/**
* @license
* Copyright The Closure Library Authors.
* SPDX-License-Identifier: Apache-2.0
*/
////////////////////////// NOTE ABOUT EDITING THIS FILE ///////////////////////
// //
// Any edits to this file must be applied to vec3f.js by running: //
// swap_type.sh vec3d.js > vec3f.js //
// //
////////////////////////// NOTE ABOUT EDITING THIS FILE ///////////////////////
/**
* @fileoverview Provides functions for operating on 3 element double (64bit)
* vectors.
*
* The last parameter will typically be the output object and an object
* can be both an input and output parameter to all methods except where
* noted.
*
* See the README for notes about the design and structure of the API
* (especially related to performance).
*/
goog.provide('goog.vec.vec3d');
goog.provide('goog.vec.vec3d.Type');
/** @suppress {extraRequire} */
goog.require('goog.vec');
/** @typedef {!goog.vec.Float64} */ goog.vec.vec3d.Type;
/**
* Creates a vec3d with all elements initialized to zero.
*
* @return {!goog.vec.vec3d.Type} The new vec3d.
*/
goog.vec.vec3d.create = function() {
'use strict';
return new Float64Array(3);
};
/**
* Creates a new vec3d initialized with the value from the given array.
*
* @param {!Array<number>} vec The source 3 element array.
* @return {!goog.vec.vec3d.Type} The new vec3d.
*/
goog.vec.vec3d.createFromArray = function(vec) {
'use strict';
const newVec = goog.vec.vec3d.create();
goog.vec.vec3d.setFromArray(newVec, vec);
return newVec;
};
/**
* Creates a new vec3d 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.
* @return {!goog.vec.vec3d.Type} The new vector.
*/
goog.vec.vec3d.createFromValues = function(v0, v1, v2) {
'use strict';
const vec = goog.vec.vec3d.create();
goog.vec.vec3d.setFromValues(vec, v0, v1, v2);
return vec;
};
/**
* Creates a clone of the given vec3d.
*
* @param {!goog.vec.vec3d.Type} vec The source vec3d.
* @return {!goog.vec.vec3d.Type} The new cloned vec3d.
*/
goog.vec.vec3d.clone = function(vec) {
'use strict';
const newVec = goog.vec.vec3d.create();
goog.vec.vec3d.setFromVec3d(newVec, vec);
return newVec;
};
/**
* Initializes the vector with the given values.
*
* @param {!goog.vec.vec3d.Type} vec The vector 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.
* @return {!goog.vec.vec3d.Type} Return vec so that operations can be
* chained together.
*/
goog.vec.vec3d.setFromValues = function(vec, v0, v1, v2) {
'use strict';
vec[0] = v0;
vec[1] = v1;
vec[2] = v2;
return vec;
};
/**
* Initializes vec3d vec from vec3d src.
*
* @param {!goog.vec.vec3d.Type} vec The destination vector.
* @param {!goog.vec.vec3d.Type} src The source vector.
* @return {!goog.vec.vec3d.Type} Return vec so that operations can be
* chained together.
*/
goog.vec.vec3d.setFromVec3d = function(vec, src) {
'use strict';
vec[0] = src[0];
vec[1] = src[1];
vec[2] = src[2];
return vec;
};
/**
* Initializes vec3d vec from vec3f src (typed as a Float32Array to
* avoid circular goog.requires).
*
* @param {!goog.vec.vec3d.Type} vec The destination vector.
* @param {Float32Array} src The source vector.
* @return {!goog.vec.vec3d.Type} Return vec so that operations can be
* chained together.
*/
goog.vec.vec3d.setFromVec3f = function(vec, src) {
'use strict';
vec[0] = src[0];
vec[1] = src[1];
vec[2] = src[2];
return vec;
};
/**
* Initializes vec3d vec from Array src.
*
* @param {!goog.vec.vec3d.Type} vec The destination vector.
* @param {Array<number>} src The source vector.
* @return {!goog.vec.vec3d.Type} Return vec so that operations can be
* chained together.
*/
goog.vec.vec3d.setFromArray = function(vec, src) {
'use strict';
vec[0] = src[0];
vec[1] = src[1];
vec[2] = src[2];
return vec;
};
/**
* Performs a component-wise addition of vec0 and vec1 together storing the
* result into resultVec.
*
* @param {!goog.vec.vec3d.Type} vec0 The first addend.
* @param {!goog.vec.vec3d.Type} vec1 The second addend.
* @param {!goog.vec.vec3d.Type} resultVec The vector to
* receive the result. May be vec0 or vec1.
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.add = function(vec0, vec1, resultVec) {
'use strict';
resultVec[0] = vec0[0] + vec1[0];
resultVec[1] = vec0[1] + vec1[1];
resultVec[2] = vec0[2] + vec1[2];
return resultVec;
};
/**
* Performs a component-wise subtraction of vec1 from vec0 storing the
* result into resultVec.
*
* @param {!goog.vec.vec3d.Type} vec0 The minuend.
* @param {!goog.vec.vec3d.Type} vec1 The subtrahend.
* @param {!goog.vec.vec3d.Type} resultVec The vector to
* receive the result. May be vec0 or vec1.
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.subtract = function(vec0, vec1, resultVec) {
'use strict';
resultVec[0] = vec0[0] - vec1[0];
resultVec[1] = vec0[1] - vec1[1];
resultVec[2] = vec0[2] - vec1[2];
return resultVec;
};
/**
* Negates vec0, storing the result into resultVec.
*
* @param {!goog.vec.vec3d.Type} vec0 The vector to negate.
* @param {!goog.vec.vec3d.Type} resultVec The vector to
* receive the result. May be vec0.
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.negate = function(vec0, resultVec) {
'use strict';
resultVec[0] = -vec0[0];
resultVec[1] = -vec0[1];
resultVec[2] = -vec0[2];
return resultVec;
};
/**
* Takes the absolute value of each component of vec0 storing the result in
* resultVec.
*
* @param {!goog.vec.vec3d.Type} vec0 The source vector.
* @param {!goog.vec.vec3d.Type} resultVec The vector to receive the result.
* May be vec0.
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.abs = function(vec0, resultVec) {
'use strict';
resultVec[0] = Math.abs(vec0[0]);
resultVec[1] = Math.abs(vec0[1]);
resultVec[2] = Math.abs(vec0[2]);
return resultVec;
};
/**
* Multiplies each component of vec0 with scalar storing the product into
* resultVec.
*
* @param {!goog.vec.vec3d.Type} vec0 The source vector.
* @param {number} scalar The value to multiply with each component of vec0.
* @param {!goog.vec.vec3d.Type} resultVec The vector to
* receive the result. May be vec0.
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.scale = function(vec0, scalar, resultVec) {
'use strict';
resultVec[0] = vec0[0] * scalar;
resultVec[1] = vec0[1] * scalar;
resultVec[2] = vec0[2] * scalar;
return resultVec;
};
/**
* Returns the magnitudeSquared of the given vector.
*
* @param {!goog.vec.vec3d.Type} vec0 The vector.
* @return {number} The magnitude of the vector.
*/
goog.vec.vec3d.magnitudeSquared = function(vec0) {
'use strict';
const x = vec0[0];
const y = vec0[1];
const z = vec0[2];
return x * x + y * y + z * z;
};
/**
* Returns the magnitude of the given vector.
*
* @param {!goog.vec.vec3d.Type} vec0 The vector.
* @return {number} The magnitude of the vector.
*/
goog.vec.vec3d.magnitude = function(vec0) {
'use strict';
const x = vec0[0];
const y = vec0[1];
const z = vec0[2];
return Math.sqrt(x * x + y * y + z * z);
};
/**
* Normalizes the given vector storing the result into resultVec.
*
* @param {!goog.vec.vec3d.Type} vec0 The vector to normalize.
* @param {!goog.vec.vec3d.Type} resultVec The vector to
* receive the result. May be vec0.
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.normalize = function(vec0, resultVec) {
'use strict';
const x = vec0[0];
const y = vec0[1];
const z = vec0[2];
const ilen = 1 / Math.sqrt(x * x + y * y + z * z);
resultVec[0] = x * ilen;
resultVec[1] = y * ilen;
resultVec[2] = z * ilen;
return resultVec;
};
/**
* Returns the scalar product of vectors v0 and v1.
*
* @param {!goog.vec.vec3d.Type} v0 The first vector.
* @param {!goog.vec.vec3d.Type} v1 The second vector.
* @return {number} The scalar product.
*/
goog.vec.vec3d.dot = function(v0, v1) {
'use strict';
return v0[0] * v1[0] + v0[1] * v1[1] + v0[2] * v1[2];
};
/**
* Computes the vector (cross) product of v0 and v1 storing the result into
* resultVec.
*
* @param {!goog.vec.vec3d.Type} v0 The first vector.
* @param {!goog.vec.vec3d.Type} v1 The second vector.
* @param {!goog.vec.vec3d.Type} resultVec The vector to receive the
* results. May be either v0 or v1.
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.cross = function(v0, v1, resultVec) {
'use strict';
const x0 = v0[0];
const y0 = v0[1];
const z0 = v0[2];
const x1 = v1[0];
const y1 = v1[1];
const z1 = v1[2];
resultVec[0] = y0 * z1 - z0 * y1;
resultVec[1] = z0 * x1 - x0 * z1;
resultVec[2] = x0 * y1 - y0 * x1;
return resultVec;
};
/**
* Returns the squared distance between two points.
*
* @param {!goog.vec.vec3d.Type} vec0 First point.
* @param {!goog.vec.vec3d.Type} vec1 Second point.
* @return {number} The squared distance between the points.
*/
goog.vec.vec3d.distanceSquared = function(vec0, vec1) {
'use strict';
const x = vec0[0] - vec1[0];
const y = vec0[1] - vec1[1];
const z = vec0[2] - vec1[2];
return x * x + y * y + z * z;
};
/**
* Returns the distance between two points.
*
* @param {!goog.vec.vec3d.Type} vec0 First point.
* @param {!goog.vec.vec3d.Type} vec1 Second point.
* @return {number} The distance between the points.
*/
goog.vec.vec3d.distance = function(vec0, vec1) {
'use strict';
return Math.sqrt(goog.vec.vec3d.distanceSquared(vec0, vec1));
};
/**
* Returns a unit vector pointing from one point to another.
* If the input points are equal then the result will be all zeros.
*
* @param {!goog.vec.vec3d.Type} vec0 Origin point.
* @param {!goog.vec.vec3d.Type} vec1 Target point.
* @param {!goog.vec.vec3d.Type} resultVec The vector to receive the
* results (may be vec0 or vec1).
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.direction = function(vec0, vec1, resultVec) {
'use strict';
const x = vec1[0] - vec0[0];
const y = vec1[1] - vec0[1];
const z = vec1[2] - vec0[2];
let d = Math.sqrt(x * x + y * y + z * z);
if (d) {
d = 1 / d;
resultVec[0] = x * d;
resultVec[1] = y * d;
resultVec[2] = z * d;
} else {
resultVec[0] = resultVec[1] = resultVec[2] = 0;
}
return resultVec;
};
/**
* Linearly interpolate from vec0 to v1 according to f. The value of f should be
* in the range [0..1] otherwise the results are undefined.
*
* @param {!goog.vec.vec3d.Type} v0 The first vector.
* @param {!goog.vec.vec3d.Type} v1 The second vector.
* @param {number} f The interpolation factor.
* @param {!goog.vec.vec3d.Type} resultVec The vector to receive the
* results (may be v0 or v1).
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.lerp = function(v0, v1, f, resultVec) {
'use strict';
const x = v0[0];
const y = v0[1];
const z = v0[2];
resultVec[0] = (v1[0] - x) * f + x;
resultVec[1] = (v1[1] - y) * f + y;
resultVec[2] = (v1[2] - z) * f + z;
return resultVec;
};
/**
* Perform a spherical linear interpolation from v0 to v1 according to f. The
* value of f should be in the range [0..1] otherwise the results are undefined.
*
* Slerp is normally used to interpolate quaternions, but there is a geometric
* formula for interpolating vectors directly, see "Geometric Slerp" in:
* https://en.wikipedia.org/wiki/Slerp.
*
* This interpolates the vectors' directions via slerp, but linearly
* interpolates the vectors' magnitudes.
*
* Results are undefined if v0 or v1 are of zero magnitude.
*
* @param {!goog.vec.vec3d.Type} v0 The first vector.
* @param {!goog.vec.vec3d.Type} v1 The second vector.
* @param {number} f The interpolation factor.
* @param {!goog.vec.vec3d.Type} resultVec The vector to receive the
* results (may be v0 or v1).
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.slerp = function(v0, v1, f, resultVec) {
'use strict';
const v0Magnitude = goog.vec.vec3d.magnitude(v0);
let v1Magnitude = goog.vec.vec3d.magnitude(v1);
let cosAngle = goog.vec.vec3d.dot(v0, v1) / (v0Magnitude * v1Magnitude);
// If v0 and v1 are almost the same direction, fall back on a straight lerp.
if (cosAngle > 1 - goog.vec.EPSILON) {
return goog.vec.vec3d.lerp(v0, v1, f, resultVec);
}
let angle = 0;
let sinAngle = 0;
// If v0 and v1 are opposite directions, pick an arbitrary 'mid' vector that
// is perpendicular to both, and slerp from v0 -> mid -> v1.
if (cosAngle < -1 + goog.vec.EPSILON) {
const mid = goog.vec.vec3d.create();
let magnitudeFactor = (v0Magnitude + v1Magnitude) / 2;
if (v0[0]) { // v0 not parallel to [0,0,1].
magnitudeFactor /= Math.sqrt(v0[0] * v0[0] + v0[1] + v0[1]);
mid[0] = -v0[1] * magnitudeFactor;
mid[1] = v0[0] * magnitudeFactor;
mid[2] = 0;
} else { // v0 not parallel to [1,0,0].
magnitudeFactor /= Math.sqrt(v0[2] * v0[2] + v0[1] + v0[1]);
mid[0] = 0;
mid[1] = -v0[2] * magnitudeFactor;
mid[2] = v0[1] * magnitudeFactor;
}
// Depending on f, slerp between either v0 and mid, or mid and v1.
if (f <= 0.5) {
v1Magnitude = v0Magnitude;
v1 = mid;
f *= 2;
} else {
v0 = mid;
f = 2 * f - 1;
}
angle = Math.PI / 2;
cosAngle = 0;
sinAngle = 1;
} else {
angle = Math.acos(cosAngle);
sinAngle = Math.sqrt(1 - cosAngle * cosAngle);
}
const coeff0 = (Math.sin((1 - f) * angle) / sinAngle) / v0Magnitude;
const coeff1 = (Math.sin(f * angle) / sinAngle) / v1Magnitude;
const magnitude = (1 - f) * v0Magnitude + f * v1Magnitude;
resultVec[0] = (v0[0] * coeff0 + v1[0] * coeff1) * magnitude;
resultVec[1] = (v0[1] * coeff0 + v1[1] * coeff1) * magnitude;
resultVec[2] = (v0[2] * coeff0 + v1[2] * coeff1) * magnitude;
return resultVec;
};
/**
* Compares the components of vec0 with the components of another vector or
* scalar, storing the larger values in resultVec.
*
* @param {!goog.vec.vec3d.Type} vec0 The source vector.
* @param {!goog.vec.vec3d.Type|number} limit The limit vector or scalar.
* @param {!goog.vec.vec3d.Type} resultVec The vector to receive the
* results (may be vec0 or limit).
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.max = function(vec0, limit, resultVec) {
'use strict';
if (typeof limit === 'number') {
resultVec[0] = Math.max(vec0[0], limit);
resultVec[1] = Math.max(vec0[1], limit);
resultVec[2] = Math.max(vec0[2], limit);
} else {
resultVec[0] = Math.max(vec0[0], limit[0]);
resultVec[1] = Math.max(vec0[1], limit[1]);
resultVec[2] = Math.max(vec0[2], limit[2]);
}
return resultVec;
};
/**
* Compares the components of vec0 with the components of another vector or
* scalar, storing the smaller values in resultVec.
*
* @param {!goog.vec.vec3d.Type} vec0 The source vector.
* @param {!goog.vec.vec3d.Type|number} limit The limit vector or scalar.
* @param {!goog.vec.vec3d.Type} resultVec The vector to receive the
* results (may be vec0 or limit).
* @return {!goog.vec.vec3d.Type} Return resultVec so that operations can be
* chained together.
*/
goog.vec.vec3d.min = function(vec0, limit, resultVec) {
'use strict';
if (typeof limit === 'number') {
resultVec[0] = Math.min(vec0[0], limit);
resultVec[1] = Math.min(vec0[1], limit);
resultVec[2] = Math.min(vec0[2], limit);
} else {
resultVec[0] = Math.min(vec0[0], limit[0]);
resultVec[1] = Math.min(vec0[1], limit[1]);
resultVec[2] = Math.min(vec0[2], limit[2]);
}
return resultVec;
};
/**
* Returns true if the components of v0 are equal to the components of v1.
*
* @param {!goog.vec.vec3d.Type} v0 The first vector.
* @param {!goog.vec.vec3d.Type} v1 The second vector.
* @return {boolean} True if the vectors are equal, false otherwise.
*/
goog.vec.vec3d.equals = function(v0, v1) {
'use strict';
return v0.length == v1.length && v0[0] == v1[0] && v0[1] == v1[1] &&
v0[2] == v1[2];
};
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