kicad/libs/kimath/include/math/vector2d.h

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18 KiB
C++

/*
* This program source code file is part of KICAD, a free EDA CAD application.
*
* Copyright (C) 2010 Virtenio GmbH, Torsten Hueter, torsten.hueter <at> virtenio.de
* Copyright (C) 2012 SoftPLC Corporation, Dick Hollenbeck <dick@softplc.com>
* Copyright (C) 2012-2021 KiCad Developers, see AUTHORS.txt for contributors.
* Copyright (C) 2013 CERN
* @author Tomasz Wlostowski <tomasz.wlostowski@cern.ch>
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, you may find one here:
* http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
* or you may search the http://www.gnu.org website for the version 2 license,
* or you may write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
*/
#ifndef VECTOR2D_H_
#define VECTOR2D_H_
#include <limits>
#include <iostream>
#include <sstream>
#include <type_traits>
#include <math/util.h>
/**
* Traits class for VECTOR2.
*/
template <class T>
struct VECTOR2_TRAITS
{
/// extended range/precision types used by operations involving multiple
/// multiplications to prevent overflow.
typedef T extended_type;
};
template <>
struct VECTOR2_TRAITS<int>
{
typedef int64_t extended_type;
};
// Forward declarations for template friends
template <class T>
class VECTOR2;
template <class T>
std::ostream& operator<<( std::ostream& aStream, const VECTOR2<T>& aVector );
/**
* Define a general 2D-vector/point.
*
* This class uses templates to be universal. Several operators are provided to help
* easy implementing of linear algebra equations.
*
*/
template <class T = int>
class VECTOR2
{
public:
typedef typename VECTOR2_TRAITS<T>::extended_type extended_type;
typedef T coord_type;
static constexpr extended_type ECOORD_MAX = std::numeric_limits<extended_type>::max();
static constexpr extended_type ECOORD_MIN = std::numeric_limits<extended_type>::min();
T x, y;
/// Construct a 2D-vector with x, y = 0
VECTOR2();
/// Construct a vector with given components x, y
VECTOR2( T x, T y );
/// Initializes a vector from another specialization. Beware of rounding issues.
template <typename CastingType>
VECTOR2( const VECTOR2<CastingType>& aVec )
{
if( std::is_floating_point<T>() )
{
x = static_cast<T>( aVec.x );
y = static_cast<T>( aVec.y );
}
else if( std::is_floating_point<CastingType>() )
{
CastingType minI = static_cast<CastingType>( std::numeric_limits<T>::min() );
CastingType maxI = static_cast<CastingType>( std::numeric_limits<T>::max() );
x = static_cast<T>( Clamp( minI, aVec.x, maxI ) );
y = static_cast<T>( Clamp( minI, aVec.y, maxI ) );
}
else if( std::is_integral<T>() && std::is_integral<CastingType>() )
{
int64_t minI = static_cast<int64_t>( std::numeric_limits<T>::min() );
int64_t maxI = static_cast<int64_t>( std::numeric_limits<T>::max() );
x = static_cast<T>( Clamp( minI, static_cast<int64_t>( aVec.x ), maxI ) );
y = static_cast<T>( Clamp( minI, static_cast<int64_t>(aVec.y), maxI ) );
}
else
{
x = static_cast<T>( aVec.x );
y = static_cast<T>( aVec.y );
}
}
/// Copy a vector
VECTOR2( const VECTOR2<T>& aVec )
{
x = aVec.x;
y = aVec.y;
}
/// Cast a vector to another specialized subclass. Beware of rounding issues.
template <typename U>
VECTOR2<U> operator()() const
{
if( std::is_floating_point<U>::value )
{
return VECTOR2<U>( static_cast<U>( x ), static_cast<U>( y ) );
}
else if( std::is_floating_point<T>() )
{
T minI = static_cast<T>( std::numeric_limits<U>::min() );
T maxI = static_cast<T>( std::numeric_limits<U>::max() );
return VECTOR2<U>( static_cast<U>( Clamp( minI, x, maxI ) ),
static_cast<U>( Clamp( minI, y, maxI ) ) );
}
else if( std::is_integral<T>() && std::is_integral<U>() )
{
int64_t minI = static_cast<int64_t>( std::numeric_limits<U>::min() );
int64_t maxI = static_cast<int64_t>( std::numeric_limits<U>::max() );
return VECTOR2<U>(
static_cast<U>( Clamp( minI, static_cast<int64_t>( x ), maxI ) ),
static_cast<U>( Clamp( minI, static_cast<int64_t>( y ), maxI ) ) );
}
else
{
return VECTOR2<U>( static_cast<U>( x ), static_cast<U>( y ) );
}
}
// virtual ~VECTOR2();
/**
* Compute the Euclidean norm of the vector, which is defined as sqrt(x ** 2 + y ** 2).
*
* It is used to calculate the length of the vector.
*
* @return Scalar, the euclidean norm
*/
T EuclideanNorm() const;
/**
* Compute the squared euclidean norm of the vector, which is defined as (x ** 2 + y ** 2).
*
* It is used to calculate the length of the vector.
*
* @return Scalar, the euclidean norm
*/
extended_type SquaredEuclideanNorm() const;
/**
* Compute the perpendicular vector.
*
* @return Perpendicular vector
*/
VECTOR2<T> Perpendicular() const;
/**
* Return a vector of the same direction, but length specified in \a aNewLength.
*
* @param aNewLength is the length of the rescaled vector.
* @return the rescaled vector.
*/
VECTOR2<T> Resize( T aNewLength ) const;
/**
* Return the vector formatted as a string.
*
* @return the formatted string
*/
const std::string Format() const;
/**
* Compute cross product of self with \a aVector.
*/
extended_type Cross( const VECTOR2<T>& aVector ) const;
/**
* Compute dot product of self with \a aVector.
*/
extended_type Dot( const VECTOR2<T>& aVector ) const;
/**
* Compute the distance between two vectors. This is a double precision
* value because the distance is frequently non-integer.
*/
double Distance( const VECTOR2<extended_type>& aVector ) const;
// Operators
/// Assignment operator
VECTOR2<T>& operator=( const VECTOR2<T>& aVector );
/// Compound assignment operator
VECTOR2<T>& operator+=( const VECTOR2<T>& aVector );
/// Compound assignment operator
VECTOR2<T>& operator*=( const VECTOR2<T>& aVector );
VECTOR2<T>& operator*=( const T& aScalar );
/// Compound assignment operator
VECTOR2<T>& operator+=( const T& aScalar );
/// Compound assignment operator
VECTOR2<T>& operator-=( const VECTOR2<T>& aVector );
/// Compound assignment operator
VECTOR2<T>& operator-=( const T& aScalar );
/// Negate Vector operator
VECTOR2<T> operator-();
/// Division with a factor
VECTOR2<T> operator/( double aFactor ) const;
/// Equality operator
bool operator==( const VECTOR2<T>& aVector ) const;
/// Not equality operator
bool operator!=( const VECTOR2<T>& aVector ) const;
/// Smaller than operator
bool operator<( const VECTOR2<T>& aVector ) const;
bool operator<=( const VECTOR2<T>& aVector ) const;
/// Greater than operator
bool operator>( const VECTOR2<T>& aVector ) const;
bool operator>=( const VECTOR2<T>& aVector ) const;
};
// ----------------------
// --- Implementation ---
// ----------------------
template <class T>
VECTOR2<T>::VECTOR2() : x{}, y{}
{
}
template <class T>
VECTOR2<T>::VECTOR2( T aX, T aY )
{
x = aX;
y = aY;
}
template <class T>
T VECTOR2<T>::EuclideanNorm() const
{
// 45° are common in KiCad, so we can optimize the calculation
if( std::abs( x ) == std::abs( y ) )
{
if( std::is_integral<T>::value )
return KiROUND<double, T>( std::abs( x ) * M_SQRT2 );
return static_cast<T>( std::abs( x ) * M_SQRT2 );
}
if( x == 0 )
return static_cast<T>( std::abs( y ) );
if( y == 0 )
return static_cast<T>( std::abs( x ) );
if( std::is_integral<T>::value )
return KiROUND<double, T>( std::hypot( x, y ) );
return static_cast<T>( std::hypot( x, y ) );
}
template <class T>
typename VECTOR2<T>::extended_type VECTOR2<T>::SquaredEuclideanNorm() const
{
return (extended_type) x * x + (extended_type) y * y;
}
template <class T>
VECTOR2<T> VECTOR2<T>::Perpendicular() const
{
VECTOR2<T> perpendicular( -y, x );
return perpendicular;
}
template <class T>
VECTOR2<T>& VECTOR2<T>::operator=( const VECTOR2<T>& aVector )
{
x = aVector.x;
y = aVector.y;
return *this;
}
template <class T>
VECTOR2<T>& VECTOR2<T>::operator+=( const VECTOR2<T>& aVector )
{
x += aVector.x;
y += aVector.y;
return *this;
}
template <class T>
VECTOR2<T>& VECTOR2<T>::operator*=( const VECTOR2<T>& aVector )
{
x *= aVector.x;
y *= aVector.y;
return *this;
}
template <class T>
VECTOR2<T>& VECTOR2<T>::operator*=( const T& aScalar )
{
x *= aScalar;
y *= aScalar;
return *this;
}
template <class T>
VECTOR2<T>& VECTOR2<T>::operator+=( const T& aScalar )
{
x += aScalar;
y += aScalar;
return *this;
}
template <class T>
VECTOR2<T>& VECTOR2<T>::operator-=( const VECTOR2<T>& aVector )
{
x -= aVector.x;
y -= aVector.y;
return *this;
}
template <class T>
VECTOR2<T>& VECTOR2<T>::operator-=( const T& aScalar )
{
x -= aScalar;
y -= aScalar;
return *this;
}
template <class T>
VECTOR2<T> VECTOR2<T>::Resize( T aNewLength ) const
{
if( x == 0 && y == 0 )
return VECTOR2<T> ( 0, 0 );
double newX;
double newY;
if( std::abs( x ) == std::abs( y ) )
{
newX = newY = std::abs( aNewLength ) * M_SQRT1_2;
}
else
{
extended_type x_sq = (extended_type) x * x;
extended_type y_sq = (extended_type) y * y;
extended_type l_sq = x_sq + y_sq;
extended_type newLength_sq = (extended_type) aNewLength * aNewLength;
newX = std::sqrt( rescale( newLength_sq, x_sq, l_sq ) );
newY = std::sqrt( rescale( newLength_sq, y_sq, l_sq ) );
}
if( std::is_integral<T>::value )
{
return VECTOR2<T>( static_cast<T>( x < 0 ? -KiROUND( newX ) : KiROUND( newX ) ),
static_cast<T>( y < 0 ? -KiROUND( newY ) : KiROUND( newY ) ) )
* sign( aNewLength );
}
else
{
return VECTOR2<T>( static_cast<T>( x < 0 ? -newX : newX ),
static_cast<T>( y < 0 ? -newY : newY ) )
* sign( aNewLength );
}
}
template <class T>
const std::string VECTOR2<T>::Format() const
{
std::stringstream ss;
ss << "( xy " << x << " " << y << " )";
return ss.str();
}
template <class T>
concept FloatingPoint = std::is_floating_point<T>::value;
template <class T>
concept Integral = std::is_integral<T>::value;
template <class T, class U>
VECTOR2<std::common_type_t<T, U>> operator+( const VECTOR2<T>& aLHS, const VECTOR2<U>& aRHS )
{
return VECTOR2<std::common_type_t<T, U>>( aLHS.x + aRHS.x, aLHS.y + aRHS.y );
}
template <FloatingPoint T, class U>
VECTOR2<T> operator+( const VECTOR2<T>& aLHS, const U& aScalar )
{
return VECTOR2<T>( aLHS.x + aScalar, aLHS.y + aScalar );
}
template <Integral T, Integral U>
VECTOR2<T> operator+( const VECTOR2<T>& aLHS, const U& aScalar )
{
return VECTOR2<T>( aLHS.x + aScalar, aLHS.y + aScalar );
}
template <Integral T, FloatingPoint U>
VECTOR2<T> operator+( const VECTOR2<T>& aLHS, const U& aScalar )
{
return VECTOR2<T>( KiROUND( aLHS.x + aScalar ), KiROUND( aLHS.y + aScalar ) );
}
template <class T, class U>
VECTOR2<std::common_type_t<T, U>> operator-( const VECTOR2<T>& aLHS, const VECTOR2<U>& aRHS )
{
return VECTOR2<std::common_type_t<T, U>>( aLHS.x - aRHS.x, aLHS.y - aRHS.y );
}
template <FloatingPoint T, class U>
VECTOR2<T> operator-( const VECTOR2<T>& aLHS, U aScalar )
{
return VECTOR2<T>( aLHS.x - aScalar, aLHS.y - aScalar );
}
template <Integral T, Integral U>
VECTOR2<T> operator-( const VECTOR2<T>& aLHS, U aScalar )
{
return VECTOR2<T>( aLHS.x - aScalar, aLHS.y - aScalar );
}
template <Integral T, FloatingPoint U>
VECTOR2<T> operator-( const VECTOR2<T>& aLHS, const U& aScalar )
{
return VECTOR2<T>( KiROUND( aLHS.x - aScalar ), KiROUND( aLHS.y - aScalar ) );
}
template <class T>
VECTOR2<T> VECTOR2<T>::operator-()
{
return VECTOR2<T> ( -x, -y );
}
template <class T, class U>
#ifdef SWIG
double operator*( const VECTOR2<T>& aLHS, const VECTOR2<U>& aRHS )
#else
auto operator*( const VECTOR2<T>& aLHS, const VECTOR2<U>& aRHS )
#endif
{
using extended_type = typename VECTOR2<std::common_type_t<T, U>>::extended_type;
return (extended_type)aLHS.x * aRHS.x + (extended_type)aLHS.y * aRHS.y;
}
template <class T, class U>
VECTOR2<std::common_type_t<T, U>> operator*( const VECTOR2<T>& aLHS, const U& aScalar )
{
return VECTOR2<std::common_type_t<T, U>>( aLHS.x * aScalar, aLHS.y * aScalar );
}
template <class T, class U>
VECTOR2<std::common_type_t<T, U>> operator*( const T& aScalar, const VECTOR2<U>& aVector )
{
return VECTOR2<std::common_type_t<T, U>>( aScalar * aVector.x, aScalar * aVector.y );
}
template <class T>
VECTOR2<T> VECTOR2<T>::operator/( double aFactor ) const
{
if( std::is_integral<T>::value )
return VECTOR2<T>( KiROUND( x / aFactor ), KiROUND( y / aFactor ) );
else
return VECTOR2<T>( static_cast<T>( x / aFactor ), static_cast<T>( y / aFactor ) );
}
template <class T>
typename VECTOR2<T>::extended_type VECTOR2<T>::Cross( const VECTOR2<T>& aVector ) const
{
return (extended_type) x * (extended_type) aVector.y -
(extended_type) y * (extended_type) aVector.x;
}
template <class T>
typename VECTOR2<T>::extended_type VECTOR2<T>::Dot( const VECTOR2<T>& aVector ) const
{
return (extended_type) x * (extended_type) aVector.x +
(extended_type) y * (extended_type) aVector.y;
}
template <class T>
double VECTOR2<T>::Distance( const VECTOR2<extended_type>& aVector ) const
{
VECTOR2<double> diff( aVector.x - x, aVector.y - y );
return diff.EuclideanNorm();
}
template <class T>
bool VECTOR2<T>::operator<( const VECTOR2<T>& aVector ) const
{
return ( *this * *this ) < ( aVector * aVector );
}
template <class T>
bool VECTOR2<T>::operator<=( const VECTOR2<T>& aVector ) const
{
return ( *this * *this ) <= ( aVector * aVector );
}
template <class T>
bool VECTOR2<T>::operator>( const VECTOR2<T>& aVector ) const
{
return ( *this * *this ) > ( aVector * aVector );
}
template <class T>
bool VECTOR2<T>::operator>=( const VECTOR2<T>& aVector ) const
{
return ( *this * *this ) >= ( aVector * aVector );
}
template <class T>
bool VECTOR2<T>::operator==( VECTOR2<T> const& aVector ) const
{
return ( aVector.x == x ) && ( aVector.y == y );
}
template <class T>
bool VECTOR2<T>::operator!=( VECTOR2<T> const& aVector ) const
{
return ( aVector.x != x ) || ( aVector.y != y );
}
template <class T>
const VECTOR2<T> LexicographicalMax( const VECTOR2<T>& aA, const VECTOR2<T>& aB )
{
if( aA.x > aB.x )
return aA;
else if( aA.x == aB.x && aA.y > aB.y )
return aA;
return aB;
}
template <class T>
const VECTOR2<T> LexicographicalMin( const VECTOR2<T>& aA, const VECTOR2<T>& aB )
{
if( aA.x < aB.x )
return aA;
else if( aA.x == aB.x && aA.y < aB.y )
return aA;
return aB;
}
template <class T>
int LexicographicalCompare( const VECTOR2<T>& aA, const VECTOR2<T>& aB )
{
if( aA.x < aB.x )
return -1;
else if( aA.x > aB.x )
return 1;
else // aA.x == aB.x
{
if( aA.y < aB.y )
return -1;
else if( aA.y > aB.y )
return 1;
else
return 0;
}
}
/**
* Template to compare two VECTOR2<T> values for equality within a required epsilon.
*
* @param aFirst value to compare.
* @param aSecond value to compare.
* @param aEpsilon allowed error.
* @return true if the values considered equal within the specified epsilon, otherwise false.
*/
template <class T>
typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type
equals( VECTOR2<T> const& aFirst, VECTOR2<T> const& aSecond,
T aEpsilon = std::numeric_limits<T>::epsilon() )
{
if( !equals( aFirst.x, aSecond.x, aEpsilon ) )
{
return false;
}
return equals( aFirst.y, aSecond.y, aEpsilon );
}
template <class T>
std::ostream& operator<<( std::ostream& aStream, const VECTOR2<T>& aVector )
{
aStream << "[ " << aVector.x << " | " << aVector.y << " ]";
return aStream;
}
/* Default specializations */
typedef VECTOR2<double> VECTOR2D;
typedef VECTOR2<int32_t> VECTOR2I;
typedef VECTOR2<int64_t> VECTOR2L;
/* KiROUND specialization for vectors */
inline VECTOR2I KiROUND( const VECTOR2D& vec )
{
return VECTOR2I( KiROUND( vec.x ), KiROUND( vec.y ) );
}
/* STL specializations */
namespace std
{
// Required to enable correct use in std::map/unordered_map
// DO NOT USE hash tables with VECTOR2 elements. It is inefficient
// and degenerates to a linear search. Use the std::map/std::set
// trees instead that utilize the less operator below
// This function is purposely deleted after substantial testing
template <>
struct hash<VECTOR2I>
{
size_t operator()( const VECTOR2I& k ) const = delete;
};
// 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_