/****************************************************************************** * TrngEval.c - triangular surface evaluation routines. * ******************************************************************************* * (C) Gershon Elber, Technion, Israel Institute of Technology * ******************************************************************************* * Written by Gershon Elber, Aug. 96. * ******************************************************************************/ #include #include "trng_loc.h" #define MAX_MULTS_VAL 20 /* Maximal order of triangular Bezier supported. */ /***************************************************************************** * DESCRIPTION: * * Evaluates the following (in floating point arithmetic): * * N N! * * ( ) = ---------------------- * * i j i! * j! * (N - i - j)! * * * * PARAMETERS: * * i, j, N: Coefficients of combinatorial expression. * * * * RETURN VALUE: * * CagdRType: Result of ij choose N, in floating point, to prevent from * * overflows. * * * * KEYWORDS: * * TrngIJChooseN, evaluation, combinatorics * *****************************************************************************/ CagdRType TrngIJChooseN(int i, int j, int N) { static CagdRType Facts[MAX_MULTS_VAL] = { -1.0 }; if (Facts[0] < 0.0) { int l = 0; Facts[0] = 1; for (l = 1; l < MAX_MULTS_VAL; l++) Facts[l] = l * Facts[l - 1]; } if (N >= MAX_MULTS_VAL) { fprintf(stderr, "TrngLib: Fatal: Order of triangular Bezier too large - increase MAX_MULTS_VAL\n"); return 1.0; } return Facts[N] / (Facts[i] * Facts[j] * Facts[N - i - j]); } /***************************************************************************** * DESCRIPTION: M * Evaluates the given triangular surface at a given point. M * * * PARAMETERS: M * TriSrf: To evaluate at given (u, v, w) parametric location. M * u, v, w: Parametric location to evaluate TriSrf at. M * * * RETURN VALUE: M * CagdRType *: A vector holding all the coefficients of all components M * of the triangualr surface's point type. If for example M * point type is P2, the W, X, and Y will be saved in the M * first three locations of the returned vector. The first M * location (index 0) of the returned vector is reserved for M * the rational coefficient W and XYZ always starts at second M * location of the returned vector (index 1). M * * * KEYWORDS: M * TrngTriSrfEval, evaluation, triangular surfaces M *****************************************************************************/ CagdRType *TrngTriSrfEval(TrngTriangSrfStruct *TriSrf, CagdRType u, CagdRType v, CagdRType w) { static CagdRType Pt[CAGD_MAX_PT_COORD]; int i, j, MaxCoord = CAGD_NUM_OF_PT_COORD(TriSrf -> PType), Length = TriSrf -> Length; CagdBType IsNotRational = !TRNG_IS_RATIONAL_TRISRF(TriSrf); CagdRType B, uu, vv, ww, **Points = TriSrf -> Points; for (j = IsNotRational; j <= MaxCoord; j++) Pt[j] = 0.0; if (TRNG_IS_BEZIER_TRISRF(TriSrf)) { for (i = 0, uu = 1.0; i < Length; i++, uu *= u) { for (j = 0, vv = 1.0; j < Length - i; j++, vv *= v) { int l, kk, k = Length - i - j - 1, Index = TRNG_MESH_IJK(TriSrf, i, j, k); for (kk = 0, ww = 1.0; kk < k; kk++) ww *= w; B = TrngIJChooseN(i, j, Length - 1) * uu * vv * ww; for (l = IsNotRational; l <= MaxCoord; l++) Pt[l] += B * Points[l][Index]; } } } else if (TRNG_IS_BSPLINE_TRISRF(TriSrf)) { TRNG_FATAL_ERROR(TRNG_ERR_BSPLINE_NO_SUPPORT); return NULL; } return Pt; } /***************************************************************************** * DESCRIPTION: M * Evaluates the given triangular surface at a given point. Same as function M * TrngTriSrfEval with w computed using 'w = 1 - u - v' for Bezier triangular M * surfaces. M * * * PARAMETERS: M * TriSrf: To evaluate at given (u, v) parametric location. M * u, v: Parametric location to evaluate TriSrf at. M * * * RETURN VALUE: M * CagdRType *: A vector holding all the coefficients of all components M * of the triangualr surface's point type. If for example M * point type is P2, the W, X, and Y will be saved in the M * first three locations of the returned vector. The first M * location (index 0) of the returned vector is reserved for M * the rational coefficient W and XYZ always starts at second M * location of the returned vector (index 1). M * * * KEYWORDS: M * TrngTriSrfEval2, evaluation, triangular surfaces M *****************************************************************************/ CagdRType *TrngTriSrfEval2(TrngTriangSrfStruct *TriSrf, CagdRType u, CagdRType v) { if (TRNG_IS_BEZIER_TRISRF(TriSrf)) { return TrngTriSrfEval(TriSrf, u, v, 1.0 - u - v); } else if (TRNG_IS_BSPLINE_TRISRF(TriSrf)) { TRNG_FATAL_ERROR(TRNG_ERR_BSPLINE_NO_SUPPORT); return NULL; } return NULL; } /***************************************************************************** * DESCRIPTION: M * Evaluates the normal of the given triangular surface at a given point. M * * * PARAMETERS: M * TriSrf: To evaluate at given (u, v, w) parametric location. M * u, v, w: Parametric location to evaluate normal of TriSrf at. M * * * RETURN VALUE: M * CagdVecStruct *: A pointer to a static vector holding the unit normal M * information. M * * * SEE ALSO: M * CagdSrfNormal, BzrSrfNormal, BspSrfNormal, SymbSrfNormalSrf M * * * KEYWORDS: M * BzrSrfNormal, normal M * * * KEYWORDS: M * TrngTriSrfEval, evaluation, triangular surfaces M *****************************************************************************/ CagdVecStruct *TrngTriSrfNrml(TrngTriangSrfStruct *TriSrf, CagdRType u, CagdRType v) { static CagdVecStruct Normal; CagdVType Vec1, Vec2; CagdPType Pt1, Pt2; CagdRType *R, UMin, UMax, VMin, VMax, WMin, WMax, Du, Dv; TrngTriSrfDomain(TriSrf, &UMin, &UMax, &VMin, &VMax, &WMin, &WMax); R = TrngTriSrfEval2(TriSrf, u, v); CagdCoerceToE3(Pt1, &R, -1, TriSrf -> PType); Du = UMax - u > u - UMin ? u + IRIT_EPS : u - IRIT_EPS; R = TrngTriSrfEval2(TriSrf, Du, v); CagdCoerceToE3(Pt2, &R, -1, TriSrf -> PType); PT_SUB(Vec1, Pt1, Pt2); PT_SCALE(Vec1, 1 / (Du - u)); Dv = VMax - v > v - VMin ? v + IRIT_EPS : v - IRIT_EPS; R = TrngTriSrfEval2(TriSrf, u, Dv); CagdCoerceToE3(Pt2, &R, -1, TriSrf -> PType); PT_SUB(Vec2, Pt1, Pt2); PT_SCALE(Vec2, 1 / (Dv - v)); CROSS_PROD(Normal.Vec, Vec1, Vec2); PT_NORMALIZE(Normal.Vec); return &Normal; }