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THREEi_ONLY_SphereWithSomeHoles.js
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THREEi_ONLY_SphereWithSomeHoles.js
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// THREEi_ONLY_SphereWithSomeHoles.js ( rev 109.0 )
// NOTE! This version contains only the older, simplified functions
// * buildSphereWithHolesObj, buildSphereWithHoles( ),
// * this requires less effort in code and execution,
// but
// * does not check whether the current front overlaps,
// * in very many cases with few holes this is not a problem,
// * it can lead to errors in more complicated cases
/**
* @author hofk / http://threejs.hofk.de/
*/
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
typeof define === 'function' && define.amd ? define(['exports'], factory) :
(factory((global.THREEi = global.THREEi || {})));
}(this, (function (exports) {
'use strict';
var g; // THREE.BufferGeometry
//#################################################################################################
// Algorithm based on (simplified for sphere with holes)
// de: https://www2.mathematik.tu-darmstadt.de/~ehartmann/cdg0/cdg0n.pdf
// en: https://www2.mathematik.tu-darmstadt.de/~ehartmann/cdgen0104.pdf
//
// ............................ Sphere with Holes (Triangulation) .................................
function createSphereWithHoles( arg1, arg2 ) {
g = this; // THREE.BufferGeometry() - geometry object from three.js
g.buildSphereWithHolesObj = buildSphereWithHolesObj;
g.buildSphereWithHoles = buildSphereWithHoles;
if( typeof arg1 === 'number' ) { // variant detail, holes are optional, radius = 1 is fixed - use three.js .scale
// Variant with less effort in the algorithm! Other angle calculation too.
g.detail = arg1; // count of triangles for half a great circle
g.holes = arg2 !== undefined ? arg2 : []; // optional
/* holes, example:
holes = [
// circular hole, 3 elements: [ theta, phi, count ]
[ 2.44, 0.41, 12 ],
[ 0.72, 2.55, 19 ],
// points hole,: array of points theta, phi, ... (last point is connected to first)
[ 0,0, 0.5,-0.8, 0.25,-0.27, 0.4,0.3, 0.3,0.72 ]
];
*/
g.buildSphereWithHoles( );
} else { // variant parameters object { d: div4: holes: } all elements optional
g.d = arg1.d !== undefined ? arg1.d : 2 * Math.sin( Math.PI / 24 ); // to g.div4 default
g.div4 = arg1.div4 !== undefined ? arg1.div4 : 6; // 6 * 4 = 24 great circle divisions
g.holes = arg1.holes !== undefined ? arg1.holes : [];
g.detail = g.div4 * 4; // division of the great circle
g.radius = g.d / Math.sin( Math.PI / g.detail ) / 2; // sphere radius, for external use as well
/* holes, example:
holes: [
// circular hole, 3 elements: [ theta, phi, div4Hole ], div4Hole <= div4
[ 1.82, 0.41, 12 ],
// points hole,: array of points theta, phi, ... (last point is connected to first)
[ 0,0, 0.5,-0.8, 0.25,-0.27, 0.4,0.3, 0.3,0.72 ]
]
*/
g.buildSphereWithHolesObj( );
}
}
function buildSphereWithHolesObj( ) {
const dd = g.d * g.d;
const squareLength = ( x,y,z ) => ( x*x + y*y + z*z );
const length = ( x, y, z ) => ( Math.sqrt( x * x + y * y + z * z ) );
const prevFront = ( i ) => ( i !== 0 ? i - 1 : front.length - 1 );
const nextFront = ( i ) => ( i !== front.length - 1 ? i + 1 : 0 );
const determinant = ( xa,ya,za, xb,yb,zb, xc,yc,zc ) => ( xa*yb*zc + ya*zb*xc + za*xb*yc - za*yb*xc - xa*zb*yc - ya*xb*zc );
let m; // index of the current front point
let n; // number of new points
let nT; // number of new triangles
let nIns; // number of new points (after union or split)
let dAng; // partial angle
let len, d1, d2, d12; // lengths
let iSplit, jSplit; // split front indices
let iUnite, jUnite, fUnite; // unite front indices, front number (to unite)
// points and vectors:
let x, y, z, xp, yp, zp; // coordinates point and actual point p
let x1, y1, z1, x2, y2, z2; // previous and next point to p in front
let xn, yn, zn; // normal, gradient (sphere: normalized point)
let xt1, yt1, zt1, xt2, yt2, zt2; // tangents
let xs1, ys1, xs2, ys2; // p in tangential system (only x, y required)
let xc, yc, zc; // actual point as center point for new points
// preparation
const faceCount = g.detail * g.detail * 8 ;
const posCount = g.detail * g.detail * 6 ;
g.indices = new Uint32Array( faceCount * 3 );
g.positions = new Float32Array( posCount * 3 );
//g.normals = new Float32Array( posCount * 3 );
g.setIndex( new THREE.BufferAttribute( g.indices, 1 ) );
g.addAttribute( 'position', new THREE.BufferAttribute( g.positions, 3 ) );
let posIdx = 0;
let indIdx = 0;
let frontPosIdx, unionIdxA, unionIdxB, splitIdx;
let front = []; // active front // front[ i ]: object { idx: 0, ang: 0 }
let partFront = []; // separated part of the active front (to split)
let insertFront = []; // new front points to insert into active front
let fronts = []; // all fronts
let partBounds = []; // bounding box of partFront [ xmin, xmax, ymin, ymax, zmin, zmax ]
let boundings = []; // fronts bounding boxes
let smallAngles = []; // new angles < 1.5
let frontNo, frontStock;
let unite = false;
let split = false;
frontNo = 0; // active front number
frontStock = 0; // number of fronts still to be processed
// define holes fronts
if ( g.holes.length === 0 ) {
makeFirstTriangle( );
} else {
g.circles = []; // array of arrays [ xc, yc, zc, rHole, div4Hole ], values for external use
for ( let i = 0; i < g.holes.length; i ++ ) {
if ( g.holes[ i ].length === 3 ) {
makeCircularHole( i ); // [ theta, phi, div4Hole ]
} else {
makePointsHole( i ); // points: [ theta, phi, ... ]
}
}
}
frontNo = 0;
front = fronts[ frontNo ];
//////////////// DEBUG triangles //////////////////////////////////////
// let stp = 0;
///////////////////////////////////////////////////////////////////////
// ------ triangulation cycle -------------
while ( frontStock > 0 ) {
if ( !unite ) { // triangulation on the front
smallAngles = [];
for ( let i = 0; i < front.length; i ++ ) {
if( front[ i ].ang === 0 ) calculateFrontAngle( i ); // is to be recalculated (angle was set to zero)
}
m = getMinimalAngleIndex( ); // front angle
makeNewTriangles( m );
if ( front.length > 9 && smallAngles.length === 0 ) {
checkDistancesToUnite( m );
}
if ( front.length === 3 ) {
makeLastTriangle( ); // last triangle closes the front
chooseNextFront( ); // if aviable
}
} else { // unite the active front to another front
uniteFront( m, iUnite, fUnite, jUnite );
trianglesAtUnionPoints( );
unite = false;
}
}
// ..... detail functions .....
function makeFirstTriangle ( ) {
fronts[ frontNo ] = [];
boundings[ frontNo ] = [];
storePoint( 0, 0 ); // ( theta, phi )
storePoint( Math.PI / 2 / g.div4, -Math.PI / 6 );
storePoint( Math.PI / 2 / g.div4, Math.PI / 6 );
g.indices[ 0 ] = 0;
g.indices[ 1 ] = 1;
g.indices[ 2 ] = 2;
indIdx += 3;
fronts[ frontNo ].push( { idx: 0, ang: 0 }, { idx: 1, ang: 0 }, { idx: 2, ang: 0 } );
frontNo ++;
frontStock ++;
}
function makePointsHole( i ) {
let theta, phi, count, xmin, ymin, zmin, xmax, ymax, zmax, xv2, yv2, zv2;
xmin = ymin = zmin = Infinity;
xmax = ymax = zmax = -Infinity;
fronts[ frontNo ] = [];
boundings[ frontNo ] = [];
theta = g.holes[ i ][ 0 ];
phi = g.holes[ i ][ 1 ];
x1 = g.radius * Math.sin( theta ) * Math.cos( phi );
y1 = g.radius * Math.cos( theta );
z1 = -g.radius * Math.sin( theta ) * Math.sin( phi );
for ( let j = 1; j < g.holes[ i ].length / 2 + 1; j ++ ) {
g.positions[ posIdx ] = x1;
g.positions[ posIdx + 1 ] = y1;
g.positions[ posIdx + 2 ] = z1;
fronts[ frontNo ].push( { idx: posIdx / 3, ang: 0 } );
xmin = x1 < xmin ? x1 : xmin;
ymin = y1 < ymin ? y1 : ymin;
zmin = z1 < zmin ? z1 : zmin;
xmax = x1 > xmax ? x1 : xmax;
ymax = y1 > ymax ? y1 : ymax;
zmax = z1 > zmax ? z1 : zmax;
posIdx += 3;
theta = g.holes[ i ][ j < g.holes[ i ].length / 2 ? j * 2 : 0 ]; // 0 => connect to start
phi = g.holes[ i ][ j < g.holes[ i ].length / 2 ? j * 2 + 1 : 1 ]; // 1 => connect to start
x2 = g.radius * Math.sin( theta ) * Math.cos( phi );
y2 = g.radius * Math.cos( theta );
z2 = -g.radius * Math.sin( theta ) * Math.sin( phi );
xv2 = x2 - x1;
yv2 = y2 - y1;
zv2 = z2 - z1;
len = length( xv2, yv2, zv2 );
if ( len > g.d ) {
count = Math.ceil( len / g.d );
for ( let k = 1; k < count; k ++ ) {
x = x1 + k * xv2 / count;
y = y1 + k * yv2 / count;
z = z1 + k * zv2 / count;
len = length( x, y, z ); // to bring the point to the surface (g.radius * ..)
g.positions[ posIdx ] = g.radius * x / len;
g.positions[ posIdx + 1 ] = g.radius * y / len;
g.positions[ posIdx + 2 ] = g.radius * z / len;
fronts[ frontNo ].push( { idx: posIdx / 3, ang: 0 } );
xmin = x < xmin ? x : xmin;
ymin = y < ymin ? y : ymin;
zmin = z < zmin ? z : zmin;
xmax = x > xmax ? x : xmax;
ymax = y > ymax ? y : ymax;
zmax = z > zmax ? z : zmax;
posIdx += 3;
}
}
x1 = x2;
y1 = y2;
z1 = z2;
}
boundings[ frontNo ].push( xmin, xmax, ymin, ymax, zmin, zmax );
frontNo ++;
frontStock ++;
}
function makeCircularHole( i ) {
let xa, ya, za, xb, yb; // for rotation around z, y
const theta = g.holes[ i ][ 0 ];
const phi = g.holes[ i ][ 1 ];
const div4Hole = g.holes[ i ][ 2 ];
const countH = div4Hole * 4;
let xmin, ymin, zmin, xmax, ymax, zmax;
xmin = ymin = zmin = Infinity;
xmax = ymax = zmax = -Infinity;
const rHole = g.d / ( Math.sin( Math.PI / countH ) * 2 ); // radius cutting circle
const h = Math.sqrt( g.radius * g.radius - rHole * rHole ); // distance: sphere center to cutting circle
// ... hole values for external use
xp = g.radius * Math.sin( theta ) * Math.cos( phi );
yp = g.radius * Math.cos( theta );
zp = -g.radius * -Math.sin( theta ) * Math.sin( phi );
xc = h / g.radius * xp;
yc = h / g.radius * yp;
zc = h / g.radius * zp;
g.circles.push( [ xc, yc, zc, rHole, div4Hole ] ); // values for external use
fronts[ frontNo ] = [];
boundings[ frontNo ] = [];
ya = h;
for ( let i = 0, alpha = 0; i < countH; i ++, alpha += 2 * Math.PI / countH ) {
// cutting circle on top
xa = rHole * Math.cos( alpha );
za = rHole * Math.sin( alpha );
// rotate around z axis
xb = xa * Math.cos( theta ) - ya * Math.sin( theta );
yb = xa * Math.sin( theta ) + ya * Math.cos( theta );
// rotate around y axis
x = -xb * Math.cos( phi ) + za * Math.sin( phi );
z = xb * Math.sin( phi ) + za * Math.cos( phi );
y = yb; // for storing and checking bounds
g.positions[ posIdx ] = x;
g.positions[ posIdx + 1 ] = y;
g.positions[ posIdx + 2 ] = z;
fronts[ frontNo ].push( { idx: posIdx / 3, ang: 0 } );
xmin = x < xmin ? x : xmin;
ymin = y < ymin ? y : ymin;
zmin = z < zmin ? z : zmin;
xmax = x > xmax ? x : xmax;
ymax = y > ymax ? y : ymax;
zmax = z > zmax ? z : zmax;
posIdx += 3;
}
boundings[ frontNo ].push( xmin, xmax, ymin, ymax, zmin, zmax );
frontNo ++;
frontStock ++;
}
function checkDistancesToUnite( m ) { // for new active front points
let idxJ, xChk, yChk, zChk, ddUnite;
let ddUniteMin = Infinity;
unite = false;
for ( let i = 0; i < insertFront.length; i ++ ) {
getPoint( m + i );
for ( let f = 0; f < fronts.length; f ++ ) {
if ( f !== frontNo ) {
xChk = ( xp > boundings[ f ][ 0 ] - g.d ) && ( xp < boundings[ f ][ 3 ] + g.d );
yChk = ( yp > boundings[ f ][ 1 ] - g.d ) && ( yp < boundings[ f ][ 4 ] + g.d );
zChk = ( zp > boundings[ f ][ 2 ] - g.d ) && ( zp < boundings[ f ][ 5 ] + g.d );
if ( xChk || yChk || zChk ) {
for ( let j = 0; j < fronts[ f ].length; j ++ ) {
idxJ = fronts[ f ][ j ].idx * 3;
// Hint: here (2) is exceptionally point in other front!
x2 = g.positions[ idxJ ];
y2 = g.positions[ idxJ + 1 ];
z2 = g.positions[ idxJ + 2 ];
ddUnite = squareLength ( x2 - xp, y2 - yp, z2 - zp );
if ( ddUnite < dd && ddUnite < ddUniteMin ) {
ddUniteMin = ddUnite;
iUnite = i;
jUnite = j;
fUnite = f;
unite = true;
}
}
}
}
}
}
}
function uniteFront( m, i, f, j ) {
let tmp = [];
tmp[ 0 ] = front.slice( 0, m + i + 1 );
tmp[ 1 ] = fronts[ f ].slice( j , fronts[ f ].length );
tmp[ 2 ] = fronts[ f ].slice( 0 , j + 1 );
tmp[ 3 ] = front.slice( m + i, front.length );
unionIdxA = m + i;
unionIdxB = m + i + 1 + fronts[ f ].length
front = [];
for ( let t = 0; t < 4; t ++ ) {
for ( let k = 0; k < tmp[ t ].length ; k ++ ) {
front.push( tmp[ t ][ k ] );
}
}
fronts[ f ] = []; // empty united front
frontStock -= 1; // front is eliminated
}
function trianglesAtUnionPoints( ) {
nIns = 0; // count inserted points
calculateFrontAngle( unionIdxA );
calculateFrontAngle( unionIdxA + 1 );
if ( front[ unionIdxA ].ang < front[ unionIdxA + 1 ].ang ) {
makeNewTriangles( unionIdxA );
nIns += n - 1;
calculateFrontAngle( unionIdxA + 1 + nIns );
makeNewTriangles( unionIdxA + 1 + nIns );
nIns += n - 1;
} else {
makeNewTriangles( unionIdxA + 1 );
nIns += n - 1;
calculateFrontAngle( unionIdxA );
makeNewTriangles( unionIdxA );
nIns += n - 1;
}
calculateFrontAngle( unionIdxB + nIns );
calculateFrontAngle( unionIdxB + 1 + nIns );
if ( front[ unionIdxB + nIns ].ang < front[ unionIdxB + 1 + nIns ].ang ) {
makeNewTriangles( unionIdxB + nIns );
nIns += n - 1;
calculateFrontAngle( unionIdxB + 1 + nIns );
makeNewTriangles( unionIdxB + 1 + nIns );
} else {
makeNewTriangles( unionIdxB + 1 + nIns );
calculateFrontAngle( unionIdxB + nIns );
makeNewTriangles( unionIdxB + nIns );
}
}
function getMinimalAngleIndex( ) {
let angle = Infinity;
let m;
for ( let i = 0; i < front.length; i ++ ) {
if( front[ i ].ang < angle ) {
angle = front[ i ].ang ;
m = i;
}
}
return m;
}
function makeNewTriangles( m ) {
// m: minimal angle (index)
insertFront = []; // new front points
nT = Math.floor( 3 * front[ m ].ang / Math.PI ) + 1; // number of new triangles
dAng = front[ m ].ang / nT;
getSystemAtPoint( m );
getNextPoint( m );
d1 = length( x1 - xp, y1 - yp, z1 - zp );
d2 = length( x2 - xp, y2 - yp, z2 - zp );
d12 = length( x2 - x1, y2 - y1, z2 - z1 );
// correction of dAng, nT in extreme cases
if ( dAng < 0.8 && nT > 1 ) {
nT --;
dAng = front[ m ].ang / nT;
}
if ( dAng > 0.8 && nT === 1 && d12 > 1.25 * g.d ) {
nT = 2;
dAng = front[ m ].ang / nT;
}
if ( d1 * d1 < 0.2 * dd || d2 * d2 < 0.2 * dd ) {
nT = 1;
}
n = nT - 1; // n number of new points
if ( n === 0 ) { // one triangle
g.indices[ indIdx ] = front[ m ].idx;
g.indices[ indIdx + 1 ] = front[ prevFront( m ) ].idx;
g.indices[ indIdx + 2 ] = front[ nextFront( m ) ].idx;
indIdx += 3;
/////////////// DEBUG triangles //////////////////////
// stp ++;
////////////////////////////////////////////////////////
front[ prevFront( m ) ].ang = 0;
front[ nextFront( m ) ].ang = 0;
front.splice( m, 1 ); // delete point with index m from the front
} else { // more then one triangle
xc = xp;
yc = yp;
zc = zp;
for ( let i = 0, phi = dAng; i < n; i ++, phi += dAng ) {
xp = xc + Math.cos( phi ) * g.d * xt1 + Math.sin( phi ) * g.d * xt2;
yp = yc + Math.cos( phi ) * g.d * yt1 + Math.sin( phi ) * g.d * yt2;
zp = zc + Math.cos( phi ) * g.d * zt1 + Math.sin( phi ) * g.d * zt2;
len = length( xp, yp, zp ); // to bring the point to the surface (g.radius * ..)
g.positions[ posIdx ] = g.radius * xp / len;
g.positions[ posIdx + 1 ] = g.radius * yp / len;
g.positions[ posIdx + 2 ] = g.radius * zp / len;
insertFront.push( { idx: posIdx / 3, ang: 0 } );
posIdx += 3;
}
g.indices[ indIdx ] = front[ m ].idx;
g.indices[ indIdx + 1 ] = front[ prevFront( m ) ].idx
g.indices[ indIdx + 2 ] = insertFront[ 0 ].idx;
indIdx += 3;
/////////////// DEBUG triangles //////////////////////
// stp ++;
////////////////////////////////////////////////////////
front[ prevFront( m ) ].ang = 0;
for ( let i = 0; i < n - 1; i ++ ) {
g.indices[ indIdx ] = front[ m ].idx;
g.indices[ indIdx + 1 ] = insertFront[ i ].idx;
g.indices[ indIdx + 2 ] = insertFront[ i + 1 ].idx;
indIdx += 3;
/////////////// DEBUG triangles //////////////////////
// stp ++;
////////////////////////////////////////////////////////
}
g.indices[ indIdx ] = front[ m ].idx;
g.indices[ indIdx + 1 ] = insertFront[ n - 1 ].idx;
g.indices[ indIdx + 2 ] = front[ nextFront( m ) ].idx;
front[ nextFront( m ) ].ang = 0;
indIdx += 3;
/////////////// DEBUG triangles //////////////////////
// stp ++;
////////////////////////////////////////////////////////
replaceFront( m, insertFront ); // replaces front[ m ] with new points
}
}
function makeLastTriangle( ) {
g.indices[ indIdx ] = front[ 2 ].idx;
g.indices[ indIdx + 1 ] = front[ 1 ].idx
g.indices[ indIdx + 2 ] = front[ 0 ].idx;
indIdx += 3;
/////////////// DEBUG triangles //////////////////////
// stp ++;
////////////////////////////////////////////////////////
front = [];
fronts[ frontNo ] = [];
frontStock -= 1; // close front
}
function chooseNextFront( ) {
if ( frontStock > 0 ) {
for ( let i = 0; i < fronts.length; i ++ ) {
if ( fronts[ i ].length > 0 ) {
frontNo = i;
break;
}
}
front = fronts[ frontNo ];
smallAngles = [];
for ( let i = 0; i < front.length; i ++ ) {
calculateFrontAngle( i ); // recalculate angles of next front
}
}
}
function atan2PI( x, y ) {
let phi = Math.atan2( y, x );
if ( phi < 0 ) phi = phi + Math.PI * 2;
return phi;
}
function coordTangentialSystem( ) {
let det = determinant( xt1, yt1, zt1, xt2, yt2, zt2, xn, yn, zn );
xs1 = determinant( x1 - xp, y1 - yp, z1 - zp, xt2, yt2, zt2, xn, yn, zn ) / det;
ys1 = determinant( xt1, yt1, zt1, x1 - xp, y1 - yp, z1 - zp, xn, yn, zn ) / det;
//zs1 = determinant( xt1, yt1, zt1, xt2, yt2, zt2, x1 - xp, y1 - yp, z1 - zp ) / det; // not needed
xs2 = determinant( x2 - xp, y2 - yp, z2 - zp, xt2, yt2, zt2, xn, yn, zn ) / det;
ys2 = determinant( xt1, yt1, zt1, x2 - xp, y2 - yp, z2 - zp, xn, yn, zn ) / det;
//zs2 = determinant( xt1, yt1, zt1, xt2, yt2, zt2, x2 - xp, y2 - yp, z2 - zp ) / det; // not needed
}
function calculateFrontAngle( i ) {
let ang1, ang2;
getSystemAtPoint( i );
getNextPoint( i );
coordTangentialSystem( );
ang1 = atan2PI( xs1, ys1 );
ang2 = atan2PI( xs2, ys2 );
if ( ang2 < ang1 ) ang2 += Math.PI * 2;
front[ i ].ang = ang2 - ang1;
if ( front[ i ].ang < 1.5 ) smallAngles.push( i );
}
function partFrontBounds( ) {
let idx, xmin, ymin, zmin, xmax, ymax, zmax;
partBounds = [];
xmin = ymin = zmin = Infinity;
xmax = ymax = zmax = -Infinity;
for( let i = 0; i < partFront.length; i ++ ) {
idx = partFront[ i ].idx * 3;
x = g.positions[ idx ];
y = g.positions[ idx + 1 ];
z = g.positions[ idx + 2 ];
xmin = x < xmin ? x : xmin;
ymin = y < ymin ? y : ymin;
zmin = z < zmin ? z : zmin;
xmax = x > xmax ? x : xmax;
ymax = y > ymax ? y : ymax;
zmax = z > zmax ? z : zmax;
}
partBounds.push( xmin, ymin, zmin, xmax, ymax, zmax );
boundings.push( partBounds );
}
function replaceFront( m, fNew ) {
let rear = front.splice( m, front.length - m );
for ( let i = 0; i < fNew.length; i ++ ) {
front.push( fNew[ i ] ); // new front points
}
for ( let i = 1; i < rear.length; i ++ ) { // i = 1: without old front point m
front.push( rear[ i ] );
}
}
function getSystemAtPoint( i ) {
getPrevPoint( i );
getPoint( i );
len = length( xp, yp, zp ); // to normalize
xn = xp / len;
yn = yp / len
zn = zp / len;
// centerAngle = Math.acos( Math.abs( x1 * xp + y1 * yp + z1 * zp ) / ( g.radius * g.radius ) );
const h = Math.abs( x1 * xp + y1 * yp + z1 * zp ) / g.radius; // distance: sphere center to cutting circle
// center cutting circle (refers to previous point)
xc = h / g.radius * xp;
yc = h / g.radius * yp;
zc = h / g.radius * zp;
// first tangent
xt1 = x1 - xc;
yt1 = y1 - yc;
zt1 = z1 - zc;
len = length( xt1, yt1, zt1 ); // to normalize
xt1 = xt1 / len;
yt1 = yt1 / len;
zt1 = zt1 / len;
// cross, second tangent
xt2 = yn * zt1 - zn * yt1;
yt2 = zn * xt1 - xn * zt1;
zt2 = xn * yt1 - yn * xt1;
}
function storePoint( theta, phi ) {
g.positions[ posIdx ] = g.radius * Math.sin( theta ) * Math.cos( phi );
g.positions[ posIdx + 1 ] = g.radius * Math.cos( theta );
g.positions[ posIdx + 2 ] = -g.radius * Math.sin( theta ) * Math.sin( phi );
posIdx += 3;
}
function getPrevPoint( i ) {
frontPosIdx = front[ prevFront( i ) ].idx * 3;
x1 = g.positions[ frontPosIdx ];
y1 = g.positions[ frontPosIdx + 1 ];
z1 = g.positions[ frontPosIdx + 2 ];
}
function getPoint( i ) {
frontPosIdx = front[ i ].idx * 3;
xp = g.positions[ frontPosIdx ];
yp = g.positions[ frontPosIdx + 1 ];
zp = g.positions[ frontPosIdx + 2 ];
}
function getNextPoint( i ) {
frontPosIdx = front[ nextFront( i ) ].idx * 3;
x2 = g.positions[ frontPosIdx ];
y2 = g.positions[ frontPosIdx + 1 ];
z2 = g.positions[ frontPosIdx + 2 ];
}
}
function buildSphereWithHoles( ) {
const length = ( x, y, z ) => ( Math.sqrt( x * x + y * y + z * z ) );
const prevFront = ( i ) => ( i !== 0 ? i - 1 : front.length - 1 );
const nextFront = ( i ) => ( i !== front.length - 1 ? i + 1 : 0 );
let d; // rough edge length of the triangles
let m; // index of the current front point
let n; // number of new points
let nT; // number of new triangles
let nUnion; // number of new points (after union)
let dAng; // partial angle
let len, d1, d2, d12, dd1, dd2, dd12; // lengths and their squares
let h; // distance center to circle
let acute, concave; // front angle properties
// points and vectors:
let x, y, z, xp, yp, zp, xc, yc, zc, x1, y1, z1, x2, y2, z2, xt1, yt1, zt1, xt2, yt2, zt2, xv1, yv1, zv1, xv2, yv2, zv2;
// preparation
const faceCount = g.detail * g.detail * 4;
const posCount = g.detail * g.detail * 3;
g.indices = new Uint32Array( faceCount * 3 );
g.positions = new Float32Array( posCount * 3 );
//g.normals = new Float32Array( posCount * 3 );
g.setIndex( new THREE.BufferAttribute( g.indices, 1 ) );
g.addAttribute( 'position', new THREE.BufferAttribute( g.positions, 3 ) );
d = Math.PI / g.detail; // rough side length of the triangles
let posIdx = 0;
let indIdx = 0;
let frontPosIdx, unionIdxA, unionIdxB;
let front = []; // active front // front[ i ]: object { idx: 0, ang: 0 }
let partFront = []; // separated part of the active front
let insertFront = []; // new front points to insert into active front
let fronts = []; // all fronts
let partBounds = []; // bounding box of partFront [ xmin, xmax, ymin, ymax, zmin, zmax ]
let boundings = []; // fronts bounding boxes
let smallAngles = []; // new angles < 1.5
let start = true;
let united = false;
// define holes
let holeNumber;
if ( g.holes.length === 0 ) {
makeFirstTriangle( );
} else {
g.circles = []; // [ center, r, count ] of holes for external use
holeNumber = 0;
for ( let i = 0; i < g.holes.length; i ++ ) {
if ( g.holes[ i ].length === 3 ) {
makeCircularHole( i ); // [ theta, phi, count ]
} else {
makePointsHole( i ); // points: [ theta, phi, ... ]
}
}
}
let activeFrontNo = 0;
front = fronts[ activeFrontNo ];
// ------ triangulation cycle -------------
while ( front.length > 3 || start ) {
if ( start ) start = false;
if ( front.length > 9 && smallAngles.length === 0 ) {
// checkDistancesInFront( );
checkDistancesToFronts( m );
}
if ( united ) {
trianglesAtUnionPoints( );
} else {