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/**
* @author mrdoob / http://mrdoob.com/
* @author alteredq / http://alteredqualia.com/
*/
THREE.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 THREE.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 THREE.Vector3();
return function ( vectorA, vectorB, vectorC ) {
var point = new THREE.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 THREE.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 = THREE.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 ] = THREE.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 THREE.Vector3();
vB = new THREE.Vector3();
vC = new THREE.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 += THREE.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 ] = THREE.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 ] = THREE.GeometryUtils.randomPointInTriangle( vA, vB, vC );
}
return result;
},
// Get triangle area (half of parallelogram)
// http://mathworld.wolfram.com/TriangleArea.html
triangleArea: function () {
var vector1 = new THREE.Vector3();
var vector2 = new THREE.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();
}
};
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