b311480e |
1 | // Copyright (c) 1995-1999 Matra Datavision |
973c2be1 |
2 | // Copyright (c) 1999-2014 OPEN CASCADE SAS |
b311480e |
3 | // |
973c2be1 |
4 | // This file is part of Open CASCADE Technology software library. |
b311480e |
5 | // |
973c2be1 |
6 | // This library is free software; you can redistribute it and / or modify it |
7 | // under the terms of the GNU Lesser General Public version 2.1 as published |
8 | // by the Free Software Foundation, with special exception defined in the file |
9 | // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT |
10 | // distribution for complete text of the license and disclaimer of any warranty. |
b311480e |
11 | // |
973c2be1 |
12 | // Alternatively, this file may be used under the terms of Open CASCADE |
13 | // commercial license or contractual agreement. |
7fd59977 |
14 | |
15 | #define No_Standard_RangeError |
16 | #define No_Standard_OutOfRange |
17 | |
18 | #include <AppParCurves.ixx> |
19 | #include <BSplCLib.hxx> |
20 | #include <TColStd_Array1OfReal.hxx> |
21 | #include <gp_Pnt2d.hxx> |
22 | #include <gp_Vec2d.hxx> |
23 | |
24 | |
25 | void AppParCurves::BernsteinMatrix(const Standard_Integer NbPoles, |
26 | const math_Vector& U, |
27 | math_Matrix& A) { |
28 | |
29 | Standard_Integer i, j, id; |
30 | Standard_Real u0, u1, y0, y1, xs; |
31 | Standard_Integer first = U.Lower(), last = U.Upper(); |
32 | math_Vector B(1, NbPoles-1); |
33 | |
34 | |
35 | for (i = first; i <= last; i++) { |
36 | B(1) = 1; |
37 | u0 = U(i); |
38 | u1 = 1.-u0; |
39 | |
40 | for (id = 2; id <= NbPoles-1; id++) { |
41 | y0 = B(1); |
42 | y1 = u0*y0; |
43 | B(1) = y0-y1; |
44 | for (j = 2; j <= id-1; j++) { |
45 | xs = y1; |
46 | y0 = B(j); |
47 | y1 = u0*y0; |
48 | B(j) = y0-y1+xs; |
49 | } |
50 | B(id) = y1; |
51 | } |
52 | A(i, 1) = u1*B(1); |
53 | A(i, NbPoles) = u0*B(NbPoles-1); |
54 | for (j = 2; j <= NbPoles-1; j++) { |
55 | A(i, j) = u1*B(j)+u0*B(j-1); |
56 | } |
57 | } |
58 | } |
59 | |
60 | |
61 | void AppParCurves::Bernstein(const Standard_Integer NbPoles, |
62 | const math_Vector& U, |
63 | math_Matrix& A, |
64 | math_Matrix& DA) { |
65 | |
66 | Standard_Integer i, j, id, Ndeg = NbPoles-1; |
67 | Standard_Real u0, u1, y0, y1, xs, bj, bj1;; |
68 | Standard_Integer first = U.Lower(), last = U.Upper(); |
69 | math_Vector B(1, NbPoles-1); |
70 | |
71 | |
72 | for (i = first; i <= last; i++) { |
73 | B(1) = 1; |
74 | u0 = U(i); |
75 | u1 = 1.-u0; |
76 | |
77 | for (id = 2; id <= NbPoles-1; id++) { |
78 | y0 = B(1); |
79 | y1 = u0*y0; |
80 | B(1) = y0-y1; |
81 | for (j = 2; j <= id-1; j++) { |
82 | xs = y1; |
83 | y0 = B(j); |
84 | y1 = u0*y0; |
85 | B(j) = y0-y1+xs; |
86 | } |
87 | B(id) = y1; |
88 | } |
89 | DA(i, 1) = -Ndeg*B(1); |
90 | DA(i, NbPoles) = Ndeg*B(NbPoles-1); |
91 | A(i, 1) = u1*B(1); |
92 | A(i, NbPoles) = u0*B(NbPoles-1); |
93 | for (j = 2; j <= NbPoles-1; j++) { |
94 | bj = B(j); bj1 = B(j-1); |
95 | DA(i,j) = Ndeg*(bj1-bj); |
96 | A(i, j) = u1*bj+u0*bj1; |
97 | } |
98 | } |
99 | } |
100 | |
101 | |
102 | void AppParCurves::SecondDerivativeBernstein(const Standard_Real U, |
103 | math_Vector& DDA) { |
104 | // Standard_Real U1 = 1-U, Y0, Y1, Xs; |
105 | Standard_Real Y0, Y1, Xs; |
106 | Standard_Integer NbPoles = DDA.Length(); |
107 | Standard_Integer id, j, N2, N3, N4, deg = NbPoles-1; |
108 | N2 = deg-1; N3 = deg-2, N4 = deg*(deg-1); |
109 | math_Vector B(1, deg-1); |
110 | B(1) = 1.; |
111 | |
112 | // Cas particulier si degre = 1: |
113 | if (deg == 1) { |
114 | DDA(1) = 0.0; |
115 | DDA(2) = 0.0; |
116 | } |
117 | else if (deg == 2) { |
118 | DDA(1) = 2.0; |
119 | DDA(2) = -4.0; |
120 | DDA(3) = 2.0; |
121 | } |
122 | else { |
123 | |
124 | for (id = 2; id <= deg-1; id++) { |
125 | Y0 = B(1); |
126 | Y1 = U*Y0; |
127 | B(1) = Y0-Y1; |
128 | for (j = 2; j <= id-1; j++) { |
129 | Xs = Y1; |
130 | Y0 = B(j); |
131 | Y1 = U*Y0; |
132 | B(j) = Y0 - Y1 +Xs; |
133 | } |
134 | B(id) = Y1; |
135 | } |
136 | |
137 | DDA(1) = N4*B(1); |
138 | DDA(2) = N4*(-2*B(1) + B(2)); |
139 | DDA(deg) = N4*(B(deg-2) - 2*B(deg-1)); |
140 | DDA(deg+1) = N4*B(deg-1); |
141 | |
142 | for(j = 2; j <= deg-2; j++) { |
143 | DDA(j+1) = N4*(B(j-1)-2*B(j)+B(j+1)); |
144 | } |
145 | } |
146 | } |
147 | |
148 | |
149 | |
150 | void AppParCurves::SplineFunction(const Standard_Integer nbpoles, |
151 | const Standard_Integer deg, |
152 | const math_Vector& Parameters, |
153 | const math_Vector& flatknots, |
154 | math_Matrix& A, |
155 | math_Matrix& DA, |
156 | math_IntegerVector& index) |
157 | { |
158 | // Standard_Real U, NewU, co, diff, t1, t2; |
159 | Standard_Real U, NewU; |
160 | // gp_Pnt2d Pt, P0; |
161 | // gp_Vec2d V1; |
162 | // Standard_Integer i, j, k, iter, in, ik, deg1 = deg+1; |
163 | Standard_Integer i, j, deg1 = deg+1; |
164 | // Standard_Integer oldkindex, kindex, theindex, ttindex; |
165 | Standard_Integer oldkindex, kindex, theindex; |
166 | math_Vector locpoles(1 , deg1); |
167 | math_Vector locdpoles(1 , deg1); |
168 | Standard_Integer firstp = Parameters.Lower(), lastp = Parameters.Upper(); |
169 | |
170 | TColStd_Array1OfReal Aflatknots(flatknots.Lower(), flatknots.Upper()); |
171 | for (i = flatknots.Lower(); i <= flatknots.Upper(); i++) { |
172 | Aflatknots(i) = flatknots(i); |
173 | } |
174 | |
175 | |
176 | oldkindex = 1; |
177 | |
178 | Standard_Integer pp, qq; |
179 | Standard_Real Saved, Inverse, LocalInverse, locqq, locdqq, val; |
180 | |
181 | for (i = firstp; i <= lastp; i++) { |
182 | U = Parameters(i); |
183 | NewU = U; |
184 | kindex = oldkindex; |
185 | BSplCLib::LocateParameter(deg, Aflatknots, U, Standard_False, |
186 | deg1, nbpoles+1, kindex, NewU); |
187 | |
188 | oldkindex = kindex; |
189 | |
190 | // On stocke les index: |
191 | index(i) = kindex - deg-1; |
192 | |
193 | locpoles(1) = 1.0; |
194 | |
195 | for (qq = 2; qq <= deg; qq++) { |
196 | locpoles(qq) = 0.0; |
197 | for (pp = 1; pp <= qq-1; pp++) { |
198 | Inverse = 1.0 / (flatknots(kindex + pp) - flatknots(kindex - qq + pp + 1)) ; |
199 | Saved = (U - flatknots(kindex - qq + pp + 1)) * Inverse * locpoles(pp); |
200 | locpoles(pp) *= (flatknots(kindex + pp) - U) * Inverse ; |
201 | locpoles(pp) += locpoles(qq) ; |
202 | locpoles(qq) = Saved ; |
203 | } |
204 | } |
205 | |
206 | qq = deg+1; |
207 | for (pp = 1; pp <= deg; pp++) { |
208 | locdpoles(pp)= locpoles(pp); |
209 | } |
210 | |
211 | locqq = 0.0; |
212 | locdqq = 0.0; |
213 | for (pp = 1; pp <= deg; pp++) { |
214 | Inverse = 1.0 / (flatknots(kindex + pp) - flatknots(kindex - qq + pp + 1)); |
215 | Saved = (U - flatknots(kindex - qq + pp + 1)) * Inverse * locpoles(pp); |
216 | locpoles(pp) *= (flatknots(kindex + pp) - U) * Inverse; |
217 | locpoles(pp) += locqq; |
218 | locqq = Saved ; |
219 | LocalInverse = (Standard_Real) (deg) * Inverse; |
220 | Saved = LocalInverse * locdpoles(pp); |
221 | locdpoles(pp) *= - LocalInverse ; |
222 | locdpoles(pp) += locdqq; |
223 | locdqq = Saved ; |
224 | } |
225 | |
226 | locpoles(qq) = locqq; |
227 | locdpoles(qq) = locdqq; |
228 | |
229 | for (j = 1; j <= deg1; j++) { |
230 | val = locpoles(j); |
231 | theindex = j+oldkindex-deg1; |
232 | A(i, theindex) = val; |
233 | DA(i, theindex) = locdpoles(j); |
234 | } |
235 | |
236 | for (j = 1; j < oldkindex-deg; j++) |
237 | A(i, j) = DA(i, j) = 0.0; |
238 | for (j = oldkindex+1; j <= nbpoles; j++) |
239 | A(i, j) = DA(i, j) = 0.0; |
240 | |
241 | } |
242 | |
243 | } |