;
const yz = z2 * y;
const 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;
};
/**
* Rotates a quaternion by the given angle about the X axis.
*
* @param {!goog.vec.Quaternion.AnyType} quat The quaternion.
* @param {number} angle The angle in radians.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result.
* @return {!goog.vec.Quaternion.AnyType} Return resultQuat so that
* operations can be chained together.
*/
goog.vec.Quaternion.rotateX = function(quat, angle, resultQuat) {
'use strict';
angle *= 0.5;
const aw = quat[3];
const ax = quat[0];
const ay = quat[1];
const az = quat[2];
const bw = Math.cos(angle);
const bx = Math.sin(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;
};
/**
* Rotates a quaternion by the given angle about the Y axis.
*
* @param {!goog.vec.Quaternion.AnyType} quat The quaternion.
* @param {number} angle The angle in radians.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result.
* @return {!goog.vec.Quaternion.AnyType} Return resultQuat so that
* operations can be chained together.
*/
goog.vec.Quaternion.rotateY = function(quat, angle, resultQuat) {
'use strict';
angle *= 0.5;
const aw = quat[3];
const ax = quat[0];
const ay = quat[1];
const az = quat[2];
const bw = Math.cos(angle);
const by = Math.sin(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;
};
/**
* Rotates a quaternion by the given angle about the Z axis.
*
* @param {!goog.vec.Quaternion.AnyType} quat The quaternion.
* @param {number} angle The angle in radians.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result.
* @return {!goog.vec.Quaternion.AnyType} Return resultQuat so that
* operations can be chained together.
*/
goog.vec.Quaternion.rotateZ = function(quat, angle, resultQuat) {
'use strict';
angle *= 0.5;
const aw = quat[3];
const ax = quat[0];
const ay = quat[1];
const az = quat[2];
const bw = Math.cos(angle);
const bz = Math.sin(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;
};
/**
* Transforms a vec with a quaternion. Works on both vec3s and vec4s.
*
* @param {!goog.vec.AnyType} vec The vec to transform.
* @param {!goog.vec.Quaternion.AnyType} quat The quaternion.
* @param {!goog.vec.AnyType} resultVec The vec to receive the result.
* @return {!goog.vec.AnyType} Return resultVec so that operations can be
* chained together. Note that the caller is responsible for type-casting.
*/
goog.vec.Quaternion.transformVec = function(vec, quat, resultVec) {
'use strict';
const x = vec[0];
const y = vec[1];
const z = vec[2];
const qw = quat[3];
const qx = quat[0];
const qy = quat[1];
const qz = quat[2];
// Calculate quat * vec.
const ix = qw * x + qy * z - qz * y;
const iy = qw * y + qz * x - qx * z;
const iz = qw * z + qx * y - qy * x;
const iw = -qx * x - qy * y - qz * z;
// Calculate result * inverse quat.
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;
};
/**
* Computes the spherical linear interpolated value from the given quaternions
* q0 and q1 according to the coefficient t. The resulting quaternion is stored
* in resultQuat.
*
* @param {!goog.vec.Quaternion.AnyType} q0 The first quaternion.
* @param {!goog.vec.Quaternion.AnyType} q1 The second quaternion.
* @param {number} t The interpolating coefficient.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the result.
* @return {!goog.vec.Quaternion.AnyType} Return resultQuat so that
* operations can be chained together.
*/
goog.vec.Quaternion.slerp = function(q0, q1, t, resultQuat) {
'use strict';
// Compute the dot product between q0 and q1 (cos of the angle between q0 and
// q1). If it's outside the interval [-1,1], then the arccos is not defined.
// The usual reason for this is that q0 and q1 are colinear. In this case
// the angle between the two is zero, so just return q1.
let cosVal = goog.vec.Quaternion.dot(q0, q1);
if (cosVal > 1 || cosVal < -1) {
goog.vec.Vec4.setFromArray(resultQuat, q1);
return resultQuat;
}
// Quaternions are a double cover on the space of rotations. That is, q and -q
// represent the same rotation. Thus we have two possibilities when
// interpolating between q0 and q1: going the short way or the long way. We
// prefer the short way since that is the likely expectation from users.
let factor = 1;
if (cosVal < 0) {
factor = -1;
cosVal = -cosVal;
}
// Compute the angle between q0 and q1. If it's very small, then just return
// q1 to avoid a very large denominator below.
const angle = Math.acos(cosVal);
if (angle <= goog.vec.EPSILON) {
goog.vec.Vec4.setFromArray(resultQuat, q1);
return resultQuat;
}
// Compute the coefficients and interpolate.
const invSinVal = 1 / Math.sin(angle);
const c0 = Math.sin((1 - t) * angle) * invSinVal;
const 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;
};
/**
* Compute the simple linear interpolation of the two quaternions q0 and q1
* according to the coefficient t. The resulting quaternion is stored in
* resultVec.
*
* @param {!goog.vec.Quaternion.AnyType} q0 The first quaternion.
* @param {!goog.vec.Quaternion.AnyType} q1 The second quaternion.
* @param {number} t The interpolation factor.
* @param {!goog.vec.Quaternion.AnyType} resultQuat The quaternion to
* receive the results (may be q0 or q1).
*/
goog.vec.Quaternion.nlerp = goog.vec.Vec4.lerp;
Codebase Browser
chromium