#include <BsplineBasis.h>
Inheritance diagram for Go::BsplineBasis:
Public Member Functions | |
| BsplineBasis () | |
| Default constructor, making an empty basis. | |
| template<typename RandomIterator> | |
| BsplineBasis (int number, int order, RandomIterator knotstart) | |
| Constructor. | |
| template<typename RandomIterator> | |
| BsplineBasis (int order, RandomIterator knotstart, RandomIterator knotend) | |
| Constructor. | |
| virtual | ~BsplineBasis () |
| Virtual destructor, enables safe inheritance. | |
| template<typename RandomIterator> | |
| void | setData (int number, int order, RandomIterator knotstart) |
| Change the defining data of an already-existing BsplineBasis. | |
| void | swap (BsplineBasis &other) |
| Quick swap of two BsplineBasises. | |
| virtual void | read (std::istream &is) |
| Read the BsplineBasis from a stream (ASCII mode). | |
| virtual void | write (std::ostream &os) const |
| Write the BsplineBasis to a stream (ASCII mode). | |
| virtual void | read_bin (std::istream &is) |
| Read the BsplineBasis from a stream (binary mode). | |
| virtual void | write_bin (std::ostream &os) const |
| Write the BsplineBasis to a stream (binary mode). | |
| int | knotInterval (double t) const |
| Find the interval in which the parameter value 't' lies. | |
| std::vector< double > | computeBasisValues (double t, int derivs=0) const |
| Create a vector containing the basis values in a given parameter. | |
| void | computeBasisValues (double t, double *basisvals_start, int derivs=0, double resolution=1.0e-12) const |
| Space for the basis values is allocated outside and passed in. | |
| void | computeBasisValues (const double *parvals_start, const double *parvals_end, double *basisvals_start, int *knotinter_start, int derivs=0) const |
| Compute basis values for many points simultaneously. | |
| std::vector< double > | computeBasisValuesLeft (double tval, int derivs) const |
| This function is similar to computeBasisValues(double, int), except that the values are calculated from the left, as opposed to the default right-evaluation. | |
| void | computeBasisValuesLeft (const double *parvals_start, const double *parvals_end, double *basisvals_start, int *knotinter_start, int derivs) const |
| This function is similar to computeBasisValues(const double*, const double*, double*, int*, int), except that the values are calculated from the left, as opposed to the default right-evaluation. | |
| void | reverseParameterDirection () |
| We want the new knot vector to be a mirror image of the old one, translated so that is starts and ends in the same values as before. | |
| void | rescale (double new_start, double new_end) |
| Rescales the knotvector so that parameter values lay in the specified interval. | |
| void | insertKnot (double apar) |
| Insert a knot into the knotvector. | |
| int | knotIntervalFuzzy (double &t, double tol=DEFAULT_PARAMETER_EPSILON) const |
| Find the interval in which a given parameter lies. | |
| void | insertKnot (const std::vector< double > &new_knots) |
| Insert several knots into the knotvector. | |
| void | removeKnot (double old_knot) |
| Remove a knot from the knotvector. | |
| int | lastKnotInterval () const |
| Return the index of the left knot of the last knot interval accessed for some reason (evaluation, etc. | |
| double | grevilleParameter (int index) const |
| Get the greville parameter starting from a certain knot. | |
| int | knotMultiplicity (const double parval) const |
| If there is a knot in the knotvector with the value 'parval', its multiplicity is returned. | |
| int | endMultiplicity (bool atstart) const |
| return the multiplicity of the first or the last knot | |
| bool | isKreg () const |
| query whether the basis has a k-regular knotvector (start and end knot has multiplicity equal to order(). | |
| void | coefsAffectingParam (double tpar, int &first_coef, int &last_coef) const |
| Get the range of basis functions that are involved when evaluating at a given parameter. | |
| int | numCoefs () const |
| Query the number of basis functions. | |
| int | order () const |
| Query the order of the basis functions. | |
| double | startparam () const |
| Query the start value of the parameter range. | |
| double | endparam () const |
| Query the end value of the parameter range. | |
| std::vector< double >::const_iterator | begin () const |
| Get a const-iterator to the beginning of the knotvector. | |
| std::vector< double >::const_iterator | end () const |
| Get a const-iterator to the end of the knotvector. | |
| std::vector< double >::iterator | begin () |
| Get an iterator to the beginning of the knotvector. | |
| std::vector< double >::iterator | end () |
| Get an iterator to the end of the knotvector. | |
| void | check () const |
| Checks the validity of the object. | |
Related Functions | |
| (Note that these are not member functions.) | |
| void | computeBasisValuesLeft (double tval, double *basisvals_start, int derivs, double resolution=1.0e-12) const |
| This function is similar to computeBasisValues(double, double*, int), except that the values are calculated from the left, as opposed to the default right-evaluation. | |
This basis is defined by its order, its dimension (number of basis functions) and its knotvector.
Definition at line 57 of file BsplineBasis.h.
| Go::BsplineBasis::BsplineBasis | ( | int | number, | |
| int | order, | |||
| RandomIterator | knotstart | |||
| ) | [inline] |
Constructor.
| number | Number of basis functions in space | |
| order | order of the basis functions (polynomial degree + 1) | |
| knotstart | iterator pointing to start of defining knotvector The length of the knotvector is deduced automatically, and should be equal to 'order' + 'number'. |
Definition at line 73 of file BsplineBasis.h.
References check().
| Go::BsplineBasis::BsplineBasis | ( | int | order, | |
| RandomIterator | knotstart, | |||
| RandomIterator | knotend | |||
| ) | [inline] |
Constructor.
| order | order of the basis functions (polynomial degree + 1) | |
| knotstart | iterator pointing to start of defining knotvector | |
| knotend | iterator pointing to one-past-end of defining knotvector. The number of basis functions will be deduced automatically by subtracting the 'order' from the length of the knotvector. |
Definition at line 90 of file BsplineBasis.h.
References check().
| void Go::BsplineBasis::setData | ( | int | number, | |
| int | order, | |||
| RandomIterator | knotstart | |||
| ) | [inline] |
Change the defining data of an already-existing BsplineBasis.
| number | Number of basis functions in space | |
| order | of the basis functions (polynomial degree + 1) | |
| knotstart | iterator pointing to start of defining knotvector. |
Definition at line 109 of file BsplineBasis.h.
| void Go::BsplineBasis::swap | ( | BsplineBasis & | other | ) |
| virtual void Go::BsplineBasis::read | ( | std::istream & | is | ) | [virtual] |
Read the BsplineBasis from a stream (ASCII mode).
| is | the stream from which the BsplineBasis is read. |
Implements Go::Streamable.
| virtual void Go::BsplineBasis::write | ( | std::ostream & | os | ) | const [virtual] |
Write the BsplineBasis to a stream (ASCII mode).
| os | the stream to which the BsplineBasis is written |
Implements Go::Streamable.
| virtual void Go::BsplineBasis::read_bin | ( | std::istream & | is | ) | [virtual] |
Read the BsplineBasis from a stream (binary mode).
| is | the stream from which the BsplineBasis is read. |
| virtual void Go::BsplineBasis::write_bin | ( | std::ostream & | os | ) | const [virtual] |
Write the BsplineBasis to a stream (binary mode).
| os | the stream to which the BsplineBasis is written |
| int Go::BsplineBasis::knotInterval | ( | double | t | ) | const |
Find the interval in which the parameter value 't' lies.
| t | the parameter value to test. |
| std::vector<double> Go::BsplineBasis::computeBasisValues | ( | double | t, | |
| int | derivs = 0 | |||
| ) | const |
Create a vector containing the basis values in a given parameter.
| t | the parameter at which to evaluate the basis functions | |
| derivs | the number of function derivatives to calculate for each nonzero basis function at 't'. |
| void Go::BsplineBasis::computeBasisValues | ( | double | t, | |
| double * | basisvals_start, | |||
| int | derivs = 0, |
|||
| double | resolution = 1.0e-12 | |||
| ) | const |
Space for the basis values is allocated outside and passed in.
Needed space is equal to order()*('derivs'+1) doubles.
| t | the parameter at which to evaluate the basis function | |
| basisvals_start | pointer to the memory area where the result will be written. This must be allocated by the user. The order in which the result values are written is similar to computeBasisValues(double, int) | |
| derivs | number of derivatives that should be evaluated for each nonzero basis function (derivs = 0 => only function values will be computed). | |
| resolution | accuracy for determining whether a given parametric value lies exactly 'on' a knot. |
| void Go::BsplineBasis::computeBasisValues | ( | const double * | parvals_start, | |
| const double * | parvals_end, | |||
| double * | basisvals_start, | |||
| int * | knotinter_start, | |||
| int | derivs = 0 | |||
| ) | const |
Compute basis values for many points simultaneously.
| parvals_start | pointer to the start of list of parameters where you want to evaluate the basis functions | |
| parvals_end | pointer to one-past-end of list of parameters where you want to evaluate the basis functions | |
| basisvals_start | pointer to range where the result of the evaluations will be written. The necessary memory is equal to 'derivs' multiplied by order() multiplied by length of parameter list, and should be allocated by user before calling the function. The order in which these values are stored is: first all values concerning the first parameter in the input range, then all values concerning the second parameter in the input range, etc. For each such parameter, the concerned values are stored in the order described in computeBasisValues(double, int) | |
| knotinter_start | pointer to range where the indexes to the parameter intervals in which the evaluated parameter values are located. ie. the index at knotinter_start[i] refer to the parameter interval where the i'th parameter in the range [parvals_start, parvals_end] is located. The total size of this range is therefore equal to (parvals_end - parvals_start), and should be allocated by the user. | |
| derivs | number of derivatives that should be evaluated for each nonzero basis function (derivs = 0 => only function values will be computed). |
| std::vector<double> Go::BsplineBasis::computeBasisValuesLeft | ( | double | tval, | |
| int | derivs | |||
| ) | const |
This function is similar to computeBasisValues(double, int), except that the values are calculated from the left, as opposed to the default right-evaluation.
| void Go::BsplineBasis::rescale | ( | double | new_start, | |
| double | new_end | |||
| ) |
Rescales the knotvector so that parameter values lay in the specified interval.
| new_start | start of specified interval. | |
| new_end | end of specified interval. |
| void Go::BsplineBasis::insertKnot | ( | double | apar | ) |
Insert a knot into the knotvector.
| apar | parameter value of the new knot. |
| int Go::BsplineBasis::knotIntervalFuzzy | ( | double & | t, | |
| double | tol = DEFAULT_PARAMETER_EPSILON | |||
| ) | const |
Find the interval in which a given parameter lies.
| t | the parameter we want to locate within an interval | |
| tol | if 't' is within DEFAULT_PARAMETER_EPSILON of an existing knot, 't' will be changed to that knot. To some callers of this function, that may be the primary wanted effect of this function. |
| void Go::BsplineBasis::insertKnot | ( | const std::vector< double > & | new_knots | ) |
Insert several knots into the knotvector.
| new_knots | a STL vector containing the new knots to insert into the vector |
| void Go::BsplineBasis::removeKnot | ( | double | old_knot | ) |
Remove a knot from the knotvector.
| old_knot | Parameter value indicating the knot to be removed. The corresponding knot is the largest one which is less than or equal to 'old_knot'. |
| int Go::BsplineBasis::knotMultiplicity | ( | const double | parval | ) | const |
If there is a knot in the knotvector with the value 'parval', its multiplicity is returned.
Otherwise, 0 i returned.
| parval | the parameter value for which we want to know the knot multiplicity |
| int Go::BsplineBasis::endMultiplicity | ( | bool | atstart | ) | const |
return the multiplicity of the first or the last knot
| atstart | if this is 'true' then the multiplicity of the first knot will be returned. Otherwise, the multiplicity of the last knot will be returned. |
Referenced by isKreg().
| bool Go::BsplineBasis::isKreg | ( | ) | const [inline] |
query whether the basis has a k-regular knotvector (start and end knot has multiplicity equal to order().
Definition at line 281 of file BsplineBasis.h.
References endMultiplicity().
| void Go::BsplineBasis::coefsAffectingParam | ( | double | tpar, | |
| int & | first_coef, | |||
| int & | last_coef | |||
| ) | const |
Get the range of basis functions that are involved when evaluating at a given parameter.
| tpar | the parameter where we want to determine the influential range | |
| first_coef | on function completion, will point to start of relevant range | |
| last_coef | on function completion, will point to end of relevant range |
| int Go::BsplineBasis::numCoefs | ( | ) | const [inline] |
Query the number of basis functions.
Definition at line 296 of file BsplineBasis.h.
Referenced by Go::SplineCurve::numCoefs(), Go::SplineSurface::numCoefs_u(), Go::SplineSurface::numCoefs_v(), and Go::SplineSurface::SplineSurface().
| int Go::BsplineBasis::order | ( | ) | const [inline] |
Query the order of the basis functions.
Definition at line 301 of file BsplineBasis.h.
Referenced by grevilleParameter(), Go::SplineCurve::order(), Go::SplineSurface::order_u(), and Go::SplineSurface::order_v().
| double Go::BsplineBasis::startparam | ( | ) | const [inline] |
Query the start value of the parameter range.
Definition at line 306 of file BsplineBasis.h.
| double Go::BsplineBasis::endparam | ( | ) | const [inline] |
Query the end value of the parameter range.
Definition at line 311 of file BsplineBasis.h.
| std::vector<double>::const_iterator Go::BsplineBasis::begin | ( | ) | const [inline] |
Get a const-iterator to the beginning of the knotvector.
Definition at line 316 of file BsplineBasis.h.
Referenced by Go::SplineCurve::knotsBegin().
| std::vector<double>::const_iterator Go::BsplineBasis::end | ( | ) | const [inline] |
Get a const-iterator to the end of the knotvector.
Definition at line 321 of file BsplineBasis.h.
Referenced by Go::SplineCurve::knotsEnd().
| std::vector<double>::iterator Go::BsplineBasis::begin | ( | ) | [inline] |
Get an iterator to the beginning of the knotvector.
Definition at line 326 of file BsplineBasis.h.
| std::vector<double>::iterator Go::BsplineBasis::end | ( | ) | [inline] |
Get an iterator to the end of the knotvector.
Definition at line 330 of file BsplineBasis.h.
| void computeBasisValuesLeft | ( | double | tval, | |
| double * | basisvals_start, | |||
| int | derivs, | |||
| double | resolution = 1.0e-12 | |||
| ) | const [related] |
This function is similar to computeBasisValues(double, double*, int), except that the values are calculated from the left, as opposed to the default right-evaluation.
| resolution | tolerance deciding whether a parameter value is situated "directly on" a knot. (In such situations, it might matter whether we evaluate from left or from left). |
1.5.1