* @see {@link Curve#getPointAt} */ getTangentAt( u, optionalTarget ) { const t = this.getUtoTmapping( u ); return this.getTangent( t, optionalTarget ); } /** * Generates the Frenet Frames. Requires a curve definition in 3D space. Used * in geometries like {@link TubeGeometry} or {@link ExtrudeGeometry}. * * @param {number} segments - The number of segments. * @param {boolean} [closed=false] - Whether the curve is closed or not. * @return {{tangents: Array, normals: Array, binormals: Array}} The Frenet Frames. */ computeFrenetFrames( segments, closed = false ) { // see http://www.cs.indiana.edu/pub/techreports/TR425.pdf const normal = new Vector3(); const tangents = []; const normals = []; const binormals = []; const vec = new Vector3(); const mat = new Matrix4(); // compute the tangent vectors for each segment on the curve for ( let i = 0; i <= segments; i ++ ) { const u = i / segments; tangents[ i ] = this.getTangentAt( u, new Vector3() ); } // select an initial normal vector perpendicular to the first tangent vector, // and in the direction of the minimum tangent xyz component normals[ 0 ] = new Vector3(); binormals[ 0 ] = new Vector3(); let min = Number.MAX_VALUE; const tx = Math.abs( tangents[ 0 ].x ); const ty = Math.abs( tangents[ 0 ].y ); const tz = Math.abs( tangents[ 0 ].z ); if ( tx <= min ) { min = tx; normal.set( 1, 0, 0 ); } if ( ty <= min ) { min = ty; normal.set( 0, 1, 0 ); } if ( tz <= min ) { normal.set( 0, 0, 1 ); } vec.crossVectors( tangents[ 0 ], normal ).normalize(); normals[ 0 ].crossVectors( tangents[ 0 ], vec ); binormals[ 0 ].crossVectors( tangents[ 0 ], normals[ 0 ] ); // compute the slowly-varying normal and binormal vectors for each segment on the curve for ( let i = 1; i <= segments; i ++ ) { normals[ i ] = normals[ i - 1 ].clone(); binormals[ i ] = binormals[ i - 1 ].clone(); vec.crossVectors( tangents[ i - 1 ], tangents[ i ] ); if ( vec.length() > Number.EPSILON ) { vec.normalize(); const theta = Math.acos( clamp( tangents[ i - 1 ].dot( tangents[ i ] ), -1, 1 ) ); // clamp for floating pt errors normals[ i ].applyMatrix4( mat.makeRotationAxis( vec, theta ) ); } binormals[ i ].crossVectors( tangents[ i ], normals[ i ] ); } // if the curve is closed, postprocess the vectors so the first and last normal vectors are the same if ( closed === true ) { let theta = Math.acos( clamp( normals[ 0 ].dot( normals[ segments ] ), -1, 1 ) ); theta /= segments; if ( tangents[ 0 ].dot( vec.crossVectors( normals[ 0 ], normals[ segments ] ) ) > 0 ) { theta = - theta; } for ( let i = 1; i <= segments; i ++ ) { // twist a little... normals[ i ].applyMatrix4( mat.makeRotationAxis( tangents[ i ], theta * i ) ); binormals[ i ].crossVectors( tangents[ i ], normals[ i ] ); } } return { tangents: tangents, normals: normals, binormals: binormals }; } /** * Returns a new curve with copied values from this instance. * * @return {Curve} A clone of this instance. */ clone() { return new this.constructor().copy( this ); } /** * Copies the values of the given curve to this instance. * * @param {Curve} source - The curve to copy. * @return {Curve} A reference to this curve. */ copy( source ) { this.arcLengthDivisions = source.arcLengthDivisions; return this; } /** * Serializes the curve into JSON. * * @return {Object} A JSON object representing the serialized curve. * @see {@link ObjectLoader#parse} */ toJSON() { const data = { metadata: { version: 4.7, type: 'Curve', generator: 'Curve.toJSON' } }; data.arcLengthDivisions = this.arcLengthDivisions; data.type = this.type; return data; } /** * Deserializes the curve from the given JSON. * * @param {Object} json - The JSON holding the serialized curve. * @return {Curve} A reference to this curve. */ fromJSON( json ) { this.arcLengthDivisions = json.arcLengthDivisions; return this; } } /** * A curve representing an ellipse. * * ```js * const curve = new THREE.EllipseCurve( * 0, 0, * 10, 10, * 0, 2 * Math.PI, * false, * 0 * ); * * const points = curve.getPoints( 50 ); * const geometry = new THREE.BufferGeometry().setFromPoints( points ); * * const material = new THREE.LineBasicMaterial( { color: 0xff0000 } ); * * // Create the final object to add to the scene * const ellipse = new THREE.Line( geometry, material ); * ``` * * @augments Curve */ class EllipseCurve extends Curve { /** * Constructs a new ellipse curve. * * @param {number} [aX=0] - The X center of the ellipse. * @param {number} [aY=0] - The Y center of the ellipse. * @param {number} [xRadius=1] - The radius of the ellipse in the x direction. * @param {number} [yRadius=1]