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Warning, file /include/opencascade/CSLib.hxx was not indexed or was modified since last indexation (in which case cross-reference links may be missing, inaccurate or erroneous).
0001 // Created on: 1991-09-09 0002 // Created by: Michel Chauvat 0003 // Copyright (c) 1991-1999 Matra Datavision 0004 // Copyright (c) 1999-2014 OPEN CASCADE SAS 0005 // 0006 // This file is part of Open CASCADE Technology software library. 0007 // 0008 // This library is free software; you can redistribute it and/or modify it under 0009 // the terms of the GNU Lesser General Public License version 2.1 as published 0010 // by the Free Software Foundation, with special exception defined in the file 0011 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT 0012 // distribution for complete text of the license and disclaimer of any warranty. 0013 // 0014 // Alternatively, this file may be used under the terms of Open CASCADE 0015 // commercial license or contractual agreement. 0016 0017 #ifndef _CSLib_HeaderFile 0018 #define _CSLib_HeaderFile 0019 0020 #include <CSLib_DerivativeStatus.hxx> 0021 #include <CSLib_NormalStatus.hxx> 0022 #include <Standard.hxx> 0023 #include <Standard_DefineAlloc.hxx> 0024 #include <gp_Vec.hxx> 0025 #include <NCollection_Array2.hxx> 0026 0027 class gp_Dir; 0028 class gp_Vec; 0029 0030 //! Provides functions for basic geometric computation on curves and surfaces. 0031 //! 0032 //! This package implements functions for computing surface normals 0033 //! and their derivatives at parametric points. The tolerance criteria 0034 //! used are Resolution from gp and RealEpsilon from double. 0035 //! 0036 //! Key functionality: 0037 //! - Normal computation from surface first derivatives (D1U, D1V) 0038 //! - Approximate normal in singular cases using second derivatives 0039 //! - Derivatives of the non-normalized and normalized normal vectors 0040 class CSLib 0041 { 0042 public: 0043 DEFINE_STANDARD_ALLOC 0044 0045 //! Computes the normal direction of a surface as the cross product D1U ^ D1V. 0046 //! 0047 //! The normal is undefined if: 0048 //! - D1U has null length, or 0049 //! - D1V has null length, or 0050 //! - D1U and D1V are parallel. 0051 //! 0052 //! To check parallelism, the sine of the angle between D1U and D1V 0053 //! is computed and compared with theSinTol. 0054 //! 0055 //! @param[in] theD1U First derivative in U direction 0056 //! @param[in] theD1V First derivative in V direction 0057 //! @param[in] theSinTol Sine tolerance for parallelism check 0058 //! @param[out] theStatus Result status indicating success or failure reason 0059 //! @param[out] theNormal Computed normal direction (valid only if theStatus == CSLib_Done) 0060 Standard_EXPORT static void Normal(const gp_Vec& theD1U, 0061 const gp_Vec& theD1V, 0062 double theSinTol, 0063 CSLib_DerivativeStatus& theStatus, 0064 gp_Dir& theNormal); 0065 0066 //! Computes an approximate normal direction at a singular point using second derivatives. 0067 //! 0068 //! When the standard method cannot compute the normal (D1U ^ D1V is null or too small), 0069 //! this method uses a limited Taylor expansion: 0070 //! N(u0+du, v0+dv) = N0 + dN/du * du + dN/dv * dv + O(du^2, dv^2) 0071 //! 0072 //! The normal is approximated from dN/du and dN/dv where N = D1U ^ D1V. 0073 //! 0074 //! @param[in] theD1U First derivative in U direction 0075 //! @param[in] theD1V First derivative in V direction 0076 //! @param[in] theD2U Second derivative in U direction (d^2S/du^2) 0077 //! @param[in] theD2V Second derivative in V direction (d^2S/dv^2) 0078 //! @param[in] theD2UV Mixed second derivative (d^2S/dudv) 0079 //! @param[in] theSinTol Sine tolerance for parallelism check 0080 //! @param[out] theDone True if normal was successfully computed 0081 //! @param[out] theStatus Result status with detailed information 0082 //! @param[out] theNormal Computed normal direction (valid only if theDone is true) 0083 Standard_EXPORT static void Normal(const gp_Vec& theD1U, 0084 const gp_Vec& theD1V, 0085 const gp_Vec& theD2U, 0086 const gp_Vec& theD2V, 0087 const gp_Vec& theD2UV, 0088 double theSinTol, 0089 bool& theDone, 0090 CSLib_NormalStatus& theStatus, 0091 gp_Dir& theNormal); 0092 0093 //! Computes the normal direction using magnitude tolerance. 0094 //! 0095 //! A simpler version that checks if the cross product magnitude 0096 //! and derivative magnitudes exceed the given tolerance. 0097 //! 0098 //! @param[in] theD1U First derivative in U direction 0099 //! @param[in] theD1V First derivative in V direction 0100 //! @param[in] theMagTol Magnitude tolerance for singularity detection 0101 //! @param[out] theStatus Result status (CSLib_Defined or CSLib_Singular) 0102 //! @param[out] theNormal Computed normal direction (valid only if theStatus == CSLib_Defined) 0103 Standard_EXPORT static void Normal(const gp_Vec& theD1U, 0104 const gp_Vec& theD1V, 0105 double theMagTol, 0106 CSLib_NormalStatus& theStatus, 0107 gp_Dir& theNormal); 0108 0109 //! Computes the normal at a singular point using higher-order derivatives. 0110 //! 0111 //! Finds the first order k0 where the derivatives of N = D1U ^ D1V become non-null 0112 //! and collinear, ensuring a unique normal direction. 0113 //! 0114 //! @param[in] theMaxOrder Maximum derivative order to examine 0115 //! @param[in] theDerNUV Array of derivatives of N (indices correspond to derivative orders) 0116 //! @param[in] theMagTol Magnitude tolerance 0117 //! @param[in] theU, theV Current parameter values 0118 //! @param[in] theUmin, theUmax, theVmin, theVmax Parameter bounds 0119 //! @param[out] theStatus Result status 0120 //! @param[out] theNormal Computed normal direction 0121 //! @param[out] theOrderU, theOrderV Orders of the first non-null derivative used 0122 Standard_EXPORT static void Normal(int theMaxOrder, 0123 const NCollection_Array2<gp_Vec>& theDerNUV, 0124 double theMagTol, 0125 double theU, 0126 double theV, 0127 double theUmin, 0128 double theUmax, 0129 double theVmin, 0130 double theVmax, 0131 CSLib_NormalStatus& theStatus, 0132 gp_Dir& theNormal, 0133 int& theOrderU, 0134 int& theOrderV); 0135 0136 //! Computes the derivative of order (theNu, theNv) of the non-normalized normal vector. 0137 //! 0138 //! The non-normalized normal is N = dS/du ^ dS/dv. 0139 //! This function computes d^(Nu+Nv)N / (du^Nu * dv^Nv). 0140 //! 0141 //! @param[in] theNu Derivative order in U direction 0142 //! @param[in] theNv Derivative order in V direction 0143 //! @param[in] theDerSurf Surface derivatives array where theDerSurf(i,j) = d^(i+j)S/(du^i * dv^j) 0144 //! for i = 0..theNu+1, j = 0..theNv+1 0145 //! @return The derivative vector d^(Nu+Nv)N / (du^Nu * dv^Nv) 0146 Standard_EXPORT static gp_Vec DNNUV(int theNu, 0147 int theNv, 0148 const NCollection_Array2<gp_Vec>& theDerSurf); 0149 0150 //! Computes the derivative of the non-normalized vector N = dS1/du ^ dS2/dv. 0151 //! 0152 //! This variant is used for osculating surfaces where the normal 0153 //! is computed from derivatives of two different surfaces. 0154 //! 0155 //! @param[in] theNu Derivative order in U direction 0156 //! @param[in] theNv Derivative order in V direction 0157 //! @param[in] theDerSurf1 Derivatives of the first surface S1 0158 //! @param[in] theDerSurf2 Derivatives of the second surface S2 0159 //! @return The derivative vector 0160 Standard_EXPORT static gp_Vec DNNUV(int theNu, 0161 int theNv, 0162 const NCollection_Array2<gp_Vec>& theDerSurf1, 0163 const NCollection_Array2<gp_Vec>& theDerSurf2); 0164 0165 //! Computes the derivative of order (theNu, theNv) of the normalized normal vector. 0166 //! 0167 //! @param[in] theNu Derivative order in U direction 0168 //! @param[in] theNv Derivative order in V direction 0169 //! @param[in] theDerNUV Array of derivatives of the non-normalized normal. 0170 //! Contains derivatives d^(i+j)(D1U^D1V)/(du^i * dv^j) 0171 //! for i = theIduref..theNu+theIduref, j = theIdvref..theNv+theIdvref 0172 //! @param[in] theIduref Reference index offset in U (default 0 for regular cases) 0173 //! @param[in] theIdvref Reference index offset in V (default 0 for regular cases) 0174 //! @return The derivative of the normalized normal vector 0175 Standard_EXPORT static gp_Vec DNNormal(int theNu, 0176 int theNv, 0177 const NCollection_Array2<gp_Vec>& theDerNUV, 0178 int theIduref = 0, 0179 int theIdvref = 0); 0180 }; 0181 0182 #endif // _CSLib_HeaderFile
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