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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]{@link 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 {
/**
* 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 ) {
/**
* This flag can be used for type testing.
*
* @type {boolean}
* @readonly
* @default true
*/
Matrix3.prototype.isMatrix3 = true;
/**
* 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]{@link 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 };
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