613 lines
15 KiB
C++
613 lines
15 KiB
C++
/*
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* This program source code file is part of KICAD, a free EDA CAD application.
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*
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* Copyright (C) 2010 Virtenio GmbH, Torsten Hueter, torsten.hueter <at> virtenio.de
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* Copyright (C) 2012 SoftPLC Corporation, Dick Hollenbeck <dick@softplc.com>
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* Copyright (C) 2012-2021 KiCad Developers, see AUTHORS.txt for contributors.
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* Copyright (C) 2013 CERN
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* @author Tomasz Wlostowski <tomasz.wlostowski@cern.ch>
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, you may find one here:
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* http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
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* or you may search the http://www.gnu.org website for the version 2 license,
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* or you may write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
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*/
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#ifndef VECTOR2D_H_
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#define VECTOR2D_H_
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#include <limits>
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#include <iostream>
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#include <sstream>
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#include <type_traits>
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#include <math/util.h>
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/**
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* Traits class for VECTOR2.
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*/
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template <class T>
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struct VECTOR2_TRAITS
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{
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/// extended range/precision types used by operations involving multiple
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/// multiplications to prevent overflow.
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typedef T extended_type;
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};
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template <>
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struct VECTOR2_TRAITS<int>
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{
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typedef int64_t extended_type;
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};
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// Forward declarations for template friends
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template <class T>
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class VECTOR2;
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template <class T>
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std::ostream& operator<<( std::ostream& aStream, const VECTOR2<T>& aVector );
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/**
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* Define a general 2D-vector/point.
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*
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* This class uses templates to be universal. Several operators are provided to help
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* easy implementing of linear algebra equations.
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*
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*/
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template <class T = int>
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class VECTOR2
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{
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public:
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typedef typename VECTOR2_TRAITS<T>::extended_type extended_type;
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typedef T coord_type;
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static constexpr extended_type ECOORD_MAX = std::numeric_limits<extended_type>::max();
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static constexpr extended_type ECOORD_MIN = std::numeric_limits<extended_type>::min();
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T x, y;
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/// Construct a 2D-vector with x, y = 0
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VECTOR2();
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/// Construct a vector with given components x, y
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VECTOR2( T x, T y );
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/// Initializes a vector from another specialization. Beware of rounding issues.
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template <typename CastingType>
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VECTOR2( const VECTOR2<CastingType>& aVec )
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{
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if( std::is_same<T, int>::value )
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{
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CastingType minI = static_cast<CastingType>( std::numeric_limits<int>::min() );
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CastingType maxI = static_cast<CastingType>( std::numeric_limits<int>::max() );
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x = static_cast<int>( Clamp( minI, aVec.x, maxI ) );
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y = static_cast<int>( Clamp( minI, aVec.y, maxI ) );
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}
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else
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{
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x = static_cast<T>( aVec.x );
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y = static_cast<T>( aVec.y );
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}
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}
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/// Copy a vector
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VECTOR2( const VECTOR2<T>& aVec )
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{
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x = aVec.x;
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y = aVec.y;
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}
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/// Cast a vector to another specialized subclass. Beware of rounding issues.
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template <typename CastedType>
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VECTOR2<CastedType> operator()() const
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{
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if( std::is_same<CastedType, int>::value )
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{
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T minI = static_cast<T>( std::numeric_limits<int>::min() );
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T maxI = static_cast<T>( std::numeric_limits<int>::max() );
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return VECTOR2<int>( static_cast<int>( Clamp( minI, x, maxI ) ),
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static_cast<int>( Clamp( minI, y, maxI ) ) );
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}
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else
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{
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return VECTOR2<CastedType>( static_cast<CastedType>( x ), static_cast<CastedType>( y ) );
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}
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}
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// virtual ~VECTOR2();
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/**
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* Compute the Euclidean norm of the vector, which is defined as sqrt(x ** 2 + y ** 2).
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*
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* It is used to calculate the length of the vector.
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*
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* @return Scalar, the euclidean norm
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*/
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T EuclideanNorm() const;
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/**
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* Compute the squared euclidean norm of the vector, which is defined as (x ** 2 + y ** 2).
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*
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* It is used to calculate the length of the vector.
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*
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* @return Scalar, the euclidean norm
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*/
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extended_type SquaredEuclideanNorm() const;
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/**
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* Compute the perpendicular vector.
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*
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* @return Perpendicular vector
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*/
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VECTOR2<T> Perpendicular() const;
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/**
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* Return a vector of the same direction, but length specified in \a aNewLength.
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*
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* @param aNewLength is the length of the rescaled vector.
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* @return the rescaled vector.
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*/
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VECTOR2<T> Resize( T aNewLength ) const;
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/**
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* Return the vector formatted as a string.
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*
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* @return the formatted string
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*/
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const std::string Format() const;
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/**
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* Compute cross product of self with \a aVector.
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*/
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extended_type Cross( const VECTOR2<T>& aVector ) const;
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/**
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* Compute dot product of self with \a aVector.
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*/
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extended_type Dot( const VECTOR2<T>& aVector ) const;
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// Operators
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/// Assignment operator
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VECTOR2<T>& operator=( const VECTOR2<T>& aVector );
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/// Vector addition operator
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VECTOR2<T> operator+( const VECTOR2<T>& aVector ) const;
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/// Scalar addition operator
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VECTOR2<T> operator+( const T& aScalar ) const;
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/// Compound assignment operator
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VECTOR2<T>& operator+=( const VECTOR2<T>& aVector );
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/// Compound assignment operator
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VECTOR2<T>& operator*=( const VECTOR2<T>& aVector );
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VECTOR2<T>& operator*=( const T& aScalar );
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/// Compound assignment operator
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VECTOR2<T>& operator+=( const T& aScalar );
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/// Vector subtraction operator
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VECTOR2<T> operator-( const VECTOR2<T>& aVector ) const;
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/// Scalar subtraction operator
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VECTOR2<T> operator-( const T& aScalar ) const;
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/// Compound assignment operator
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VECTOR2<T>& operator-=( const VECTOR2<T>& aVector );
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/// Compound assignment operator
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VECTOR2<T>& operator-=( const T& aScalar );
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/// Negate Vector operator
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VECTOR2<T> operator-();
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/// Scalar product operator
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extended_type operator*( const VECTOR2<T>& aVector ) const;
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/// Multiplication with a factor
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VECTOR2<T> operator*( const T& aFactor ) const;
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/// Division with a factor
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VECTOR2<T> operator/( double aFactor ) const;
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/// Equality operator
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bool operator==( const VECTOR2<T>& aVector ) const;
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/// Not equality operator
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bool operator!=( const VECTOR2<T>& aVector ) const;
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/// Smaller than operator
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bool operator<( const VECTOR2<T>& aVector ) const;
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bool operator<=( const VECTOR2<T>& aVector ) const;
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/// Greater than operator
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bool operator>( const VECTOR2<T>& aVector ) const;
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bool operator>=( const VECTOR2<T>& aVector ) const;
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};
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// ----------------------
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// --- Implementation ---
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// ----------------------
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template <class T>
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VECTOR2<T>::VECTOR2() : x{}, y{}
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{
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}
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template <class T>
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VECTOR2<T>::VECTOR2( T aX, T aY )
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{
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x = aX;
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y = aY;
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}
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template <class T>
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T VECTOR2<T>::EuclideanNorm() const
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{
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return static_cast<T>( sqrt( (extended_type) x * x + (extended_type) y * y ) );
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}
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template <class T>
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typename VECTOR2<T>::extended_type VECTOR2<T>::SquaredEuclideanNorm() const
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{
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return (extended_type) x * x + (extended_type) y * y;
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::Perpendicular() const
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{
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VECTOR2<T> perpendicular( -y, x );
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return perpendicular;
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}
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template <class T>
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VECTOR2<T>& VECTOR2<T>::operator=( const VECTOR2<T>& aVector )
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{
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x = aVector.x;
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y = aVector.y;
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return *this;
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}
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template <class T>
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VECTOR2<T>& VECTOR2<T>::operator+=( const VECTOR2<T>& aVector )
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{
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x += aVector.x;
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y += aVector.y;
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return *this;
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}
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template <class T>
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VECTOR2<T>& VECTOR2<T>::operator*=( const VECTOR2<T>& aVector )
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{
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x *= aVector.x;
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y *= aVector.y;
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return *this;
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}
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template <class T>
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VECTOR2<T>& VECTOR2<T>::operator*=( const T& aScalar )
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{
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x *= aScalar;
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y *= aScalar;
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return *this;
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}
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template <class T>
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VECTOR2<T>& VECTOR2<T>::operator+=( const T& aScalar )
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{
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x += aScalar;
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y += aScalar;
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return *this;
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}
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template <class T>
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VECTOR2<T>& VECTOR2<T>::operator-=( const VECTOR2<T>& aVector )
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{
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x -= aVector.x;
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y -= aVector.y;
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return *this;
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}
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template <class T>
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VECTOR2<T>& VECTOR2<T>::operator-=( const T& aScalar )
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{
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x -= aScalar;
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y -= aScalar;
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return *this;
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::Resize( T aNewLength ) const
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{
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if( x == 0 && y == 0 )
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return VECTOR2<T> ( 0, 0 );
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extended_type x_sq = (extended_type) x * x;
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extended_type y_sq = (extended_type) y * y;
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extended_type l_sq = x_sq + y_sq;
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extended_type newLength_sq = (extended_type) aNewLength * aNewLength;
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double newX = std::sqrt( rescale( newLength_sq, x_sq, l_sq ) );
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double newY = std::sqrt( rescale( newLength_sq, y_sq, l_sq ) );
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if( std::is_integral<T>::value )
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{
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return VECTOR2<T>( static_cast<T>( x < 0 ? -KiROUND( newX ) : KiROUND( newX ) ),
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static_cast<T>( y < 0 ? -KiROUND( newY ) : KiROUND( newY ) ) )
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* sign( aNewLength );
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}
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else
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{
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return VECTOR2<T>( static_cast<T>( x < 0 ? -newX : newX ),
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static_cast<T>( y < 0 ? -newY : newY ) )
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* sign( aNewLength );
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}
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}
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template <class T>
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const std::string VECTOR2<T>::Format() const
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{
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std::stringstream ss;
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ss << "( xy " << x << " " << y << " )";
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return ss.str();
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::operator+( const VECTOR2<T>& aVector ) const
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{
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return VECTOR2<T> ( x + aVector.x, y + aVector.y );
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::operator+( const T& aScalar ) const
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{
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return VECTOR2<T> ( x + aScalar, y + aScalar );
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::operator-( const VECTOR2<T>& aVector ) const
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{
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return VECTOR2<T> ( x - aVector.x, y - aVector.y );
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::operator-( const T& aScalar ) const
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{
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return VECTOR2<T> ( x - aScalar, y - aScalar );
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::operator-()
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{
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return VECTOR2<T> ( -x, -y );
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}
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template <class T>
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typename VECTOR2<T>::extended_type VECTOR2<T>::operator*( const VECTOR2<T>& aVector ) const
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{
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return (extended_type)aVector.x * x + (extended_type)aVector.y * y;
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::operator*( const T& aFactor ) const
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{
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VECTOR2<T> vector( x * aFactor, y * aFactor );
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return vector;
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}
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template <class T>
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VECTOR2<T> VECTOR2<T>::operator/( double aFactor ) const
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{
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if( std::is_integral<T>::value )
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return VECTOR2<T>( KiROUND( x / aFactor ), KiROUND( y / aFactor ) );
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else
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return VECTOR2<T>( static_cast<T>( x / aFactor ), static_cast<T>( y / aFactor ) );
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}
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template <class T>
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VECTOR2<T> operator*( const T& aFactor, const VECTOR2<T>& aVector )
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{
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VECTOR2<T> vector( aVector.x * aFactor, aVector.y * aFactor );
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return vector;
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}
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template <class T>
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typename VECTOR2<T>::extended_type VECTOR2<T>::Cross( const VECTOR2<T>& aVector ) const
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{
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return (extended_type) x * (extended_type) aVector.y -
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(extended_type) y * (extended_type) aVector.x;
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}
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template <class T>
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typename VECTOR2<T>::extended_type VECTOR2<T>::Dot( const VECTOR2<T>& aVector ) const
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{
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return (extended_type) x * (extended_type) aVector.x +
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(extended_type) y * (extended_type) aVector.y;
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}
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template <class T>
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bool VECTOR2<T>::operator<( const VECTOR2<T>& aVector ) const
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{
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return ( *this * *this ) < ( aVector * aVector );
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}
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template <class T>
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bool VECTOR2<T>::operator<=( const VECTOR2<T>& aVector ) const
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{
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return ( *this * *this ) <= ( aVector * aVector );
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}
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template <class T>
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bool VECTOR2<T>::operator>( const VECTOR2<T>& aVector ) const
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{
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return ( *this * *this ) > ( aVector * aVector );
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}
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template <class T>
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bool VECTOR2<T>::operator>=( const VECTOR2<T>& aVector ) const
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{
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return ( *this * *this ) >= ( aVector * aVector );
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}
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template <class T>
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bool VECTOR2<T>::operator==( VECTOR2<T> const& aVector ) const
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{
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return ( aVector.x == x ) && ( aVector.y == y );
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}
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template <class T>
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bool VECTOR2<T>::operator!=( VECTOR2<T> const& aVector ) const
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{
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return ( aVector.x != x ) || ( aVector.y != y );
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}
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template <class T>
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const VECTOR2<T> LexicographicalMax( const VECTOR2<T>& aA, const VECTOR2<T>& aB )
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{
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if( aA.x > aB.x )
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return aA;
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else if( aA.x == aB.x && aA.y > aB.y )
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return aA;
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return aB;
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}
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template <class T>
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const VECTOR2<T> LexicographicalMin( const VECTOR2<T>& aA, const VECTOR2<T>& aB )
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{
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if( aA.x < aB.x )
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return aA;
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else if( aA.x == aB.x && aA.y < aB.y )
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return aA;
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return aB;
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}
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template <class T>
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int LexicographicalCompare( const VECTOR2<T>& aA, const VECTOR2<T>& aB )
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{
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if( aA.x < aB.x )
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return -1;
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else if( aA.x > aB.x )
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return 1;
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else // aA.x == aB.x
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{
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if( aA.y < aB.y )
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return -1;
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else if( aA.y > aB.y )
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return 1;
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else
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return 0;
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}
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}
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|
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/**
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* Template to compare two VECTOR2<T> values for equality within a required epsilon.
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*
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* @param aFirst value to compare.
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* @param aSecond value to compare.
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* @param aEpsilon allowed error.
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* @return true if the values considered equal within the specified epsilon, otherwise false.
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*/
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template <class T>
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typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type
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equals( VECTOR2<T> const& aFirst, VECTOR2<T> const& aSecond,
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T aEpsilon = std::numeric_limits<T>::epsilon() )
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{
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if( !equals( aFirst.x, aSecond.x, aEpsilon ) )
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{
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return false;
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|
}
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|
|
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return equals( aFirst.y, aSecond.y, aEpsilon );
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}
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|
|
|
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template <class T>
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std::ostream& operator<<( std::ostream& aStream, const VECTOR2<T>& aVector )
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{
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aStream << "[ " << aVector.x << " | " << aVector.y << " ]";
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return aStream;
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|
}
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|
|
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/* Default specializations */
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typedef VECTOR2<double> VECTOR2D;
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typedef VECTOR2<int> VECTOR2I;
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|
|
|
/* STL specializations */
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|
namespace std
|
|
{
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|
// Required to enable correct use in std::map/unordered_map
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|
// DO NOT USE hash tables with VECTOR2 elements. It is inefficient
|
|
// and degenerates to a linear search. Use the std::map/std::set
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|
// trees instead that utilize the less operator below
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|
// This function is purposely deleted after substantial testing
|
|
template <>
|
|
struct hash<VECTOR2I>
|
|
{
|
|
size_t operator()( const VECTOR2I& k ) const = delete;
|
|
};
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|
|
|
// Required to enable use of std::hash with maps.
|
|
template <>
|
|
struct less<VECTOR2I>
|
|
{
|
|
bool operator()( const VECTOR2I& aA, const VECTOR2I& aB ) const;
|
|
};
|
|
}
|
|
|
|
#endif // VECTOR2D_H_
|