/**
* @author mrdoob / http://mrdoob.com/
* @author alteredq / http://alteredqualia.com/
*/
import {
Mesh,
Vector3
} from "../../../build/three.module.js";
var GeometryUtils = {
// Merge two geometries or geometry and geometry from object (using object's transform)
merge: function ( geometry1, geometry2, materialIndexOffset ) {
console.warn( 'THREE.GeometryUtils: .merge() has been moved to Geometry. Use geometry.merge( geometry2, matrix, materialIndexOffset ) instead.' );
var matrix;
if ( geometry2 instanceof Mesh ) {
geometry2.matrixAutoUpdate && geometry2.updateMatrix();
matrix = geometry2.matrix;
geometry2 = geometry2.geometry;
}
geometry1.merge( geometry2, matrix, materialIndexOffset );
},
// Get random point in triangle (via barycentric coordinates)
// (uniform distribution)
// http://www.cgafaq.info/wiki/Random_Point_In_Triangle
randomPointInTriangle: function () {
var vector = new Vector3();
return function ( vectorA, vectorB, vectorC ) {
var point = new Vector3();
var a = Math.random();
var b = Math.random();
if ( ( a + b ) > 1 ) {
a = 1 - a;
b = 1 - b;
}
var c = 1 - a - b;
point.copy( vectorA );
point.multiplyScalar( a );
vector.copy( vectorB );
vector.multiplyScalar( b );
point.add( vector );
vector.copy( vectorC );
vector.multiplyScalar( c );
point.add( vector );
return point;
};
}(),
// Get random point in face (triangle)
// (uniform distribution)
randomPointInFace: function ( face, geometry ) {
var vA, vB, vC;
vA = geometry.vertices[ face.a ];
vB = geometry.vertices[ face.b ];
vC = geometry.vertices[ face.c ];
return GeometryUtils.randomPointInTriangle( vA, vB, vC );
},
// Get uniformly distributed random points in mesh
// - create array with cumulative sums of face areas
// - pick random number from 0 to total area
// - find corresponding place in area array by binary search
// - get random point in face
randomPointsInGeometry: function ( geometry, n ) {
var face, i,
faces = geometry.faces,
vertices = geometry.vertices,
il = faces.length,
totalArea = 0,
cumulativeAreas = [],
vA, vB, vC;
// precompute face areas
for ( i = 0; i < il; i ++ ) {
face = faces[ i ];
vA = vertices[ face.a ];
vB = vertices[ face.b ];
vC = vertices[ face.c ];
face._area = GeometryUtils.triangleArea( vA, vB, vC );
totalArea += face._area;
cumulativeAreas[ i ] = totalArea;
}
// binary search cumulative areas array
function binarySearchIndices( value ) {
function binarySearch( start, end ) {
// return closest larger index
// if exact number is not found
if ( end < start )
return start;
var mid = start + Math.floor( ( end - start ) / 2 );
if ( cumulativeAreas[ mid ] > value ) {
return binarySearch( start, mid - 1 );
} else if ( cumulativeAreas[ mid ] < value ) {
return binarySearch( mid + 1, end );
} else {
return mid;
}
}
var result = binarySearch( 0, cumulativeAreas.length - 1 );
return result;
}
// pick random face weighted by face area
var r, index,
result = [];
var stats = {};
for ( i = 0; i < n; i ++ ) {
r = Math.random() * totalArea;
index = binarySearchIndices( r );
result[ i ] = GeometryUtils.randomPointInFace( faces[ index ], geometry );
if ( ! stats[ index ] ) {
stats[ index ] = 1;
} else {
stats[ index ] += 1;
}
}
return result;
},
randomPointsInBufferGeometry: function ( geometry, n ) {
var i,
vertices = geometry.attributes.position.array,
totalArea = 0,
cumulativeAreas = [],
vA, vB, vC;
// precompute face areas
vA = new Vector3();
vB = new Vector3();
vC = new Vector3();
// geometry._areas = [];
var il = vertices.length / 9;
for ( i = 0; i < il; i ++ ) {
vA.set( vertices[ i * 9 + 0 ], vertices[ i * 9 + 1 ], vertices[ i * 9 + 2 ] );
vB.set( vertices[ i * 9 + 3 ], vertices[ i * 9 + 4 ], vertices[ i * 9 + 5 ] );
vC.set( vertices[ i * 9 + 6 ], vertices[ i * 9 + 7 ], vertices[ i * 9 + 8 ] );
totalArea += GeometryUtils.triangleArea( vA, vB, vC );
cumulativeAreas.push( totalArea );
}
// binary search cumulative areas array
function binarySearchIndices( value ) {
function binarySearch( start, end ) {
// return closest larger index
// if exact number is not found
if ( end < start )
return start;
var mid = start + Math.floor( ( end - start ) / 2 );
if ( cumulativeAreas[ mid ] > value ) {
return binarySearch( start, mid - 1 );
} else if ( cumulativeAreas[ mid ] < value ) {
return binarySearch( mid + 1, end );
} else {
return mid;
}
}
var result = binarySearch( 0, cumulativeAreas.length - 1 );
return result;
}
// pick random face weighted by face area
var r, index,
result = [];
for ( i = 0; i < n; i ++ ) {
r = Math.random() * totalArea;
index = binarySearchIndices( r );
// result[ i ] = GeometryUtils.randomPointInFace( faces[ index ], geometry, true );
vA.set( vertices[ index * 9 + 0 ], vertices[ index * 9 + 1 ], vertices[ index * 9 + 2 ] );
vB.set( vertices[ index * 9 + 3 ], vertices[ index * 9 + 4 ], vertices[ index * 9 + 5 ] );
vC.set( vertices[ index * 9 + 6 ], vertices[ index * 9 + 7 ], vertices[ index * 9 + 8 ] );
result[ i ] = GeometryUtils.randomPointInTriangle( vA, vB, vC );
}
return result;
},
// Get triangle area (half of parallelogram)
// http://mathworld.wolfram.com/TriangleArea.html
triangleArea: function () {
var vector1 = new Vector3();
var vector2 = new Vector3();
return function ( vectorA, vectorB, vectorC ) {
vector1.subVectors( vectorB, vectorA );
vector2.subVectors( vectorC, vectorA );
vector1.cross( vector2 );
return 0.5 * vector1.length();
};
}(),
center: function ( geometry ) {
console.warn( 'THREE.GeometryUtils: .center() has been moved to Geometry. Use geometry.center() instead.' );
return geometry.center();
},
/**
* Generates 2D-Coordinates in a very fast way.
*
* @author Dylan Grafmyre
*
* Based on work by:
* @author Thomas Diewald
* @link http://www.openprocessing.org/sketch/15493
*
* @param center Center of Hilbert curve.
* @param size Total width of Hilbert curve.
* @param iterations Number of subdivisions.
* @param v0 Corner index -X, -Z.
* @param v1 Corner index -X, +Z.
* @param v2 Corner index +X, +Z.
* @param v3 Corner index +X, -Z.
*/
hilbert2D: function ( center, size, iterations, v0, v1, v2, v3 ) {
// Default Vars
var center = center !== undefined ? center : new Vector3( 0, 0, 0 ),
size = size !== undefined ? size : 10,
half = size / 2,
iterations = iterations !== undefined ? iterations : 1,
v0 = v0 !== undefined ? v0 : 0,
v1 = v1 !== undefined ? v1 : 1,
v2 = v2 !== undefined ? v2 : 2,
v3 = v3 !== undefined ? v3 : 3
;
var vec_s = [
new Vector3( center.x - half, center.y, center.z - half ),
new Vector3( center.x - half, center.y, center.z + half ),
new Vector3( center.x + half, center.y, center.z + half ),
new Vector3( center.x + half, center.y, center.z - half )
];
var vec = [
vec_s[ v0 ],
vec_s[ v1 ],
vec_s[ v2 ],
vec_s[ v3 ]
];
// Recurse iterations
if ( 0 <= -- iterations ) {
var tmp = [];
Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 0 ], half, iterations, v0, v3, v2, v1 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 1 ], half, iterations, v0, v1, v2, v3 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 2 ], half, iterations, v0, v1, v2, v3 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert2D( vec[ 3 ], half, iterations, v2, v1, v0, v3 ) );
// Return recursive call
return tmp;
}
// Return complete Hilbert Curve.
return vec;
},
/**
* Generates 3D-Coordinates in a very fast way.
*
* @author Dylan Grafmyre
*
* Based on work by:
* @author Thomas Diewald
* @link http://www.openprocessing.org/visuals/?visualID=15599
*
* @param center Center of Hilbert curve.
* @param size Total width of Hilbert curve.
* @param iterations Number of subdivisions.
* @param v0 Corner index -X, +Y, -Z.
* @param v1 Corner index -X, +Y, +Z.
* @param v2 Corner index -X, -Y, +Z.
* @param v3 Corner index -X, -Y, -Z.
* @param v4 Corner index +X, -Y, -Z.
* @param v5 Corner index +X, -Y, +Z.
* @param v6 Corner index +X, +Y, +Z.
* @param v7 Corner index +X, +Y, -Z.
*/
hilbert3D: function ( center, size, iterations, v0, v1, v2, v3, v4, v5, v6, v7 ) {
// Default Vars
var center = center !== undefined ? center : new Vector3( 0, 0, 0 ),
size = size !== undefined ? size : 10,
half = size / 2,
iterations = iterations !== undefined ? iterations : 1,
v0 = v0 !== undefined ? v0 : 0,
v1 = v1 !== undefined ? v1 : 1,
v2 = v2 !== undefined ? v2 : 2,
v3 = v3 !== undefined ? v3 : 3,
v4 = v4 !== undefined ? v4 : 4,
v5 = v5 !== undefined ? v5 : 5,
v6 = v6 !== undefined ? v6 : 6,
v7 = v7 !== undefined ? v7 : 7
;
var vec_s = [
new Vector3( center.x - half, center.y + half, center.z - half ),
new Vector3( center.x - half, center.y + half, center.z + half ),
new Vector3( center.x - half, center.y - half, center.z + half ),
new Vector3( center.x - half, center.y - half, center.z - half ),
new Vector3( center.x + half, center.y - half, center.z - half ),
new Vector3( center.x + half, center.y - half, center.z + half ),
new Vector3( center.x + half, center.y + half, center.z + half ),
new Vector3( center.x + half, center.y + half, center.z - half )
];
var vec = [
vec_s[ v0 ],
vec_s[ v1 ],
vec_s[ v2 ],
vec_s[ v3 ],
vec_s[ v4 ],
vec_s[ v5 ],
vec_s[ v6 ],
vec_s[ v7 ]
];
// Recurse iterations
if ( -- iterations >= 0 ) {
var tmp = [];
Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 0 ], half, iterations, v0, v3, v4, v7, v6, v5, v2, v1 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 1 ], half, iterations, v0, v7, v6, v1, v2, v5, v4, v3 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 2 ], half, iterations, v0, v7, v6, v1, v2, v5, v4, v3 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 3 ], half, iterations, v2, v3, v0, v1, v6, v7, v4, v5 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 4 ], half, iterations, v2, v3, v0, v1, v6, v7, v4, v5 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 5 ], half, iterations, v4, v3, v2, v5, v6, v1, v0, v7 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 6 ], half, iterations, v4, v3, v2, v5, v6, v1, v0, v7 ) );
Array.prototype.push.apply( tmp, GeometryUtils.hilbert3D( vec[ 7 ], half, iterations, v6, v5, v2, v1, v0, v3, v4, v7 ) );
// Return recursive call
return tmp;
}
// Return complete Hilbert Curve.
return vec;
}
};
export { GeometryUtils };
