Eigen::Quaternions now satisfy IsManifold, IsGroup, and IsLieGroup! Also reverted back to a simpler treatment of Charts.
Merge branch 'traits/quaternion' into feature/tighteningTraitsrelease/4.3a0
dellaert
commit
e0e2a9b063
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@ -146,30 +146,6 @@ TESTABLE, MANIFOLD, GROUP, LIE_GROUP, and VECTOR_SPACE concepts.
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and we also define a limited number of `gtsam::tags` to select the correct implementation
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of certain functions at compile time (tag dispatching). Charts are done more conventionally, so we start there...
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Interfaces
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----------
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Because Charts are always written by the user (or automatically generated, see below for vector spaces),
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we enforce the Chart concept using an abstract base class, acting as an interface:
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```
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#!c++
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template <class T, class Derived>
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struct Chart {
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typedef T ManifoldType;
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typedef typename traits::TangentVector<T>::type TangentVector;
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static TangentVector Local(const ManifoldType& p, const ManifoldType& q) {return Derived::local(p,q);}
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static ManifoldType Retract(const ManifoldType& p, const TangentVector& v) {return Derived::retract(p,v);}
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protected:
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Chart(){ (void)&Local; (void)&Retract; } // enforce early instantiation.
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}
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```
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The [CRTP](http://en.wikipedia.org/wiki/Curiously_recurring_template_pattern) and the protected constructor
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automatically check for the existence of the methods in the Derived class, whenever a new Chart is created by
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struct MyChart : Chart<MyType,MyChart> { ... }
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Traits
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------
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@ -34,6 +34,7 @@
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#pragma once
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#include <boost/shared_ptr.hpp>
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#include <boost/concept_check.hpp>
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#include <stdio.h>
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#include <string>
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@ -50,17 +51,20 @@ namespace gtsam {
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* @tparam T is the type this constrains to be testable - assumes print() and equals()
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*/
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template <class T>
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class TestableConcept {
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static bool checkTestableConcept(const T& d) {
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class Testable {
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T t;
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bool r1,r2;
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public:
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BOOST_CONCEPT_USAGE(Testable) {
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// check print function, with optional string
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d.print(std::string());
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d.print();
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t.print(std::string());
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t.print();
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// check print, with optional threshold
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double tol = 1.0;
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bool r1 = d.equals(d, tol);
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bool r2 = d.equals(d);
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return r1 && r2;
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r1 = t.equals(t, tol);
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r2 = t.equals(t);
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}
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};
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@ -129,6 +133,7 @@ namespace gtsam {
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*
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* NOTE: intentionally not in the gtsam namespace to allow for classes not in
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* the gtsam namespace to be more easily enforced as testable
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* @deprecated please use BOOST_CONCEPT_ASSERT and
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*/
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#define GTSAM_CONCEPT_TESTABLE_INST(T) template class gtsam::TestableConcept<T>;
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#define GTSAM_CONCEPT_TESTABLE_TYPE(T) typedef gtsam::TestableConcept<T> _gtsam_TestableConcept_##T;
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#define GTSAM_CONCEPT_TESTABLE_INST(T) template class gtsam::Testable<T>;
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#define GTSAM_CONCEPT_TESTABLE_TYPE(T) typedef gtsam::Testable<T> _gtsam_Testable_##T;
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@ -11,7 +11,9 @@
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//#include "manifold.h"
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//#include "chart.h"
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#include <gtsam/base/Matrix.h>
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#include <gtsam/base/Testable.h>
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#include <boost/concept_check.hpp>
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#include <boost/concept/requires.hpp>
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#include <boost/static_assert.hpp>
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#include <boost/type_traits/is_base_of.hpp>
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@ -24,9 +26,7 @@ namespace traits {
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* @brief Associate a unique tag with each of the main GTSAM concepts
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*/
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//@{
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template<class T>
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struct structure_category;
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// specializations should be derived from one of the following tags
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template<typename T> struct structure_category;
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//@}
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/**
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@ -34,81 +34,98 @@ struct structure_category;
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* @brief Possible values for traits::structure_category<T>::type
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*/
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//@{
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struct manifold_tag {
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};
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struct group_tag {
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};
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struct lie_group_tag: public manifold_tag, public group_tag {
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};
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struct vector_space_tag: public lie_group_tag {
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};
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struct manifold_tag {};
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struct group_tag {};
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struct lie_group_tag: public manifold_tag, public group_tag {};
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struct vector_space_tag: public lie_group_tag {};
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//@}
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}// namespace traits
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namespace manifold {
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/** @name Free functions any Manifold needs to define */
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//@{
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//@}
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namespace traits {
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/** @name Manifold Traits */
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//@{
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template<class Manifold> struct TangentVector;
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template<class Manifold> struct DefaultChart;
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template<typename Manifold> struct dimension;
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template<typename Manifold> struct TangentVector;
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template<typename Manifold> struct DefaultChart;
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//@}
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}// namespace traits
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}// \ namespace traits
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/*
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template<class T>
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class ManifoldConcept {
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public:
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typedef T Manifold;
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typedef typename traits::TangentVector<T>::type TangentVector;
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typedef typename traits::DefaultChart<T>::type DefaultChart;
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static const size_t dim = traits::dimension<T>::value;
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BOOST_CONCEPT_USAGE(ManifoldConcept) {
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BOOST_STATIC_ASSERT(boost::is_base_of<traits::manifold_tag, traits::structure<Manifold> >);
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BOOST_STATIC_ASSERT(TangentVector::SizeAtCompileTime == dim);
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// no direct usage for manifold since most usage is through a chart
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}
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private:
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Manifold p;
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TangentVector v;
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};
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template<class C>
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class ChartConcept {
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public:
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typedef C Chart;
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typedef typename traits::Manifold<Chart>::type Manifold;
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typedef typename traits::TangentVector<Manifold>::type TangentVector;
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BOOST_CONCEPT_USAGE(ChartConcept) {
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v = Chart::local(p,q); // returns local coordinates of q w.r.t. origin p
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q = Chart::retract(p,v); // returns retracted update of p with v
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/// Check invariants for Manifold type
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template<typename T>
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BOOST_CONCEPT_REQUIRES(((Testable<T>)),(bool)) //
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check_invariants(const T& a, const T& b) {
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typedef typename traits::DefaultChart<T>::type Chart;
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return true;
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}
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private:
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Manifold p,q;
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TangentVector v;
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} // \ namespace manifold
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};
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/**
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* Chart concept
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*/
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template<typename T>
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class IsChart {
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public:
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typedef typename T::ManifoldType ManifoldType;
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typedef typename manifold::traits::TangentVector<ManifoldType>::type V;
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BOOST_CONCEPT_USAGE(IsChart) {
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// make sure Derived methods in Chart are defined
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v = T::Local(p,q);
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q = T::Retract(p,v);
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}
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private:
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ManifoldType p,q;
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V v;
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};
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/**
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* Manifold concept
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*/
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template<typename T>
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class IsManifold {
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public:
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typedef typename traits::structure_category<T>::type structure_category_tag;
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static const size_t dim = manifold::traits::dimension<T>::value;
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typedef typename manifold::traits::TangentVector<T>::type TangentVector;
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typedef typename manifold::traits::DefaultChart<T>::type DefaultChart;
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BOOST_CONCEPT_USAGE(IsManifold) {
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BOOST_STATIC_ASSERT_MSG(
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(boost::is_base_of<traits::manifold_tag, structure_category_tag>::value),
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"This type's structure_category trait does not assert it as a manifold (or derived)");
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BOOST_STATIC_ASSERT(TangentVector::SizeAtCompileTime == dim);
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BOOST_CONCEPT_ASSERT((IsChart<DefaultChart >));
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}
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private:
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T p,q;
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TangentVector v;
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};
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namespace group {
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/** @name Free functions any Group needs to define */
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//@{
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template<typename G> G compose(const G&g, const G& h);
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template<typename G> G between(const G&g, const G& h);
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template<typename G> G inverse(const G&g);
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template<typename T> T compose(const T&g, const T& h);
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template<typename T> T between(const T&g, const T& h);
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template<typename T> T inverse(const T&g);
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//@}
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namespace traits {
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/** @name Group Traits */
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//@{
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template<class G> struct identity;
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template<class G> struct flavor;
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template<typename T> struct identity;
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template<typename T> struct flavor;
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//@}
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/** @name Group Flavor Tags */
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@ -120,93 +137,130 @@ struct multiplicative_tag {
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//@}
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}// \ namespace traits
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/// Check invariants
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template<typename T>
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BOOST_CONCEPT_REQUIRES(((Testable<T>)),(bool)) //
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check_invariants(const T& a, const T& b, double tol = 1e-9) {
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T e = traits::identity<T>::value;
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return compose(a, inverse(a)).equals(e, tol)
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&& between(a, b).equals(compose(inverse(a), b), tol)
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&& compose(a, between(a, b)).equals<T>(b, tol);
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}
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} // \ namespace group
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/**
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* Group Concept
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*/
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template<typename G>
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class Group {
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template<typename T>
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class IsGroup {
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public:
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typedef typename traits::structure_category<G>::type structure_category_tag;
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typedef typename group::traits::identity<G>::value_type identity_value_type;
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typedef typename group::traits::flavor<G>::type flavor_tag;
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typedef typename traits::structure_category<T>::type structure_category_tag;
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typedef typename group::traits::identity<T>::value_type identity_value_type;
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typedef typename group::traits::flavor<T>::type flavor_tag;
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BOOST_CONCEPT_USAGE(Group) {
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void operator_usage(group::traits::multiplicative_tag) {
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g = g * h;
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}
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void operator_usage(group::traits::additive_tag) {
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g = g + h;
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g = h - g;
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g = -g;
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}
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BOOST_CONCEPT_USAGE(IsGroup) {
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using group::compose;
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using group::between;
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using group::inverse;
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BOOST_STATIC_ASSERT(
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boost::is_base_of<traits::group_tag, structure_category_tag>::value);
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e = group::traits::identity<G>::value;
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d = compose(g, h);
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d = between(g, h);
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ig = inverse(g);
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test = operator_usage(g, h, flavor);
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BOOST_STATIC_ASSERT_MSG(
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(boost::is_base_of<traits::group_tag, structure_category_tag>::value),
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"This type's structure_category trait does not assert it as a group (or derived)");
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e = group::traits::identity<T>::value;
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g = compose(g, h);
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g = between(g, h);
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g = inverse(g);
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operator_usage(flavor);
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}
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// TODO: these all require default constructors :-(
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// Also, requires equal which is not required of a group
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// Group():e(group::traits::identity<G>::value) {
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// }
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//
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// bool check_invariants(const G& a, const G& b) {
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// return (equal(compose(a, inverse(a)), e))
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// && (equal(between(a, b), compose(inverse(a), b)))
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// && (equal(compose(a, between(a, b)), b))
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// && operator_usage(a, b, flavor);
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// }
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private:
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flavor_tag flavor;
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G e, g, h, gh, ig, d;
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bool test, test2;
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bool operator_usage(const G& a, const G& b,
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group::traits::multiplicative_tag) {
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// return group::compose(a, b) == a * b;
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return true;
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}
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bool operator_usage(const G& a, const G& b, group::traits::additive_tag) {
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return group::compose(a, b) == a + b;
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}
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T e, g, h;
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};
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/*
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template <class L>
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class LieGroupConcept : public GroupConcept<L>, public ManifoldConcept<L> {
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namespace lie_group {
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BOOST_CONCEPT_USAGE(LieGroupConcept) {
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BOOST_STATIC_ASSERT(boost::is_base_of<traits::lie_group_tag, traits::structure<L> >);
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/** @name Free functions any Group needs to define */
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//@{
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// TODO need Jacobians
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//template<typename T> T compose(const T&g, const T& h);
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//template<typename T> T between(const T&g, const T& h);
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//template<typename T> T inverse(const T&g);
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//@}
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namespace traits {
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/** @name Lie Group Traits */
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//@{
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//@}
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}// \ namespace traits
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/// Check invariants
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//template<typename T>
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//BOOST_CONCEPT_REQUIRES(((Testable<T>)),(bool)) check_invariants(const T& a,
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// const T& b) {
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// bool check_invariants(const V& a, const V& b) {
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// return equal(Chart::retract(a, b), a + b)
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// && equal(Chart::local(a, b), b - a);
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// }
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//}
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}// \ namespace lie_group
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/**
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* Lie Group Concept
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*/
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template<typename T>
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class IsLieGroup: public IsGroup<T>, public IsManifold<T> {
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public:
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typedef typename traits::structure_category<T>::type structure_category_tag;
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BOOST_CONCEPT_USAGE(IsLieGroup) {
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BOOST_STATIC_ASSERT_MSG(
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(boost::is_base_of<traits::lie_group_tag, structure_category_tag>::value),
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"This type's trait does not assert it as a Lie group (or derived)");
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// TODO Check with Jacobian
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// using lie_group::compose;
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// using lie_group::between;
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// using lie_group::inverse;
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// g = compose(g, h);
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// g = between(g, h);
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// g = inverse(g);
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}
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private:
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T g, h;
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};
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template <class V>
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class VectorSpaceConcept : public LieGroupConcept {
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typedef typename traits::DefaultChart<V>::type Chart;
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typedef typename GroupConcept<V>::identity identity;
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template<typename T>
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class IsVectorSpace: public IsLieGroup<T> {
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public:
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BOOST_CONCEPT_USAGE(VectorSpaceConcept) {
|
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BOOST_STATIC_ASSERT(boost::is_base_of<traits::vector_space_tag, traits::structure<L> >);
|
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typedef typename traits::structure_category<T>::type structure_category_tag;
|
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|
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BOOST_CONCEPT_USAGE(IsVectorSpace) {
|
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BOOST_STATIC_ASSERT_MSG(
|
||||
(boost::is_base_of<traits::vector_space_tag, structure_category_tag>::value),
|
||||
"This type's trait does not assert it as a vector space (or derived)");
|
||||
r = p + q;
|
||||
r = -p;
|
||||
r = p - q;
|
||||
}
|
||||
|
||||
bool check_invariants(const V& a, const V& b) {
|
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return equal(compose(a, b), a+b)
|
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&& equal(inverse(a), -a)
|
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&& equal(between(a, b), b-a)
|
||||
&& equal(Chart::retract(a, b), a+b)
|
||||
&& equal(Chart::local(a, b), b-a);
|
||||
}
|
||||
|
||||
private:
|
||||
V g,q,r;
|
||||
T p, q, r;
|
||||
};
|
||||
*/
|
||||
|
||||
} // namespace gtsam
|
||||
|
||||
|
|
|
|||
|
|
@ -26,7 +26,7 @@ typedef Cyclic<6> G; // Let's use the cyclic group of order 6
|
|||
|
||||
//******************************************************************************
|
||||
TEST(Cyclic, Concept) {
|
||||
BOOST_CONCEPT_ASSERT((Group<G>));
|
||||
BOOST_CONCEPT_ASSERT((IsGroup<G>));
|
||||
EXPECT_LONGS_EQUAL(0, group::traits::identity<G>::value);
|
||||
G g(2), h(3);
|
||||
// EXPECT(Group<G>().check_invariants(g,h))
|
||||
|
|
@ -81,6 +81,12 @@ TEST(Cyclic, Ivnverse) {
|
|||
EXPECT_LONGS_EQUAL(1, group::inverse(G(5)));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Cyclic , Invariants) {
|
||||
G g(2), h(5);
|
||||
group::check_invariants(g,h);
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
int main() {
|
||||
TestResult tr;
|
||||
|
|
|
|||
|
|
@ -19,47 +19,134 @@
|
|||
|
||||
namespace gtsam {
|
||||
|
||||
/// Typedef to an Eigen Quaternion<double>, we disable alignment because
|
||||
/// geometry objects are stored in boost pool allocators, in Values
|
||||
/// containers, and and these pool allocators do not support alignment.
|
||||
typedef Eigen::Quaternion<double, Eigen::DontAlign> Quaternion;
|
||||
namespace traits {
|
||||
|
||||
/// Define Eigen::Quaternion to be a model of the Lie Group concept
|
||||
template<typename S, int O>
|
||||
struct structure_category<Eigen::Quaternion<S, O> > {
|
||||
typedef lie_group_tag type;
|
||||
};
|
||||
|
||||
} // \namespace gtsam::traits
|
||||
|
||||
namespace manifold {
|
||||
|
||||
/// Chart for Eigen Quaternions
|
||||
template<typename S, int O>
|
||||
struct QuaternionChart {
|
||||
|
||||
// required
|
||||
typedef Eigen::Quaternion<S, O> ManifoldType;
|
||||
|
||||
// internal
|
||||
typedef ManifoldType Q;
|
||||
typedef typename traits::TangentVector<Q>::type Omega;
|
||||
|
||||
/// Exponential map, simply be converting omega to AngleAxis
|
||||
static Q Expmap(const Omega& omega) {
|
||||
double theta = omega.norm();
|
||||
if (std::abs(theta) < 1e-10)
|
||||
return Q::Identity();
|
||||
return Q(Eigen::AngleAxisd(theta, omega / theta));
|
||||
}
|
||||
|
||||
/// retract, simply be converting omega to AngleAxis
|
||||
static Q Retract(const Q& p, const Omega& omega) {
|
||||
return p * Expmap(omega);
|
||||
}
|
||||
|
||||
/// We use our own Logmap, as there is a slight bug in Eigen
|
||||
static Omega Logmap(const Q& q) {
|
||||
using std::acos;
|
||||
using std::sqrt;
|
||||
static const double twoPi = 2.0 * M_PI,
|
||||
// define these compile time constants to avoid std::abs:
|
||||
NearlyOne = 1.0 - 1e-10, NearlyNegativeOne = -1.0 + 1e-10;
|
||||
|
||||
const double qw = q.w();
|
||||
if (qw > NearlyOne) {
|
||||
// Taylor expansion of (angle / s) at 1
|
||||
return (2 - 2 * (qw - 1) / 3) * q.vec();
|
||||
} else if (qw < NearlyNegativeOne) {
|
||||
// Angle is zero, return zero vector
|
||||
return Vector3::Zero();
|
||||
} else {
|
||||
// Normal, away from zero case
|
||||
double angle = 2 * acos(qw), s = sqrt(1 - qw * qw);
|
||||
// Important: convert to [-pi,pi] to keep error continuous
|
||||
if (angle > M_PI)
|
||||
angle -= twoPi;
|
||||
else if (angle < -M_PI)
|
||||
angle += twoPi;
|
||||
return (angle / s) * q.vec();
|
||||
}
|
||||
}
|
||||
|
||||
/// local is our own, as there is a slight bug in Eigen
|
||||
static Omega Local(const Q& q1, const Q& q2) {
|
||||
return Logmap(q1.inverse() * q2);
|
||||
}
|
||||
};
|
||||
|
||||
namespace traits {
|
||||
/// Define Quaternion to be a model of the Group concept
|
||||
template<>
|
||||
struct structure_category<Quaternion> {
|
||||
typedef group_tag type;
|
||||
|
||||
/// Define the trait that asserts Quaternion manifold has dimension 3
|
||||
template<typename S, int O>
|
||||
struct dimension<Eigen::Quaternion<S, O> > : public boost::integral_constant<
|
||||
int, 3> {
|
||||
};
|
||||
} // \namespace gtsam::traits
|
||||
|
||||
/// Define the trait that asserts Quaternion TangentVector is Vector3
|
||||
template<typename S, int O>
|
||||
struct TangentVector<Eigen::Quaternion<S, O> > {
|
||||
typedef Eigen::Matrix<S, 3, 1, O, 3, 1> type;
|
||||
};
|
||||
|
||||
/// Define the trait that asserts Quaternion TangentVector is Vector3
|
||||
template<typename S, int O>
|
||||
struct DefaultChart<Eigen::Quaternion<S, O> > {
|
||||
typedef QuaternionChart<S, O> type;
|
||||
};
|
||||
|
||||
} // \namespace gtsam::manifold::traits
|
||||
} // \namespace gtsam::manifold
|
||||
|
||||
namespace group {
|
||||
|
||||
Quaternion compose(const Quaternion&g, const Quaternion& h) {
|
||||
template<typename S, int O>
|
||||
Eigen::Quaternion<S, O> compose(const Eigen::Quaternion<S, O> &g,
|
||||
const Eigen::Quaternion<S, O> & h) {
|
||||
return g * h;
|
||||
}
|
||||
|
||||
Quaternion between(const Quaternion&g, const Quaternion& h) {
|
||||
template<typename S, int O>
|
||||
Eigen::Quaternion<S, O> between(const Eigen::Quaternion<S, O> &g,
|
||||
const Eigen::Quaternion<S, O> & h) {
|
||||
return g.inverse() * h;
|
||||
}
|
||||
|
||||
Quaternion inverse(const Quaternion&g) {
|
||||
template<typename S, int O>
|
||||
Eigen::Quaternion<S, O> inverse(const Eigen::Quaternion<S, O> &g) {
|
||||
return g.inverse();
|
||||
}
|
||||
|
||||
namespace traits {
|
||||
|
||||
/// Define the trait that specifies Quaternion's identity element
|
||||
template<>
|
||||
struct identity<Quaternion> {
|
||||
static const Quaternion value;
|
||||
typedef Quaternion value_type;
|
||||
/// Declare the trait that specifies a quaternion's identity element
|
||||
template<typename S, int O>
|
||||
struct identity<Eigen::Quaternion<S, O> > {
|
||||
static const Eigen::Quaternion<S, O> value;
|
||||
typedef Eigen::Quaternion<S, O> value_type;
|
||||
};
|
||||
|
||||
const Quaternion identity<Quaternion>::value = Quaternion(0);
|
||||
/// Out of line definition of identity
|
||||
template<typename S, int O>
|
||||
const Eigen::Quaternion<S, O> identity<Eigen::Quaternion<S, O> >::value =
|
||||
Eigen::Quaternion<S, O>::Identity();
|
||||
|
||||
/// Define the trait that asserts Quaternion is an additive group
|
||||
template<>
|
||||
struct flavor<Quaternion> {
|
||||
/// Define the trait that asserts quaternions are a multiplicative group
|
||||
template<typename S, int O>
|
||||
struct flavor<Eigen::Quaternion<S, O> > {
|
||||
typedef multiplicative_tag type;
|
||||
};
|
||||
|
||||
|
|
@ -67,6 +154,13 @@ struct flavor<Quaternion> {
|
|||
} // \namespace gtsam::group
|
||||
} // \namespace gtsam
|
||||
|
||||
/**
|
||||
* GSAM typedef to an Eigen::Quaternion<double>, we disable alignment because
|
||||
* geometry objects are stored in boost pool allocators, in Values containers,
|
||||
* and and these pool allocators do not support alignment.
|
||||
*/
|
||||
typedef Eigen::Quaternion<double, Eigen::DontAlign> Quaternion;
|
||||
|
||||
/**
|
||||
* @file testCyclic.cpp
|
||||
* @brief Unit tests for cyclic group
|
||||
|
|
@ -75,6 +169,7 @@ struct flavor<Quaternion> {
|
|||
|
||||
//#include <gtsam/geometry/Quaternion.h>
|
||||
#include <gtsam/base/Testable.h>
|
||||
#include <gtsam/base/Vector.h>
|
||||
#include <CppUnitLite/TestHarness.h>
|
||||
|
||||
using namespace std;
|
||||
|
|
@ -84,12 +179,43 @@ typedef Quaternion Q; // Typedef
|
|||
|
||||
//******************************************************************************
|
||||
TEST(Quaternion , Concept) {
|
||||
BOOST_CONCEPT_ASSERT((Group<Q>));
|
||||
BOOST_CONCEPT_ASSERT((IsGroup<Quaternion >));
|
||||
BOOST_CONCEPT_ASSERT((IsManifold<Quaternion >));
|
||||
BOOST_CONCEPT_ASSERT((IsLieGroup<Quaternion >));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Quaternion , Constructor) {
|
||||
Q g(0);
|
||||
Q q(Eigen::AngleAxisd(1, Vector3(0, 0, 1)));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Quaternion , Invariants) {
|
||||
Q q1(Eigen::AngleAxisd(1, Vector3(0, 0, 1)));
|
||||
Q q2(Eigen::AngleAxisd(2, Vector3(0, 1, 0)));
|
||||
// group::check_invariants(q1,q2); Does not satisfy Testable concept (yet!)
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Quaternion , Local) {
|
||||
Vector3 z_axis(0, 0, 1);
|
||||
Q q1(Eigen::AngleAxisd(0, z_axis));
|
||||
Q q2(Eigen::AngleAxisd(0.1, z_axis));
|
||||
typedef manifold::traits::DefaultChart<Q>::type Chart;
|
||||
Vector3 expected(0, 0, 0.1);
|
||||
Vector3 actual = Chart::Local(q1, q2);
|
||||
EXPECT(assert_equal((Vector)expected,actual));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Quaternion , Retract) {
|
||||
Vector3 z_axis(0, 0, 1);
|
||||
Q q(Eigen::AngleAxisd(0, z_axis));
|
||||
Q expected(Eigen::AngleAxisd(0.1, z_axis));
|
||||
typedef manifold::traits::DefaultChart<Q>::type Chart;
|
||||
Vector3 v(0, 0, 0.1);
|
||||
Q actual = Chart::Retract(q, v);
|
||||
EXPECT(actual.isApprox(expected));
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
|
|
@ -101,7 +227,7 @@ TEST(Quaternion, Between) {
|
|||
}
|
||||
|
||||
//******************************************************************************
|
||||
TEST(Quaternion, Ivnverse) {
|
||||
TEST(Quaternion , Inverse) {
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
|
|
|
|||
Loading…
Reference in New Issue