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<h1 class="page-title">Source: vec3.js</h1>
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<pre class="prettyprint source linenums"><code>import * as glMatrix from "./common.js";
/**
* 3 Dimensional Vector
* @module vec3
*/
/**
* Creates a new, empty vec3
*
* @returns {vec3} a new 3D vector
*/
export function create() {
let out = new glMatrix.ARRAY_TYPE(3);
out[0] = 0;
out[1] = 0;
out[2] = 0;
return out;
}
/**
* Creates a new vec3 initialized with values from an existing vector
*
* @param {vec3} a vector to clone
* @returns {vec3} a new 3D vector
*/
export function clone(a) {
var out = new glMatrix.ARRAY_TYPE(3);
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
return out;
}
/**
* Calculates the length of a vec3
*
* @param {vec3} a vector to calculate length of
* @returns {Number} length of a
*/
export function length(a) {
let x = a[0];
let y = a[1];
let z = a[2];
return Math.sqrt(x*x + y*y + z*z);
}
/**
* Creates a new vec3 initialized with the given values
*
* @param {Number} x X component
* @param {Number} y Y component
* @param {Number} z Z component
* @returns {vec3} a new 3D vector
*/
export function fromValues(x, y, z) {
let out = new glMatrix.ARRAY_TYPE(3);
out[0] = x;
out[1] = y;
out[2] = z;
return out;
}
/**
* Copy the values from one vec3 to another
*
* @param {vec3} out the receiving vector
* @param {vec3} a the source vector
* @returns {vec3} out
*/
export function copy(out, a) {
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
return out;
}
/**
* Set the components of a vec3 to the given values
*
* @param {vec3} out the receiving vector
* @param {Number} x X component
* @param {Number} y Y component
* @param {Number} z Z component
* @returns {vec3} out
*/
export function set(out, x, y, z) {
out[0] = x;
out[1] = y;
out[2] = z;
return out;
}
/**
* Adds two vec3's
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {vec3} out
*/
export function add(out, a, b) {
out[0] = a[0] + b[0];
out[1] = a[1] + b[1];
out[2] = a[2] + b[2];
return out;
}
/**
* Subtracts vector b from vector a
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {vec3} out
*/
export function subtract(out, a, b) {
out[0] = a[0] - b[0];
out[1] = a[1] - b[1];
out[2] = a[2] - b[2];
return out;
}
/**
* Multiplies two vec3's
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {vec3} out
*/
export function multiply(out, a, b) {
out[0] = a[0] * b[0];
out[1] = a[1] * b[1];
out[2] = a[2] * b[2];
return out;
}
/**
* Divides two vec3's
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {vec3} out
*/
export function divide(out, a, b) {
out[0] = a[0] / b[0];
out[1] = a[1] / b[1];
out[2] = a[2] / b[2];
return out;
}
/**
* Math.ceil the components of a vec3
*
* @param {vec3} out the receiving vector
* @param {vec3} a vector to ceil
* @returns {vec3} out
*/
export function ceil(out, a) {
out[0] = Math.ceil(a[0]);
out[1] = Math.ceil(a[1]);
out[2] = Math.ceil(a[2]);
return out;
}
/**
* Math.floor the components of a vec3
*
* @param {vec3} out the receiving vector
* @param {vec3} a vector to floor
* @returns {vec3} out
*/
export function floor(out, a) {
out[0] = Math.floor(a[0]);
out[1] = Math.floor(a[1]);
out[2] = Math.floor(a[2]);
return out;
}
/**
* Returns the minimum of two vec3's
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {vec3} out
*/
export function min(out, a, b) {
out[0] = Math.min(a[0], b[0]);
out[1] = Math.min(a[1], b[1]);
out[2] = Math.min(a[2], b[2]);
return out;
}
/**
* Returns the maximum of two vec3's
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {vec3} out
*/
export function max(out, a, b) {
out[0] = Math.max(a[0], b[0]);
out[1] = Math.max(a[1], b[1]);
out[2] = Math.max(a[2], b[2]);
return out;
}
/**
* Math.round the components of a vec3
*
* @param {vec3} out the receiving vector
* @param {vec3} a vector to round
* @returns {vec3} out
*/
export function round(out, a) {
out[0] = Math.round(a[0]);
out[1] = Math.round(a[1]);
out[2] = Math.round(a[2]);
return out;
}
/**
* Scales a vec3 by a scalar number
*
* @param {vec3} out the receiving vector
* @param {vec3} a the vector to scale
* @param {Number} b amount to scale the vector by
* @returns {vec3} out
*/
export function scale(out, a, b) {
out[0] = a[0] * b;
out[1] = a[1] * b;
out[2] = a[2] * b;
return out;
}
/**
* Adds two vec3's after scaling the second operand by a scalar value
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @param {Number} scale the amount to scale b by before adding
* @returns {vec3} out
*/
export function scaleAndAdd(out, a, b, scale) {
out[0] = a[0] + (b[0] * scale);
out[1] = a[1] + (b[1] * scale);
out[2] = a[2] + (b[2] * scale);
return out;
}
/**
* Calculates the euclidian distance between two vec3's
*
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {Number} distance between a and b
*/
export function distance(a, b) {
let x = b[0] - a[0];
let y = b[1] - a[1];
let z = b[2] - a[2];
return Math.sqrt(x*x + y*y + z*z);
}
/**
* Calculates the squared euclidian distance between two vec3's
*
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {Number} squared distance between a and b
*/
export function squaredDistance(a, b) {
let x = b[0] - a[0];
let y = b[1] - a[1];
let z = b[2] - a[2];
return x*x + y*y + z*z;
}
/**
* Calculates the squared length of a vec3
*
* @param {vec3} a vector to calculate squared length of
* @returns {Number} squared length of a
*/
export function squaredLength(a) {
let x = a[0];
let y = a[1];
let z = a[2];
return x*x + y*y + z*z;
}
/**
* Negates the components of a vec3
*
* @param {vec3} out the receiving vector
* @param {vec3} a vector to negate
* @returns {vec3} out
*/
export function negate(out, a) {
out[0] = -a[0];
out[1] = -a[1];
out[2] = -a[2];
return out;
}
/**
* Returns the inverse of the components of a vec3
*
* @param {vec3} out the receiving vector
* @param {vec3} a vector to invert
* @returns {vec3} out
*/
export function inverse(out, a) {
out[0] = 1.0 / a[0];
out[1] = 1.0 / a[1];
out[2] = 1.0 / a[2];
return out;
}
/**
* Normalize a vec3
*
* @param {vec3} out the receiving vector
* @param {vec3} a vector to normalize
* @returns {vec3} out
*/
export function normalize(out, a) {
let x = a[0];
let y = a[1];
let z = a[2];
let len = x*x + y*y + z*z;
if (len > 0) {
//TODO: evaluate use of glm_invsqrt here?
len = 1 / Math.sqrt(len);
out[0] = a[0] * len;
out[1] = a[1] * len;
out[2] = a[2] * len;
}
return out;
}
/**
* Calculates the dot product of two vec3's
*
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {Number} dot product of a and b
*/
export function dot(a, b) {
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}
/**
* Computes the cross product of two vec3's
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @returns {vec3} out
*/
export function cross(out, a, b) {
let ax = a[0], ay = a[1], az = a[2];
let bx = b[0], by = b[1], bz = b[2];
out[0] = ay * bz - az * by;
out[1] = az * bx - ax * bz;
out[2] = ax * by - ay * bx;
return out;
}
/**
* Performs a linear interpolation between two vec3's
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {vec3} out
*/
export function lerp(out, a, b, t) {
let ax = a[0];
let ay = a[1];
let az = a[2];
out[0] = ax + t * (b[0] - ax);
out[1] = ay + t * (b[1] - ay);
out[2] = az + t * (b[2] - az);
return out;
}
/**
* Performs a hermite interpolation with two control points
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @param {vec3} c the third operand
* @param {vec3} d the fourth operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {vec3} out
*/
export function hermite(out, a, b, c, d, t) {
let factorTimes2 = t * t;
let factor1 = factorTimes2 * (2 * t - 3) + 1;
let factor2 = factorTimes2 * (t - 2) + t;
let factor3 = factorTimes2 * (t - 1);
let factor4 = factorTimes2 * (3 - 2 * t);
out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4;
out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4;
out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4;
return out;
}
/**
* Performs a bezier interpolation with two control points
*
* @param {vec3} out the receiving vector
* @param {vec3} a the first operand
* @param {vec3} b the second operand
* @param {vec3} c the third operand
* @param {vec3} d the fourth operand
* @param {Number} t interpolation amount, in the range [0-1], between the two inputs
* @returns {vec3} out
*/
export function bezier(out, a, b, c, d, t) {
let inverseFactor = 1 - t;
let inverseFactorTimesTwo = inverseFactor * inverseFactor;
let factorTimes2 = t * t;
let factor1 = inverseFactorTimesTwo * inverseFactor;
let factor2 = 3 * t * inverseFactorTimesTwo;
let factor3 = 3 * factorTimes2 * inverseFactor;
let factor4 = factorTimes2 * t;
out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4;
out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4;
out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4;
return out;
}
/**
* Generates a random vector with the given scale
*
* @param {vec3} out the receiving vector
* @param {Number} [scale] Length of the resulting vector. If ommitted, a unit vector will be returned
* @returns {vec3} out
*/
export function random(out, scale) {
scale = scale || 1.0;
let r = glMatrix.RANDOM() * 2.0 * Math.PI;
let z = (glMatrix.RANDOM() * 2.0) - 1.0;
let zScale = Math.sqrt(1.0-z*z) * scale;
out[0] = Math.cos(r) * zScale;
out[1] = Math.sin(r) * zScale;
out[2] = z * scale;
return out;
}
/**
* Transforms the vec3 with a mat4.
* 4th vector component is implicitly '1'
*
* @param {vec3} out the receiving vector
* @param {vec3} a the vector to transform
* @param {mat4} m matrix to transform with
* @returns {vec3} out
*/
export function transformMat4(out, a, m) {
let x = a[0], y = a[1], z = a[2];
let w = m[3] * x + m[7] * y + m[11] * z + m[15];
w = w || 1.0;
out[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;
out[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;
out[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;
return out;
}
/**
* Transforms the vec3 with a mat3.
*
* @param {vec3} out the receiving vector
* @param {vec3} a the vector to transform
* @param {mat3} m the 3x3 matrix to transform with
* @returns {vec3} out
*/
export function transformMat3(out, a, m) {
let x = a[0], y = a[1], z = a[2];
out[0] = x * m[0] + y * m[3] + z * m[6];
out[1] = x * m[1] + y * m[4] + z * m[7];
out[2] = x * m[2] + y * m[5] + z * m[8];
return out;
}
/**
* Transforms the vec3 with a quat
* Can also be used for dual quaternions. (Multiply it with the real part)
*
* @param {vec3} out the receiving vector
* @param {vec3} a the vector to transform
* @param {quat} q quaternion to transform with
* @returns {vec3} out
*/
export function transformQuat(out, a, q) {
// benchmarks: https://jsperf.com/quaternion-transform-vec3-implementations-fixed
let qx = q[0], qy = q[1], qz = q[2], qw = q[3];
let x = a[0], y = a[1], z = a[2];
// var qvec = [qx, qy, qz];
// var uv = vec3.cross([], qvec, a);
let uvx = qy * z - qz * y,
uvy = qz * x - qx * z,
uvz = qx * y - qy * x;
// var uuv = vec3.cross([], qvec, uv);
let uuvx = qy * uvz - qz * uvy,
uuvy = qz * uvx - qx * uvz,
uuvz = qx * uvy - qy * uvx;
// vec3.scale(uv, uv, 2 * w);
let w2 = qw * 2;
uvx *= w2;
uvy *= w2;
uvz *= w2;
// vec3.scale(uuv, uuv, 2);
uuvx *= 2;
uuvy *= 2;
uuvz *= 2;
// return vec3.add(out, a, vec3.add(out, uv, uuv));
out[0] = x + uvx + uuvx;
out[1] = y + uvy + uuvy;
out[2] = z + uvz + uuvz;
return out;
}
/**
* Rotate a 3D vector around the x-axis
* @param {vec3} out The receiving vec3
* @param {vec3} a The vec3 point to rotate
* @param {vec3} b The origin of the rotation
* @param {Number} c The angle of rotation
* @returns {vec3} out
*/
export function rotateX(out, a, b, c){
let p = [], r=[];
//Translate point to the origin
p[0] = a[0] - b[0];
p[1] = a[1] - b[1];
p[2] = a[2] - b[2];
//perform rotation
r[0] = p[0];
r[1] = p[1]*Math.cos(c) - p[2]*Math.sin(c);
r[2] = p[1]*Math.sin(c) + p[2]*Math.cos(c);
//translate to correct position
out[0] = r[0] + b[0];
out[1] = r[1] + b[1];
out[2] = r[2] + b[2];
return out;
}
/**
* Rotate a 3D vector around the y-axis
* @param {vec3} out The receiving vec3
* @param {vec3} a The vec3 point to rotate
* @param {vec3} b The origin of the rotation
* @param {Number} c The angle of rotation
* @returns {vec3} out
*/
export function rotateY(out, a, b, c){
let p = [], r=[];
//Translate point to the origin
p[0] = a[0] - b[0];
p[1] = a[1] - b[1];
p[2] = a[2] - b[2];
//perform rotation
r[0] = p[2]*Math.sin(c) + p[0]*Math.cos(c);
r[1] = p[1];
r[2] = p[2]*Math.cos(c) - p[0]*Math.sin(c);
//translate to correct position
out[0] = r[0] + b[0];
out[1] = r[1] + b[1];
out[2] = r[2] + b[2];
return out;
}
/**
* Rotate a 3D vector around the z-axis
* @param {vec3} out The receiving vec3
* @param {vec3} a The vec3 point to rotate
* @param {vec3} b The origin of the rotation
* @param {Number} c The angle of rotation
* @returns {vec3} out
*/
export function rotateZ(out, a, b, c){
let p = [], r=[];
//Translate point to the origin
p[0] = a[0] - b[0];
p[1] = a[1] - b[1];
p[2] = a[2] - b[2];
//perform rotation
r[0] = p[0]*Math.cos(c) - p[1]*Math.sin(c);
r[1] = p[0]*Math.sin(c) + p[1]*Math.cos(c);
r[2] = p[2];
//translate to correct position
out[0] = r[0] + b[0];
out[1] = r[1] + b[1];
out[2] = r[2] + b[2];
return out;
}
/**
* Get the angle between two 3D vectors
* @param {vec3} a The first operand
* @param {vec3} b The second operand
* @returns {Number} The angle in radians
*/
export function angle(a, b) {
let tempA = fromValues(a[0], a[1], a[2]);
let tempB = fromValues(b[0], b[1], b[2]);
normalize(tempA, tempA);
normalize(tempB, tempB);
let cosine = dot(tempA, tempB);
if(cosine > 1.0) {
return 0;
}
else if(cosine < -1.0) {
return Math.PI;
} else {
return Math.acos(cosine);
}
}
/**
* Returns a string representation of a vector
*
* @param {vec3} a vector to represent as a string
* @returns {String} string representation of the vector
*/
export function str(a) {
return 'vec3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ')';
}
/**
* Returns whether or not the vectors have exactly the same elements in the same position (when compared with ===)
*
* @param {vec3} a The first vector.
* @param {vec3} b The second vector.
* @returns {Boolean} True if the vectors are equal, false otherwise.
*/
export function exactEquals(a, b) {
return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];
}
/**
* Returns whether or not the vectors have approximately the same elements in the same position.
*
* @param {vec3} a The first vector.
* @param {vec3} b The second vector.
* @returns {Boolean} True if the vectors are equal, false otherwise.
*/
export function equals(a, b) {
let a0 = a[0], a1 = a[1], a2 = a[2];
let b0 = b[0], b1 = b[1], b2 = b[2];
return (Math.abs(a0 - b0) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a0), Math.abs(b0)) &&
Math.abs(a1 - b1) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a1), Math.abs(b1)) &&
Math.abs(a2 - b2) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a2), Math.abs(b2)));
}
/**
* Alias for {@link vec3.subtract}
* @function
*/
export const sub = subtract;
/**
* Alias for {@link vec3.multiply}
* @function
*/
export const mul = multiply;
/**
* Alias for {@link vec3.divide}
* @function
*/
export const div = divide;
/**
* Alias for {@link vec3.distance}
* @function
*/
export const dist = distance;
/**
* Alias for {@link vec3.squaredDistance}
* @function
*/
export const sqrDist = squaredDistance;
/**
* Alias for {@link vec3.length}
* @function
*/
export const len = length;
/**
* Alias for {@link vec3.squaredLength}
* @function
*/
export const sqrLen = squaredLength;
/**
* Perform some operation over an array of vec3s.
*
* @param {Array} a the array of vectors to iterate over
* @param {Number} stride Number of elements between the start of each vec3. If 0 assumes tightly packed
* @param {Number} offset Number of elements to skip at the beginning of the array
* @param {Number} count Number of vec3s to iterate over. If 0 iterates over entire array
* @param {Function} fn Function to call for each vector in the array
* @param {Object} [arg] additional argument to pass to fn
* @returns {Array} a
* @function
*/
export const forEach = (function() {
let vec = create();
return function(a, stride, offset, count, fn, arg) {
let i, l;
if(!stride) {
stride = 3;
}
if(!offset) {
offset = 0;
}
if(count) {
l = Math.min((count * stride) + offset, a.length);
} else {
l = a.length;
}
for(i = offset; i < l; i += stride) {
vec[0] = a[i]; vec[1] = a[i+1]; vec[2] = a[i+2];
fn(vec, vec, arg);
a[i] = vec[0]; a[i+1] = vec[1]; a[i+2] = vec[2];
}
return a;
};
})();
</code></pre>
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