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