| 1 |
- {"ast":null,"code":"import { Vector3, Vector4 } from 'three';\n\n/**\n * NURBS utils\n *\n * See NURBSCurve and NURBSSurface.\n **/\n\n/**************************************************************\n *\tNURBS Utils\n **************************************************************/\n\n/*\nFinds knot vector span.\n\np : degree\nu : parametric value\nU : knot vector\n\nreturns the span\n*/\nfunction findSpan(p, u, U) {\n const n = U.length - p - 1;\n if (u >= U[n]) {\n return n - 1;\n }\n if (u <= U[p]) {\n return p;\n }\n let low = p;\n let high = n;\n let mid = Math.floor((low + high) / 2);\n while (u < U[mid] || u >= U[mid + 1]) {\n if (u < U[mid]) {\n high = mid;\n } else {\n low = mid;\n }\n mid = Math.floor((low + high) / 2);\n }\n return mid;\n}\n\n/*\nCalculate basis functions. See The NURBS Book, page 70, algorithm A2.2\n\nspan : span in which u lies\nu : parametric point\np : degree\nU : knot vector\n\nreturns array[p+1] with basis functions values.\n*/\nfunction calcBasisFunctions(span, u, p, U) {\n const N = [];\n const left = [];\n const right = [];\n N[0] = 1.0;\n for (let j = 1; j <= p; ++j) {\n left[j] = u - U[span + 1 - j];\n right[j] = U[span + j] - u;\n let saved = 0.0;\n for (let r = 0; r < j; ++r) {\n const rv = right[r + 1];\n const lv = left[j - r];\n const temp = N[r] / (rv + lv);\n N[r] = saved + rv * temp;\n saved = lv * temp;\n }\n N[j] = saved;\n }\n return N;\n}\n\n/*\nCalculate B-Spline curve points. See The NURBS Book, page 82, algorithm A3.1.\n\np : degree of B-Spline\nU : knot vector\nP : control points (x, y, z, w)\nu : parametric point\n\nreturns point for given u\n*/\nfunction calcBSplinePoint(p, U, P, u) {\n const span = findSpan(p, u, U);\n const N = calcBasisFunctions(span, u, p, U);\n const C = new Vector4(0, 0, 0, 0);\n for (let j = 0; j <= p; ++j) {\n const point = P[span - p + j];\n const Nj = N[j];\n const wNj = point.w * Nj;\n C.x += point.x * wNj;\n C.y += point.y * wNj;\n C.z += point.z * wNj;\n C.w += point.w * Nj;\n }\n return C;\n}\n\n/*\nCalculate basis functions derivatives. See The NURBS Book, page 72, algorithm A2.3.\n\nspan : span in which u lies\nu : parametric point\np : degree\nn : number of derivatives to calculate\nU : knot vector\n\nreturns array[n+1][p+1] with basis functions derivatives\n*/\nfunction calcBasisFunctionDerivatives(span, u, p, n, U) {\n const zeroArr = [];\n for (let i = 0; i <= p; ++i) zeroArr[i] = 0.0;\n const ders = [];\n for (let i = 0; i <= n; ++i) ders[i] = zeroArr.slice(0);\n const ndu = [];\n for (let i = 0; i <= p; ++i) ndu[i] = zeroArr.slice(0);\n ndu[0][0] = 1.0;\n const left = zeroArr.slice(0);\n const right = zeroArr.slice(0);\n for (let j = 1; j <= p; ++j) {\n left[j] = u - U[span + 1 - j];\n right[j] = U[span + j] - u;\n let saved = 0.0;\n for (let r = 0; r < j; ++r) {\n const rv = right[r + 1];\n const lv = left[j - r];\n ndu[j][r] = rv + lv;\n const temp = ndu[r][j - 1] / ndu[j][r];\n ndu[r][j] = saved + rv * temp;\n saved = lv * temp;\n }\n ndu[j][j] = saved;\n }\n for (let j = 0; j <= p; ++j) {\n ders[0][j] = ndu[j][p];\n }\n for (let r = 0; r <= p; ++r) {\n let s1 = 0;\n let s2 = 1;\n const a = [];\n for (let i = 0; i <= p; ++i) {\n a[i] = zeroArr.slice(0);\n }\n a[0][0] = 1.0;\n for (let k = 1; k <= n; ++k) {\n let d = 0.0;\n const rk = r - k;\n const pk = p - k;\n if (r >= k) {\n a[s2][0] = a[s1][0] / ndu[pk + 1][rk];\n d = a[s2][0] * ndu[rk][pk];\n }\n const j1 = rk >= -1 ? 1 : -rk;\n const j2 = r - 1 <= pk ? k - 1 : p - r;\n for (let j = j1; j <= j2; ++j) {\n a[s2][j] = (a[s1][j] - a[s1][j - 1]) / ndu[pk + 1][rk + j];\n d += a[s2][j] * ndu[rk + j][pk];\n }\n if (r <= pk) {\n a[s2][k] = -a[s1][k - 1] / ndu[pk + 1][r];\n d += a[s2][k] * ndu[r][pk];\n }\n ders[k][r] = d;\n const j = s1;\n s1 = s2;\n s2 = j;\n }\n }\n let r = p;\n for (let k = 1; k <= n; ++k) {\n for (let j = 0; j <= p; ++j) {\n ders[k][j] *= r;\n }\n r *= p - k;\n }\n return ders;\n}\n\n/*\n\tCalculate derivatives of a B-Spline. See The NURBS Book, page 93, algorithm A3.2.\n\n\tp : degree\n\tU : knot vector\n\tP : control points\n\tu : Parametric points\n\tnd : number of derivatives\n\n\treturns array[d+1] with derivatives\n\t*/\nfunction calcBSplineDerivatives(p, U, P, u, nd) {\n const du = nd < p ? nd : p;\n const CK = [];\n const span = findSpan(p, u, U);\n const nders = calcBasisFunctionDerivatives(span, u, p, du, U);\n const Pw = [];\n for (let i = 0; i < P.length; ++i) {\n const point = P[i].clone();\n const w = point.w;\n point.x *= w;\n point.y *= w;\n point.z *= w;\n Pw[i] = point;\n }\n for (let k = 0; k <= du; ++k) {\n const point = Pw[span - p].clone().multiplyScalar(nders[k][0]);\n for (let j = 1; j <= p; ++j) {\n point.add(Pw[span - p + j].clone().multiplyScalar(nders[k][j]));\n }\n CK[k] = point;\n }\n for (let k = du + 1; k <= nd + 1; ++k) {\n CK[k] = new Vector4(0, 0, 0);\n }\n return CK;\n}\n\n/*\nCalculate \"K over I\"\n\nreturns k!/(i!(k-i)!)\n*/\nfunction calcKoverI(k, i) {\n let nom = 1;\n for (let j = 2; j <= k; ++j) {\n nom *= j;\n }\n let denom = 1;\n for (let j = 2; j <= i; ++j) {\n denom *= j;\n }\n for (let j = 2; j <= k - i; ++j) {\n denom *= j;\n }\n return nom / denom;\n}\n\n/*\nCalculate derivatives (0-nd) of rational curve. See The NURBS Book, page 127, algorithm A4.2.\n\nPders : result of function calcBSplineDerivatives\n\nreturns array with derivatives for rational curve.\n*/\nfunction calcRationalCurveDerivatives(Pders) {\n const nd = Pders.length;\n const Aders = [];\n const wders = [];\n for (let i = 0; i < nd; ++i) {\n const point = Pders[i];\n Aders[i] = new Vector3(point.x, point.y, point.z);\n wders[i] = point.w;\n }\n const CK = [];\n for (let k = 0; k < nd; ++k) {\n const v = Aders[k].clone();\n for (let i = 1; i <= k; ++i) {\n v.sub(CK[k - i].clone().multiplyScalar(calcKoverI(k, i) * wders[i]));\n }\n CK[k] = v.divideScalar(wders[0]);\n }\n return CK;\n}\n\n/*\nCalculate NURBS curve derivatives. See The NURBS Book, page 127, algorithm A4.2.\n\np : degree\nU : knot vector\nP : control points in homogeneous space\nu : parametric points\nnd : number of derivatives\n\nreturns array with derivatives.\n*/\nfunction calcNURBSDerivatives(p, U, P, u, nd) {\n const Pders = calcBSplineDerivatives(p, U, P, u, nd);\n return calcRationalCurveDerivatives(Pders);\n}\n\n/*\nCalculate rational B-Spline surface point. See The NURBS Book, page 134, algorithm A4.3.\n\np1, p2 : degrees of B-Spline surface\nU1, U2 : knot vectors\nP : control points (x, y, z, w)\nu, v : parametric values\n\nreturns point for given (u, v)\n*/\nfunction calcSurfacePoint(p, q, U, V, P, u, v, target) {\n const uspan = findSpan(p, u, U);\n const vspan = findSpan(q, v, V);\n const Nu = calcBasisFunctions(uspan, u, p, U);\n const Nv = calcBasisFunctions(vspan, v, q, V);\n const temp = [];\n for (let l = 0; l <= q; ++l) {\n temp[l] = new Vector4(0, 0, 0, 0);\n for (let k = 0; k <= p; ++k) {\n const point = P[uspan - p + k][vspan - q + l].clone();\n const w = point.w;\n point.x *= w;\n point.y *= w;\n point.z *= w;\n temp[l].add(point.multiplyScalar(Nu[k]));\n }\n }\n const Sw = new Vector4(0, 0, 0, 0);\n for (let l = 0; l <= q; ++l) {\n Sw.add(temp[l].multiplyScalar(Nv[l]));\n }\n Sw.divideScalar(Sw.w);\n target.set(Sw.x, Sw.y, Sw.z);\n}\nexport { findSpan, calcBasisFunctions, calcBSplinePoint, calcBasisFunctionDerivatives, calcBSplineDerivatives, calcKoverI, calcRationalCurveDerivatives, calcNURBSDerivatives, calcSurfacePoint };","map":{"version":3,"names":["Vector3","Vector4","findSpan","p","u","U","n","length","low","high","mid","Math","floor","calcBasisFunctions","span","N","left","right","j","saved","r","rv","lv","temp","calcBSplinePoint","P","C","point","Nj","wNj","w","x","y","z","calcBasisFunctionDerivatives","zeroArr","i","ders","slice","ndu","s1","s2","a","k","d","rk","pk","j1","j2","calcBSplineDerivatives","nd","du","CK","nders","Pw","clone","multiplyScalar","add","calcKoverI","nom","denom","calcRationalCurveDerivatives","Pders","Aders","wders","v","sub","divideScalar","calcNURBSDerivatives","calcSurfacePoint","q","V","target","uspan","vspan","Nu","Nv","l","Sw","set"],"sources":["/Users/mac/projects/mime/mine/public/curves/NURBSUtils.js"],"sourcesContent":["import {\n\tVector3,\n\tVector4\n} from 'three';\n\n/**\n * NURBS utils\n *\n * See NURBSCurve and NURBSSurface.\n **/\n\n\n/**************************************************************\n *\tNURBS Utils\n **************************************************************/\n\n/*\nFinds knot vector span.\n\np : degree\nu : parametric value\nU : knot vector\n\nreturns the span\n*/\nfunction findSpan( p, u, U ) {\n\n\tconst n = U.length - p - 1;\n\n\tif ( u >= U[ n ] ) {\n\n\t\treturn n - 1;\n\n\t}\n\n\tif ( u <= U[ p ] ) {\n\n\t\treturn p;\n\n\t}\n\n\tlet low = p;\n\tlet high = n;\n\tlet mid = Math.floor( ( low + high ) / 2 );\n\n\twhile ( u < U[ mid ] || u >= U[ mid + 1 ] ) {\n\n\t\tif ( u < U[ mid ] ) {\n\n\t\t\thigh = mid;\n\n\t\t} else {\n\n\t\t\tlow = mid;\n\n\t\t}\n\n\t\tmid = Math.floor( ( low + high ) / 2 );\n\n\t}\n\n\treturn mid;\n\n}\n\n\n/*\nCalculate basis functions. See The NURBS Book, page 70, algorithm A2.2\n\nspan : span in which u lies\nu : parametric point\np : degree\nU : knot vector\n\nreturns array[p+1] with basis functions values.\n*/\nfunction calcBasisFunctions( span, u, p, U ) {\n\n\tconst N = [];\n\tconst left = [];\n\tconst right = [];\n\tN[ 0 ] = 1.0;\n\n\tfor ( let j = 1; j <= p; ++ j ) {\n\n\t\tleft[ j ] = u - U[ span + 1 - j ];\n\t\tright[ j ] = U[ span + j ] - u;\n\n\t\tlet saved = 0.0;\n\n\t\tfor ( let r = 0; r < j; ++ r ) {\n\n\t\t\tconst rv = right[ r + 1 ];\n\t\t\tconst lv = left[ j - r ];\n\t\t\tconst temp = N[ r ] / ( rv + lv );\n\t\t\tN[ r ] = saved + rv * temp;\n\t\t\tsaved = lv * temp;\n\n\t\t}\n\n\t\tN[ j ] = saved;\n\n\t}\n\n\treturn N;\n\n}\n\n\n/*\nCalculate B-Spline curve points. See The NURBS Book, page 82, algorithm A3.1.\n\np : degree of B-Spline\nU : knot vector\nP : control points (x, y, z, w)\nu : parametric point\n\nreturns point for given u\n*/\nfunction calcBSplinePoint( p, U, P, u ) {\n\n\tconst span = findSpan( p, u, U );\n\tconst N = calcBasisFunctions( span, u, p, U );\n\tconst C = new Vector4( 0, 0, 0, 0 );\n\n\tfor ( let j = 0; j <= p; ++ j ) {\n\n\t\tconst point = P[ span - p + j ];\n\t\tconst Nj = N[ j ];\n\t\tconst wNj = point.w * Nj;\n\t\tC.x += point.x * wNj;\n\t\tC.y += point.y * wNj;\n\t\tC.z += point.z * wNj;\n\t\tC.w += point.w * Nj;\n\n\t}\n\n\treturn C;\n\n}\n\n\n/*\nCalculate basis functions derivatives. See The NURBS Book, page 72, algorithm A2.3.\n\nspan : span in which u lies\nu : parametric point\np : degree\nn : number of derivatives to calculate\nU : knot vector\n\nreturns array[n+1][p+1] with basis functions derivatives\n*/\nfunction calcBasisFunctionDerivatives( span, u, p, n, U ) {\n\n\tconst zeroArr = [];\n\tfor ( let i = 0; i <= p; ++ i )\n\t\tzeroArr[ i ] = 0.0;\n\n\tconst ders = [];\n\n\tfor ( let i = 0; i <= n; ++ i )\n\t\tders[ i ] = zeroArr.slice( 0 );\n\n\tconst ndu = [];\n\n\tfor ( let i = 0; i <= p; ++ i )\n\t\tndu[ i ] = zeroArr.slice( 0 );\n\n\tndu[ 0 ][ 0 ] = 1.0;\n\n\tconst left = zeroArr.slice( 0 );\n\tconst right = zeroArr.slice( 0 );\n\n\tfor ( let j = 1; j <= p; ++ j ) {\n\n\t\tleft[ j ] = u - U[ span + 1 - j ];\n\t\tright[ j ] = U[ span + j ] - u;\n\n\t\tlet saved = 0.0;\n\n\t\tfor ( let r = 0; r < j; ++ r ) {\n\n\t\t\tconst rv = right[ r + 1 ];\n\t\t\tconst lv = left[ j - r ];\n\t\t\tndu[ j ][ r ] = rv + lv;\n\n\t\t\tconst temp = ndu[ r ][ j - 1 ] / ndu[ j ][ r ];\n\t\t\tndu[ r ][ j ] = saved + rv * temp;\n\t\t\tsaved = lv * temp;\n\n\t\t}\n\n\t\tndu[ j ][ j ] = saved;\n\n\t}\n\n\tfor ( let j = 0; j <= p; ++ j ) {\n\n\t\tders[ 0 ][ j ] = ndu[ j ][ p ];\n\n\t}\n\n\tfor ( let r = 0; r <= p; ++ r ) {\n\n\t\tlet s1 = 0;\n\t\tlet s2 = 1;\n\n\t\tconst a = [];\n\t\tfor ( let i = 0; i <= p; ++ i ) {\n\n\t\t\ta[ i ] = zeroArr.slice( 0 );\n\n\t\t}\n\n\t\ta[ 0 ][ 0 ] = 1.0;\n\n\t\tfor ( let k = 1; k <= n; ++ k ) {\n\n\t\t\tlet d = 0.0;\n\t\t\tconst rk = r - k;\n\t\t\tconst pk = p - k;\n\n\t\t\tif ( r >= k ) {\n\n\t\t\t\ta[ s2 ][ 0 ] = a[ s1 ][ 0 ] / ndu[ pk + 1 ][ rk ];\n\t\t\t\td = a[ s2 ][ 0 ] * ndu[ rk ][ pk ];\n\n\t\t\t}\n\n\t\t\tconst j1 = ( rk >= - 1 ) ? 1 : - rk;\n\t\t\tconst j2 = ( r - 1 <= pk ) ? k - 1 : p - r;\n\n\t\t\tfor ( let j = j1; j <= j2; ++ j ) {\n\n\t\t\t\ta[ s2 ][ j ] = ( a[ s1 ][ j ] - a[ s1 ][ j - 1 ] ) / ndu[ pk + 1 ][ rk + j ];\n\t\t\t\td += a[ s2 ][ j ] * ndu[ rk + j ][ pk ];\n\n\t\t\t}\n\n\t\t\tif ( r <= pk ) {\n\n\t\t\t\ta[ s2 ][ k ] = - a[ s1 ][ k - 1 ] / ndu[ pk + 1 ][ r ];\n\t\t\t\td += a[ s2 ][ k ] * ndu[ r ][ pk ];\n\n\t\t\t}\n\n\t\t\tders[ k ][ r ] = d;\n\n\t\t\tconst j = s1;\n\t\t\ts1 = s2;\n\t\t\ts2 = j;\n\n\t\t}\n\n\t}\n\n\tlet r = p;\n\n\tfor ( let k = 1; k <= n; ++ k ) {\n\n\t\tfor ( let j = 0; j <= p; ++ j ) {\n\n\t\t\tders[ k ][ j ] *= r;\n\n\t\t}\n\n\t\tr *= p - k;\n\n\t}\n\n\treturn ders;\n\n}\n\n\n/*\n\tCalculate derivatives of a B-Spline. See The NURBS Book, page 93, algorithm A3.2.\n\n\tp : degree\n\tU : knot vector\n\tP : control points\n\tu : Parametric points\n\tnd : number of derivatives\n\n\treturns array[d+1] with derivatives\n\t*/\nfunction calcBSplineDerivatives( p, U, P, u, nd ) {\n\n\tconst du = nd < p ? nd : p;\n\tconst CK = [];\n\tconst span = findSpan( p, u, U );\n\tconst nders = calcBasisFunctionDerivatives( span, u, p, du, U );\n\tconst Pw = [];\n\n\tfor ( let i = 0; i < P.length; ++ i ) {\n\n\t\tconst point = P[ i ].clone();\n\t\tconst w = point.w;\n\n\t\tpoint.x *= w;\n\t\tpoint.y *= w;\n\t\tpoint.z *= w;\n\n\t\tPw[ i ] = point;\n\n\t}\n\n\tfor ( let k = 0; k <= du; ++ k ) {\n\n\t\tconst point = Pw[ span - p ].clone().multiplyScalar( nders[ k ][ 0 ] );\n\n\t\tfor ( let j = 1; j <= p; ++ j ) {\n\n\t\t\tpoint.add( Pw[ span - p + j ].clone().multiplyScalar( nders[ k ][ j ] ) );\n\n\t\t}\n\n\t\tCK[ k ] = point;\n\n\t}\n\n\tfor ( let k = du + 1; k <= nd + 1; ++ k ) {\n\n\t\tCK[ k ] = new Vector4( 0, 0, 0 );\n\n\t}\n\n\treturn CK;\n\n}\n\n\n/*\nCalculate \"K over I\"\n\nreturns k!/(i!(k-i)!)\n*/\nfunction calcKoverI( k, i ) {\n\n\tlet nom = 1;\n\n\tfor ( let j = 2; j <= k; ++ j ) {\n\n\t\tnom *= j;\n\n\t}\n\n\tlet denom = 1;\n\n\tfor ( let j = 2; j <= i; ++ j ) {\n\n\t\tdenom *= j;\n\n\t}\n\n\tfor ( let j = 2; j <= k - i; ++ j ) {\n\n\t\tdenom *= j;\n\n\t}\n\n\treturn nom / denom;\n\n}\n\n\n/*\nCalculate derivatives (0-nd) of rational curve. See The NURBS Book, page 127, algorithm A4.2.\n\nPders : result of function calcBSplineDerivatives\n\nreturns array with derivatives for rational curve.\n*/\nfunction calcRationalCurveDerivatives( Pders ) {\n\n\tconst nd = Pders.length;\n\tconst Aders = [];\n\tconst wders = [];\n\n\tfor ( let i = 0; i < nd; ++ i ) {\n\n\t\tconst point = Pders[ i ];\n\t\tAders[ i ] = new Vector3( point.x, point.y, point.z );\n\t\twders[ i ] = point.w;\n\n\t}\n\n\tconst CK = [];\n\n\tfor ( let k = 0; k < nd; ++ k ) {\n\n\t\tconst v = Aders[ k ].clone();\n\n\t\tfor ( let i = 1; i <= k; ++ i ) {\n\n\t\t\tv.sub( CK[ k - i ].clone().multiplyScalar( calcKoverI( k, i ) * wders[ i ] ) );\n\n\t\t}\n\n\t\tCK[ k ] = v.divideScalar( wders[ 0 ] );\n\n\t}\n\n\treturn CK;\n\n}\n\n\n/*\nCalculate NURBS curve derivatives. See The NURBS Book, page 127, algorithm A4.2.\n\np : degree\nU : knot vector\nP : control points in homogeneous space\nu : parametric points\nnd : number of derivatives\n\nreturns array with derivatives.\n*/\nfunction calcNURBSDerivatives( p, U, P, u, nd ) {\n\n\tconst Pders = calcBSplineDerivatives( p, U, P, u, nd );\n\treturn calcRationalCurveDerivatives( Pders );\n\n}\n\n\n/*\nCalculate rational B-Spline surface point. See The NURBS Book, page 134, algorithm A4.3.\n\np1, p2 : degrees of B-Spline surface\nU1, U2 : knot vectors\nP : control points (x, y, z, w)\nu, v : parametric values\n\nreturns point for given (u, v)\n*/\nfunction calcSurfacePoint( p, q, U, V, P, u, v, target ) {\n\n\tconst uspan = findSpan( p, u, U );\n\tconst vspan = findSpan( q, v, V );\n\tconst Nu = calcBasisFunctions( uspan, u, p, U );\n\tconst Nv = calcBasisFunctions( vspan, v, q, V );\n\tconst temp = [];\n\n\tfor ( let l = 0; l <= q; ++ l ) {\n\n\t\ttemp[ l ] = new Vector4( 0, 0, 0, 0 );\n\t\tfor ( let k = 0; k <= p; ++ k ) {\n\n\t\t\tconst point = P[ uspan - p + k ][ vspan - q + l ].clone();\n\t\t\tconst w = point.w;\n\t\t\tpoint.x *= w;\n\t\t\tpoint.y *= w;\n\t\t\tpoint.z *= w;\n\t\t\ttemp[ l ].add( point.multiplyScalar( Nu[ k ] ) );\n\n\t\t}\n\n\t}\n\n\tconst Sw = new Vector4( 0, 0, 0, 0 );\n\tfor ( let l = 0; l <= q; ++ l ) {\n\n\t\tSw.add( temp[ l ].multiplyScalar( Nv[ l ] ) );\n\n\t}\n\n\tSw.divideScalar( Sw.w );\n\ttarget.set( Sw.x, Sw.y, Sw.z );\n\n}\n\n\n\nexport 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