JSDoc: Source: vec3.js

# Source: vec3.js

    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);
      if(glMatrix.ARRAY_TYPE != Float32Array) {
        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;
      };
    })();