import { Box3, MathUtils, Matrix4, Matrix3, Ray, Vector3 } from '../../../build/three.module.js'; // module scope helper variables const a = { c: null, // center u: [ new Vector3(), new Vector3(), new Vector3() ], // basis vectors e: [] // half width }; const b = { c: null, // center u: [ new Vector3(), new Vector3(), new Vector3() ], // basis vectors e: [] // half width }; const R = [[], [], []]; const AbsR = [[], [], []]; const t = []; const xAxis = new Vector3(); const yAxis = new Vector3(); const zAxis = new Vector3(); const v1 = new Vector3(); const size = new Vector3(); const closestPoint = new Vector3(); const rotationMatrix = new Matrix3(); const aabb = new Box3(); const matrix = new Matrix4(); const inverse = new Matrix4(); const localRay = new Ray(); // OBB class OBB { constructor( center = new Vector3(), halfSize = new Vector3(), rotation = new Matrix3() ) { this.center = center; this.halfSize = halfSize; this.rotation = rotation; } set( center, halfSize, rotation ) { this.center = center; this.halfSize = halfSize; this.rotation = rotation; return this; } copy( obb ) { this.center.copy( obb.center ); this.halfSize.copy( obb.halfSize ); this.rotation.copy( obb.rotation ); return this; } clone() { return new this.constructor().copy( this ); } getSize( result ) { return result.copy( this.halfSize ).multiplyScalar( 2 ); } /** * Reference: Closest Point on OBB to Point in Real-Time Collision Detection * by Christer Ericson (chapter 5.1.4) */ clampPoint( point, result ) { const halfSize = this.halfSize; v1.subVectors( point, this.center ); this.rotation.extractBasis( xAxis, yAxis, zAxis ); // start at the center position of the OBB result.copy( this.center ); // project the target onto the OBB axes and walk towards that point const x = MathUtils.clamp( v1.dot( xAxis ), - halfSize.x, halfSize.x ); result.add( xAxis.multiplyScalar( x ) ); const y = MathUtils.clamp( v1.dot( yAxis ), - halfSize.y, halfSize.y ); result.add( yAxis.multiplyScalar( y ) ); const z = MathUtils.clamp( v1.dot( zAxis ), - halfSize.z, halfSize.z ); result.add( zAxis.multiplyScalar( z ) ); return result; } containsPoint( point ) { v1.subVectors( point, this.center ); this.rotation.extractBasis( xAxis, yAxis, zAxis ); // project v1 onto each axis and check if these points lie inside the OBB return Math.abs( v1.dot( xAxis ) ) <= this.halfSize.x && Math.abs( v1.dot( yAxis ) ) <= this.halfSize.y && Math.abs( v1.dot( zAxis ) ) <= this.halfSize.z; } intersectsBox3( box3 ) { return this.intersectsOBB( obb.fromBox3( box3 ) ); } intersectsSphere( sphere ) { // find the point on the OBB closest to the sphere center this.clampPoint( sphere.center, closestPoint ); // if that point is inside the sphere, the OBB and sphere intersect return closestPoint.distanceToSquared( sphere.center ) <= ( sphere.radius * sphere.radius ); } /** * Reference: OBB-OBB Intersection in Real-Time Collision Detection * by Christer Ericson (chapter 4.4.1) * */ intersectsOBB( obb, epsilon = Number.EPSILON ) { // prepare data structures (the code uses the same nomenclature like the reference) a.c = this.center; a.e[ 0 ] = this.halfSize.x; a.e[ 1 ] = this.halfSize.y; a.e[ 2 ] = this.halfSize.z; this.rotation.extractBasis( a.u[ 0 ], a.u[ 1 ], a.u[ 2 ] ); b.c = obb.center; b.e[ 0 ] = obb.halfSize.x; b.e[ 1 ] = obb.halfSize.y; b.e[ 2 ] = obb.halfSize.z; obb.rotation.extractBasis( b.u[ 0 ], b.u[ 1 ], b.u[ 2 ] ); // compute rotation matrix expressing b in a's coordinate frame for ( let i = 0; i < 3; i ++ ) { for ( let j = 0; j < 3; j ++ ) { R[ i ][ j ] = a.u[ i ].dot( b.u[ j ] ); } } // compute translation vector v1.subVectors( b.c, a.c ); // bring translation into a's coordinate frame t[ 0 ] = v1.dot( a.u[ 0 ] ); t[ 1 ] = v1.dot( a.u[ 1 ] ); t[ 2 ] = v1.dot( a.u[ 2 ] ); // compute common subexpressions. Add in an epsilon term to // counteract arithmetic errors when two edges are parallel and // their cross product is (near) null for ( let i = 0; i < 3; i ++ ) { for ( let j = 0; j < 3; j ++ ) { AbsR[ i ][ j ] = Math.abs( R[ i ][ j ] ) + epsilon; } } let ra, rb; // test axes L = A0, L = A1, L = A2 for ( let i = 0; i < 3; i ++ ) { ra = a.e[ i ]; rb = b.e[ 0 ] * AbsR[ i ][ 0 ] + b.e[ 1 ] * AbsR[ i ][ 1 ] + b.e[ 2 ] * AbsR[ i ][ 2 ]; if ( Math.abs( t[ i ] ) > ra + rb ) return false; } // test axes L = B0, L = B1, L = B2 for ( let i = 0; i < 3; i ++ ) { ra = a.e[ 0 ] * AbsR[ 0 ][ i ] + a.e[ 1 ] * AbsR[ 1 ][ i ] + a.e[ 2 ] * AbsR[ 2 ][ i ]; rb = b.e[ i ]; if ( Math.abs( t[ 0 ] * R[ 0 ][ i ] + t[ 1 ] * R[ 1 ][ i ] + t[ 2 ] * R[ 2 ][ i ] ) > ra + rb ) return false; } // test axis L = A0 x B0 ra = a.e[ 1 ] * AbsR[ 2 ][ 0 ] + a.e[ 2 ] * AbsR[ 1 ][ 0 ]; rb = b.e[ 1 ] * AbsR[ 0 ][ 2 ] + b.e[ 2 ] * AbsR[ 0 ][ 1 ]; if ( Math.abs( t[ 2 ] * R[ 1 ][ 0 ] - t[ 1 ] * R[ 2 ][ 0 ] ) > ra + rb ) return false; // test axis L = A0 x B1 ra = a.e[ 1 ] * AbsR[ 2 ][ 1 ] + a.e[ 2 ] * AbsR[ 1 ][ 1 ]; rb = b.e[ 0 ] * AbsR[ 0 ][ 2 ] + b.e[ 2 ] * AbsR[ 0 ][ 0 ]; if ( Math.abs( t[ 2 ] * R[ 1 ][ 1 ] - t[ 1 ] * R[ 2 ][ 1 ] ) > ra + rb ) return false; // test axis L = A0 x B2 ra = a.e[ 1 ] * AbsR[ 2 ][ 2 ] + a.e[ 2 ] * AbsR[ 1 ][ 2 ]; rb = b.e[ 0 ] * AbsR[ 0 ][ 1 ] + b.e[ 1 ] * AbsR[ 0 ][ 0 ]; if ( Math.abs( t[ 2 ] * R[ 1 ][ 2 ] - t[ 1 ] * R[ 2 ][ 2 ] ) > ra + rb ) return false; // test axis L = A1 x B0 ra = a.e[ 0 ] * AbsR[ 2 ][ 0 ] + a.e[ 2 ] * AbsR[ 0 ][ 0 ]; rb = b.e[ 1 ] * AbsR[ 1 ][ 2 ] + b.e[ 2 ] * AbsR[ 1 ][ 1 ]; if ( Math.abs( t[ 0 ] * R[ 2 ][ 0 ] - t[ 2 ] * R[ 0 ][ 0 ] ) > ra + rb ) return false; // test axis L = A1 x B1 ra = a.e[ 0 ] * AbsR[ 2 ][ 1 ] + a.e[ 2 ] * AbsR[ 0 ][ 1 ]; rb = b.e[ 0 ] * AbsR[ 1 ][ 2 ] + b.e[ 2 ] * AbsR[ 1 ][ 0 ]; if ( Math.abs( t[ 0 ] * R[ 2 ][ 1 ] - t[ 2 ] * R[ 0 ][ 1 ] ) > ra + rb ) return false; // test axis L = A1 x B2 ra = a.e[ 0 ] * AbsR[ 2 ][ 2 ] + a.e[ 2 ] * AbsR[ 0 ][ 2 ]; rb = b.e[ 0 ] * AbsR[ 1 ][ 1 ] + b.e[ 1 ] * AbsR[ 1 ][ 0 ]; if ( Math.abs( t[ 0 ] * R[ 2 ][ 2 ] - t[ 2 ] * R[ 0 ][ 2 ] ) > ra + rb ) return false; // test axis L = A2 x B0 ra = a.e[ 0 ] * AbsR[ 1 ][ 0 ] + a.e[ 1 ] * AbsR[ 0 ][ 0 ]; rb = b.e[ 1 ] * AbsR[ 2 ][ 2 ] + b.e[ 2 ] * AbsR[ 2 ][ 1 ]; if ( Math.abs( t[ 1 ] * R[ 0 ][ 0 ] - t[ 0 ] * R[ 1 ][ 0 ] ) > ra + rb ) return false; // test axis L = A2 x B1 ra = a.e[ 0 ] * AbsR[ 1 ][ 1 ] + a.e[ 1 ] * AbsR[ 0 ][ 1 ]; rb = b.e[ 0 ] * AbsR[ 2 ][ 2 ] + b.e[ 2 ] * AbsR[ 2 ][ 0 ]; if ( Math.abs( t[ 1 ] * R[ 0 ][ 1 ] - t[ 0 ] * R[ 1 ][ 1 ] ) > ra + rb ) return false; // test axis L = A2 x B2 ra = a.e[ 0 ] * AbsR[ 1 ][ 2 ] + a.e[ 1 ] * AbsR[ 0 ][ 2 ]; rb = b.e[ 0 ] * AbsR[ 2 ][ 1 ] + b.e[ 1 ] * AbsR[ 2 ][ 0 ]; if ( Math.abs( t[ 1 ] * R[ 0 ][ 2 ] - t[ 0 ] * R[ 1 ][ 2 ] ) > ra + rb ) return false; // since no separating axis is found, the OBBs must be intersecting return true; } /** * Reference: Testing Box Against Plane in Real-Time Collision Detection * by Christer Ericson (chapter 5.2.3) */ intersectsPlane( plane ) { this.rotation.extractBasis( xAxis, yAxis, zAxis ); // compute the projection interval radius of this OBB onto L(t) = this->center + t * p.normal; const r = this.halfSize.x * Math.abs( plane.normal.dot( xAxis ) ) + this.halfSize.y * Math.abs( plane.normal.dot( yAxis ) ) + this.halfSize.z * Math.abs( plane.normal.dot( zAxis ) ); // compute distance of the OBB's center from the plane const d = plane.normal.dot( this.center ) - plane.constant; // Intersection occurs when distance d falls within [-r,+r] interval return Math.abs( d ) <= r; } /** * Performs a ray/OBB intersection test and stores the intersection point * to the given 3D vector. If no intersection is detected, *null* is returned. */ intersectRay( ray, result ) { // the idea is to perform the intersection test in the local space // of the OBB. this.getSize( size ); aabb.setFromCenterAndSize( v1.set( 0, 0, 0 ), size ); // create a 4x4 transformation matrix matrix.setFromMatrix3( this.rotation ); matrix.setPosition( this.center ); // transform ray to the local space of the OBB inverse.copy( matrix ).invert(); localRay.copy( ray ).applyMatrix4( inverse ); // perform ray <-> AABB intersection test if ( localRay.intersectBox( aabb, result ) ) { // transform the intersection point back to world space return result.applyMatrix4( matrix ); } else { return null; } } /** * Performs a ray/OBB intersection test. Returns either true or false if * there is a intersection or not. */ intersectsRay( ray ) { return this.intersectRay( ray, v1 ) !== null; } fromBox3( box3 ) { box3.getCenter( this.center ); box3.getSize( this.halfSize ).multiplyScalar( 0.5 ); this.rotation.identity(); return this; } equals( obb ) { return obb.center.equals( this.center ) && obb.halfSize.equals( this.halfSize ) && obb.rotation.equals( this.rotation ); } applyMatrix4( matrix ) { const e = matrix.elements; let sx = v1.set( e[ 0 ], e[ 1 ], e[ 2 ] ).length(); const sy = v1.set( e[ 4 ], e[ 5 ], e[ 6 ] ).length(); const sz = v1.set( e[ 8 ], e[ 9 ], e[ 10 ] ).length(); const det = matrix.determinant(); if ( det < 0 ) sx = - sx; rotationMatrix.setFromMatrix4( matrix ); const invSX = 1 / sx; const invSY = 1 / sy; const invSZ = 1 / sz; rotationMatrix.elements[ 0 ] *= invSX; rotationMatrix.elements[ 1 ] *= invSX; rotationMatrix.elements[ 2 ] *= invSX; rotationMatrix.elements[ 3 ] *= invSY; rotationMatrix.elements[ 4 ] *= invSY; rotationMatrix.elements[ 5 ] *= invSY; rotationMatrix.elements[ 6 ] *= invSZ; rotationMatrix.elements[ 7 ] *= invSZ; rotationMatrix.elements[ 8 ] *= invSZ; this.rotation.multiply( rotationMatrix ); this.halfSize.x *= sx; this.halfSize.y *= sy; this.halfSize.z *= sz; v1.setFromMatrixPosition( matrix ); this.center.add( v1 ); return this; } } const obb = new OBB(); export { OBB };