// ____ ______ __ // / __ \ / ____// / // / /_/ // / / / // / ____// /___ / /___ PixInsight Class Library // /_/ \____//_____/ PCL 2.4.23 // ---------------------------------------------------------------------------- // pcl/LinearTransformation.h - Released 2022-03-12T18:59:29Z // ---------------------------------------------------------------------------- // This file is part of the PixInsight Class Library (PCL). // PCL is a multiplatform C++ framework for development of PixInsight modules. // // Copyright (c) 2003-2022 Pleiades Astrophoto S.L. All Rights Reserved. // // Redistribution and use in both source and binary forms, with or without // modification, is permitted provided that the following conditions are met: // // 1. All redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // // 2. 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IN NO EVENT SHALL PLEIADES ASTROPHOTO OR ITS // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, // EXEMPLARY OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, BUSINESS // INTERRUPTION; PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; AND LOSS OF USE, // DATA OR PROFITS) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE // POSSIBILITY OF SUCH DAMAGE. // ---------------------------------------------------------------------------- #ifndef __PCL_LinearTransformation_h #define __PCL_LinearTransformation_h /// \file pcl/LinearTransformation.h #include #include #include #include #include /* * Based on original work contributed by Andrés del Pozo. */ namespace pcl { // ---------------------------------------------------------------------------- /*! * \class LinearTransformation * \brief A linear geometric transformation on the plane defined as a 2x3 * matrix of 64-bit floating point scalars. * * %LinearTransformation is a simple structure where the six transformation * coefficients are stored directly as \c double scalars. Since the third row * of the transformation matrix is (0, 0, 1) implicitly, this class can only * represent translations, rotations and scale changes. This class is primarily * intended to support WCS coordinate transformations. * * \ingroup astrometry_support */ class LinearTransformation { public: /*! * Default constructor. Constructs a unit linear transformation. */ LinearTransformation() = default; /*! * Copy constructor. */ LinearTransformation( const LinearTransformation& ) = default; /*! * Copy assignment operator. Returns a reference to this object. */ LinearTransformation& operator =( const LinearTransformation& ) = default; /*! * Constructs a linear transformation with the specified matrix elements. */ LinearTransformation( double a00, double a01, double a02, double a10, double a11, double a12 ) : m_a00( a00 ), m_a01( a01 ), m_a02( a02 ) , m_a10( a10 ), m_a11( a11 ), m_a12( a12 ) , m_det( a00*a11 - a01*a10 ) { } /*! * Returns true if this transformation has been defined by a singular * matrix. A singular matrix has zero or insignificant (with respect to the * machine epsilon for \c double) determinant and hence cannot be inverted. */ bool IsSingularMatrix() const { return 1 + m_det == 1; } /*! * Returns the transformation of the specified point \a p. */ DPoint Transform( const DPoint& p ) const { return DPoint( m_a00*p.x + m_a01*p.y + m_a02, m_a10*p.x + m_a11*p.y + m_a12 ); } /*! * Returns the transformation of the specified point \a p. This operator is * equivalent to the Transform() member function. */ DPoint operator ()( const DPoint& p ) const { return Transform( p ); } /*! * Returns the inverse transformation of the specified point \a p. * * If the transformation matrix is singular, this member function throws an * Error exception. */ DPoint TransformInverse( const DPoint& p ) const { if ( IsSingularMatrix() ) throw Error( "Invalid call to LinearTransformation::TransformInverse(): Singular matrix" ); return DPoint( ( m_a11*p.x - m_a01*p.y + m_a01*m_a12 - m_a02*m_a11)/m_det, (-m_a10*p.x + m_a00*p.y + m_a02*m_a10 - m_a00*m_a12)/m_det ); } /*! * Returns the product of this transformation by a transformation \a T. */ LinearTransformation Multiply( const LinearTransformation& T ) const { return LinearTransformation( m_a00*T.m_a00 + m_a01*T.m_a10, m_a00*T.m_a01 + m_a01*T.m_a11, m_a00*T.m_a02 + m_a01*T.m_a12 + m_a02, m_a10*T.m_a00 + m_a11*T.m_a10, m_a10*T.m_a01 + m_a11*T.m_a11, m_a10*T.m_a02 + m_a11*T.m_a12 + m_a12 ); } /*! * Returns the inverse of this transformation. * * If the transformation matrix is singular, this member function throws an * Error exception. */ LinearTransformation Inverse() const { if ( IsSingularMatrix() ) throw Error( "Invalid call to LinearTransformation::Inverse(): Singular matrix" ); return LinearTransformation( m_a11/m_det, -m_a01/m_det, (m_a01*m_a12 - m_a02*m_a11)/m_det, -m_a10/m_det, m_a00/m_det, (m_a02*m_a10 - m_a00*m_a12)/m_det ); } /*! * Returns the transformation coefficient at the first row, first column. */ double A00() const { return m_a00; } /*! * Returns the transformation coefficient at the first row, second column. */ double A01() const { return m_a01; } /*! * Returns the transformation coefficient at the first row, third column. */ double A02() const { return m_a02; } /*! * Returns the transformation coefficient at the second row, first column. */ double A10() const { return m_a10; } /*! * Returns the transformation coefficient at the second row, second column. */ double A11() const { return m_a11; } /*! * Returns the transformation coefficient at the third row, third column. */ double A12() const { return m_a12; } /*! * Returns a 3x3 matrix initialized with the transformation coefficients in * this object. */ Matrix ToMatrix() const { return Matrix( m_a00, m_a01, m_a02, m_a10, m_a11, m_a12, 0.0, 0.0, 1.0 ); } /*! * Returns a six-component vector initialized with the transformation * coefficients in this object. */ Vector ToVector() const { return Vector( { m_a00, m_a01, m_a02, m_a10, m_a11, m_a12 } ); } /*! * Returns a string representation of the transformation matrix. The * representation consists of two text lines, each with \a indent leading * spaces, separated by a newline character. */ String ToString( int indent = 0 ) const { String text; if ( indent > 0 ) text << String( ' ', indent ); text.AppendFormat( "%+16.8e %+16.8e %+16.8e\n", m_a00, m_a01, m_a02 ); if ( indent > 0 ) text << String( ' ', indent ); text.AppendFormat( "%+16.8e %+16.8e %+16.8e", m_a10, m_a11, m_a12 ); return text; } private: double m_a00 = 1, m_a01 = 0, m_a02 = 0, m_a10 = 0, m_a11 = 1, m_a12 = 0; double m_det = 1; }; // ---------------------------------------------------------------------------- } // pcl #endif // __PCL_LinearTransformation_h // ---------------------------------------------------------------------------- // EOF pcl/LinearTransformation.h - Released 2022-03-12T18:59:29Z