three.js/src/math/Matrix3.js at dev · supermedium/three.js · GitHub

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/**

* Represents a 3x3 matrix.

* A Note on Row-Major and Column-Major Ordering:

* The constructor and {@link Matrix3#set} method take arguments in

* [row-major](https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order)

* order, while internally they are stored in the {@link Matrix3#elements} array in column-major order.

* This means that calling:

* ```js

* const m = new THREE.Matrix();

* m.set( 11, 12, 13,

* 21, 22, 23,

* 31, 32, 33 );

* ```

* will result in the elements array containing:

* ```js

* m.elements = [ 11, 21, 31,

* 12, 22, 32,

* 13, 23, 33 ];

* ```

* and internally all calculations are performed using column-major ordering.

* However, as the actual ordering makes no difference mathematically and

* most people are used to thinking about matrices in row-major order, the

* three.js documentation shows matrices in row-major order. Just bear in

* mind that if you are reading the source code, you'll have to take the

* transpose of any matrices outlined here to make sense of the calculations.

class Matrix3 {

static {

/**

* This flag can be used for type testing.

* @type {boolean}

* @readonly

* @default true

Matrix3.prototype.isMatrix3 = true;

}

/**

* Constructs a new 3x3 matrix. The arguments are supposed to be

* in row-major order. If no arguments are provided, the constructor

* initializes the matrix as an identity matrix.

* @param {number} [n11] - 1-1 matrix element.

* @param {number} [n12] - 1-2 matrix element.

* @param {number} [n13] - 1-3 matrix element.

* @param {number} [n21] - 2-1 matrix element.

* @param {number} [n22] - 2-2 matrix element.

* @param {number} [n23] - 2-3 matrix element.

* @param {number} [n31] - 3-1 matrix element.

* @param {number} [n32] - 3-2 matrix element.

* @param {number} [n33] - 3-3 matrix element.

constructor( n11, n12, n13, n21, n22, n23, n31, n32, n33 ) {

/**

* A column-major list of matrix values.

* @type {Array<number>}

this.elements = [

1, 0, 0,

0, 1, 0,

0, 0, 1

];

if ( n11 !== undefined ) {

this.set( n11, n12, n13, n21, n22, n23, n31, n32, n33 );

}

/**

* Sets the elements of the matrix.The arguments are supposed to be

* in row-major order.

* @param {number} [n11] - 1-1 matrix element.

* @param {number} [n12] - 1-2 matrix element.

* @param {number} [n13] - 1-3 matrix element.

* @param {number} [n21] - 2-1 matrix element.

* @param {number} [n22] - 2-2 matrix element.

* @param {number} [n23] - 2-3 matrix element.

* @param {number} [n31] - 3-1 matrix element.

* @param {number} [n32] - 3-2 matrix element.

* @param {number} [n33] - 3-3 matrix element.

* @return {Matrix3} A reference to this matrix.

set( n11, n12, n13, n21, n22, n23, n31, n32, n33 ) {

const te = this.elements;

te[ 0 ] = n11; te[ 1 ] = n21; te[ 2 ] = n31;

te[ 3 ] = n12; te[ 4 ] = n22; te[ 5 ] = n32;

te[ 6 ] = n13; te[ 7 ] = n23; te[ 8 ] = n33;

return this;

}

/**

* Sets this matrix to the 3x3 identity matrix.

* @return {Matrix3} A reference to this matrix.

identity() {

this.set(

1, 0, 0,

0, 1, 0,

0, 0, 1

);

return this;

}

/**

* Copies the values of the given matrix to this instance.

* @param {Matrix3} m - The matrix to copy.

* @return {Matrix3} A reference to this matrix.

copy( m ) {

const te = this.elements;

const me = m.elements;

te[ 0 ] = me[ 0 ]; te[ 1 ] = me[ 1 ]; te[ 2 ] = me[ 2 ];

te[ 3 ] = me[ 3 ]; te[ 4 ] = me[ 4 ]; te[ 5 ] = me[ 5 ];

te[ 6 ] = me[ 6 ]; te[ 7 ] = me[ 7 ]; te[ 8 ] = me[ 8 ];

return this;

}

/**

* Extracts the basis of this matrix into the three axis vectors provided.

* @param {Vector3} xAxis - The basis's x axis.

* @param {Vector3} yAxis - The basis's y axis.

* @param {Vector3} zAxis - The basis's z axis.

* @return {Matrix3} A reference to this matrix.

extractBasis( xAxis, yAxis, zAxis ) {

xAxis.setFromMatrix3Column( this, 0 );

yAxis.setFromMatrix3Column( this, 1 );

zAxis.setFromMatrix3Column( this, 2 );

return this;

}

/**

* Set this matrix to the upper 3x3 matrix of the given 4x4 matrix.

* @param {Matrix4} m - The 4x4 matrix.

* @return {Matrix3} A reference to this matrix.

setFromMatrix4( m ) {

const me = m.elements;

this.set(

me[ 0 ], me[ 4 ], me[ 8 ],

me[ 1 ], me[ 5 ], me[ 9 ],

me[ 2 ], me[ 6 ], me[ 10 ]

);

return this;

}

/**

* Post-multiplies this matrix by the given 3x3 matrix.

* @param {Matrix3} m - The matrix to multiply with.

* @return {Matrix3} A reference to this matrix.

multiply( m ) {

return this.multiplyMatrices( this, m );

}

/**

* Pre-multiplies this matrix by the given 3x3 matrix.

* @param {Matrix3} m - The matrix to multiply with.

* @return {Matrix3} A reference to this matrix.

premultiply( m ) {

return this.multiplyMatrices( m, this );

}

/**

* Multiples the given 3x3 matrices and stores the result

* in this matrix.

* @param {Matrix3} a - The first matrix.

* @param {Matrix3} b - The second matrix.

* @return {Matrix3} A reference to this matrix.

multiplyMatrices( a, b ) {

const ae = a.elements;

const be = b.elements;

const te = this.elements;

const a11 = ae[ 0 ], a12 = ae[ 3 ], a13 = ae[ 6 ];

const a21 = ae[ 1 ], a22 = ae[ 4 ], a23 = ae[ 7 ];

const a31 = ae[ 2 ], a32 = ae[ 5 ], a33 = ae[ 8 ];

const b11 = be[ 0 ], b12 = be[ 3 ], b13 = be[ 6 ];

const b21 = be[ 1 ], b22 = be[ 4 ], b23 = be[ 7 ];

const b31 = be[ 2 ], b32 = be[ 5 ], b33 = be[ 8 ];

te[ 0 ] = a11 * b11 + a12 * b21 + a13 * b31;

te[ 3 ] = a11 * b12 + a12 * b22 + a13 * b32;

te[ 6 ] = a11 * b13 + a12 * b23 + a13 * b33;

te[ 1 ] = a21 * b11 + a22 * b21 + a23 * b31;

te[ 4 ] = a21 * b12 + a22 * b22 + a23 * b32;

te[ 7 ] = a21 * b13 + a22 * b23 + a23 * b33;

te[ 2 ] = a31 * b11 + a32 * b21 + a33 * b31;

te[ 5 ] = a31 * b12 + a32 * b22 + a33 * b32;

te[ 8 ] = a31 * b13 + a32 * b23 + a33 * b33;

return this;

}

/**

* Multiplies every component of the matrix by the given scalar.

* @param {number} s - The scalar.

* @return {Matrix3} A reference to this matrix.

multiplyScalar( s ) {

const te = this.elements;

te[ 0 ] *= s; te[ 3 ] *= s; te[ 6 ] *= s;

te[ 1 ] *= s; te[ 4 ] *= s; te[ 7 ] *= s;

te[ 2 ] *= s; te[ 5 ] *= s; te[ 8 ] *= s;

return this;

}

/**

* Computes and returns the determinant of this matrix.

* @return {number} The determinant.

determinant() {

const te = this.elements;

const a = te[ 0 ], b = te[ 1 ], c = te[ 2 ],

d = te[ 3 ], e = te[ 4 ], f = te[ 5 ],

g = te[ 6 ], h = te[ 7 ], i = te[ 8 ];

return a * e * i - a * f * h - b * d * i + b * f * g + c * d * h - c * e * g;

}

/**

* Inverts this matrix, using the [analytic method](https://en.wikipedia.org/wiki/Invertible_matrix#Analytic_solution).

* You can not invert with a determinant of zero. If you attempt this, the method produces

* a zero matrix instead.

* @return {Matrix3} A reference to this matrix.

invert() {

const te = this.elements,

n11 = te[ 0 ], n21 = te[ 1 ], n31 = te[ 2 ],

n12 = te[ 3 ], n22 = te[ 4 ], n32 = te[ 5 ],

n13 = te[ 6 ], n23 = te[ 7 ], n33 = te[ 8 ],

t11 = n33 * n22 - n32 * n23,

t12 = n32 * n13 - n33 * n12,

t13 = n23 * n12 - n22 * n13,

det = n11 * t11 + n21 * t12 + n31 * t13;

if ( det === 0 ) return this.set( 0, 0, 0, 0, 0, 0, 0, 0, 0 );

const detInv = 1 / det;

te[ 0 ] = t11 * detInv;

te[ 1 ] = ( n31 * n23 - n33 * n21 ) * detInv;

te[ 2 ] = ( n32 * n21 - n31 * n22 ) * detInv;

te[ 3 ] = t12 * detInv;

te[ 4 ] = ( n33 * n11 - n31 * n13 ) * detInv;

te[ 5 ] = ( n31 * n12 - n32 * n11 ) * detInv;

te[ 6 ] = t13 * detInv;

te[ 7 ] = ( n21 * n13 - n23 * n11 ) * detInv;

te[ 8 ] = ( n22 * n11 - n21 * n12 ) * detInv;

return this;

}

/**

* Transposes this matrix in place.

* @return {Matrix3} A reference to this matrix.

transpose() {

let tmp;

const m = this.elements;

tmp = m[ 1 ]; m[ 1 ] = m[ 3 ]; m[ 3 ] = tmp;

tmp = m[ 2 ]; m[ 2 ] = m[ 6 ]; m[ 6 ] = tmp;

tmp = m[ 5 ]; m[ 5 ] = m[ 7 ]; m[ 7 ] = tmp;

return this;

}

/**

* Computes the normal matrix which is the inverse transpose of the upper

* left 3x3 portion of the given 4x4 matrix.

* @param {Matrix4} matrix4 - The 4x4 matrix.

* @return {Matrix3} A reference to this matrix.

getNormalMatrix( matrix4 ) {

return this.setFromMatrix4( matrix4 ).invert().transpose();

}

/**

* Transposes this matrix into the supplied array, and returns itself unchanged.

* @param {Array<number>} r - An array to store the transposed matrix elements.

* @return {Matrix3} A reference to this matrix.

transposeIntoArray( r ) {

const m = this.elements;

r[ 0 ] = m[ 0 ];

r[ 1 ] = m[ 3 ];

r[ 2 ] = m[ 6 ];

r[ 3 ] = m[ 1 ];

r[ 4 ] = m[ 4 ];

r[ 5 ] = m[ 7 ];

r[ 6 ] = m[ 2 ];

r[ 7 ] = m[ 5 ];

r[ 8 ] = m[ 8 ];

return this;

}

/**

* Sets the UV transform matrix from offset, repeat, rotation, and center.

* @param {number} tx - Offset x.

* @param {number} ty - Offset y.

* @param {number} sx - Repeat x.

* @param {number} sy - Repeat y.

* @param {number} rotation - Rotation, in radians. Positive values rotate counterclockwise.

* @param {number} cx - Center x of rotation.

* @param {number} cy - Center y of rotation

* @return {Matrix3} A reference to this matrix.

setUvTransform( tx, ty, sx, sy, rotation, cx, cy ) {

const c = Math.cos( rotation );

const s = Math.sin( rotation );

this.set(

sx * c, sx * s, - sx * ( c * cx + s * cy ) + cx + tx,

- sy * s, sy * c, - sy * ( - s * cx + c * cy ) + cy + ty,

0, 0, 1

);

return this;

}

/**

* Scales this matrix with the given scalar values.

* @param {number} sx - The amount to scale in the X axis.

* @param {number} sy - The amount to scale in the Y axis.

* @return {Matrix3} A reference to this matrix.

scale( sx, sy ) {

this.premultiply( _m3.makeScale( sx, sy ) );

return this;

}

/**

* Rotates this matrix by the given angle.

* @param {number} theta - The rotation in radians.

* @return {Matrix3} A reference to this matrix.

rotate( theta ) {

this.premultiply( _m3.makeRotation( - theta ) );

return this;

}

/**

* Translates this matrix by the given scalar values.

* @param {number} tx - The amount to translate in the X axis.

* @param {number} ty - The amount to translate in the Y axis.

* @return {Matrix3} A reference to this matrix.

translate( tx, ty ) {

this.premultiply( _m3.makeTranslation( tx, ty ) );

return this;

}

// for 2D Transforms

/**

* Sets this matrix as a 2D translation transform.

* @param {number|Vector2} x - The amount to translate in the X axis or alternatively a translation vector.

* @param {number} y - The amount to translate in the Y axis.

* @return {Matrix3} A reference to this matrix.

makeTranslation( x, y ) {

if ( x.isVector2 ) {

this.set(

1, 0, x.x,

0, 1, x.y,

0, 0, 1

);

} else {

this.set(

1, 0, x,

0, 1, y,

0, 0, 1

);

}

return this;

}

/**

* Sets this matrix as a 2D rotational transformation.

* @param {number} theta - The rotation in radians.

* @return {Matrix3} A reference to this matrix.

makeRotation( theta ) {

// counterclockwise

const c = Math.cos( theta );

const s = Math.sin( theta );

this.set(

c, - s, 0,

s, c, 0,

0, 0, 1

);

return this;

}

/**

* Sets this matrix as a 2D scale transform.

* @param {number} x - The amount to scale in the X axis.

* @param {number} y - The amount to scale in the Y axis.

* @return {Matrix3} A reference to this matrix.

makeScale( x, y ) {

this.set(

x, 0, 0,

0, y, 0,

0, 0, 1

);

return this;

}

/**

* Returns `true` if this matrix is equal with the given one.

* @param {Matrix3} matrix - The matrix to test for equality.

* @return {boolean} Whether this matrix is equal with the given one.

equals( matrix ) {

const te = this.elements;

const me = matrix.elements;

for ( let i = 0; i < 9; i ++ ) {

if ( te[ i ] !== me[ i ] ) return false;

}

return true;

}

/**

* Sets the elements of the matrix from the given array.

* @param {Array<number>} array - The matrix elements in column-major order.

* @param {number} [offset=0] - Index of the first element in the array.

* @return {Matrix3} A reference to this matrix.

fromArray( array, offset = 0 ) {

for ( let i = 0; i < 9; i ++ ) {

this.elements[ i ] = array[ i + offset ];

}

return this;

}

/**

* Writes the elements of this matrix to the given array. If no array is provided,

* the method returns a new instance.

* @param {Array<number>} [array=[]] - The target array holding the matrix elements in column-major order.

* @param {number} [offset=0] - Index of the first element in the array.

* @return {Array<number>} The matrix elements in column-major order.

toArray( array = [], offset = 0 ) {

const te = this.elements;

array[ offset ] = te[ 0 ];

array[ offset + 1 ] = te[ 1 ];

array[ offset + 2 ] = te[ 2 ];

array[ offset + 3 ] = te[ 3 ];

array[ offset + 4 ] = te[ 4 ];

array[ offset + 5 ] = te[ 5 ];

array[ offset + 6 ] = te[ 6 ];

array[ offset + 7 ] = te[ 7 ];

array[ offset + 8 ] = te[ 8 ];

return array;

}

/**

* Returns a matrix with copied values from this instance.

* @return {Matrix3} A clone of this instance.

clone() {

return new this.constructor().fromArray( this.elements );

}

const _m3 = /*@__PURE__*/ new Matrix3();

export { Matrix3 };

three.js/src/math/Matrix3.js at dev · supermedium/three.js · GitHub

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