添加关照、全局等高线、修改图层问题

dist/electron/static/sdk/three/jsm/curves/NURBSUtils.js

@@ -0,0 +1,542 @@
+import {
+	Vector3,
+	Vector4
+} from 'three';
+
+/**
+ * NURBS utils
+ *
+ * See NURBSCurve and NURBSSurface.
+ **/
+
+
+/**************************************************************
+ *	NURBS Utils
+ **************************************************************/
+
+/*
+Finds knot vector span.
+
+p : degree
+u : parametric value
+U : knot vector
+
+returns the span
+*/
+function findSpan( p, u, U ) {
+
+	const n = U.length - p - 1;
+
+	if ( u >= U[ n ] ) {
+
+		return n - 1;
+
+	}
+
+	if ( u <= U[ p ] ) {
+
+		return p;
+
+	}
+
+	let low = p;
+	let high = n;
+	let mid = Math.floor( ( low + high ) / 2 );
+
+	while ( u < U[ mid ] || u >= U[ mid + 1 ] ) {
+
+		if ( u < U[ mid ] ) {
+
+			high = mid;
+
+		} else {
+
+			low = mid;
+
+		}
+
+		mid = Math.floor( ( low + high ) / 2 );
+
+	}
+
+	return mid;
+
+}
+
+
+/*
+Calculate basis functions. See The NURBS Book, page 70, algorithm A2.2
+
+span : span in which u lies
+u    : parametric point
+p    : degree
+U    : knot vector
+
+returns array[p+1] with basis functions values.
+*/
+function calcBasisFunctions( span, u, p, U ) {
+
+	const N = [];
+	const left = [];
+	const right = [];
+	N[ 0 ] = 1.0;
+
+	for ( let j = 1; j <= p; ++ j ) {
+
+		left[ j ] = u - U[ span + 1 - j ];
+		right[ j ] = U[ span + j ] - u;
+
+		let saved = 0.0;
+
+		for ( let r = 0; r < j; ++ r ) {
+
+			const rv = right[ r + 1 ];
+			const lv = left[ j - r ];
+			const temp = N[ r ] / ( rv + lv );
+			N[ r ] = saved + rv * temp;
+			saved = lv * temp;
+
+		}
+
+		N[ j ] = saved;
+
+	}
+
+	return N;
+
+}
+
+
+/*
+Calculate B-Spline curve points. See The NURBS Book, page 82, algorithm A3.1.
+
+p : degree of B-Spline
+U : knot vector
+P : control points (x, y, z, w)
+u : parametric point
+
+returns point for given u
+*/
+function calcBSplinePoint( p, U, P, u ) {
+
+	const span = findSpan( p, u, U );
+	const N = calcBasisFunctions( span, u, p, U );
+	const C = new Vector4( 0, 0, 0, 0 );
+
+	for ( let j = 0; j <= p; ++ j ) {
+
+		const point = P[ span - p + j ];
+		const Nj = N[ j ];
+		const wNj = point.w * Nj;
+		C.x += point.x * wNj;
+		C.y += point.y * wNj;
+		C.z += point.z * wNj;
+		C.w += point.w * Nj;
+
+	}
+
+	return C;
+
+}
+
+
+/*
+Calculate basis functions derivatives. See The NURBS Book, page 72, algorithm A2.3.
+
+span : span in which u lies
+u    : parametric point
+p    : degree
+n    : number of derivatives to calculate
+U    : knot vector
+
+returns array[n+1][p+1] with basis functions derivatives
+*/
+function calcBasisFunctionDerivatives( span, u, p, n, U ) {
+
+	const zeroArr = [];
+	for ( let i = 0; i <= p; ++ i )
+		zeroArr[ i ] = 0.0;
+
+	const ders = [];
+
+	for ( let i = 0; i <= n; ++ i )
+		ders[ i ] = zeroArr.slice( 0 );
+
+	const ndu = [];
+
+	for ( let i = 0; i <= p; ++ i )
+		ndu[ i ] = zeroArr.slice( 0 );
+
+	ndu[ 0 ][ 0 ] = 1.0;
+
+	const left = zeroArr.slice( 0 );
+	const right = zeroArr.slice( 0 );
+
+	for ( let j = 1; j <= p; ++ j ) {
+
+		left[ j ] = u - U[ span + 1 - j ];
+		right[ j ] = U[ span + j ] - u;
+
+		let saved = 0.0;
+
+		for ( let r = 0; r < j; ++ r ) {
+
+			const rv = right[ r + 1 ];
+			const lv = left[ j - r ];
+			ndu[ j ][ r ] = rv + lv;
+
+			const temp = ndu[ r ][ j - 1 ] / ndu[ j ][ r ];
+			ndu[ r ][ j ] = saved + rv * temp;
+			saved = lv * temp;
+
+		}
+
+		ndu[ j ][ j ] = saved;
+
+	}
+
+	for ( let j = 0; j <= p; ++ j ) {
+
+		ders[ 0 ][ j ] = ndu[ j ][ p ];
+
+	}
+
+	for ( let r = 0; r <= p; ++ r ) {
+
+		let s1 = 0;
+		let s2 = 1;
+
+		const a = [];
+		for ( let i = 0; i <= p; ++ i ) {
+
+			a[ i ] = zeroArr.slice( 0 );
+
+		}
+
+		a[ 0 ][ 0 ] = 1.0;
+
+		for ( let k = 1; k <= n; ++ k ) {
+
+			let d = 0.0;
+			const rk = r - k;
+			const pk = p - k;
+
+			if ( r >= k ) {
+
+				a[ s2 ][ 0 ] = a[ s1 ][ 0 ] / ndu[ pk + 1 ][ rk ];
+				d = a[ s2 ][ 0 ] * ndu[ rk ][ pk ];
+
+			}
+
+			const j1 = ( rk >= - 1 ) ? 1 : - rk;
+			const j2 = ( r - 1 <= pk ) ? k - 1 : p - r;
+
+			for ( let j = j1; j <= j2; ++ j ) {
+
+				a[ s2 ][ j ] = ( a[ s1 ][ j ] - a[ s1 ][ j - 1 ] ) / ndu[ pk + 1 ][ rk + j ];
+				d += a[ s2 ][ j ] * ndu[ rk + j ][ pk ];
+
+			}
+
+			if ( r <= pk ) {
+
+				a[ s2 ][ k ] = - a[ s1 ][ k - 1 ] / ndu[ pk + 1 ][ r ];
+				d += a[ s2 ][ k ] * ndu[ r ][ pk ];
+
+			}
+
+			ders[ k ][ r ] = d;
+
+			const j = s1;
+			s1 = s2;
+			s2 = j;
+
+		}
+
+	}
+
+	let r = p;
+
+	for ( let k = 1; k <= n; ++ k ) {
+
+		for ( let j = 0; j <= p; ++ j ) {
+
+			ders[ k ][ j ] *= r;
+
+		}
+
+		r *= p - k;
+
+	}
+
+	return ders;
+
+}
+
+
+/*
+	Calculate derivatives of a B-Spline. See The NURBS Book, page 93, algorithm A3.2.
+
+	p  : degree
+	U  : knot vector
+	P  : control points
+	u  : Parametric points
+	nd : number of derivatives
+
+	returns array[d+1] with derivatives
+	*/
+function calcBSplineDerivatives( p, U, P, u, nd ) {
+
+	const du = nd < p ? nd : p;
+	const CK = [];
+	const span = findSpan( p, u, U );
+	const nders = calcBasisFunctionDerivatives( span, u, p, du, U );
+	const Pw = [];
+
+	for ( let i = 0; i < P.length; ++ i ) {
+
+		const point = P[ i ].clone();
+		const w = point.w;
+
+		point.x *= w;
+		point.y *= w;
+		point.z *= w;
+
+		Pw[ i ] = point;
+
+	}
+
+	for ( let k = 0; k <= du; ++ k ) {
+
+		const point = Pw[ span - p ].clone().multiplyScalar( nders[ k ][ 0 ] );
+
+		for ( let j = 1; j <= p; ++ j ) {
+
+			point.add( Pw[ span - p + j ].clone().multiplyScalar( nders[ k ][ j ] ) );
+
+		}
+
+		CK[ k ] = point;
+
+	}
+
+	for ( let k = du + 1; k <= nd + 1; ++ k ) {
+
+		CK[ k ] = new Vector4( 0, 0, 0 );
+
+	}
+
+	return CK;
+
+}
+
+
+/*
+Calculate "K over I"
+
+returns k!/(i!(k-i)!)
+*/
+function calcKoverI( k, i ) {
+
+	let nom = 1;
+
+	for ( let j = 2; j <= k; ++ j ) {
+
+		nom *= j;
+
+	}
+
+	let denom = 1;
+
+	for ( let j = 2; j <= i; ++ j ) {
+
+		denom *= j;
+
+	}
+
+	for ( let j = 2; j <= k - i; ++ j ) {
+
+		denom *= j;
+
+	}
+
+	return nom / denom;
+
+}
+
+
+/*
+Calculate derivatives (0-nd) of rational curve. See The NURBS Book, page 127, algorithm A4.2.
+
+Pders : result of function calcBSplineDerivatives
+
+returns array with derivatives for rational curve.
+*/
+function calcRationalCurveDerivatives( Pders ) {
+
+	const nd = Pders.length;
+	const Aders = [];
+	const wders = [];
+
+	for ( let i = 0; i < nd; ++ i ) {
+
+		const point = Pders[ i ];
+		Aders[ i ] = new Vector3( point.x, point.y, point.z );
+		wders[ i ] = point.w;
+
+	}
+
+	const CK = [];
+
+	for ( let k = 0; k < nd; ++ k ) {
+
+		const v = Aders[ k ].clone();
+
+		for ( let i = 1; i <= k; ++ i ) {
+
+			v.sub( CK[ k - i ].clone().multiplyScalar( calcKoverI( k, i ) * wders[ i ] ) );
+
+		}
+
+		CK[ k ] = v.divideScalar( wders[ 0 ] );
+
+	}
+
+	return CK;
+
+}
+
+
+/*
+Calculate NURBS curve derivatives. See The NURBS Book, page 127, algorithm A4.2.
+
+p  : degree
+U  : knot vector
+P  : control points in homogeneous space
+u  : parametric points
+nd : number of derivatives
+
+returns array with derivatives.
+*/
+function calcNURBSDerivatives( p, U, P, u, nd ) {
+
+	const Pders = calcBSplineDerivatives( p, U, P, u, nd );
+	return calcRationalCurveDerivatives( Pders );
+
+}
+
+
+/*
+Calculate rational B-Spline surface point. See The NURBS Book, page 134, algorithm A4.3.
+
+p, q : degrees of B-Spline surface
+U, V : knot vectors
+P    : control points (x, y, z, w)
+u, v : parametric values
+
+returns point for given (u, v)
+*/
+function calcSurfacePoint( p, q, U, V, P, u, v, target ) {
+
+	const uspan = findSpan( p, u, U );
+	const vspan = findSpan( q, v, V );
+	const Nu = calcBasisFunctions( uspan, u, p, U );
+	const Nv = calcBasisFunctions( vspan, v, q, V );
+	const temp = [];
+
+	for ( let l = 0; l <= q; ++ l ) {
+
+		temp[ l ] = new Vector4( 0, 0, 0, 0 );
+		for ( let k = 0; k <= p; ++ k ) {
+
+			const point = P[ uspan - p + k ][ vspan - q + l ].clone();
+			const w = point.w;
+			point.x *= w;
+			point.y *= w;
+			point.z *= w;
+			temp[ l ].add( point.multiplyScalar( Nu[ k ] ) );
+
+		}
+
+	}
+
+	const Sw = new Vector4( 0, 0, 0, 0 );
+	for ( let l = 0; l <= q; ++ l ) {
+
+		Sw.add( temp[ l ].multiplyScalar( Nv[ l ] ) );
+
+	}
+
+	Sw.divideScalar( Sw.w );
+	target.set( Sw.x, Sw.y, Sw.z );
+
+}
+
+/*
+Calculate rational B-Spline volume point. See The NURBS Book, page 134, algorithm A4.3.
+
+p, q, r   : degrees of B-Splinevolume
+U, V, W   : knot vectors
+P         : control points (x, y, z, w)
+u, v, w   : parametric values
+
+returns point for given (u, v, w)
+*/
+function calcVolumePoint( p, q, r, U, V, W, P, u, v, w, target ) {
+
+	const uspan = findSpan( p, u, U );
+	const vspan = findSpan( q, v, V );
+	const wspan = findSpan( r, w, W );
+	const Nu = calcBasisFunctions( uspan, u, p, U );
+	const Nv = calcBasisFunctions( vspan, v, q, V );
+	const Nw = calcBasisFunctions( wspan, w, r, W );
+	const temp = [];
+
+	for ( let m = 0; m <= r; ++ m ) {
+
+		temp[ m ] = [];
+
+		for ( let l = 0; l <= q; ++ l ) {
+
+			temp[ m ][ l ] = new Vector4( 0, 0, 0, 0 );
+			for ( let k = 0; k <= p; ++ k ) {
+
+				const point = P[ uspan - p + k ][ vspan - q + l ][ wspan - r + m ].clone();
+				const w = point.w;
+				point.x *= w;
+				point.y *= w;
+				point.z *= w;
+				temp[ m ][ l ].add( point.multiplyScalar( Nu[ k ] ) );
+
+			}
+
+		}
+
+	}
+	const Sw = new Vector4( 0, 0, 0, 0 );
+	for ( let m = 0; m <= r; ++ m ) {
+		for ( let l = 0; l <= q; ++ l ) {
+
+			Sw.add( temp[ m ][ l ].multiplyScalar( Nw[ m ] ).multiplyScalar( Nv[ l ] ) );
+
+		}
+	}
+
+	Sw.divideScalar( Sw.w );
+	target.set( Sw.x, Sw.y, Sw.z );
+
+}
+
+
+export {
+	findSpan,
+	calcBasisFunctions,
+	calcBSplinePoint,
+	calcBasisFunctionDerivatives,
+	calcBSplineDerivatives,
+	calcKoverI,
+	calcRationalCurveDerivatives,
+	calcNURBSDerivatives,
+	calcSurfacePoint,
+	calcVolumePoint,
+};