/****************************************************************************** * Trng_Iso.c - Computes iso parametric curves of triangular surfaces. * ******************************************************************************* * (C) Gershon Elber, Technion, Israel Institute of Technology * ******************************************************************************* * Written by Gershon Elber, Aug. 96. * ******************************************************************************/ #include "trng_loc.h" /***************************************************************************** * DESCRIPTION: M * Routine to convert a single triangular surface to NumOfIsolines M * polylines in each parametric direction with SamplesPerCurve in each M * isoparametric curve. M * Polyline are always E3 of CagdPolylineStruct type. M * Iso parametric curves are sampled equally spaced in parametric space. M * NULL is returned in case of an error, otherwise list of M * CagdPolylineStruct. Attempt is made to extract isolines along C1 M * discontinuities first. M * * * PARAMETERS: M * TriSrf: To extract isoparametric curves from. M * NumOfIsocurves: In each (U or V or W) direction. M * SamplesPerCurve: Fineness control on piecewise linear curve M * approximation. M * Optimal: Use optimal approximation of isocurves. M * * * RETURN VALUE: M * CagdPolylineStruct *: List of polylines representing a piecewise linear M * approximation of the extracted isoparamteric M * curves or NULL is case of an error. M * * * KEYWORDS: M * TrngTriSrf2Polylines, isoparametric curves M *****************************************************************************/ CagdPolylineStruct *TrngTriSrf2Polylines(TrngTriangSrfStruct *TriSrf, int NumOfIsocurves[3], int SamplesPerCurve, int Optimal) { int i, j; CagdPolylineStruct *PolylineList = NULL; for (i = 0; i < 3; i++) if (NumOfIsocurves[i] < 2) NumOfIsocurves[i] = 2; if (SamplesPerCurve < 2) SamplesPerCurve = 2; if (TRNG_IS_BEZIER_TRISRF(TriSrf)) { for (i = 0; i < NumOfIsocurves[0]; i++) { /* Constant u isolines. */ CagdRType u = i / ((CagdRType) (NumOfIsocurves[0] - 1)), u1 = 1.0 - u; CagdPolylineStruct *Polyline = CagdPolylineNew(SamplesPerCurve); CagdPolylnStruct *Pts = Polyline -> Polyline; for (j = 0; j < SamplesPerCurve; j++) { CagdRType v = u1 * j / ((CagdRType) (SamplesPerCurve - 1)), *R = TrngTriSrfEval2(TriSrf, u, v); CagdCoerceToE3(Pts[j].Pt, &R, -1, TriSrf -> PType); } LIST_PUSH(Polyline, PolylineList); } for (i = 0; i < NumOfIsocurves[1]; i++) { /* Constant v isolines. */ CagdRType v = i / ((CagdRType) (NumOfIsocurves[1] - 1)), v1 = 1.0 - v; CagdPolylineStruct *Polyline = CagdPolylineNew(SamplesPerCurve); CagdPolylnStruct *Pts = Polyline -> Polyline; for (j = 0; j < SamplesPerCurve; j++) { CagdRType u = v1 * j / ((CagdRType) (SamplesPerCurve - 1)), *R = TrngTriSrfEval2(TriSrf, u, v); CagdCoerceToE3(Pts[j].Pt, &R, -1, TriSrf -> PType); } LIST_PUSH(Polyline, PolylineList); } for (i = 0; i < NumOfIsocurves[2]; i++) { /* Constant w isolines. */ CagdRType w = i / ((CagdRType) (NumOfIsocurves[2] - 1)), w1 = 1.0 - w; CagdPolylineStruct *Polyline = CagdPolylineNew(SamplesPerCurve); CagdPolylnStruct *Pts = Polyline -> Polyline; for (j = 0; j < SamplesPerCurve; j++) { CagdRType v = w1 * j / ((CagdRType) (SamplesPerCurve - 1)), *R = TrngTriSrfEval2(TriSrf, 1.0 - v - w, v); CagdCoerceToE3(Pts[j].Pt, &R, -1, TriSrf -> PType); } LIST_PUSH(Polyline, PolylineList); } return PolylineList; } return NULL; } /***************************************************************************** * DESCRIPTION: M * Routine to extract from a triangular surface NumOfIsoline isocurve list M * in each param. direction. M * Iso parametric curves are sampled equally spaced in parametric space. M * If, however, oout of the three NumOfIsocurves values, two are zero and M * one NumOfIsocurves values equals to one, extarct one isocurve at that M * direction, at value Val. M * NULL is returned in case of an error, otherwise list of CagdCrvStruct. M * M * Consider isoparametric curve of Bezier triangular surface at fixed u = u0: M * __ V * \ n! i j n-i-j V * / ------------------- u0 v (1 - u0 - v) b = V * -- i! j! (n - i - j)! ijk V * V * __ __ V * \ n! i \ (n - i)! j n-i-j V * / ------- u0 / ---------------- v (1 - u0 - v) b = V * -- i!(n-i)! -- j! (n - i - j)! ijk V * V * __ __ V * \ n! i n-i \ (n - i)! v j v n-i-j V * / ------- u0 (1-u0) / --------------- (----) (1 - ----) b V * -- i!(n-i)! -- j! (n - i - j)! 1-u0 1-u0 ijk V * M * Hence, the isoparametric curve of u = u0 is a weighted sum of a sequence M * of Bezier curves of degree 1 to n-1, each defined over a row of the M * triangular mesh, over the domain of v = [0, 1-u0]. M * * * PARAMETERS: M * TriSrf: To extract isoparametric curves from. M * NumOfIsocurves: In each (U or V or W) direction. M * Val: If only one isocurve to extract - do so at value Val. M * * * RETURN VALUE: M * CagdCrvStruct *: List of extracted isoparametric curves. These curves M * inherit the order and continuity of the original Srf. M * NULL is returned in case of an error. M * * * SEE ALSO: M * TrngTriSrf2Curves, TrngCrvFromTriSrf M * * * KEYWORDS: M * TrngTriBzrSrf2Curves, curves, isoparametric curves M *****************************************************************************/ CagdCrvStruct *TrngTriBzrSrf2Curves(TrngTriangSrfStruct *TriSrf, int NumOfIsocurves[3], RealType Val) { CagdPointType PType = TriSrf -> PType; int d, MaxCoord = CAGD_NUM_OF_PT_COORD(PType), Length = TriSrf -> Length; CagdBType SingleIsoCurve = FALSE, IsNotRational = !TRNG_IS_RATIONAL_TRISRF(TriSrf); CagdRType **TriSrfPoints = TriSrf -> Points; CagdCrvStruct *CrvList = NULL; if (NumOfIsocurves[0] + NumOfIsocurves[1] + NumOfIsocurves[2] == 1) { int i; /* Needs to extract a single isocurve at value Val. */ SingleIsoCurve = TRUE; /* We need at least two isolines to generate something below. */ for (i = 0; i < 3; i++) NumOfIsocurves[i] *= 2; if (Val < 0.0 || Val > 1.0) { TRNG_FATAL_ERROR(TRNG_ERR_WRONG_DOMAIN); return FALSE; } } if (TRNG_IS_BEZIER_TRISRF(TriSrf)) { for (d = 0; d < 3; d++) { /* For 3 different isoparametric dirs. */ int i, j, l; /* The following is written for U isoparametric curves basically */ /* but we rotate the ijk indices in accessing the triangular */ /* mesh, extracting isocurves in all three directions. */ for (l = 0; l < NumOfIsocurves[d] - 1; l++) { CagdRType uu0, uu1, u0 = SingleIsoCurve ? Val : l / ((CagdRType) (NumOfIsocurves[d] - 1)), u1 = 1.0 - u0; CagdCrvStruct *Crv = BzrCrvNew(Length, PType); CagdRType **Points = Crv -> Points; for (i = IsNotRational; i <= MaxCoord; i++) { /* Clr isocrv. */ CagdRType *R = Points[i]; for (j = 0; j < Length; j++) *R++ = 0.0; } for (i = 1, uu1 = 1; i < Length; i++, uu1 *= u1); /*(1-u0)^n.*/ for (i = 0, uu0 = 1; i < Length; i++) { CagdRType Wgt = TrngIJChooseN(i, 0, Length - 1) * uu0 * uu1; CagdCrvStruct *TCrv2, *TCrv = BzrCrvNew(Length - i, PType); CagdRType **TPoints = TCrv -> Points; for (j = 0; j < Length - i; j++) { int m, Index, k = Length - i - j - 1; switch (d) { case 0: Index = TRNG_MESH_IJK(TriSrf, i, j, k); break; case 1: Index = TRNG_MESH_IJK(TriSrf, j, k, i); break; case 2: Index = TRNG_MESH_IJK(TriSrf, k, i, j); break; } for (m = IsNotRational; m <= MaxCoord; m++) TPoints[m][j] = TriSrfPoints[m][Index] * Wgt; } TCrv2 = SymbCrvAdd(Crv, TCrv); /* Also degree raise! */ CagdCrvFree(Crv); CagdCrvFree(TCrv); Crv = TCrv2; uu0 *= u0; uu1 /= (u1 == 0.0 ? IRIT_UEPS : u1); } if (SingleIsoCurve) return Crv; else LIST_PUSH(Crv, CrvList); } } return CrvList; } return NULL; } /***************************************************************************** * DESCRIPTION: M * Extracts an isoparametric curve from the triangular surface TriSrf in M * direction Dir at the parameter value of t. M * * * PARAMETERS: M * TriSrf: To extract an isoparametric curve from. M * t: Parameter value of extracted isoparametric curve. M * Dir: Direction of extracted isocurve. Either U or V or W. M * * * RETURN VALUE: M * CagdCrvStruct *: An isoparametric curve of TriSrf. This curve inherit M * the order and continuity of TriSrf in direction Dir. M * * * SEE ALSO: M * BzrSrfCrvFromSrf, BspSrfCrvFromSrf, CagdCrvFromMesh, BzrSrfCrvFromMesh, M * BspSrfCrvFromMesh, CagdCrvFromSrf, TrngTriBzrSrf2Curves M * * * KEYWORDS: M * TrngCrvFromTriSrf, isoparametric curves, curve from surface M *****************************************************************************/ CagdCrvStruct *TrngCrvFromTriSrf(TrngTriangSrfStruct *TriSrf, CagdRType t, TrngTriSrfDirType Dir) { int i, NumOfIsocurves[3]; for (i = 0; i < 3; i++) NumOfIsocurves[i] = 0; switch (Dir) { case TRNG_CONST_U_DIR: NumOfIsocurves[0] = 1; break; case TRNG_CONST_V_DIR: NumOfIsocurves[1] = 1; break; case TRNG_CONST_W_DIR: NumOfIsocurves[2] = 1; break; default: TRNG_FATAL_ERROR(TRNG_ERR_DIR_NOT_VALID); break; } return TrngTriBzrSrf2Curves(TriSrf, NumOfIsocurves, t); } /***************************************************************************** * DESCRIPTION: M * Routine to extract from a triangular surface NumOfIsoline isocurve list M * in each param. direction. M * Iso parametric curves are sampled equally spaced in parametric space. M * NULL is returned in case of an error, otherwise list of CagdCrvStruct. M * * * PARAMETERS: M * TriSrf: To extract isoparametric curves from. M * NumOfIsocurves: In each (U or V or W) direction. M * * * RETURN VALUE: M * CagdCrvStruct *: List of extracted isoparametric curves. These curves M * inherit the order and continuity of the original Srf. M * NULL is returned in case of an error. M * * * SEE ALSO: M * TrngTriBzrSrf2Curves, TrngCrvFromTriSrf M * * * KEYWORDS: M * TrngTriSrf2Curves, curves, isoparametric curves M *****************************************************************************/ CagdCrvStruct *TrngTriSrf2Curves(TrngTriangSrfStruct *TriSrf, int NumOfIsocurves[3]) { int d; for (d = 0; d < 3; d++) if (NumOfIsocurves[d] < 2) NumOfIsocurves[d] = 2; if (TRNG_IS_BEZIER_TRISRF(TriSrf)) { return TrngTriBzrSrf2Curves(TriSrf, NumOfIsocurves, 0.0); } else return NULL; }