bool Multivector::Multiply( const Multivector& multivectorA, const Multivector& multivectorB, Term::ProductType productType )
{
Term::ProductType otherProductType = Term::OtherProductType( productType );
if( multivectorA.CountProductTypes( otherProductType ) > 0 )
if( !const_cast< Multivector* >( &multivectorA )->CollectTerms( productType ) )
return false;
if( multivectorB.CountProductTypes( otherProductType ) > 0 )
if( !const_cast< Multivector* >( &multivectorB )->CollectTerms( productType ) )
return false;
Multivector* multivectorResult = this;
Multivector multivectorStorage;
if( this == &multivectorA || this == &multivectorB )
multivectorResult = &multivectorStorage;
multivectorResult->sumOfTerms.RemoveAll();
for( const SumOfTerms::Node* nodeA = multivectorA.sumOfTerms.Head(); nodeA; nodeA = nodeA->Next() )
{
const Term* termA = nodeA->data;
for( const SumOfTerms::Node* nodeB = multivectorB.sumOfTerms.Head(); nodeB; nodeB = nodeB->Next() )
{
const Term* termB = nodeB->data;
Term* termResult = new Term( productType );
multivectorResult->sumOfTerms.InsertAfter()->data = termResult;
if( !termResult->coeficient->AssignProduct( *termA->coeficient, *termB->coeficient ) )
return false;
for( const Term::ProductOfVectors::Node* node = termA->productOfVectors.Head(); node; node = node->Next() )
termResult->productOfVectors.InsertAfter()->data = node->data->Clone();
for( const Term::ProductOfVectors::Node* node = termB->productOfVectors.Head(); node; node = node->Next() )
termResult->productOfVectors.InsertAfter()->data = node->data->Clone();
}
}
if( !multivectorResult->CollectTerms( productType ) )
return false;
if( multivectorResult == &multivectorStorage )
return Assign( multivectorStorage );
return true;
}
std::string DebugString(Multivector<Scalar, Frame, rank> const& multivector) {
// This |using| is required for the |Trivector|, since we need an ambiguity
// between |geometry::DebugString(R3Element<Scalar> const&)| and
// |quantities::DebugString(Scalar const&)| in order for the template magic
// to work out.
using quantities::DebugString;
return DebugString(multivector.coordinates());
}
bool Multivector::AssignInnerProduct( const Multivector& multivectorA, const Multivector& multivectorB )
{
if( multivectorA.CountProductTypes( Term::GEOMETRIC_PRODUCT ) > 0 )
if( !const_cast< Multivector* >( &multivectorA )->CollectTerms( Term::OUTER_PRODUCT ) )
return false;
if( multivectorB.CountProductTypes( Term::GEOMETRIC_PRODUCT ) > 0 )
if( !const_cast< Multivector* >( &multivectorB )->CollectTerms( Term::OUTER_PRODUCT ) )
return false;
Multivector* multivectorResult = this;
Multivector multivectorStorage;
if( this == &multivectorA || this == &multivectorB )
multivectorResult = &multivectorStorage;
for( const SumOfTerms::Node* nodeA = multivectorA.sumOfTerms.Head(); nodeA; nodeA = nodeA->Next() )
{
const Term* termA = nodeA->data;
for( const SumOfTerms::Node* nodeB = multivectorB.sumOfTerms.Head(); nodeB; nodeB = nodeB->Next() )
{
const Term* termB = nodeB->data;
Multivector innerProductMultivector;
if( !termA->InnerProductMultiply( termB, innerProductMultivector ) )
return false;
Scalar scalar;
if( !scalar.AssignProduct( *termA->coeficient, *termB->coeficient ) )
return false;
if( !innerProductMultivector.AssignScalarProduct( scalar, innerProductMultivector ) )
return false;
multivectorResult->sumOfTerms.Absorb( &innerProductMultivector.sumOfTerms );
}
}
if( multivectorResult == &multivectorStorage )
return Assign( multivectorStorage );
return true;
}
Multivector<quantities::Quotient<LScalar, quantities::Quantity<RDimension>>,
Frame,
rank>
operator/(Multivector<LScalar, Frame, rank> const& left,
quantities::Quantity<RDimension> const& right) {
return Multivector<
quantities::Quotient<LScalar, quantities::Quantity<RDimension>>,
Frame,
rank>(left.coordinates() / right);
}
Multivector<quantities::Product<quantities::Quantity<LDimension>, RScalar>,
Frame,
rank>
operator*(quantities::Quantity<LDimension> const& left,
Multivector<RScalar, Frame, rank> const& right) {
return Multivector<
quantities::Product<quantities::Quantity<LDimension>, RScalar>,
Frame,
rank>(left * right.coordinates());
}
inline Multivector<
quantities::Product<LScalar, quantities::Quantity<RDimension>>,
Frame,
rank>
operator*(Multivector<LScalar, Frame, rank> const& left,
quantities::Quantity<RDimension> const& right) {
return Multivector<
quantities::Product<LScalar, quantities::Quantity<RDimension>>,
Frame,
rank>(left.coordinates() * right);
}
bool operator!=(Multivector<Scalar, Frame, rank> const& left,
Multivector<Scalar, Frame, rank> const& right) {
return left.coordinates() != right.coordinates();
}
Multivector<Scalar, Frame, rank> operator/(
Multivector<Scalar, Frame, rank> const& left,
double const right) {
return Multivector<Scalar, Frame, rank>(left.coordinates() / right);
}
Multivector<Scalar, Frame, rank> operator*(
double const left,
Multivector<Scalar, Frame, rank> const& right) {
return Multivector<Scalar, Frame, rank>(left * right.coordinates());
}
Multivector<Scalar, Frame, rank> operator-(
Multivector<Scalar, Frame, rank> const& left,
Multivector<Scalar, Frame, rank> const& right) {
return Multivector<Scalar, Frame, rank>(
left.coordinates() - right.coordinates());
}
Multivector<Scalar, Frame, rank> operator+(
Multivector<Scalar, Frame, rank> const& right) {
return Multivector<Scalar, Frame, rank>(+right.coordinates());
}
Multivector<double, Frame, 3> Normalize(
Multivector<Scalar, Frame, 3> const& multivector) {
Scalar const norm = multivector.Norm();
CHECK_NE(Scalar(), norm);
return multivector / norm;
}
Multivector<double, Frame, 2> Normalize(
Multivector<Scalar, Frame, 2> const& multivector) {
return Multivector<double, Frame, 2>(Normalize(multivector.coordinates()));
}
// Note that in the interest of efficiency, we do not preserve this term in this process.
// Also note that we accumulate into the given multivector.
bool Multivector::Term::PerformProductMorphism( Multivector& multivector )
{
ProductType targetProductType = OtherProductType( productType );
if( productOfVectors.Count() == 1 )
{
ProductOfVectors::Node* node = productOfVectors.Head();
productOfVectors.Remove( node, false );
Term* term = new Term( targetProductType, coeficient );
term->productOfVectors.InsertAfter( 0, node );
multivector.sumOfTerms.InsertAfter()->data = term;
return true;
}
else if( productOfVectors.Count() == 0 )
{
Term* term = new Term( targetProductType, coeficient );
multivector.sumOfTerms.InsertAfter()->data = term;
return true;
}
ProductOfVectors::Node* node = productOfVectors.Head();
Vector* vector = node->data;
productOfVectors.Remove( node, false );
bool success = false;
do
{
if( targetProductType == GEOMETRIC_PRODUCT )
{
Multivector termMultivector;
termMultivector.sumOfTerms.InsertAfter()->data = Clone();
Multivector innerProductMultivector;
if( !innerProductMultivector.InnerProductMultiply( *vector, termMultivector ) )
break;
innerProductMultivector.Negate();
while( innerProductMultivector.sumOfTerms.Count() > 0 )
{
SumOfTerms::Node* node = innerProductMultivector.sumOfTerms.Head();
Term* term = node->data;
if( !term->PerformProductMorphism( multivector ) )
break;
innerProductMultivector.sumOfTerms.Remove( node, true );
}
if( innerProductMultivector.sumOfTerms.Count() > 0 )
break;
}
Multivector subMultivector;
if( !PerformProductMorphism( subMultivector ) )
break;
if( targetProductType == OUTER_PRODUCT )
{
if( !multivector.InnerProductMultiply( *vector, subMultivector ) )
break;
if( !multivector.OuterProductMultiply( *vector, subMultivector ) )
break;
}
else if( targetProductType == GEOMETRIC_PRODUCT )
{
if( !multivector.GeometricProductMultiply( *vector, subMultivector ) )
break;
}
success = true;
}
while( false );
delete node;
return success;
}
inline Multivector<double, Frame, rank> Normalize(
Multivector<Scalar, Frame, rank> const& multivector) {
return multivector / multivector.Norm();
}