ogl/src/math/functions/Mat3Func.js

WebGL Library

const EPSILON = 0.000001;

/**
 * Copies the upper-left 3x3 values into the given mat3.
 *
 * @param {mat3} out the receiving 3x3 matrix
 * @param {mat4} a   the source 4x4 matrix
 * @returns {mat3} out
 */
export function fromMat4(out, a) {
    out[0] = a[0];
    out[1] = a[1];
    out[2] = a[2];
    out[3] = a[4];
    out[4] = a[5];
    out[5] = a[6];
    out[6] = a[8];
    out[7] = a[9];
    out[8] = a[10];
    return out;
}

/**
 * Calculates a 3x3 matrix from the given quaternion
 *
 * @param {mat3} out mat3 receiving operation result
 * @param {quat} q Quaternion to create matrix from
 *
 * @returns {mat3} out
 */
export function fromQuat(out, q) {
    let x = q[0],
        y = q[1],
        z = q[2],
        w = q[3];
    let x2 = x + x;
    let y2 = y + y;
    let z2 = z + z;

    let xx = x * x2;
    let yx = y * x2;
    let yy = y * y2;
    let zx = z * x2;
    let zy = z * y2;
    let zz = z * z2;
    let wx = w * x2;
    let wy = w * y2;
    let wz = w * z2;

    out[0] = 1 - yy - zz;
    out[3] = yx - wz;
    out[6] = zx + wy;

    out[1] = yx + wz;
    out[4] = 1 - xx - zz;
    out[7] = zy - wx;

    out[2] = zx - wy;
    out[5] = zy + wx;
    out[8] = 1 - xx - yy;

    return out;
}

/**
 * Copy the values from one mat3 to another
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
export function copy(out, a) {
    out[0] = a[0];
    out[1] = a[1];
    out[2] = a[2];
    out[3] = a[3];
    out[4] = a[4];
    out[5] = a[5];
    out[6] = a[6];
    out[7] = a[7];
    out[8] = a[8];
    return out;
}

/**
 * Set the components of a mat3 to the given values
 *
 * @param {mat3} out the receiving matrix
 * @returns {mat3} out
 */
export function set(out, m00, m01, m02, m10, m11, m12, m20, m21, m22) {
    out[0] = m00;
    out[1] = m01;
    out[2] = m02;
    out[3] = m10;
    out[4] = m11;
    out[5] = m12;
    out[6] = m20;
    out[7] = m21;
    out[8] = m22;
    return out;
}

/**
 * Set a mat3 to the identity matrix
 *
 * @param {mat3} out the receiving matrix
 * @returns {mat3} out
 */
export function identity(out) {
    out[0] = 1;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = 1;
    out[5] = 0;
    out[6] = 0;
    out[7] = 0;
    out[8] = 1;
    return out;
}

/**
 * Transpose the values of a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
export function transpose(out, a) {
    // If we are transposing ourselves we can skip a few steps but have to cache some values
    if (out === a) {
        let a01 = a[1],
            a02 = a[2],
            a12 = a[5];
        out[1] = a[3];
        out[2] = a[6];
        out[3] = a01;
        out[5] = a[7];
        out[6] = a02;
        out[7] = a12;
    } else {
        out[0] = a[0];
        out[1] = a[3];
        out[2] = a[6];
        out[3] = a[1];
        out[4] = a[4];
        out[5] = a[7];
        out[6] = a[2];
        out[7] = a[5];
        out[8] = a[8];
    }

    return out;
}

/**
 * Inverts a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
export function invert(out, a) {
    let a00 = a[0],
        a01 = a[1],
        a02 = a[2];
    let a10 = a[3],
        a11 = a[4],
        a12 = a[5];
    let a20 = a[6],
        a21 = a[7],
        a22 = a[8];

    let b01 = a22 * a11 - a12 * a21;
    let b11 = -a22 * a10 + a12 * a20;
    let b21 = a21 * a10 - a11 * a20;

    // Calculate the determinant
    let det = a00 * b01 + a01 * b11 + a02 * b21;

    if (!det) {
        return null;
    }
    det = 1.0 / det;

    out[0] = b01 * det;
    out[1] = (-a22 * a01 + a02 * a21) * det;
    out[2] = (a12 * a01 - a02 * a11) * det;
    out[3] = b11 * det;
    out[4] = (a22 * a00 - a02 * a20) * det;
    out[5] = (-a12 * a00 + a02 * a10) * det;
    out[6] = b21 * det;
    out[7] = (-a21 * a00 + a01 * a20) * det;
    out[8] = (a11 * a00 - a01 * a10) * det;
    return out;
}

/**
 * Calculates the determinant of a mat3
 *
 * @param {mat3} a the source matrix
 * @returns {Number} determinant of a
 */
export function determinant(a) {
    let a00 = a[0],
        a01 = a[1],
        a02 = a[2];
    let a10 = a[3],
        a11 = a[4],
        a12 = a[5];
    let a20 = a[6],
        a21 = a[7],
        a22 = a[8];

    return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
}

/**
 * Multiplies two mat3's
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @returns {mat3} out
 */
export function multiply(out, a, b) {
    let a00 = a[0],
        a01 = a[1],
        a02 = a[2];
    let a10 = a[3],
        a11 = a[4],
        a12 = a[5];
    let a20 = a[6],
        a21 = a[7],
        a22 = a[8];

    let b00 = b[0],
        b01 = b[1],
        b02 = b[2];
    let b10 = b[3],
        b11 = b[4],
        b12 = b[5];
    let b20 = b[6],
        b21 = b[7],
        b22 = b[8];

    out[0] = b00 * a00 + b01 * a10 + b02 * a20;
    out[1] = b00 * a01 + b01 * a11 + b02 * a21;
    out[2] = b00 * a02 + b01 * a12 + b02 * a22;

    out[3] = b10 * a00 + b11 * a10 + b12 * a20;
    out[4] = b10 * a01 + b11 * a11 + b12 * a21;
    out[5] = b10 * a02 + b11 * a12 + b12 * a22;

    out[6] = b20 * a00 + b21 * a10 + b22 * a20;
    out[7] = b20 * a01 + b21 * a11 + b22 * a21;
    out[8] = b20 * a02 + b21 * a12 + b22 * a22;
    return out;
}

/**
 * Translate a mat3 by the given vector
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to translate
 * @param {vec2} v vector to translate by
 * @returns {mat3} out
 */
export function translate(out, a, v) {
    let a00 = a[0],
        a01 = a[1],
        a02 = a[2],
        a10 = a[3],
        a11 = a[4],
        a12 = a[5],
        a20 = a[6],
        a21 = a[7],
        a22 = a[8],
        x = v[0],
        y = v[1];

    out[0] = a00;
    out[1] = a01;
    out[2] = a02;

    out[3] = a10;
    out[4] = a11;
    out[5] = a12;

    out[6] = x * a00 + y * a10 + a20;
    out[7] = x * a01 + y * a11 + a21;
    out[8] = x * a02 + y * a12 + a22;
    return out;
}

/**
 * Rotates a mat3 by the given angle
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to rotate
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat3} out
 */
export function rotate(out, a, rad) {
    let a00 = a[0],
        a01 = a[1],
        a02 = a[2],
        a10 = a[3],
        a11 = a[4],
        a12 = a[5],
        a20 = a[6],
        a21 = a[7],
        a22 = a[8],
        s = Math.sin(rad),
        c = Math.cos(rad);

    out[0] = c * a00 + s * a10;
    out[1] = c * a01 + s * a11;
    out[2] = c * a02 + s * a12;

    out[3] = c * a10 - s * a00;
    out[4] = c * a11 - s * a01;
    out[5] = c * a12 - s * a02;

    out[6] = a20;
    out[7] = a21;
    out[8] = a22;
    return out;
}

/**
 * Scales the mat3 by the dimensions in the given vec2
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to rotate
 * @param {vec2} v the vec2 to scale the matrix by
 * @returns {mat3} out
 **/
export function scale(out, a, v) {
    let x = v[0],
        y = v[1];

    out[0] = x * a[0];
    out[1] = x * a[1];
    out[2] = x * a[2];

    out[3] = y * a[3];
    out[4] = y * a[4];
    out[5] = y * a[5];

    out[6] = a[6];
    out[7] = a[7];
    out[8] = a[8];
    return out;
}

/**
 * Calculates a 3x3 normal matrix (transpose inverse) from the 4x4 matrix
 *
 * @param {mat3} out mat3 receiving operation result
 * @param {mat4} a Mat4 to derive the normal matrix from
 *
 * @returns {mat3} out
 */
export function normalFromMat4(out, a) {
    let a00 = a[0],
        a01 = a[1],
        a02 = a[2],
        a03 = a[3];
    let a10 = a[4],
        a11 = a[5],
        a12 = a[6],
        a13 = a[7];
    let a20 = a[8],
        a21 = a[9],
        a22 = a[10],
        a23 = a[11];
    let a30 = a[12],
        a31 = a[13],
        a32 = a[14],
        a33 = a[15];

    let b00 = a00 * a11 - a01 * a10;
    let b01 = a00 * a12 - a02 * a10;
    let b02 = a00 * a13 - a03 * a10;
    let b03 = a01 * a12 - a02 * a11;
    let b04 = a01 * a13 - a03 * a11;
    let b05 = a02 * a13 - a03 * a12;
    let b06 = a20 * a31 - a21 * a30;
    let b07 = a20 * a32 - a22 * a30;
    let b08 = a20 * a33 - a23 * a30;
    let b09 = a21 * a32 - a22 * a31;
    let b10 = a21 * a33 - a23 * a31;
    let b11 = a22 * a33 - a23 * a32;

    // Calculate the determinant
    let det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

    if (!det) {
        return null;
    }
    det = 1.0 / det;

    out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
    out[1] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
    out[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det;

    out[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
    out[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
    out[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det;

    out[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
    out[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
    out[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det;

    return out;
}

/**
 * Generates a 2D projection matrix with the given bounds
 *
 * @param {mat3} out mat3 frustum matrix will be written into
 * @param {number} width Width of your gl context
 * @param {number} height Height of gl context
 * @returns {mat3} out
 */
export function projection(out, width, height) {
    out[0] = 2 / width;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = -2 / height;
    out[5] = 0;
    out[6] = -1;
    out[7] = 1;
    out[8] = 1;
    return out;
}

/**
 * Adds two mat3's
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @returns {mat3} 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];
    out[3] = a[3] + b[3];
    out[4] = a[4] + b[4];
    out[5] = a[5] + b[5];
    out[6] = a[6] + b[6];
    out[7] = a[7] + b[7];
    out[8] = a[8] + b[8];
    return out;
}

/**
 * Subtracts matrix b from matrix a
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @returns {mat3} 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];
    out[3] = a[3] - b[3];
    out[4] = a[4] - b[4];
    out[5] = a[5] - b[5];
    out[6] = a[6] - b[6];
    out[7] = a[7] - b[7];
    out[8] = a[8] - b[8];
    return out;
}

/**
 * Multiply each element of the matrix by a scalar.
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to scale
 * @param {Number} b amount to scale the matrix's elements by
 * @returns {mat3} out
 */
export function multiplyScalar(out, a, b) {
    out[0] = a[0] * b;
    out[1] = a[1] * b;
    out[2] = a[2] * b;
    out[3] = a[3] * b;
    out[4] = a[4] * b;
    out[5] = a[5] * b;
    out[6] = a[6] * b;
    out[7] = a[7] * b;
    out[8] = a[8] * b;
    return out;
}