ogl/src/math/functions/Vec3Func.js

WebGL Library

const EPSILON = 0.000001;

/**
 * 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);
}

/**
 * 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;
}

/**
 * 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;
}

/**
 * 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 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 frame rate independant, 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} decay decay constant for interpolation. useful range between 1 and 25, from slow to fast.
 * @param {Number} dt delta time
 * @returns {vec3} out
 */
export function smoothLerp(out, a, b, decay, dt) {
    const exp = Math.exp(-decay * dt);
    let ax = a[0];
    let ay = a[1];
    let az = a[2];

    out[0] = b[0] + (ax - b[0]) * exp;
    out[1] = b[1] + (ay - b[1]) * exp;
    out[2] = b[2] + (az - b[2]) * exp;
    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;
}

/**
 * Same as above but doesn't apply translation.
 * Useful for rays.
 */
export function scaleRotateMat4(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) / w;
    out[1] = (m[1] * x + m[5] * y + m[9] * z) / w;
    out[2] = (m[2] * x + m[6] * y + m[10] * z) / 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
 *
 * @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 x = a[0],
        y = a[1],
        z = a[2];
    let qx = q[0],
        qy = q[1],
        qz = q[2],
        qw = q[3];

    let uvx = qy * z - qz * y;
    let uvy = qz * x - qx * z;
    let uvz = qx * y - qy * x;

    let uuvx = qy * uvz - qz * uvy;
    let uuvy = qz * uvx - qx * uvz;
    let uuvz = qx * uvy - qy * uvx;

    let w2 = qw * 2;
    uvx *= w2;
    uvy *= w2;
    uvz *= w2;

    uuvx *= 2;
    uuvy *= 2;
    uuvz *= 2;

    out[0] = x + uvx + uuvx;
    out[1] = y + uvy + uuvy;
    out[2] = z + uvz + uuvz;
    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 const angle = (function () {
    const tempA = [0, 0, 0];
    const tempB = [0, 0, 0];

    return function (a, b) {
        copy(tempA, a);
        copy(tempB, b);

        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 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];
}