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IgANet
IGAnets - Isogeometric Analysis Networks
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IgANet
IGAnets - Isogeometric Analysis Networks
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B-spline (common high-level functionality). More...
#include </home/runner/work/iganet/iganet/include/iganet/splines/bspline.hpp>
Public Types | |
| template<typename real_t , short_t GeoDim, short_t... Degrees> | |
| using | derived_self_type = BSplineCommon< typename BSplineCore::template derived_self_type< real_t, GeoDim, Degrees... > > |
Deduces the derived self-type when exposed to different class template parameters real_t and GeoDim, and the Degrees parameter pack. | |
| template<template< typename, short_t, short_t... > class T, std::make_signed_t< short_t > degree_elevate = 0> | |
| using | derived_type = BSplineCommon< typename BSplineCore::template derived_type< T, degree_elevate > > |
Deduces the type of the template parameter T when exposed to the class template parameters real_t and GeoDim, and the Degrees parameter pack. The optional template parameter degree_elevate can be used to (de-)elevate the degrees by an additive constant. | |
| using | Ptr = std::shared_ptr< BSplineCommon > |
| Shared pointer for BSplineCommon. | |
| template<typename other_t > | |
| using | real_derived_self_type = BSplineCommon< typename BSplineCore::template real_derived_self_type< other_t > > |
Deduces the derived self-type when exposed to a different class template parameter real_t. | |
| template<std::make_signed_t< short_t > degree_elevate = 0> | |
| using | self_type = BSplineCommon< typename BSplineCore::template self_type< degree_elevate > > |
Deduces the self-type possibly degrees (de-)elevated by the additive constant degree_elevate. | |
| using | uPtr = std::unique_ptr< BSplineCommon > |
| Unique pointer for BSplineCommon. | |
Public Member Functions | |
| BSplineCommon (BSplineCommon &&)=default | |
| Move constructor. | |
| BSplineCommon (BSplineCommon &&other, utils::TensorArray< BSplineCore::geoDim_ > &&coeffs) | |
| Move constructor with external coefficients. | |
| BSplineCommon (const BSplineCommon &)=default | |
| Copy constructor. | |
| BSplineCommon (const BSplineCommon &other, bool clone) | |
| Copy/clone constructor. | |
| BSplineCommon (const BSplineCommon &other, const utils::TensorArray< BSplineCore::geoDim_ > &coeffs, bool clone=false) | |
| Copy constructor with external coefficients. | |
| template<typename OtherCore > requires SplineCoreType<std::remove_cvref_t<OtherCore>> | |
| BSplineCommon (OtherCore &&core) | |
| Constructs the high-level B-spline from a compatible core. | |
| auto | abs_diff (const BSplineCommon &other, int dim=-1) const |
| Computes the absolute difference between two compatible B-spline objects. | |
| auto | abs_diff_ (const BSplineCommon &other, int dim=-1) |
| Computes the absolute difference between two compatible B-spline objects in-place. | |
| auto | boundingBox () const |
| Computes the bounding box of the B-spline object. | |
| auto | clone () const |
| Returns a clone of the B-spline object. | |
| template<bool memory_optimized = false> | |
| auto | curl (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const |
| Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | curl (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const |
| Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables. | |
| auto | diff (const BSplineCommon &other, int dim=-1) const |
| Computes the difference between two compatible B-spline objects. | |
| auto | diff_ (const BSplineCommon &other, int dim=-1) |
| Computes the difference between two compatible B-spline objects in-place. | |
| template<bool memory_optimized = false> | |
| auto | div (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const |
| Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | div (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const |
| Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | grad (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | grad (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | hess (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | hess (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | icurl (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const |
Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | icurl (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const |
Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | idiv (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const |
| Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | idiv (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const |
| Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | igrad (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | igrad (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | ihess (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | ihess (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | ijac (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | ijac (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | ilapl (const Geometry &G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G, const torch::Tensor &coeff_indices_G) const |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false, typename Geometry > | |
| auto | ilapl (const Geometry G, const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const utils::TensorArray< Geometry::parDim()> &knot_indices_G) const |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables. | |
| template<bool memory_optimized = false> | |
| auto | jac (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | jac (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | lapl (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables. | |
| template<bool memory_optimized = false> | |
| auto | lapl (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables. | |
| auto | norm () const |
| Computes the norm of the B-spline object by computing the mean-squared sum of the function values evaluated at the Greville abscissae. | |
| template<bool memory_optimized = false> | |
| auto | nv (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices) const |
| Returns a block-tensor with the outward pointing normal vector of the B-spline object. | |
| template<bool memory_optimized = false> | |
| auto | nv (const utils::TensorArray< BSplineCore::parDim_ > &xi, const utils::TensorArray< BSplineCore::parDim_ > &knot_indices, const torch::Tensor &coeff_indices) const |
| Returns a block-tensor with the outward pointing normal vector of the B-spline object. | |
| BSplineCommon | operator* (BSplineCore::value_type s) const |
| Returns a new B-spline object whose coefficients are scaled by a scalar. | |
| BSplineCommon | operator* (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) const |
| Returns a new B-spline object whose coefficients are scaled by a vector. | |
| BSplineCommon & | operator*= (BSplineCore::value_type s) |
| Scales the coefficients by a scalar. | |
| BSplineCommon & | operator*= (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) |
| Scales the coefficients by a vector. | |
| BSplineCommon | operator+ (const BSplineCommon &other) const |
| Returns a new B-spline object whose coefficients are the sum of that of two compatible B-spline objects. | |
| BSplineCommon & | operator+= (const BSplineCommon &other) |
| Adds the coefficients of another B-spline object. | |
| BSplineCommon | operator- (const BSplineCommon &other) const |
| Returns a new B-spline object whose coefficients are the difference of that of two compatible B-spline objects. | |
| BSplineCommon & | operator-= (const BSplineCommon &other) |
| Substracts the coefficients of another B-spline object. | |
| BSplineCommon | operator/ (BSplineCore::value_type s) const |
| Returns a new B-spline object whose coefficients are scaled by a scalar. | |
| BSplineCommon | operator/ (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) const |
| Returns a new B-spline object whose coefficients are scaled by a vector. | |
| BSplineCommon & | operator/= (BSplineCore::value_type s) |
| Scales the coefficients by a scalar. | |
| BSplineCommon & | operator/= (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) |
| Scales the coefficients by a vector. | |
| template<typename Backend = void, typename BSplineCoreColor > | |
| auto | plot (const BSplineCommon< BSplineCoreColor > &color, const nlohmann::json &json={}) const |
| Plots the B-spline object colored by another B-spline object. | |
| template<typename Backend = void, typename BSplineCoreColor > | |
| auto | plot (const BSplineCommon< BSplineCoreColor > &color, const std::initializer_list< utils::TensorArray< BSplineCore::parDim_ > > &xi, const nlohmann::json &json={}) const |
| Plots the B-spline object colored by another B-spline object together with a set of sampling points. | |
| template<typename Backend = void, typename BSplineCoreColor > | |
| auto | plot (const BSplineCommon< BSplineCoreColor > &color, const utils::TensorArray< BSplineCore::parDim_ > &xi, const nlohmann::json &json={}) const |
| Plots the B-spline object colored by another B-spline object together with a set of sampling points. | |
| template<typename Backend = void> | |
| auto | plot (const nlohmann::json &json={}) const |
| Plots the B-spline object. | |
| template<typename Backend = void> | |
| auto | plot (const std::initializer_list< utils::TensorArray< BSplineCore::parDim_ > > &xi, const nlohmann::json &json={}) const |
| Plots the B-spline object together with a set of sampling points. | |
| template<typename Backend = void> | |
| auto | plot (const utils::TensorArray< BSplineCore::parDim_ > &xi, const nlohmann::json &json={}) const |
| Plots the B-spline object together with a set of sampling points. | |
| void | pretty_print (std::ostream &os) const noexcept override |
| Returns a string representation of the BSplineCommon object. | |
| auto | rotate (BSplineCore::value_type angle) const |
| Rotates the B-spline object by an angle in 2d. | |
| auto | rotate (std::array< typename BSplineCore::value_type, 3 > angle) const |
| Rotates the B-spline object by three angles in 3d. | |
| auto | rotate_ (BSplineCore::value_type angle) |
| Rotates the B-spline object by an angle in 2d in-place. | |
| auto | rotate_ (std::array< typename BSplineCore::value_type, 3 > angle) |
| Rotates the B-spline object by three angles in 3d in-place. | |
| auto | scale (BSplineCore::value_type s, int dim=-1) const |
| Scales the B-spline object by a scalar. | |
| auto | scale (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) const |
| Scales the B-spline object by a vector. | |
| auto | scale_ (BSplineCore::value_type s, int dim=-1) |
| Scales the B-spline object by a scalar in-place. | |
| auto | scale_ (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) |
| Scales the B-spline object by a vector in-place. | |
| template<typename real_t > | |
| auto | to () const |
| Returns a copy of the B-spline object with real_t type. | |
| template<typename real_t > | |
| auto | to (Options< real_t > options) const |
| Returns a copy of the B-spline object with settings from options. | |
| auto | to (torch::Device device) const |
| Returns a copy of the B-spline object with settings from device. | |
| auto | to_nonuniform () && |
| Converts a uniform B-spline into a non-uniform B-spline. | |
| auto | to_uniform () && |
| Converts a non-uniform B-spline into a uniform B-spline. | |
| auto | translate (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) const |
| Translates the B-spline object by a vector. | |
| auto | translate_ (std::array< typename BSplineCore::value_type, BSplineCore::geoDim()> v) |
| Translates the B-spline object by a vector in-place. | |
| BSplineCommon & | uniform_refine (int numRefine=1, int dim=-1) |
| Returns the B-spline object with uniformly refined knot and coefficient vectors. | |
Additional Inherited Members | |
 Protected Member Functions inherited from iganet::utils::FullQualifiedName | |
| virtual | ~FullQualifiedName ()=default |
| virtual const std::string & | name () const noexcept |
| Returns the full qualified name of the object. | |
| Protected Attributes inherited from iganet::utils::FullQualifiedName | |
| at::optional< std::string > | name_ |
| String storing the full qualified name of the object. | |
B-spline (common high-level functionality).
This class implements some high-level common functionality of all B-spline classes, e.g., plotting which rely on low-level functionality that is implemented differently for uniform and non-uniform B-splines. C++ would normally use virtual methods for this purpose and implement the common functionality in a base class. However, this is not performant for low-level functionality, e.g., point-wise function evaluation which is called repeatedly. Moreover, virtual methods do not work with templated functions, which is why we implement high-level common functionality here and 'inject' the core functionality by deriving from a particular base class.
| using iganet::BSplineCommon< BSplineCore >::derived_self_type = BSplineCommon<typename BSplineCore::template derived_self_type< real_t, GeoDim, Degrees...> > |
Deduces the derived self-type when exposed to different class template parameters real_t and GeoDim, and the Degrees parameter pack.
| using iganet::BSplineCommon< BSplineCore >::derived_type = BSplineCommon< typename BSplineCore::template derived_type<T, degree_elevate> > |
Deduces the type of the template parameter T when exposed to the class template parameters real_t and GeoDim, and the Degrees parameter pack. The optional template parameter degree_elevate can be used to (de-)elevate the degrees by an additive constant.
| using iganet::BSplineCommon< BSplineCore >::Ptr = std::shared_ptr<BSplineCommon> |
Shared pointer for BSplineCommon.
| using iganet::BSplineCommon< BSplineCore >::real_derived_self_type = BSplineCommon< typename BSplineCore::template real_derived_self_type<other_t> > |
Deduces the derived self-type when exposed to a different class template parameter real_t.
| using iganet::BSplineCommon< BSplineCore >::self_type = BSplineCommon<typename BSplineCore::template self_type<degree_elevate> > |
Deduces the self-type possibly degrees (de-)elevated by the additive constant degree_elevate.
| using iganet::BSplineCommon< BSplineCore >::uPtr = std::unique_ptr<BSplineCommon> |
Unique pointer for BSplineCommon.
|
default |
Copy constructor.
|
inline |
Copy/clone constructor.
| other | Second input value. |
| clone | Value of clone. |
|
inline |
Copy constructor with external coefficients.
| other | Second input value. |
| coeffs | Value of coeffs. |
| clone | Value of clone. |
|
default |
Move constructor.
|
inlineexplicit |
Constructs the high-level B-spline from a compatible core.
| OtherCore | Template parameter OtherCore. |
| core | Value of core. |
|
inline |
Move constructor with external coefficients.
| other | Second input value. |
| coeffs | Value of coeffs. |
|
inline |
Computes the absolute difference between two compatible B-spline objects.
If dim = -1 the full coefficient vector of other is subtracted from that of the current B-spline object. Otherwise, only the specified direction is subtracted.
| other | Second input value. |
| dim | Value of dim. |
|
inline |
Computes the absolute difference between two compatible B-spline objects in-place.
If dim = -1 the full coefficient vector of other is subtracted from that of the current B-spline object. Otherwise, only the specified direction is subtracted.
| other | Second input value. |
| dim | Value of dim. |
|
inline |
Computes the bounding box of the B-spline object.
|
inline |
Returns a clone of the B-spline object.
|
inline |
Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the curl. |
xi. \[ \nabla_{\boldsymbol{\xi}} \times \mathbf{u} = \begin{bmatrix} \mathbf{i}_0 & \cdots & \mathbf{i}_{d_\text{par}} \\ \frac{\partial}{\partial\xi_0} & \cdots & \frac{\partial}{\partial\xi_{d_\text{par}}} \\ u_0 & \cdots & u_{d_\text{par}} \end{bmatrix} \]
|
inline |
Provides the curl operation.
| memory_optimized | Template parameter memory_optimized. |
| memory_optimized | Template parameter memory_optimized. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the curl. |
| [in] | knot_indices | Knot indices where to evaluate the curl. |
\[ \nabla_{\boldsymbol{\xi}} \times \mathbf{u} = \begin{bmatrix} \mathbf{i}_0 & \cdots & \mathbf{i}_{d_\text{par}} \\ \frac{\partial}{\partial\xi_0} & \cdots & \frac{\partial}{\partial\xi_{d_\text{par}}} \\ u_0 & \cdots & u_{d_\text{par}} \end{bmatrix} \]
|
inline |
Returns a block-tensor with the curl of the B-spline object with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the curl. |
| [in] | knot_indices | Knot indices where to evaluate the curl. |
| [in] | coeff_indices | Coefficient indices where to evaluate the curl. |
\[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]
curl = 0, 0, du_y / dx - du_x / dy.
Only the third component is returned.
curl = du_z / dy - du_y / dz, du_x / dz - du_z / dx, du_y / dx - du_x / dy.
|
inline |
Computes the difference between two compatible B-spline objects.
If dim = -1 the full coefficient vector of other is subtracted from that of the current B-spline object. Otherwise, only the specified direction is subtracted.
| other | Second input value. |
| dim | Value of dim. |
|
inline |
Computes the difference between two compatible B-spline objects in-place.
If dim = -1 the full coefficient vector of other is subtracted from that of the current B-spline object. Otherwise, only the specified direction is subtracted.
| other | Second input value. |
| dim | Value of dim. |
|
inline |
Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the divergence. |
xi. \[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]
|
inline |
Provides the div operation.
| memory_optimized | Template parameter memory_optimized. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the divergence. |
| [in] | knot_indices | Knot indices where to evaluate the divergence. |
\[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]
|
inline |
Returns a block-tensor with the divergence of the B-spline object with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the divergence. |
| [in] | knot_indices | Knot indices where to evaluate the divergence. |
| [in] | coeff_indices | Coefficient indices where to evaluate the divergence. |
\[ \nabla_{\boldsymbol{\xi}} \cdot \mathbf{u} = \text{trace} ( J_{\boldsymbol{\xi}}(u) ) = \frac{\partial u_0}{\partial \xi_0} + \frac{\partial u_1}{\partial \xi_1} + \dots \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \]
|
inline |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the gradient. |
xi. \[ \nabla_{\boldsymbol{\xi}}u = \left(\frac{\partial u}{\partial \xi_0}, \frac{\partial u}{\partial \xi_1}, \dots \frac{\partial u}{\partial \xi_{d_\text{par}}}\right) \]
|
inline |
Provides the grad operation.
| memory_optimized | Template parameter memory_optimized. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the gradient. |
| [in] | knot_indices | Knot indices where to evaluate the gradient. |
\[ \nabla_{\boldsymbol{\xi}}u = \left(\frac{\partial u}{\partial \xi_0}, \frac{\partial u}{\partial \xi_1}, \dots \frac{\partial u}{\partial \xi_{d_\text{par}}}\right) \]
|
inline |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the gradient. |
| [in] | knot_indices | Knot indices where to evaluate the gradient. |
| [in] | coeff_indices | Coefficient indices where to evaluate the gradient. |
\[ \nabla_{\boldsymbol{\xi}}u = \left(\frac{\partial u}{\partial \xi_0}, \frac{\partial u}{\partial \xi_1}, \dots \frac{\partial u}{\partial \xi_{d_\text{par}}}\right) \]
|
inline |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the Hessian. |
xi. \[ H_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial^2 u}{\partial^2 \xi_0}& \frac{\partial^2 u}{\partial \xi_0\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_0\partial \xi_{d_\text{par}}} \\ \frac{\partial^2 u}{\partial \xi_1\partial \xi_0}& \frac{\partial^2 u}{\partial^2 \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_1\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_0}& \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial^2 \xi_{d_\text{par}}} \end{bmatrix} \]
|
inline |
Provides the hess operation.
| memory_optimized | Template parameter memory_optimized. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the gradient. |
| [in] | knot_indices | Knot indices where to evaluate the Hessian. |
\[ H_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial^2 u}{\partial^2 \xi_0}& \frac{\partial^2 u}{\partial \xi_0\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_0\partial \xi_{d_\text{par}}} \\ \frac{\partial^2 u}{\partial \xi_1\partial \xi_0}& \frac{\partial^2 u}{\partial^2 \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_1\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_0}& \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial^2 \xi_{d_\text{par}}} \end{bmatrix} \]
|
inline |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the Hessian. |
| [in] | knot_indices | Knot indices where to evaluate the Hessian. |
| [in] | coeff_indices | Coefficient indices where to evaluate the Hessian. |
\[ H_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial^2 u}{\partial^2 \xi_0}& \frac{\partial^2 u}{\partial \xi_0\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_0\partial \xi_{d_\text{par}}} \\ \frac{\partial^2 u}{\partial \xi_1\partial \xi_0}& \frac{\partial^2 u}{\partial^2 \xi_1}& \dots& \frac{\partial^2 u}{\partial \xi_1\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_0}& \frac{\partial^2 u}{\partial \xi_{d_\text{par}}\partial \xi_1}& \dots& \frac{\partial^2 u}{\partial^2 \xi_{d_\text{par}}} \end{bmatrix} \]
|
inline |
Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the curl. |
\[ \nabla \times {\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} \times u \, \operatorname{det}(\operatorname{det}(J_{\boldsymbol{\xi}}(G))^{-1} \, J_{\boldsymbol{\xi}}(G) , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Provides the icurl operation.
| memory_optimized | Template parameter memory_optimized. |
| Geometry | Template parameter Geometry. |
| G | Value of G. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the gradient. |
| [in] | knot_indices | Knot indices where to evaluate the gradient. |
| [in] | knot_indices_G | Knot indices where to evaluate the Jacobian of G. |
| [in] | coeff_indices | Coefficient indices where to evaluate the gradient. |
| [in] | coeff_indices_G | Coefficient indices where to evaluate the Jacobian of G. |
\[ \nabla \times {\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} \times u \, \operatorname{det}(\operatorname{det}(J_{\boldsymbol{\xi}}(G))^{-1} \, J_{\boldsymbol{\xi}}(G) , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the curl of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the gradient. |
| [in] | knot_indices | Knot indices where to evaluate the gradient. |
| [in] | knot_indices_G | Knot indices where to evaluate Jacobian of G. |
\[ \nabla \times {\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} \times u \, \operatorname{det}(\operatorname{det}(J_{\boldsymbol{\xi}}(G))^{-1} \, J_{\boldsymbol{\xi}}(G) , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the divergence. |
\[ \nabla_{\mathbf{x}} \cdot \mathbf{u} = \text{trace} ( J_{\mathbf{x}}(u) ) = \frac{\partial u_0}{\partial x_0} + \frac{\partial u_1}{\partial x_1} + \frac{\partial u_{d_\text{geo}}}{\partial x_{d_\text{par}}} \]
|
inline |
Provides the idiv operation.
| memory_optimized | Template parameter memory_optimized. |
| Geometry | Template parameter Geometry. |
| G | Value of G. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the divergence. |
| [in] | knot_indices | Knot indices where to evaluate the divergence. |
| [in] | knot_indices_G | Knot indices where to evaluate the Jacobian of G. |
| [in] | coeff_indices | Coefficient indices where to evaluate the divergence. |
| [in] | coeff_indices_G | Coefficient indices where to evaluate the Jacobian of G. |
\[ \nabla_{\mathbf{x}} \cdot \mathbf{u} = \text{trace} ( J_{\mathbf{x}}(u) ) = \frac{\partial u_0}{\partial x_0} + \frac{\partial u_1}{\partial x_1} + \frac{\partial u_{d_\text{geo}}}{\partial x_{d_\text{par}}} \]
|
inline |
Returns a block-tensor with the divergence of the B-spline object with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the divergence. |
| [in] | knot_indices | Knot indices where to evaluate the divergence. |
| [in] | knot_indices_G | Knot indices where to evaluate the Jacobian of G. |
\[ \nabla_{\mathbf{x}} \cdot \mathbf{u} = \text{trace} ( J_{\mathbf{x}}(u) ) = \frac{\partial u_0}{\partial x_0} + \frac{\partial u_1}{\partial x_1} + \frac{\partial u_{d_\text{geo}}}{\partial x_{d_\text{par}}} \]
|
inline |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the gradient. |
\[ \nabla_{\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} u \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Provides the igrad operation.
| memory_optimized | Template parameter memory_optimized. |
| Geometry | Template parameter Geometry. |
| G | Value of G. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the gradient. |
| [in] | knot_indices | Knot indices where to evaluate the gradient. |
| [in] | knot_indices_G | Knot indices where to evaluate the Jacobian of G. |
| [in] | coeff_indices | Coefficient indices where to evaluate the gradient. |
| [in] | coeff_indices_G | Coefficient indices where to evaluate the Jacobian of G. |
\[ \nabla_{\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} u \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the gradient of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the gradient. |
| [in] | knot_indices | Knot indices where to evaluate the gradient. |
| [in] | knot_indices_G | Knot indices where to evaluate Jacobian of G. |
\[ \nabla_{\mathbf{x}} u = \nabla_{\boldsymbol{\xi}} u \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Hessian. |
\[ H_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Provides the ihess operation.
| memory_optimized | Template parameter memory_optimized. |
| Geometry | Template parameter Geometry. |
| G | Value of G. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Hessian. |
| [in] | knot_indices | Knot indices where to evaluate the Hessian. |
| [in] | knot_indices_G | Knot indices where to evaluate the Jacobian of G. |
| [in] | coeff_indices | Coefficient indices where to evaluate the Hessian. |
| [in] | coeff_indices_G | Coefficient indices where to evaluate the Jacobian of G. |
\[ H_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the Hessian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Hessian. |
| [in] | knot_indices | Knot indices where to evaluate the Hessian. |
| [in] | knot_indices_G | Knot indices where to evaluate Jacobian of G. |
\[ H_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Jacobian. |
\[ J_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(u) \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Provides the ijac operation.
| memory_optimized | Template parameter memory_optimized. |
| Geometry | Template parameter Geometry. |
| G | Value of G. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Jacobian. |
| [in] | knot_indices | Knot indices where to evaluate the Jacobain. |
| [in] | knot_indices_G | Knot indices where to evaluate the Jacobian of G. |
| [in] | coeff_indices | Coefficient indices where to evaluate the Jacobian. |
| [in] | coeff_indices_G | Coefficient indices where to evaluate the Jacobian of G. |
\[ J_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(u) \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Jacobian. |
| [in] | knot_indices | Knot indices where to evaluate the Jacobian. |
| [in] | knot_indices_G | Knot indices where to evaluate the Jacobian of G. |
\[ J_{\mathbf{x}}(u) = J_{\boldsymbol{\xi}}(u) \, J_{\boldsymbol{\xi}}(G)^{-T} , \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Laplacian. |
\[ L_{\mathbf{x}}(u) = \text{trace} \left( J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} \right), \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Provides the ilapl operation.
| memory_optimized | Template parameter memory_optimized. |
| Geometry | Template parameter Geometry. |
| G | Value of G. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Laplacian. |
| [in] | knot_indices | Knot indices where to evaluate the Laplacian. |
| [in] | knot_indices_G | Knot indices where to evaluate the Jacobian of G. |
| [in] | coeff_indices | Coefficient indices where to evaluate the Laplacian. |
| [in] | coeff_indices_G | Coefficient indices where to evaluate the Jacobian of G. |
\[ L_{\mathbf{x}}(u) = \text{trace} \left( J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} \right), \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the physical variables.
| Geometry | Type of the geometry B-spline object. |
| [in] | G | B-spline geometry object. |
| [in] | xi | Point(s) where to evaluate the Laplacian. |
| [in] | knot_indices | Knot indices where to evaluate the Laplacian. |
| [in] | knot_indices_G | Knot indices where to evaluate Jacobian of G. |
\[ L_{\mathbf{x}}(u) = \text{trace} \left( J_{\boldsymbol{\xi}}(G)^{-T} \left( H_\boldsymbol{\xi}(u) - \sum_k \nabla_{\mathbf{x},k}u H_{\boldsymbol{\xi}}(G_k) \right) J_{\boldsymbol{\xi}}(G)^{-1} \right), \quad \mathbf{x} = G(\boldsymbol{\xi}) \]
|
inline |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the Jacobian. |
\[ J_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial u_0}{\partial \xi_0}& \frac{\partial u_0}{\partial \xi_1}& \dots& \frac{\partial u_0}{\partial \xi_{d_\text{par}}} \\ \frac{\partial u_1}{\partial \xi_0}& \frac{\partial u_1}{\partial \xi_1}& \dots& \frac{\partial u_1}{\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial u_{d_\text{geo}}}{\partial \xi_0}& \frac{\partial u_{d_\text{geo}}}{\partial \xi_1}& \dots& \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \end{bmatrix} \]
|
inline |
Provides the jac operation.
| memory_optimized | Template parameter memory_optimized. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the Jacobian. |
| [in] | knot_indices | Knot indices where to evaluate the Jacobian. |
\[ J_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial u_0}{\partial \xi_0}& \frac{\partial u_0}{\partial \xi_1}& \dots& \frac{\partial u_0}{\partial \xi_{d_\text{par}}} \\ \frac{\partial u_1}{\partial \xi_0}& \frac{\partial u_1}{\partial \xi_1}& \dots& \frac{\partial u_1}{\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial u_{d_\text{geo}}}{\partial \xi_0}& \frac{\partial u_{d_\text{geo}}}{\partial \xi_1}& \dots& \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \end{bmatrix} \]
|
inline |
Returns a block-tensor with the Jacobian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the Jacobian. |
| [in] | knot_indices | Knot indices where to evaluate the Jacobian. |
| [in] | coeff_indices | Coefficient indices where to evaluate the Jacobian. |
\[ J_{\boldsymbol{\xi}}(u) = \begin{bmatrix} \frac{\partial u_0}{\partial \xi_0}& \frac{\partial u_0}{\partial \xi_1}& \dots& \frac{\partial u_0}{\partial \xi_{d_\text{par}}} \\ \frac{\partial u_1}{\partial \xi_0}& \frac{\partial u_1}{\partial \xi_1}& \dots& \frac{\partial u_1}{\partial \xi_{d_\text{par}}} \\ \vdots& \vdots & \ddots & \vdots \\ \frac{\partial u_{d_\text{geo}}}{\partial \xi_0}& \frac{\partial u_{d_\text{geo}}}{\partial \xi_1}& \dots& \frac{\partial u_{d_\text{geo}}}{\partial \xi_{d_\text{par}}} \end{bmatrix} \]
|
inline |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the Laplacian. |
xi. \[ L_{\boldsymbol{\xi}}(u) = \sum_{i,j=0\atop|i+j|=2}^2 \frac{\partial^2 u}{\partial \xi_i\partial \xi_{j}} \]
|
inline |
Provides the lapl operation.
| memory_optimized | Template parameter memory_optimized. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the Laplacian. |
| [in] | knot_indices | Knot indices where to evaluate the Laplacian. |
\[ L_{\boldsymbol{\xi}}(u) = \sum_{i,j=0\atop|i+j|=2}^2 \frac{\partial^2 u}{\partial \xi_i\partial \xi_{j}} \]
|
inline |
Returns a block-tensor with the Laplacian of the B-spline object in the points xi with respect to the parametric variables.
| [in] | xi | Point(s) where to evaluate the Laplacian. |
| [in] | knot_indices | Knot indices where to evaluate the Laplacian. |
| [in] | coeff_indices | Coefficient indices where to evaluate the Laplacian. |
\[ L_{\boldsymbol{\xi}}(u) = \sum_{i,j=0\atop|i+j|=2}^2 \frac{\partial^2 u}{\partial \xi_i\partial \xi_{j}} \]
|
inlinestatic |
Provides the make_shared operation.
| ncoeffs | Value of ncoeffs. |
| coeffs | Value of coeffs. |
| clone | Value of clone. |
| options | Configuration options. |
|
inlinestatic |
Provides the make_shared operation.
| ncoeffs | Value of ncoeffs. |
| init | Value of init. |
| options | Configuration options. |
|
inlinestatic |
Provides the make_shared operation.
| ncoeffs | Value of ncoeffs. |
| coeffs | Value of coeffs. |
| options | Configuration options. |
|
inlinestatic |
Provides the make_shared operation.
| kv | Value of kv. |
| coeffs | Value of coeffs. |
| clone | Value of clone. |
| options | Configuration options. |
|
inlinestatic |
Provides the make_shared operation.
| kv | Value of kv. |
| init | Value of init. |
| options | Configuration options. |
|
inlinestatic |
Creates a new B-spline object as shared pointer.
| options | Configuration options. |
|
inlinestatic |
Provides the make_unique operation.
| ncoeffs | Value of ncoeffs. |
| coeffs | Value of coeffs. |
| clone | Value of clone. |
| options | Configuration options. |
|
inlinestatic |
Provides the make_unique operation.
| ncoeffs | Value of ncoeffs. |
| init | Value of init. |
| options | Configuration options. |
|
inlinestatic |
Provides the make_unique operation.
| ncoeffs | Value of ncoeffs. |
| coeffs | Value of coeffs. |
| options | Configuration options. |
|
inlinestatic |
Provides the make_unique operation.
| kv | Value of kv. |
| coeffs | Value of coeffs. |
| clone | Value of clone. |
| options | Configuration options. |
|
inlinestatic |
Provides the make_unique operation.
| kv | Value of kv. |
| init | Value of init. |
| options | Configuration options. |
|
inlinestatic |
Creates a new B-spline object as unique pointer.
| options | Configuration options. |
|
inline |
Computes the norm of the B-spline object by computing the mean-squared sum of the function values evaluated at the Greville abscissae.
|
inline |
Returns a block-tensor with the outward pointing normal vector of the B-spline object.
| [in] | xi | Point(s) where to evaluate the normal vector. |
|
inline |
Provides the nv operation.
| memory_optimized | Template parameter memory_optimized. |
| memory_optimized | Template parameter memory_optimized. |
| xi | Parametric coordinates. |
|
inline |
Returns a block-tensor with the outward pointing normal vector of the B-spline object.
| [in] | xi | Point(s) where to evaluate the normal vector. |
| [in] | knot_indices | Knot indices where to evaluate the normal vector. |
|
inline |
Returns a block-tensor with the outward pointing normal vector of the B-spline object.
| [in] | xi | Point(s) where to evaluate the normal vector. |
| [in] | knot_indices | Knot indices where to evaluate the normal vector. |
| [in] | coeff_indices | Coefficient indices where to evaluate the normal vector. |
|
inline |
Returns a new B-spline object whose coefficients are scaled by a scalar.
| s | Value of s. |
|
inline |
Returns a new B-spline object whose coefficients are scaled by a vector.
| v | Value of v. |
|
inline |
Scales the coefficients by a scalar.
| s | Value of s. |
|
inline |
Scales the coefficients by a vector.
| v | Value of v. |
|
inline |
Returns a new B-spline object whose coefficients are the sum of that of two compatible B-spline objects.
| other | Second input value. |
|
inline |
Adds the coefficients of another B-spline object.
| other | Second input value. |
|
inline |
Returns a new B-spline object whose coefficients are the difference of that of two compatible B-spline objects.
| other | Second input value. |
|
inline |
Substracts the coefficients of another B-spline object.
| other | Second input value. |
|
inline |
Returns a new B-spline object whose coefficients are scaled by a scalar.
| s | Value of s. |
|
inline |
Returns a new B-spline object whose coefficients are scaled by a vector.
| v | Value of v. |
|
inline |
Scales the coefficients by a scalar.
| s | Value of s. |
|
inline |
Scales the coefficients by a vector.
| v | Value of v. |
|
inline |
Plots the B-spline object colored by another B-spline object.
| [in] | color | B-spline object representing the color. |
| [in] | json | JSON configuration. |
|
inline |
Plots the B-spline object colored by another B-spline object together with a set of sampling points.
| [in] | color | B-spline object representing the color. |
| [in] | xi | Vector of sampling points. |
| [in] | json | JSON configuration. |
|
inline |
Plots the B-spline object colored by another B-spline object together with a set of sampling points.
| [in] | color | B-spline object representing the color. |
| [in] | xi | Sampling points. |
| [in] | json | JSON configuration. |
|
inline |
Plots the B-spline object.
| [in] | json | JSON configuration. |
|
inline |
Plots the B-spline object together with a set of sampling points.
| [in] | xi | Vector of sampling points. |
| [in] | json | JSON configuration. |
|
inline |
Plots the B-spline object together with a set of sampling points.
| [in] | xi | Sampling points. |
| [in] | json | JSON configuration. |
|
inlineoverridevirtualnoexcept |
Returns a string representation of the BSplineCommon object.
| os | Output stream. |
Implements iganet::utils::FullQualifiedName.
|
inline |
Rotates the B-spline object by an angle in 2d.
| angle | Value of angle. |
|
inline |
Rotates the B-spline object by three angles in 3d.
| angle | Value of angle. |
|
inline |
Rotates the B-spline object by an angle in 2d in-place.
| angle | Value of angle. |
|
inline |
Rotates the B-spline object by three angles in 3d in-place.
| angle | Value of angle. |
|
inline |
Scales the B-spline object by a scalar.
| s | Value of s. |
| dim | Value of dim. |
|
inline |
Scales the B-spline object by a vector.
| v | Value of v. |
|
inline |
Scales the B-spline object by a scalar in-place.
| s | Value of s. |
| dim | Value of dim. |
|
inline |
Scales the B-spline object by a vector in-place.
| v | Value of v. |
|
inline |
Returns a copy of the B-spline object with real_t type.
| real_t | Template parameter real_t. |
|
inline |
Returns a copy of the B-spline object with settings from options.
| real_t | Template parameter real_t. |
| options | Configuration options. |
|
inline |
Returns a copy of the B-spline object with settings from device.
| device | Target device. |
|
inline |
Converts a uniform B-spline into a non-uniform B-spline.
All run-time state is moved into the returned object. Consequently, this operation is only available for rvalues and leaves the source object in a valid but unspecified state.
|
inline |
Converts a non-uniform B-spline into a uniform B-spline.
The conversion succeeds only if all knot vectors are canonical open uniform knot vectors. Validation is performed before any state is moved.
|
inline |
Translates the B-spline object by a vector.
| v | Value of v. |
|
inline |
Translates the B-spline object by a vector in-place.
| v | Value of v. |
|
inline |
Returns the B-spline object with uniformly refined knot and coefficient vectors.
If dim = -1, new knot values are inserted uniformly in each knot span in all spatial dimensions. Otherwise, i.e., dim != -1 new knots are only inserted in the specified dimension.
| numRefine | Value of numRefine. |
| dim | Value of dim. |
1.9.8