Matrix3: Added lookAt()

src/core/Object3D.js

@@ -307,7 +307,8 @@ Object3D.prototype = Object.assign( Object.create( EventDispatcher.prototype ),
 
 		// This method does not support objects with rotated and/or translated parent(s)
 
-		var m1 = new Matrix4();
+		var m1 = new Matrix3();
+		var targetDirection = new Vector3();
 		var vector = new Vector3();
 
 		return function lookAt( x, y, z ) {
@@ -322,15 +323,9 @@ Object3D.prototype = Object.assign( Object.create( EventDispatcher.prototype ),
 
 			}
 
-			if ( this.isCamera ) {
-
-				m1.lookAt( this.position, vector, this.up );
-
-			} else {
-
-				m1.lookAt( vector, this.position, this.up );
+			targetDirection.subVectors( vector, this.position ).normalize();
 
-			}
+			m1.lookAt( this.forward, targetDirection, this.up );
 
 			this.quaternion.setFromRotationMatrix( m1 );
 

src/math/Matrix3.js

@@ -114,6 +114,62 @@ Object.assign( Matrix3.prototype, {
 
 	}(),
 
+	makeBasis: function ( xAxis, yAxis, zAxis ) {
+
+		this.set(
+			xAxis.x, yAxis.x, zAxis.x,
+			xAxis.y, yAxis.y, zAxis.y,
+			xAxis.z, yAxis.z, zAxis.z
+		);
+
+		return this;
+
+	},
+
+	lookAt: function () {
+
+		var localRight = new Vector3();
+		var worldRight = new Vector3();
+		var worldUp = new Vector3( 0, 1, 0 );
+		var perpWorldUp = new Vector3();
+		var temp = new Vector3();
+
+		var m1 = new Matrix3();
+		var m2 = new Matrix3();
+
+		return function lookAt( localForward, targetDirection, localUp ) {
+
+			localRight.crossVectors( localUp, localForward ).normalize();
+
+			// orthonormal linear basis A { localRight, localUp, localForward } for the object local space
+
+			worldRight.crossVectors( worldUp, targetDirection ).normalize();
+
+			if ( worldRight.lengthSq() === 0 ) {
+
+				// handle case when it's not possible to build a basis from targetDirection and worldUp
+				// slightly shift targetDirection in order to avoid collinearity
+
+				temp.copy( targetDirection ).addScalar( Number.EPSILON );
+				worldRight.crossVectors( worldUp, temp ).normalize();
+
+			}
+
+			perpWorldUp.crossVectors( targetDirection, worldRight ).normalize();
+
+			// orthonormal linear basis B { worldRight, perpWorldUp, targetDirection } for the desired target orientation
+
+			m1.makeBasis( worldRight, perpWorldUp, targetDirection );
+			m2.makeBasis( localRight, localUp, localForward );
+
+			// construct a matrix that maps basis A to B
+
+			this.multiplyMatrices( m1, m2.transpose() );
+
+		};
+
+	}(),
+
 	multiply: function ( m ) {
 
 		return this.multiplyMatrices( this, m );

src/math/Quaternion.js

@@ -295,14 +295,25 @@ Object.assign( Quaternion.prototype, {
 
 		// assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
 
-		var te = m.elements,
+		var te = m.elements;
 
-			m11 = te[ 0 ], m12 = te[ 4 ], m13 = te[ 8 ],
-			m21 = te[ 1 ], m22 = te[ 5 ], m23 = te[ 9 ],
-			m31 = te[ 2 ], m32 = te[ 6 ], m33 = te[ 10 ],
+		var m11, m12, m13, m21, m22, m23, m31, m32, m33;
 
-			trace = m11 + m22 + m33,
-			s;
+		if ( m.isMatrix3 ) {
+
+			m11 = te[ 0 ]; m12 = te[ 3 ]; m13 = te[ 6 ];
+			m21 = te[ 1 ]; m22 = te[ 4 ]; m23 = te[ 7 ];
+			m31 = te[ 2 ]; m32 = te[ 5 ]; m33 = te[ 8 ];
+
+		} else {
+
+			m11 = te[ 0 ]; m12 = te[ 4 ]; m13 = te[ 8 ];
+			m21 = te[ 1 ]; m22 = te[ 5 ]; m23 = te[ 9 ];
+			m31 = te[ 2 ]; m32 = te[ 6 ]; m33 = te[ 10 ];
+
+		}
+
+		var trace = m11 + m22 + m33, s;
 
 		if ( trace > 0 ) {