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