feature: add vec3OrthoNormalize

src/math/vec3/index.ts

@@ -2,3 +2,4 @@ export type { RawVector3 } from './RawVector3';
 export { vec3ApplyMatrix4 } from './vec3ApplyMatrix4';
 export { vec3ApplyQuaternion } from './vec3ApplyQuaternion';
 export { vec3Cross } from './vec3Cross';
+export { vec3OrthoNormalize } from './vec3OrthoNormalize';

src/math/vec3/tests/vec3OrthoNormalize.test.ts

@@ -0,0 +1,26 @@
+import '../../../tests/matchers/toBeCloseToArray';
+import { vec3OrthoNormalize } from '../vec3OrthoNormalize';
+import type { RawVector3 } from '../RawVector3';
+
+describe( 'vec3OrthoNormalize', () => {
+  it( 'returns a orthogonal tangent', () => {
+    const normal: RawVector3 = [ 0.0, 0.0, 5.0 ];
+    const tangent: RawVector3 = [ 1.0, 1.0, 1.0 ];
+    const subject = vec3OrthoNormalize( normal, tangent );
+
+    expect( subject.normal ).toBeCloseToArray( [ 0.0, 0.0, 1.0 ] );
+    expect( subject.tangent ).toBeCloseToArray( [ 0.707, 0.707, 0.0 ] );
+    expect( subject.binormal ).toBeCloseToArray( [ -0.707, 0.707, 0.0 ] );
+  } );
+
+  it( 'returns a orthogonal tangent and binormal', () => {
+    const normal: RawVector3 = [ 0.0, 0.0, 5.0 ];
+    const tangent: RawVector3 = [ 1.0, 1.0, 1.0 ];
+    const binormal: RawVector3 = [ 0.0, -1.0, 0.0 ];
+    const subject = vec3OrthoNormalize( normal, tangent, binormal );
+
+    expect( subject.normal ).toBeCloseToArray( [ 0.0, 0.0, 1.0 ] );
+    expect( subject.tangent ).toBeCloseToArray( [ 0.707, 0.707, 0.0 ] );
+    expect( subject.binormal ).toBeCloseToArray( [ 0.707, -0.707, 0.0 ] );
+  } );
+} );

src/math/vec3/vec3OrthoNormalize.ts

@@ -0,0 +1,33 @@
+import { vec3Cross } from '.';
+import { vecDot, vecNeg, vecNormalize, vecScale, vecSub } from '..';
+import type { RawVector3 } from './RawVector3';
+
+/**
+ * Return a tangent which is orthogonal to normal.
+ * If binormal is specified, it is also returned and it's orthogonal to both normal and tangent.
+ */
+export function vec3OrthoNormalize(
+  normal: RawVector3,
+  tangent: RawVector3,
+  binormal?: RawVector3,
+): {
+    normal: RawVector3,
+    tangent: RawVector3,
+    binormal: RawVector3,
+  } {
+  const n = vecNormalize( normal );
+
+  const dotNT = vecDot( n, tangent );
+  const t = vecNormalize( vecSub( tangent, vecScale( n, dotNT ) ) );
+
+  let b = vec3Cross( n, t );
+  if ( binormal && vecDot( b, binormal ) < 0.0 ) {
+    b = vecNeg( b );
+  }
+
+  return {
+    normal: n,
+    tangent: t,
+    binormal: b,
+  };
+}