1 /* $NoKeywords: $ */ 2 /* 3 // 4 // Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved. 5 // OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert 6 // McNeel & Associates. 7 // 8 // THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY. 9 // ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF 10 // MERCHANTABILITY ARE HEREBY DISCLAIMED. 11 // 12 // For complete openNURBS copyright information see <http://www.opennurbs.org>. 13 // 14 //////////////////////////////////////////////////////////////// 15 */ 16 17 #if !defined(OPENNURBS_OPTIMIZE_INC_) 18 #define OPENNURBS_OPTIMIZE_INC_ 19 20 // find a local minimum of a 1 parameter function 21 ON_BOOL32 ON_FindLocalMinimum( // returns 0 - failed to converge, 1 - success, 2 - failed to converge to requested tolerances 22 int (*)(void*,double,double*,double*), // f(void*, double t, double* value, double* derivative ); 23 void*, // passed as the void* argument to the above function 24 double, double, double, // ax,bx,cx, 3 abcissa ax<bx<cx or ax>bx>cx, and 25 // f(bx) < f(ax), and f(bx) < f(cx) 26 double, // tol > 0 (minimum relative step size (use ON_EPSILON when in doubt) 27 double, // zeps > 0 (minimum absolute step size (use 1/2*(desired absolute precision)) 28 int, // maximum number of iterations ( use 100 when in doubt) 29 double* // abcissa of local minimum returned here 30 ); 31 32 // find a local zero of a 1 parameter function 33 class ON_LocalZero1 34 { 35 public: 36 ON_LocalZero1(); 37 virtual ~ON_LocalZero1(); 38 39 virtual 40 ON_BOOL32 Evaluate( // returns true if successful 41 double, // evaluation parameter 42 double*, // f(t) returned here - NULL never passed 43 double*, // If not NULL, then f'(t) returned here 44 int // < 0: evaluate from below 45 // >= 0: evaluate from above 46 ) = 0; 47 48 49 ON_BOOL32 FindZero( double* ); // Searches domain between m_t0 and m_t1 50 // domain for a root. Returns true if 51 // a root is found. 52 53 // m_t0 and m_t1 specify the domain to search and must satisfy 54 // 55 // 1) m_t0 != m_t1 56 // 2) f(m_t0) and f(m_t1) must have different signs 57 // or one must have absolute value <= m_f_tolerance 58 double m_t0, m_t1; 59 60 double m_f_tolerance; // (>= 0.0) If this value is > 0.0, then 61 // the search is terminated when a parameter 62 // "t" is found where |f(t)| <= m_f_tolerance. 63 64 double m_t_tolerance; // (>= 0.0) If this value is > 0.0, then 65 // the search is terminated when a parameter 66 // the root is bracketed in a domain with width 67 // <= m_t_tolerance. 68 69 // m_k[] is either NULL or monotone increasing array of length m_k_count. 70 // 71 // This zero finder works on continuous piecewise c2 functions. 72 // If the function is c2 on the interior of the domain 73 // 74 // [min(t0,t1), max(m_t0,m_t1)] 75 // 76 // then there is no need to initialize m_k[]. If the function 77 // is not c2 on the domain in question, then the m_k[m_count] array 78 // is a list of parameters that define the c2 domains. When m_k[] 79 // is not NULL, m_count must be >= 2 and m_k[] must be monotone 80 // increasing and satisfy 81 // 82 // m_k[0] <= min(m_t0,m_t1) 83 // and 84 // m_k[m_count-1] >= max(m_t0,m_t1). 85 // 86 // Duplicate values in m_k[] are permitted so that NURBS knot 87 // vector arrays may be used directly. 88 const double* m_k; 89 90 // length of m_k[] array ( 0 or >= 2 ). 91 int m_k_count; 92 93 private: 94 double m_s0, m_f0, m_s1, m_f1; 95 ON_BOOL32 BracketZero(double,double,double,double,int=0); 96 ON_BOOL32 BracketSpan(double,double,double,double); 97 ON_BOOL32 NewtonRaphson( double, double, double, double, int, double* ); 98 }; 99 100 #endif 101 102