Drake
Drake C++ Documentation BsplineBasis< T > Class Template Referencefinal

## Detailed Description

### template<typename T> class drake::math::BsplineBasis< T >

Given a set of non-descending breakpoints t₀ ≤ t₁ ≤ ⋅⋅⋅ ≤ tₘ, a B-spline basis of order k is a set of n + 1 (where n = m - k) piecewise polynomials of degree k - 1 defined over those breakpoints.

The elements of this set are called "B-splines". The vector (t₀, t₁, ..., tₘ)' is referred to as the "knot vector" of the basis and its elements are referred to as "knots".

At a breakpoint with multiplicity p (i.e. a breakpoint that appears p times in the knot vector), B-splines are guaranteed to have Cᵏ⁻ᵖ⁻¹ continuity.

A B-spline curve using a B-spline basis B, is a parametric curve mapping parameter values in [tₖ₋₁, tₙ₊₁] to a vector space V. For t ∈ [tₖ₋₁, tₙ₊₁] the value of the curve is given by the linear combination of n + 1 control points, pᵢ ∈ V, with the elements of B evaluated at t.

For more information on B-splines and their uses, see (for example) Patrikalakis et al. .

#include <drake/math/bspline_basis.h>

## Public Member Functions

BsplineBasis ()

BsplineBasis (int order, std::vector< T > knots)
Constructs a B-spline basis with the specified order and knots. More...

BsplineBasis (int order, int num_basis_functions, KnotVectorType type=KnotVectorType::kClampedUniform, const T &initial_parameter_value=0, const T &final_parameter_value=1)
Constructs a B-spline basis with the specified order, num_basis_functions, initial_parameter_value, final_parameter_value, and an auto-generated knot vector of the specified type. More...

BsplineBasis (const BsplineBasis< double > &other)
Conversion constructor. More...

int order () const
The order of this B-spline basis (k in the class description). More...

int degree () const
The degree of the piecewise polynomials comprising this B-spline basis (k - 1 in the class description). More...

int num_basis_functions () const
The number of basis functions in this B-spline basis (n + 1 in the class description). More...

const std::vector< T > & knots () const
The knot vector of this B-spline basis (the vector (t₀, t₁, ..., tₘ)' in the class description). More...

const T & initial_parameter_value () const
The minimum allowable parameter value for B-spline curves using this basis (tₖ₋₁ in the class description). More...

const T & final_parameter_value () const
The maximum allowable parameter value for B-spline curves using this basis (tₙ₊₁ in the class description). More...

int FindContainingInterval (const T &parameter_value) const
For a parameter_value = t, the interval that contains it is the pair of knot values [tᵢ, tᵢ₊₁] for the greatest i such that tᵢ ≤ t and tᵢ < final_parameter_value(). More...

std::vector< intComputeActiveBasisFunctionIndices (const std::array< T, 2 > &parameter_interval) const
Returns the indices of the basis functions which may evaluate to non-zero values for some parameter value in parameter_interval; all other basis functions are strictly zero over parameter_interval. More...

std::vector< intComputeActiveBasisFunctionIndices (const T &parameter_value) const
Returns the indices of the basis functions which may evaluate to non-zero values for parameter_value; all other basis functions are strictly zero at this point. More...

template<typename T_control_point >
T_control_point EvaluateCurve (const std::vector< T_control_point > &control_points, const T &parameter_value) const
Evaluates the B-spline curve defined by this and control_points at the given parameter_value. More...

EvaluateBasisFunctionI (int i, const T &parameter_value) const
Returns the value of the i-th basis function evaluated at parameter_value. More...

boolean< T > operator== (const BsplineBasis &other) const

boolean< T > operator!= (const BsplineBasis &other) const

template<typename Archive >
void Serialize (Archive *a)
Passes this object to an Archive. More...

Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
BsplineBasis (const BsplineBasis &)=default

BsplineBasisoperator= (const BsplineBasis &)=default

BsplineBasis (BsplineBasis &&)=default

BsplineBasisoperator= (BsplineBasis &&)=default

## ◆ BsplineBasis() [1/6]

 BsplineBasis ( const BsplineBasis< T > & )
default

## ◆ BsplineBasis() [2/6]

 BsplineBasis ( BsplineBasis< T > && )
default

## ◆ BsplineBasis() [3/6]

 BsplineBasis ( )

## ◆ BsplineBasis() [4/6]

 BsplineBasis ( int order, std::vector< T > knots )

Constructs a B-spline basis with the specified order and knots.

Precondition
knots is sorted in non-descending order.
Exceptions
 std::exception if knots.size() < 2 * order.

## ◆ BsplineBasis() [5/6]

 BsplineBasis ( int order, int num_basis_functions, KnotVectorType type = KnotVectorType::kClampedUniform, const T & initial_parameter_value = 0, const T & final_parameter_value = 1 )

Constructs a B-spline basis with the specified order, num_basis_functions, initial_parameter_value, final_parameter_value, and an auto-generated knot vector of the specified type.

Exceptions
 std::exception if num_basis_functions < order
Precondition
initial_parameter_value ≤ final_parameter_value

## ◆ BsplineBasis() [6/6]

 BsplineBasis ( const BsplineBasis< double > & other )
explicit

Conversion constructor.

Constructs an instance of BsplineBasis<T> from a double-valued basis.

## ◆ ComputeActiveBasisFunctionIndices() [1/2]

 std::vector ComputeActiveBasisFunctionIndices ( const std::array< T, 2 > & parameter_interval ) const

Returns the indices of the basis functions which may evaluate to non-zero values for some parameter value in parameter_interval; all other basis functions are strictly zero over parameter_interval.

Precondition
parameter_interval ≤ parameter_interval
parameter_interval ≥ initial_parameter_value()
parameter_interval ≤ final_parameter_value()

## ◆ ComputeActiveBasisFunctionIndices() [2/2]

 std::vector ComputeActiveBasisFunctionIndices ( const T & parameter_value ) const

Returns the indices of the basis functions which may evaluate to non-zero values for parameter_value; all other basis functions are strictly zero at this point.

Precondition
parameter_value ≥ initial_parameter_value()
parameter_value ≤ final_parameter_value()

## ◆ degree()

 int degree ( ) const

The degree of the piecewise polynomials comprising this B-spline basis (k - 1 in the class description).

## ◆ EvaluateBasisFunctionI()

 T EvaluateBasisFunctionI ( int i, const T & parameter_value ) const

Returns the value of the i-th basis function evaluated at parameter_value.

## ◆ EvaluateCurve()

 T_control_point EvaluateCurve ( const std::vector< T_control_point > & control_points, const T & parameter_value ) const

Evaluates the B-spline curve defined by this and control_points at the given parameter_value.

Parameters
 control_points Control points of the B-spline curve. parameter_value Parameter value at which to evaluate the B-spline curve defined by this and control_points.
Precondition
control_points.size() == num_basis_functions()
parameter_value ≥ initial_parameter_value()
parameter_value ≤ final_parameter_value()

## ◆ final_parameter_value()

 const T& final_parameter_value ( ) const

The maximum allowable parameter value for B-spline curves using this basis (tₙ₊₁ in the class description).

## ◆ FindContainingInterval()

 int FindContainingInterval ( const T & parameter_value ) const

For a parameter_value = t, the interval that contains it is the pair of knot values [tᵢ, tᵢ₊₁] for the greatest i such that tᵢ ≤ t and tᵢ < final_parameter_value().

This function returns that value of i.

Precondition
parameter_value ≥ initial_parameter_value()
parameter_value ≤ final_parameter_value()

## ◆ initial_parameter_value()

 const T& initial_parameter_value ( ) const

The minimum allowable parameter value for B-spline curves using this basis (tₖ₋₁ in the class description).

## ◆ knots()

 const std::vector& knots ( ) const

The knot vector of this B-spline basis (the vector (t₀, t₁, ..., tₘ)' in the class description).

## ◆ num_basis_functions()

 int num_basis_functions ( ) const

The number of basis functions in this B-spline basis (n + 1 in the class description).

## ◆ operator!=()

 boolean operator!= ( const BsplineBasis< T > & other ) const

## ◆ operator=() [1/2]

 BsplineBasis& operator= ( BsplineBasis< T > && )
default

## ◆ operator=() [2/2]

 BsplineBasis& operator= ( const BsplineBasis< T > & )
default

## ◆ operator==()

 boolean operator== ( const BsplineBasis< T > & other ) const

## ◆ order()

 int order ( ) const

The order of this B-spline basis (k in the class description).

## ◆ Serialize()

 void Serialize ( Archive * a )

Passes this object to an Archive.

Refer to YAML Serialization for background. This method is only available when T = double.

The documentation for this class was generated from the following file: