52 map.first->eval_into(x, px);
53 map.second->eval_into(x, py);
63 tangent = p.col(0)-line.col(0);
65 h = tangent.norm()/n_points ;
67 tangent/=tangent.norm();
75 for(
int i=0; i!=n_points; i++)
76 { next = next + h*tangent;
84 Jmap.row(0) = map.first->jacobian(current );
85 Jmap.row(1) = map.second->jacobian(current);
87 if (
math::abs( Jmap.determinant() ) < 0.0001)
89 gsDebug<<
"\n trace line: \n Jacobian vanished at : " << current.transpose() <<
"\n"
90 "with Jacobian = "<<
math::abs( Jmap.determinant() )<<
"\n \n";
96 delta = Jmap.inverse()*(next.col(0)-line.col(0));
99 map.first->eval_into(current,px);
100 map.second->eval_into(current,py);
108 while((--loops > 0) && ( (line-next).norm() > tolerance ) );
134 void gsTraceCurve( std::pair<gsFunction<T>*,gsFunction<T>*> & map,
135 gsMatrix<T>
const & x, gsBSpline<T> * bs,gsMatrix<T> & result,
const int n_points = 50,
136 const T tolerance = 0.0001)
142 result.resize(2,n_points-1);
144 gsMatrix<T> current (2,1);
145 gsMatrix<T> next (2,1), delta;
146 gsMatrix<T> line(2,1), px, py;
147 gsMatrix<T> Jmap (2,2);
150 gsMatrix<T> pts = gsPointGrid<T>(0,1,n_points);
152 gsMatrix<T> ev = bs->eval(pts);
165 result.col(n_points-2)= current;
170 map.first->eval_into(current, px);
171 map.second->eval_into(current, py);
179 for(
int i=2; i!=n_points; i++)
190 Jmap.row(0) = map.first->jacobian(current);
191 Jmap.row(1) = map.second->jacobian(current);
194 delta = Jmap.inverse()*(next.col(0)-line.col(0));
202 map.first->eval_into(current,px);
203 map.second->eval_into(current,py);
212 while((--loops > 0) && ( (line-next).norm() > tolerance ) );
215 result.col(n_points-i-1) = current;
250 const T tolerance = 0.0001)
262 gsMatrix<T> discretI = gsPointGrid<T>(t0,t1, n_points );
264 map.first->eval_into(current, px);
265 map.second->eval_into(current, py);
269 result.resize(2,ev.cols()+1);
273 for(i =1; i< ev.cols()&& cont; i++)
280 Jmap.row(0) = map.first->jacobian(current);
281 Jmap.row(1) = map.second->jacobian(current);
284 if (
math::abs( Jmap.determinant() ) < 0.01)
286 gsDebug<<
"Jacobian vanished at : " << current.transpose() <<
"\n"
287 "with Jacobian = "<<
math::abs( Jmap.determinant() )<<
"\n \n";
293 delta = Jmap.inverse()*(next.col(0)-line.col(0));
297 map.first->eval_into(current,px);
298 map.second->eval_into(current,py);
306 while((--loops > 0) && ( (line-next).norm() > tolerance ) );
308 result.col(i) = current;
312 result.conservativeResize( gsEigen::NoChange, i);
Provides declaration of FunctionExpr class.
#define gsDebug
Definition: gsDebug.h:61
void gsTraceCurvePart(std::pair< gsFunction< T > *, gsFunction< T > * > &map, gsMatrix< T > const &x, gsBSpline< T > *bs, T t0, T t1, gsMatrix< T > &result, const int n_points=50, const T tolerance=0.0001)
Definition: gsTraceCurve.hpp:247
gsMatrix< T > eval(const gsMatrix< T > &u) const
Evaluate the function,.
Definition: gsFunctionSet.hpp:120
#define index_t
Definition: gsConfig.h:32
A function from a n-dimensional domain to an m-dimensional image.
Definition: gsFunction.h:59
A B-spline function of one argument, with arbitrary target dimension.
Definition: gsBSpline.h:50
Provides declaration of BSplineBasis class.
void gsTraceLine(std::pair< gsFunction< T > *, gsFunction< T > * > &map, gsMatrix< T > const &x, gsMatrix< T > const &p, gsMatrix< T > &result)
Definition: gsTraceCurve.hpp:36
Provides functions to generate structured point data.
This is the main header file that collects wrappers of Eigen for linear algebra.
EIGEN_STRONG_INLINE abs_expr< E > abs(const E &u)
Absolute value.
Definition: gsExpressions.h:4486
Provides declaration of Function abstract interface.