424 lines
10 KiB
JavaScript
424 lines
10 KiB
JavaScript
import {
|
|
Box3,
|
|
MathUtils,
|
|
Matrix4,
|
|
Matrix3,
|
|
Ray,
|
|
Vector3
|
|
} from 'three';
|
|
|
|
// 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 };
|