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() { var 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 {ReadonlyVec3} 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 {ReadonlyVec3} a vector to calculate length of * @returns {Number} length of a */ export function length(a) { var x = a[0]; var y = a[1]; var z = a[2]; return Math.hypot(x, y, 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) { var 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 {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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 {ReadonlyVec3} 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 {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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 {ReadonlyVec3} 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 {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} b the second operand * @returns {Number} distance between a and b */ export function distance(a, b) { var x = b[0] - a[0]; var y = b[1] - a[1]; var z = b[2] - a[2]; return Math.hypot(x, y, z); } /** * Calculates the squared euclidian distance between two vec3's * * @param {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} b the second operand * @returns {Number} squared distance between a and b */ export function squaredDistance(a, b) { var x = b[0] - a[0]; var y = b[1] - a[1]; var z = b[2] - a[2]; return x * x + y * y + z * z; } /** * Calculates the squared length of a vec3 * * @param {ReadonlyVec3} a vector to calculate squared length of * @returns {Number} squared length of a */ export function squaredLength(a) { var x = a[0]; var y = a[1]; var z = a[2]; return x * x + y * y + z * z; } /** * Negates the components of a vec3 * * @param {vec3} out the receiving vector * @param {ReadonlyVec3} 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 {ReadonlyVec3} 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 {ReadonlyVec3} a vector to normalize * @returns {vec3} out */ export function normalize(out, a) { var x = a[0]; var y = a[1]; var 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} b the second operand * @returns {vec3} out */ export function cross(out, a, b) { var ax = a[0], ay = a[1], az = a[2]; var 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} 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) { var ax = a[0]; var ay = a[1]; var 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} b the second operand * @param {ReadonlyVec3} c the third operand * @param {ReadonlyVec3} 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) { var factorTimes2 = t * t; var factor1 = factorTimes2 * (2 * t - 3) + 1; var factor2 = factorTimes2 * (t - 2) + t; var factor3 = factorTimes2 * (t - 1); var 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 {ReadonlyVec3} a the first operand * @param {ReadonlyVec3} b the second operand * @param {ReadonlyVec3} c the third operand * @param {ReadonlyVec3} 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) { var inverseFactor = 1 - t; var inverseFactorTimesTwo = inverseFactor * inverseFactor; var factorTimes2 = t * t; var factor1 = inverseFactorTimesTwo * inverseFactor; var factor2 = 3 * t * inverseFactorTimesTwo; var factor3 = 3 * factorTimes2 * inverseFactor; var 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; var r = glMatrix.RANDOM() * 2.0 * Math.PI; var z = glMatrix.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 {ReadonlyVec3} a the vector to transform * @param {ReadonlyMat4} m matrix to transform with * @returns {vec3} out */ export function transformMat4(out, a, m) { var x = a[0], y = a[1], z = a[2]; var 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 {ReadonlyVec3} a the vector to transform * @param {ReadonlyMat3} m the 3x3 matrix to transform with * @returns {vec3} out */ export function transformMat3(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 * Can also be used for dual quaternions. (Multiply it with the real part) * * @param {vec3} out the receiving vector * @param {ReadonlyVec3} a the vector to transform * @param {ReadonlyQuat} q quaternion to transform with * @returns {vec3} out */ export function transformQuat(out, a, q) { // benchmarks: https://jsperf.com/quaternion-transform-vec3-implementations-fixed var qx = q[0], qy = q[1], qz = q[2], qw = q[3]; var x = a[0], y = a[1], z = a[2]; // var qvec = [qx, qy, qz]; // var uv = vec3.cross([], qvec, a); var uvx = qy * z - qz * y, uvy = qz * x - qx * z, uvz = qx * y - qy * x; // var uuv = vec3.cross([], qvec, uv); var uuvx = qy * uvz - qz * uvy, uuvy = qz * uvx - qx * uvz, uuvz = qx * uvy - qy * uvx; // vec3.scale(uv, uv, 2 * w); var 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 {ReadonlyVec3} a The vec3 point to rotate * @param {ReadonlyVec3} b The origin of the rotation * @param {Number} rad The angle of rotation in radians * @returns {vec3} out */ export function rotateX(out, a, b, rad) { 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(rad) - p[2] * Math.sin(rad); r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad); //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 {ReadonlyVec3} a The vec3 point to rotate * @param {ReadonlyVec3} b The origin of the rotation * @param {Number} rad The angle of rotation in radians * @returns {vec3} out */ export function rotateY(out, a, b, rad) { 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(rad) + p[0] * Math.cos(rad); r[1] = p[1]; r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad); //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 {ReadonlyVec3} a The vec3 point to rotate * @param {ReadonlyVec3} b The origin of the rotation * @param {Number} rad The angle of rotation in radians * @returns {vec3} out */ export function rotateZ(out, a, b, rad) { 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(rad) - p[1] * Math.sin(rad); r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad); 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 {ReadonlyVec3} a The first operand * @param {ReadonlyVec3} b The second operand * @returns {Number} The angle in radians */ export function angle(a, b) { var ax = a[0], ay = a[1], az = a[2], bx = b[0], by = b[1], bz = b[2], mag1 = Math.sqrt(ax * ax + ay * ay + az * az), mag2 = Math.sqrt(bx * bx + by * by + bz * bz), mag = mag1 * mag2, cosine = mag && dot(a, b) / mag; return Math.acos(Math.min(Math.max(cosine, -1), 1)); } /** * Set the components of a vec3 to zero * * @param {vec3} out the receiving vector * @returns {vec3} out */ export function zero(out) { out[0] = 0.0; out[1] = 0.0; out[2] = 0.0; return out; } /** * Returns a string representation of a vector * * @param {ReadonlyVec3} 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 {ReadonlyVec3} a The first vector. * @param {ReadonlyVec3} 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 {ReadonlyVec3} a The first vector. * @param {ReadonlyVec3} b The second vector. * @returns {Boolean} True if the vectors are equal, false otherwise. */ export function equals(a, b) { var a0 = a[0], a1 = a[1], a2 = a[2]; var 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 var sub = subtract; /** * Alias for {@link vec3.multiply} * @function */ export var mul = multiply; /** * Alias for {@link vec3.divide} * @function */ export var div = divide; /** * Alias for {@link vec3.distance} * @function */ export var dist = distance; /** * Alias for {@link vec3.squaredDistance} * @function */ export var sqrDist = squaredDistance; /** * Alias for {@link vec3.length} * @function */ export var len = length; /** * Alias for {@link vec3.squaredLength} * @function */ export var 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 var forEach = function () { var vec = 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; }; }();