Update wmts-hidpi, add nicer-api-docs
This commit is contained in:
Andreas Hocevar
458
nicer-api-docs/closure-library/closure/goog/vec/quaternion.js
Normal file
458
nicer-api-docs/closure-library/closure/goog/vec/quaternion.js
Normal file
@@ -0,0 +1,458 @@
|
||||
// Copyright 2011 The Closure Library Authors. All Rights Reserved.
|
||||
//
|
||||
// Licensed under the Apache License, Version 2.0 (the "License");
|
||||
// you may not use this file except in compliance with the License.
|
||||
// You may obtain a copy of the License at
|
||||
//
|
||||
// http://www.apache.org/licenses/LICENSE-2.0
|
||||
//
|
||||
// Unless required by applicable law or agreed to in writing, software
|
||||
// distributed under the License is distributed on an "AS-IS" BASIS,
|
||||
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||||
// See the License for the specific language governing permissions and
|
||||
// limitations under the License.
|
||||
|
||||
|
||||
/**
|
||||
* @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.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;
|
||||
|
||||
|
||||
/**
|
||||
* 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 conjugate of the quaternion in quat storing the result into
|
||||
* resultQuat.
|
||||
*
|
||||
* @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 q so that
|
||||
* operations can be chained together.
|
||||
*/
|
||||
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;
|
||||
};
|
||||
|
||||
|
||||
/**
|
||||
* 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 q so that
|
||||
* operations can be chained together.
|
||||
*/
|
||||
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;
|
||||
};
|
||||
|
||||
|
||||
/**
|
||||
* 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 q so that
|
||||
* operations can be chained together.
|
||||
*/
|
||||
goog.vec.Quaternion.fromAngleAxis = function(angle, axis, quat) {
|
||||
// Normalize the axis of rotation.
|
||||
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));
|
||||
|
||||
// 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) {
|
||||
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) {
|
||||
// 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 rotation matrix.
|
||||
*
|
||||
* @param {goog.vec.Quaternion.AnyType} matrix The source matrix.
|
||||
* @param {goog.vec.Quaternion.AnyType} quat The resulting quaternion.
|
||||
* @return {!goog.vec.Quaternion.AnyType} Return q so that
|
||||
* operations can be chained together.
|
||||
*/
|
||||
goog.vec.Quaternion.fromRotationMatrix4 = function(matrix, quat) {
|
||||
var sx = matrix[0], sy = matrix[5], sz = matrix[10];
|
||||
quat[3] = Math.sqrt(Math.max(0, 1 + sx + sy + sz)) / 2;
|
||||
quat[0] = Math.sqrt(Math.max(0, 1 + sx - sy - sz)) / 2;
|
||||
quat[1] = Math.sqrt(Math.max(0, 1 - sx + sy - sz)) / 2;
|
||||
quat[2] = Math.sqrt(Math.max(0, 1 - sx - sy + sz)) / 2;
|
||||
|
||||
quat[0] = (matrix[6] - matrix[9] < 0) != (quat[0] < 0) ? -quat[0] : quat[0];
|
||||
quat[1] = (matrix[8] - matrix[2] < 0) != (quat[1] < 0) ? -quat[1] : quat[1];
|
||||
quat[2] = (matrix[1] - matrix[4] < 0) != (quat[2] < 0) ? -quat[2] : quat[2];
|
||||
return quat;
|
||||
};
|
||||
|
||||
|
||||
/**
|
||||
* Generates the 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) {
|
||||
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;
|
||||
};
|
||||
|
||||
|
||||
/**
|
||||
* 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 q so that
|
||||
* operations can be chained together.
|
||||
*/
|
||||
goog.vec.Quaternion.slerp = function(q0, q1, t, resultQuat) {
|
||||
// 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.
|
||||
var 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.
|
||||
var 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.
|
||||
var angle = Math.acos(cosVal);
|
||||
if (angle <= goog.vec.EPSILON) {
|
||||
goog.vec.Vec4.setFromArray(resultQuat, q1);
|
||||
return resultQuat;
|
||||
}
|
||||
|
||||
// Compute the coefficients and interpolate.
|
||||
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;
|
||||
};
|
||||
|
||||
|
||||
/**
|
||||
* 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;
|
||||
Reference in New Issue
Block a user