THREE matrix first principle and translation rotation matrix

priority

row first

 [
    1,2,3,4
    5,6,7,8,
    9,10,11,12
]

If it is row-first, the reading order as above is 1234, 5678, 9101112

column first

 [
    1,2,3,4
    5,6,7,8,
    9,10,11,12
]

If it is row priority, the reading order as above is 159, 2610, 3711, 4812

THREE priority rule

All internally calculated and stored matrices are column-first, but row-first is more suitable for human reading order, so the Matrix.set method uses row-first reading, and reads are column-first.

 const a = new THREE.Matrix3()
a.set(1,2,3,4,5,6,7,8,9)
console.log('矩阵: ====>', a.elements) // (9) [1, 4, 7, 2, 5, 8, 3, 6, 9]

For reading, the following matrices are displayed row-first

row-first, column-first

 set( n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 ) {

 const te = this.elements;

 te[ 0 ] = n11; te[ 4 ] = n12; te[ 8 ] = n13; te[ 12 ] = n14;
 te[ 1 ] = n21; te[ 5 ] = n22; te[ 9 ] = n23; te[ 13 ] = n24;
 te[ 2 ] = n31; te[ 6 ] = n32; te[ 10 ] = n33; te[ 14 ] = n34;
 te[ 3 ] = n41; te[ 7 ] = n42; te[ 11 ] = n43; te[ 15 ] = n44;

 return this;

}

The set method converts a row-major matrix into a column-major matrix, and all matrix calculations are converted to column-major by the set method

ApplyMatrix4

 applyMatrix4( m ) {

        const x = this.x, y = this.y, z = this.z;
        const e = m.elements;

        const w = 1 / ( e[ 3 ] * x + e[ 7 ] * y + e[ 11 ] * z + e[ 15 ] );

        this.x = ( e[ 0 ] * x + e[ 4 ] * y + e[ 8 ] * z + e[ 12 ] ) * w;
        this.y = ( e[ 1 ] * x + e[ 5 ] * y + e[ 9 ] * z + e[ 13 ] ) * w;
        this.z = ( e[ 2 ] * x + e[ 6 ] * y + e[ 10 ] * z + e[ 14 ] ) * w;

        return this;

    }

The parameter m of applyMatrix4 is the column-major matrix transformed by the set method

According to the above method, it is easy to derive the translation matrix:

 const a = new THREE.Matrix4()
a.set(
  1, 0, 0, 1,
  0, 1, 0, 1,
  0, 0, 1, 1,
  0, 0, 0, 1
)

This is a matrix with xyz translated by 1 unit respectively. So know the general matrix of the translation matrix

 1, 0, 0, dx,
0, 1, 0, dy,
0, 0, 1, dz,
0, 0, 0, 1

For the rotation matrix, it is inevitable to have a relationship with trigonometric functions.

For rotation, counterclockwise rotation is a positive angle, and clockwise rotation is a negative angle.
The rotation matrix about the X axis is easy to write according to the above figure

 [
    1, 0, 0, 0,
    0, cosN, -sinN, 0,
    0, sinN, cosN, 0,
    0, 0, 0, 1
]

For any axis rotation, you can directly look at the source code of threejs

 makeRotationAxis( axis, angle ) {

 // Based on http://www.gamedev.net/reference/articles/article1199.asp

 const c = Math.cos( angle );
 const s = Math.sin( angle );
 const t = 1 - c;
 const x = axis.x, y = axis.y, z = axis.z;
 const tx = t * x, ty = t * y;

 this.set(

  tx * x + c, tx * y - s * z, tx * z + s * y, 0,
  tx * y + s * z, ty * y + c, ty * z - s * x, 0,
  tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
  0, 0, 0, 1

 );

 return this;

}