[28897] | 1 | /**
|
---|
| 2 | * @author WestLangley / https://github.com/WestLangley
|
---|
| 3 | * @author zz85 / https://github.com/zz85
|
---|
| 4 | * @author miningold / https://github.com/miningold
|
---|
| 5 | *
|
---|
| 6 | * Modified from the TorusKnotGeometry by @oosmoxiecode
|
---|
| 7 | *
|
---|
| 8 | * Creates a tube which extrudes along a 3d spline
|
---|
| 9 | *
|
---|
| 10 | * Uses parallel transport frames as described in
|
---|
| 11 | * http://www.cs.indiana.edu/pub/techreports/TR425.pdf
|
---|
| 12 | */
|
---|
| 13 |
|
---|
| 14 | THREE.TubeGeometry = function( path, segments, radius, radialSegments, closed ) {
|
---|
| 15 |
|
---|
| 16 | THREE.Geometry.call( this );
|
---|
| 17 |
|
---|
| 18 | this.path = path;
|
---|
| 19 | this.segments = segments || 64;
|
---|
| 20 | this.radius = radius || 1;
|
---|
| 21 | this.radialSegments = radialSegments || 8;
|
---|
| 22 | this.closed = closed || false;
|
---|
| 23 |
|
---|
| 24 | this.grid = [];
|
---|
| 25 |
|
---|
| 26 | var scope = this,
|
---|
| 27 |
|
---|
| 28 | tangent,
|
---|
| 29 | normal,
|
---|
| 30 | binormal,
|
---|
| 31 |
|
---|
| 32 | numpoints = this.segments + 1,
|
---|
| 33 |
|
---|
| 34 | x, y, z,
|
---|
| 35 | tx, ty, tz,
|
---|
| 36 | u, v,
|
---|
| 37 |
|
---|
| 38 | cx, cy,
|
---|
| 39 | pos, pos2 = new THREE.Vector3(),
|
---|
| 40 | i, j,
|
---|
| 41 | ip, jp,
|
---|
| 42 | a, b, c, d,
|
---|
| 43 | uva, uvb, uvc, uvd;
|
---|
| 44 |
|
---|
| 45 | var frames = new THREE.TubeGeometry.FrenetFrames( this.path, this.segments, this.closed ),
|
---|
| 46 | tangents = frames.tangents,
|
---|
| 47 | normals = frames.normals,
|
---|
| 48 | binormals = frames.binormals;
|
---|
| 49 |
|
---|
| 50 | // proxy internals
|
---|
| 51 | this.tangents = tangents;
|
---|
| 52 | this.normals = normals;
|
---|
| 53 | this.binormals = binormals;
|
---|
| 54 |
|
---|
| 55 | function vert( x, y, z ) {
|
---|
| 56 |
|
---|
| 57 | return scope.vertices.push( new THREE.Vector3( x, y, z ) ) - 1;
|
---|
| 58 |
|
---|
| 59 | }
|
---|
| 60 |
|
---|
| 61 |
|
---|
| 62 | // consruct the grid
|
---|
| 63 |
|
---|
| 64 | for ( i = 0; i < numpoints; i++ ) {
|
---|
| 65 |
|
---|
| 66 | this.grid[ i ] = [];
|
---|
| 67 |
|
---|
| 68 | u = i / ( numpoints - 1 );
|
---|
| 69 |
|
---|
| 70 | pos = path.getPointAt( u );
|
---|
| 71 |
|
---|
| 72 | tangent = tangents[ i ];
|
---|
| 73 | normal = normals[ i ];
|
---|
| 74 | binormal = binormals[ i ];
|
---|
| 75 |
|
---|
| 76 | for ( j = 0; j < this.radialSegments; j++ ) {
|
---|
| 77 |
|
---|
| 78 | v = j / this.radialSegments * 2 * Math.PI;
|
---|
| 79 |
|
---|
| 80 | cx = -this.radius * Math.cos( v ); // TODO: Hack: Negating it so it faces outside.
|
---|
| 81 | cy = this.radius * Math.sin( v );
|
---|
| 82 |
|
---|
| 83 | pos2.copy( pos );
|
---|
| 84 | pos2.x += cx * normal.x + cy * binormal.x;
|
---|
| 85 | pos2.y += cx * normal.y + cy * binormal.y;
|
---|
| 86 | pos2.z += cx * normal.z + cy * binormal.z;
|
---|
| 87 |
|
---|
| 88 | this.grid[ i ][ j ] = vert( pos2.x, pos2.y, pos2.z );
|
---|
| 89 |
|
---|
| 90 | }
|
---|
| 91 | }
|
---|
| 92 |
|
---|
| 93 |
|
---|
| 94 | // construct the mesh
|
---|
| 95 |
|
---|
| 96 | for ( i = 0; i < this.segments; i++ ) {
|
---|
| 97 |
|
---|
| 98 | for ( j = 0; j < this.radialSegments; j++ ) {
|
---|
| 99 |
|
---|
| 100 | ip = ( this.closed ) ? (i + 1) % this.segments : i + 1;
|
---|
| 101 | jp = (j + 1) % this.radialSegments;
|
---|
| 102 |
|
---|
| 103 | a = this.grid[ i ][ j ]; // *** NOT NECESSARILY PLANAR ! ***
|
---|
| 104 | b = this.grid[ ip ][ j ];
|
---|
| 105 | c = this.grid[ ip ][ jp ];
|
---|
| 106 | d = this.grid[ i ][ jp ];
|
---|
| 107 |
|
---|
| 108 | uva = new THREE.Vector2( i / this.segments, j / this.radialSegments );
|
---|
| 109 | uvb = new THREE.Vector2( ( i + 1 ) / this.segments, j / this.radialSegments );
|
---|
| 110 | uvc = new THREE.Vector2( ( i + 1 ) / this.segments, ( j + 1 ) / this.radialSegments );
|
---|
| 111 | uvd = new THREE.Vector2( i / this.segments, ( j + 1 ) / this.radialSegments );
|
---|
| 112 |
|
---|
| 113 | this.faces.push( new THREE.Face3( a, b, d ) );
|
---|
| 114 | this.faceVertexUvs[ 0 ].push( [ uva, uvb, uvd ] );
|
---|
| 115 |
|
---|
| 116 | this.faces.push( new THREE.Face3( b, c, d ) );
|
---|
| 117 | this.faceVertexUvs[ 0 ].push( [ uvb.clone(), uvc, uvd.clone() ] );
|
---|
| 118 |
|
---|
| 119 | }
|
---|
| 120 | }
|
---|
| 121 |
|
---|
| 122 | this.computeCentroids();
|
---|
| 123 | this.computeFaceNormals();
|
---|
| 124 | this.computeVertexNormals();
|
---|
| 125 |
|
---|
| 126 | };
|
---|
| 127 |
|
---|
| 128 | THREE.TubeGeometry.prototype = Object.create( THREE.Geometry.prototype );
|
---|
| 129 |
|
---|
| 130 |
|
---|
| 131 | // For computing of Frenet frames, exposing the tangents, normals and binormals the spline
|
---|
| 132 | THREE.TubeGeometry.FrenetFrames = function(path, segments, closed) {
|
---|
| 133 |
|
---|
| 134 | var tangent = new THREE.Vector3(),
|
---|
| 135 | normal = new THREE.Vector3(),
|
---|
| 136 | binormal = new THREE.Vector3(),
|
---|
| 137 |
|
---|
| 138 | tangents = [],
|
---|
| 139 | normals = [],
|
---|
| 140 | binormals = [],
|
---|
| 141 |
|
---|
| 142 | vec = new THREE.Vector3(),
|
---|
| 143 | mat = new THREE.Matrix4(),
|
---|
| 144 |
|
---|
| 145 | numpoints = segments + 1,
|
---|
| 146 | theta,
|
---|
| 147 | epsilon = 0.0001,
|
---|
| 148 | smallest,
|
---|
| 149 |
|
---|
| 150 | tx, ty, tz,
|
---|
| 151 | i, u, v;
|
---|
| 152 |
|
---|
| 153 |
|
---|
| 154 | // expose internals
|
---|
| 155 | this.tangents = tangents;
|
---|
| 156 | this.normals = normals;
|
---|
| 157 | this.binormals = binormals;
|
---|
| 158 |
|
---|
| 159 | // compute the tangent vectors for each segment on the path
|
---|
| 160 |
|
---|
| 161 | for ( i = 0; i < numpoints; i++ ) {
|
---|
| 162 |
|
---|
| 163 | u = i / ( numpoints - 1 );
|
---|
| 164 |
|
---|
| 165 | tangents[ i ] = path.getTangentAt( u );
|
---|
| 166 | tangents[ i ].normalize();
|
---|
| 167 |
|
---|
| 168 | }
|
---|
| 169 |
|
---|
| 170 | initialNormal3();
|
---|
| 171 |
|
---|
| 172 | function initialNormal1(lastBinormal) {
|
---|
| 173 | // fixed start binormal. Has dangers of 0 vectors
|
---|
| 174 | normals[ 0 ] = new THREE.Vector3();
|
---|
| 175 | binormals[ 0 ] = new THREE.Vector3();
|
---|
| 176 | if (lastBinormal===undefined) lastBinormal = new THREE.Vector3( 0, 0, 1 );
|
---|
| 177 | normals[ 0 ].crossVectors( lastBinormal, tangents[ 0 ] ).normalize();
|
---|
| 178 | binormals[ 0 ].crossVectors( tangents[ 0 ], normals[ 0 ] ).normalize();
|
---|
| 179 | }
|
---|
| 180 |
|
---|
| 181 | function initialNormal2() {
|
---|
| 182 |
|
---|
| 183 | // This uses the Frenet-Serret formula for deriving binormal
|
---|
| 184 | var t2 = path.getTangentAt( epsilon );
|
---|
| 185 |
|
---|
| 186 | normals[ 0 ] = new THREE.Vector3().subVectors( t2, tangents[ 0 ] ).normalize();
|
---|
| 187 | binormals[ 0 ] = new THREE.Vector3().crossVectors( tangents[ 0 ], normals[ 0 ] );
|
---|
| 188 |
|
---|
| 189 | normals[ 0 ].crossVectors( binormals[ 0 ], tangents[ 0 ] ).normalize(); // last binormal x tangent
|
---|
| 190 | binormals[ 0 ].crossVectors( tangents[ 0 ], normals[ 0 ] ).normalize();
|
---|
| 191 |
|
---|
| 192 | }
|
---|
| 193 |
|
---|
| 194 | function initialNormal3() {
|
---|
| 195 | // select an initial normal vector perpenicular to the first tangent vector,
|
---|
| 196 | // and in the direction of the smallest tangent xyz component
|
---|
| 197 |
|
---|
| 198 | normals[ 0 ] = new THREE.Vector3();
|
---|
| 199 | binormals[ 0 ] = new THREE.Vector3();
|
---|
| 200 | smallest = Number.MAX_VALUE;
|
---|
| 201 | tx = Math.abs( tangents[ 0 ].x );
|
---|
| 202 | ty = Math.abs( tangents[ 0 ].y );
|
---|
| 203 | tz = Math.abs( tangents[ 0 ].z );
|
---|
| 204 |
|
---|
| 205 | if ( tx <= smallest ) {
|
---|
| 206 | smallest = tx;
|
---|
| 207 | normal.set( 1, 0, 0 );
|
---|
| 208 | }
|
---|
| 209 |
|
---|
| 210 | if ( ty <= smallest ) {
|
---|
| 211 | smallest = ty;
|
---|
| 212 | normal.set( 0, 1, 0 );
|
---|
| 213 | }
|
---|
| 214 |
|
---|
| 215 | if ( tz <= smallest ) {
|
---|
| 216 | normal.set( 0, 0, 1 );
|
---|
| 217 | }
|
---|
| 218 |
|
---|
| 219 | vec.crossVectors( tangents[ 0 ], normal ).normalize();
|
---|
| 220 |
|
---|
| 221 | normals[ 0 ].crossVectors( tangents[ 0 ], vec );
|
---|
| 222 | binormals[ 0 ].crossVectors( tangents[ 0 ], normals[ 0 ] );
|
---|
| 223 | }
|
---|
| 224 |
|
---|
| 225 |
|
---|
| 226 | // compute the slowly-varying normal and binormal vectors for each segment on the path
|
---|
| 227 |
|
---|
| 228 | for ( i = 1; i < numpoints; i++ ) {
|
---|
| 229 |
|
---|
| 230 | normals[ i ] = normals[ i-1 ].clone();
|
---|
| 231 |
|
---|
| 232 | binormals[ i ] = binormals[ i-1 ].clone();
|
---|
| 233 |
|
---|
| 234 | vec.crossVectors( tangents[ i-1 ], tangents[ i ] );
|
---|
| 235 |
|
---|
| 236 | if ( vec.length() > epsilon ) {
|
---|
| 237 |
|
---|
| 238 | vec.normalize();
|
---|
| 239 |
|
---|
| 240 | theta = Math.acos( THREE.Math.clamp( tangents[ i-1 ].dot( tangents[ i ] ), -1, 1 ) ); // clamp for floating pt errors
|
---|
| 241 |
|
---|
| 242 | normals[ i ].applyMatrix4( mat.makeRotationAxis( vec, theta ) );
|
---|
| 243 |
|
---|
| 244 | }
|
---|
| 245 |
|
---|
| 246 | binormals[ i ].crossVectors( tangents[ i ], normals[ i ] );
|
---|
| 247 |
|
---|
| 248 | }
|
---|
| 249 |
|
---|
| 250 |
|
---|
| 251 | // if the curve is closed, postprocess the vectors so the first and last normal vectors are the same
|
---|
| 252 |
|
---|
| 253 | if ( closed ) {
|
---|
| 254 |
|
---|
| 255 | theta = Math.acos( THREE.Math.clamp( normals[ 0 ].dot( normals[ numpoints-1 ] ), -1, 1 ) );
|
---|
| 256 | theta /= ( numpoints - 1 );
|
---|
| 257 |
|
---|
| 258 | if ( tangents[ 0 ].dot( vec.crossVectors( normals[ 0 ], normals[ numpoints-1 ] ) ) > 0 ) {
|
---|
| 259 |
|
---|
| 260 | theta = -theta;
|
---|
| 261 |
|
---|
| 262 | }
|
---|
| 263 |
|
---|
| 264 | for ( i = 1; i < numpoints; i++ ) {
|
---|
| 265 |
|
---|
| 266 | // twist a little...
|
---|
| 267 | normals[ i ].applyMatrix4( mat.makeRotationAxis( tangents[ i ], theta * i ) );
|
---|
| 268 | binormals[ i ].crossVectors( tangents[ i ], normals[ i ] );
|
---|
| 269 |
|
---|
| 270 | }
|
---|
| 271 |
|
---|
| 272 | }
|
---|
| 273 | };
|
---|