/* Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
import { GLMAT_RANDOM, GLMAT_ARRAY_TYPE } from './common';
/**
* @class 3 Dimensional Vector
* @name vec3
*/
var vec3 = {};
/**
* Creates a new, empty vec3
*
* @returns {vec3} a new 3D vector
*/
vec3.create = function() {
var out = new GLMAT_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
*/
vec3.clone = function(a) {
var out = new GLMAT_ARRAY_TYPE(3);
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
return out;
};
/**
* 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
*/
vec3.fromValues = function(x, y, z) {
var out = new GLMAT_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
*/
vec3.copy = function(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
*/
vec3.set = function(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
*/
vec3.add = function(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
*/
vec3.subtract = function(out, a, b) {
out[0] = a[0] - b[0];
out[1] = a[1] - b[1];
out[2] = a[2] - b[2];
return out;
};
/**
* Alias for {@link vec3.subtract}
* @function
*/
vec3.sub = vec3.subtract;
/**
* 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
*/
vec3.multiply = function(out, a, b) {
out[0] = a[0] * b[0];
out[1] = a[1] * b[1];
out[2] = a[2] * b[2];
return out;
};
/**
* Alias for {@link vec3.multiply}
* @function
*/
vec3.mul = vec3.multiply;
/**
* 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
*/
vec3.divide = function(out, a, b) {
out[0] = a[0] / b[0];
out[1] = a[1] / b[1];
out[2] = a[2] / b[2];
return out;
};
/**
* Alias for {@link vec3.divide}
* @function
*/
vec3.div = vec3.divide;
/**
* 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
*/
vec3.min = function(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
*/
vec3.max = function(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;
};
/**
* 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
*/
vec3.scale = function(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
*/
vec3.scaleAndAdd = function(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
*/
vec3.distance = function(a, b) {
var x = b[0] - a[0],
y = b[1] - a[1],
z = b[2] - a[2];
return Math.sqrt(x*x + y*y + z*z);
};
/**
* Alias for {@link vec3.distance}
* @function
*/
vec3.dist = vec3.distance;
/**
* 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
*/
vec3.squaredDistance = function(a, b) {
var x = b[0] - a[0],
y = b[1] - a[1],
z = b[2] - a[2];
return x*x + y*y + z*z;
};
/**
* Alias for {@link vec3.squaredDistance}
* @function
*/
vec3.sqrDist = vec3.squaredDistance;
/**
* Calculates the length of a vec3
*
* @param {vec3} a vector to calculate length of
* @returns {Number} length of a
*/
vec3.length = function (a) {
var x = a[0],
y = a[1],
z = a[2];
return Math.sqrt(x*x + y*y + z*z);
};
/**
* Alias for {@link vec3.length}
* @function
*/
vec3.len = vec3.length;
/**
* Calculates the squared length of a vec3
*
* @param {vec3} a vector to calculate squared length of
* @returns {Number} squared length of a
*/
vec3.squaredLength = function (a) {
var x = a[0],
y = a[1],
z = a[2];
return x*x + y*y + z*z;
};
/**
* Alias for {@link vec3.squaredLength}
* @function
*/
vec3.sqrLen = vec3.squaredLength;
/**
* Negates the components of a vec3
*
* @param {vec3} out the receiving vector
* @param {vec3} a vector to negate
* @returns {vec3} out
*/
vec3.negate = function(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
*/
vec3.inverse = function(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
*/
vec3.normalize = function(out, a) {
var x = a[0],
y = a[1],
z = a[2];
var 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
*/
vec3.dot = function (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
*/
vec3.cross = function(out, a, b) {
var ax = a[0], ay = a[1], az = a[2],
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 between the two inputs
* @returns {vec3} out
*/
vec3.lerp = function (out, a, b, t) {
var ax = a[0],
ay = a[1],
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;
};
/**
* 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
*/
vec3.random = function (out, scale) {
scale = scale || 1.0;
var r = GLMAT_RANDOM() * 2.0 * Math.PI;
var z = (GLMAT_RANDOM() * 2.0) - 1.0;
var 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
*/
vec3.transformMat4 = function(out, a, m) {
var x = a[0], y = a[1], z = a[2],
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 {mat4} m the 3x3 matrix to transform with
* @returns {vec3} out
*/
vec3.transformMat3 = function(out, a, m) {
var 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
*
* @param {vec3} out the receiving vector
* @param {vec3} a the vector to transform
* @param {quat} q quaternion to transform with
* @returns {vec3} out
*/
vec3.transformQuat = function(out, a, q) {
// benchmarks: http://jsperf.com/quaternion-transform-vec3-implementations
var x = a[0], y = a[1], z = a[2],
qx = q[0], qy = q[1], qz = q[2], qw = q[3],
// calculate quat * vec
ix = qw * x + qy * z - qz * y,
iy = qw * y + qz * x - qx * z,
iz = qw * z + qx * y - qy * x,
iw = -qx * x - qy * y - qz * z;
// calculate result * inverse quat
out[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
out[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
out[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
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
*/
vec3.rotateX = function(out, a, b, c){
var 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
*/
vec3.rotateY = function(out, a, b, c){
var 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
*/
vec3.rotateZ = function(out, a, b, c){
var 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;
};
/**
* 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
*/
vec3.forEach = (function() {
var vec = vec3.create();
return function(a, stride, offset, count, fn, arg) {
var 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;
};
})();
/**
* 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
*/
vec3.angle = function(a, b) {
var tempA = vec3.fromValues(a[0], a[1], a[2]);
var tempB = vec3.fromValues(b[0], b[1], b[2]);
vec3.normalize(tempA, tempA);
vec3.normalize(tempB, tempB);
var cosine = vec3.dot(tempA, tempB);
if(cosine > 1.0){
return 0;
} else {
return Math.acos(cosine);
}
};
export default vec3;