feature: add mat3CreateNormalMatrix

and its equivalen in classes

src/math/mat3/Matrix3.ts

@@ -1,5 +1,6 @@
 import { Matrix4 } from '../mat4/Matrix4';
 import { Quaternion } from '../quat/Quaternion';
+import { mat3CreateNormalMatrix } from './mat3CreateNormalMatrix';
 import { mat3Determinant } from './mat3Determinant';
 import { mat3FromMat4 } from './mat3FromMat4';
 import { mat3FromQuaternion } from './mat3FromQuaternion';
@@ -98,6 +99,14 @@ export class Matrix3 {
     }
   }
 
+  /**
+   * Create a normal matrix out of matrix4.
+   * @param matrix4 A matrix4
+   */
+  public static createNormalMatrix( matrix4: Matrix4 ): Matrix3 {
+    return new Matrix3( mat3CreateNormalMatrix( matrix4.elements ) );
+  }
+
   /**
    * Cast a {@link Matrix4} into a Matrix3.
    * @param matrix4 A matrix4

src/math/mat3/index.ts

@@ -1,3 +1,4 @@
+export { mat3CreateNormalMatrix } from './mat3CreateNormalMatrix';
 export { mat3Determinant } from './mat3Determinant';
 export { mat3FromMat4 } from './mat3FromMat4';
 export { mat3FromMat4Transpose } from './mat3FromMat4Transpose';

src/math/mat3/mat3CreateNormalMatrix.ts

@@ -0,0 +1,13 @@
+import { mat3FromMat4Transpose } from './mat3FromMat4Transpose';
+import { mat3Inverse } from './mat3Inverse';
+import type { RawMatrix3 } from './RawMatrix3';
+import type { RawMatrix4 } from '../mat4/RawMatrix4';
+
+/**
+ * Create a normal matrix out of a matrix4.
+ *
+ * @param matrix A matrix4
+ */
+export function mat3CreateNormalMatrix( m: RawMatrix4 ): RawMatrix3 {
+  return mat3Inverse( mat3FromMat4Transpose( m ) );
+}

src/math/mat3/mat3FromMat4Transpose.ts

@@ -3,6 +3,7 @@ import type { RawMatrix4 } from '../mat4/RawMatrix4';
 
 /**
  * Who needs this?
+ * Intended to be used by {@link mat3CreateNormalMatrix}.
  */
 export function mat3FromMat4Transpose(
   source: RawMatrix4,

src/math/mat3/tests/mat3CreateNormalMatrix.test.ts

@@ -0,0 +1,24 @@
+import '../../../tests/matchers/toBeCloseToArray';
+import { mat3CreateNormalMatrix } from '../mat3CreateNormalMatrix';
+import type { RawMatrix3 } from '../RawMatrix3';
+import type { RawMatrix4 } from '../../mat4/RawMatrix4';
+
+const rawMatrixLookAtFrom345: RawMatrix4 = [
+  0.8574929257125442, 0, -0.5144957554275265, 0,
+  -0.2910427500435996, 0.824621125123532, -0.48507125007266594, 0,
+  0.4242640687119285, 0.565685424949238, 0.7071067811865475, 0,
+  3, 4, 5, 1
+];
+
+const rawMatrixLookAtFrom345Normal: RawMatrix3 = [
+  0.857, 0.0, -0.514,
+  -0.291, 0.825, -0.485,
+  0.424, 0.566, 0.707,
+];
+
+describe( 'mat3CreateNormalMatrix', () => {
+  it( 'returns a determinant of the matrix', () => {
+    const subject = mat3CreateNormalMatrix( rawMatrixLookAtFrom345 );
+    expect( subject ).toBeCloseToArray( rawMatrixLookAtFrom345Normal );
+  } );
+} );

src/math/mat4/Matrix4.ts

@@ -66,6 +66,13 @@ export class Matrix4 {
     return Matrix3.fromMatrix4( this );
   }
 
+  /**
+   * Itself but normal matrix.
+   */
+  public get normalMatrix(): Matrix3 {
+    return Matrix3.createNormalMatrix( this );
+  }
+
   public toString(): string {
     const m = this.elements.map( ( v ) => v.toFixed( 3 ) );
     return `Matrix4( ${ m[ 0 ] }, ${ m[ 4 ] }, ${ m[ 8 ] }, ${ m[ 12 ] }; ${ m[ 1 ] }, ${ m[ 5 ] }, ${ m[ 9 ] }, ${ m[ 13 ] }; ${ m[ 2 ] }, ${ m[ 6 ] }, ${ m[ 10 ] }, ${ m[ 14 ] }; ${ m[ 3 ] }, ${ m[ 7 ] }, ${ m[ 11 ] }, ${ m[ 15 ] } )`;