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kicad/libs/kimath/include/math/box2.h

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/*
* This program source code file is part of KiCad, a free EDA CAD application.
*
* Copyright (C) 2012 SoftPLC Corporation, Dick Hollenbeck <dick@softplc.com>
* Copyright (C) 2012-2022 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 __BOX2_H
#define __BOX2_H
#include <limits>
#include <algorithm>
#include <optional>
#include <math/vector2d.h>
#include <geometry/eda_angle.h>
#include <trigo.h>
/**
* A 2D bounding box built on top of an origin point and size vector.
*/
template <class Vec>
class BOX2
{
public:
typedef typename Vec::coord_type coord_type;
typedef typename Vec::extended_type ecoord_type;
typedef std::numeric_limits<coord_type> coord_limits;
BOX2() :
m_Pos( 0, 0 ),
m_Size( 0, 0 ),
m_init( false )
{};
BOX2( const Vec& aPos, const Vec& aSize = Vec(0, 0) ) :
m_Pos( aPos ),
m_Size( aSize ),
m_init( true )
{
Normalize();
}
void SetMaximum()
{
m_Pos.x = m_Pos.y = coord_limits::lowest() / 2 + coord_limits::epsilon();
m_Size.x = m_Size.y = coord_limits::max() - coord_limits::epsilon();
m_init = true;
}
Vec Centre() const
{
return Vec( m_Pos.x + ( m_Size.x / 2 ),
m_Pos.y + ( m_Size.y / 2 ) );
}
/**
* Compute the bounding box from a given list of points.
*
* @param aPointList is the list points of the object.
*/
template <class Container>
void Compute( const Container& aPointList )
{
Vec vmin, vmax;
typename Container::const_iterator i;
if( !aPointList.size() )
return;
vmin = vmax = aPointList[0];
for( i = aPointList.begin(); i != aPointList.end(); ++i )
{
Vec p( *i );
vmin.x = std::min( vmin.x, p.x );
vmin.y = std::min( vmin.y, p.y );
vmax.x = std::max( vmax.x, p.x );
vmax.y = std::max( vmax.y, p.y );
}
SetOrigin( vmin );
SetSize( vmax - vmin );
}
/**
* Move the rectangle by the \a aMoveVector.
*
* @param aMoveVector is a point that is the value to move this rectangle.
*/
void Move( const Vec& aMoveVector )
{
m_Pos += aMoveVector;
}
/**
* Ensure that the height and width are positive.
*/
BOX2<Vec>& Normalize()
{
if( m_Size.y < 0 )
{
m_Size.y = -m_Size.y;
m_Pos.y -= m_Size.y;
}
if( m_Size.x < 0 )
{
m_Size.x = -m_Size.x;
m_Pos.x -= m_Size.x;
}
return *this;
}
/**
* @param aPoint is the point to test.
*
* @return true if \a aPoint is inside the boundary box. A point on a edge is seen as inside.
*/
bool Contains( const Vec& aPoint ) const
{
Vec rel_pos = aPoint - m_Pos;
Vec size = m_Size;
if( size.x < 0 )
{
size.x = -size.x;
rel_pos.x += size.x;
}
if( size.y < 0 )
{
size.y = -size.y;
rel_pos.y += size.y;
}
return ( rel_pos.x >= 0 ) && ( rel_pos.y >= 0 ) && ( rel_pos.y <= size.y) &&
( rel_pos.x <= size.x);
}
/**
* @param x is the x coordinate of the point to test.
* @param y is the x coordinate of the point to test.
* @return true if point is inside the boundary box. A point on a edge is seen as inside.
*/
bool Contains( coord_type x, coord_type y ) const { return Contains( Vec( x, y ) ); }
/**
* @param aRect is the the area to test.
*
* @return true if \a aRect is contained. A common edge is seen as contained.
*/
bool Contains( const BOX2<Vec>& aRect ) const
{
return Contains( aRect.GetOrigin() ) && Contains( aRect.GetEnd() );
}
const Vec& GetSize() const { return m_Size; }
coord_type GetX() const { return m_Pos.x; }
coord_type GetY() const { return m_Pos.y; }
const Vec& GetOrigin() const { return m_Pos; }
const Vec& GetPosition() const { return m_Pos; }
const Vec GetEnd() const { return Vec( GetRight(), GetBottom() ); }
coord_type GetWidth() const { return m_Size.x; }
coord_type GetHeight() const { return m_Size.y; }
coord_type GetRight() const { return m_Pos.x + m_Size.x; }
coord_type GetBottom() const { return m_Pos.y + m_Size.y; }
// Compatibility aliases
coord_type GetLeft() const { return GetX(); }
coord_type GetTop() const { return GetY(); }
const Vec GetCenter() const { return Centre(); }
/**
* @return the width or height, whichever is greater.
*/
int GetSizeMax() const { return ( m_Size.x > m_Size.y ) ? m_Size.x : m_Size.y; }
void SetOrigin( const Vec& pos )
{
m_Pos = pos;
m_init = true;
}
void SetOrigin( coord_type x, coord_type y )
{
SetOrigin( Vec( x, y ) );
}
void SetSize( const Vec& size )
{
m_Size = size;
m_init = true;
}
void SetSize( coord_type w, coord_type h )
{
SetSize( Vec( w, h ) );
}
void Offset( coord_type dx, coord_type dy )
{
m_Pos.x += dx;
m_Pos.y += dy;
}
void Offset( const Vec& offset )
{
Offset( offset.x, offset.y );
}
void SetX( coord_type val )
{
SetOrigin( val, m_Pos.y );
}
void SetY( coord_type val )
{
SetOrigin( m_Pos.x, val );
}
void SetWidth( coord_type val )
{
SetSize( val, m_Size.y );
}
void SetHeight( coord_type val )
{
SetSize( m_Size.x, val );
}
void SetEnd( coord_type x, coord_type y )
{
SetEnd( Vec( x, y ) );
}
void SetEnd( const Vec& pos )
{
SetSize( pos - m_Pos );
}
/**
* @return true if the argument rectangle intersects this rectangle.
* (i.e. if the 2 rectangles have at least a common point)
*/
bool Intersects( const BOX2<Vec>& aRect ) const
{
// this logic taken from wxWidgets' geometry.cpp file:
bool rc;
BOX2<Vec> me( *this );
BOX2<Vec> rect( aRect );
me.Normalize(); // ensure size is >= 0
rect.Normalize(); // ensure size is >= 0
// calculate the left common area coordinate:
int left = std::max( me.m_Pos.x, rect.m_Pos.x );
// calculate the right common area coordinate:
int right = std::min( me.m_Pos.x + me.m_Size.x, rect.m_Pos.x + rect.m_Size.x );
// calculate the upper common area coordinate:
int top = std::max( me.m_Pos.y, rect.m_Pos.y );
// calculate the lower common area coordinate:
int bottom = std::min( me.m_Pos.y + me.m_Size.y, rect.m_Pos.y + rect.m_Size.y );
// if a common area exists, it must have a positive (null accepted) size
if( left <= right && top <= bottom )
rc = true;
else
rc = false;
return rc;
}
/**
* @return true if this rectangle intersects \a aRect.
*/
BOX2<Vec> Intersect( const BOX2<Vec>& aRect )
{
BOX2<Vec> me( *this );
BOX2<Vec> rect( aRect );
me.Normalize(); // ensure size is >= 0
rect.Normalize(); // ensure size is >= 0
Vec topLeft, bottomRight;
topLeft.x = std::max( me.m_Pos.x, rect.m_Pos.x );
bottomRight.x = std::min( me.m_Pos.x + me.m_Size.x, rect.m_Pos.x + rect.m_Size.x );
topLeft.y = std::max( me.m_Pos.y, rect.m_Pos.y );
bottomRight.y = std::min( me.m_Pos.y + me.m_Size.y, rect.m_Pos.y + rect.m_Size.y );
if ( topLeft.x < bottomRight.x && topLeft.y < bottomRight.y )
return BOX2<Vec>( topLeft, bottomRight - topLeft );
else
return BOX2<Vec>( Vec( 0, 0 ), Vec( 0, 0 ) );
}
/**
* @return true if this rectangle intersects a line from \a aPoint1 to \a aPoint2
*/
bool Intersects( const Vec& aPoint1, const Vec& aPoint2 ) const
{
Vec point2, point4;
if( Contains( aPoint1 ) || Contains( aPoint2 ) )
return true;
point2.x = GetEnd().x;
point2.y = GetOrigin().y;
point4.x = GetOrigin().x;
point4.y = GetEnd().y;
//Only need to test 3 sides since a straight line can't enter and exit on same side
if( SegmentIntersectsSegment( aPoint1, aPoint2, GetOrigin(), point2 ) )
return true;
if( SegmentIntersectsSegment( aPoint1, aPoint2, point2, GetEnd() ) )
return true;
if( SegmentIntersectsSegment( aPoint1, aPoint2, GetEnd(), point4 ) )
return true;
return false;
}
/**
* @return true if this rectangle intersects a rotated rect given by \a aRect and
* \a aRotaiton.
*/
bool Intersects( const BOX2<Vec>& aRect, const EDA_ANGLE& aRotation ) const
{
if( !m_init )
return false;
EDA_ANGLE rotation = aRotation;
rotation.Normalize();
/*
* Most rectangles will be axis aligned. It is quicker to check for this case and pass
* the rect to the simpler intersection test.
*/
// Prevent floating point comparison errors
static const EDA_ANGLE ROT_EPSILON( 0.000000001, DEGREES_T );
static const EDA_ANGLE ROT_PARALLEL[] = { ANGLE_0, ANGLE_180, ANGLE_360 };
static const EDA_ANGLE ROT_PERPENDICULAR[] = { ANGLE_0, ANGLE_90, ANGLE_270 };
// Test for non-rotated rectangle
for( EDA_ANGLE ii : ROT_PARALLEL )
{
if( std::abs( rotation - ii ) < ROT_EPSILON )
return Intersects( aRect );
}
// Test for rectangle rotated by multiple of 90 degrees
for( EDA_ANGLE jj : ROT_PERPENDICULAR )
{
if( std::abs( rotation - jj ) < ROT_EPSILON )
{
BOX2<Vec> rotRect;
// Rotate the supplied rect by 90 degrees
rotRect.SetOrigin( aRect.Centre() );
rotRect.Inflate( aRect.GetHeight(), aRect.GetWidth() );
return Intersects( rotRect );
}
}
/* There is some non-orthogonal rotation.
* There are three cases to test:
* A) One point of this rect is inside the rotated rect
* B) One point of the rotated rect is inside this rect
* C) One of the sides of the rotated rect intersect this
*/
VECTOR2I corners[4];
/* Test A : Any corners exist in rotated rect? */
corners[0] = m_Pos;
corners[1] = m_Pos + VECTOR2I( m_Size.x, 0 );
corners[2] = m_Pos + VECTOR2I( m_Size.x, m_Size.y );
corners[3] = m_Pos + VECTOR2I( 0, m_Size.y );
VECTOR2I rCentre = aRect.Centre();
for( int i = 0; i < 4; i++ )
{
VECTOR2I delta = corners[i] - rCentre;
RotatePoint( delta, -rotation );
delta += rCentre;
if( aRect.Contains( delta ) )
return true;
}
/* Test B : Any corners of rotated rect exist in this one? */
int w = aRect.GetWidth() / 2;
int h = aRect.GetHeight() / 2;
// Construct corners around center of shape
corners[0] = VECTOR2I( -w, -h );
corners[1] = VECTOR2I( w, -h );
corners[2] = VECTOR2I( w, h );
corners[3] = VECTOR2I( -w, h );
// Rotate and test each corner
for( int j = 0; j < 4; j++ )
{
RotatePoint( corners[j], rotation );
corners[j] += rCentre;
if( Contains( corners[j] ) )
return true;
}
/* Test C : Any sides of rotated rect intersect this */
if( Intersects( corners[0], corners[1] ) || Intersects( corners[1], corners[2] )
|| Intersects( corners[2], corners[3] ) || Intersects( corners[3], corners[0] ) )
{
return true;
}
return false;
}
/**
* @return true if this rectangle intersects the circle defined by \a aCenter and \a aRadius.
*/
bool IntersectsCircle( const Vec& aCenter, const int aRadius ) const
{
if( !m_init )
return false;
Vec closest = ClosestPointTo( aCenter );
double dx = static_cast<double>( aCenter.x ) - closest.x;
double dy = static_cast<double>( aCenter.y ) - closest.y;
double r = static_cast<double>( aRadius );
return ( dx * dx + dy * dy ) <= ( r * r );
}
/**
* @return true if this rectangle intersects the edge of a circle defined by \a aCenter
* and \a aRadius.
*/
bool IntersectsCircleEdge( const Vec& aCenter, const int aRadius, const int aWidth ) const
{
if( !m_init )
return false;
BOX2<Vec> me( *this );
me.Normalize(); // ensure size is >= 0
// Test if the circle intersects at all
if( !IntersectsCircle( aCenter, aRadius + aWidth / 2 ) )
return false;
Vec farpt = FarthestPointTo( aCenter );
// Farthest point must be further than the inside of the line
double fx = (double) farpt.x - aCenter.x;
double fy = (double) farpt.y - aCenter.y;
double r = (double) aRadius - (double) aWidth / 2;
return ( fx * fx + fy * fy ) > ( r * r );
}
const std::string Format() const
{
std::stringstream ss;
ss << "( box corner " << m_Pos.Format() << " w " << m_Size.x << " h " << m_Size.y << " )";
return ss.str();
}
/**
* Inflates the rectangle horizontally by \a dx and vertically by \a dy. If \a dx
* and/or \a dy is negative the rectangle is deflated.
*/
BOX2<Vec>& Inflate( coord_type dx, coord_type dy )
{
if( m_Size.x >= 0 )
{
if( m_Size.x < -2 * dx )
{
// Don't allow deflate to eat more width than we have,
m_Pos.x += m_Size.x / 2;
m_Size.x = 0;
}
else
{
// The inflate is valid.
m_Pos.x -= dx;
m_Size.x += 2 * dx;
}
}
else // size.x < 0:
{
if( m_Size.x > 2 * dx )
{
// Don't allow deflate to eat more width than we have,
m_Pos.x -= m_Size.x / 2;
m_Size.x = 0;
}
else
{
// The inflate is valid.
m_Pos.x += dx;
m_Size.x -= 2 * dx; // m_Size.x <0: inflate when dx > 0
}
}
if( m_Size.y >= 0 )
{
if( m_Size.y < -2 * dy )
{
// Don't allow deflate to eat more height than we have,
m_Pos.y += m_Size.y / 2;
m_Size.y = 0;
}
else
{
// The inflate is valid.
m_Pos.y -= dy;
m_Size.y += 2 * dy;
}
}
else // size.y < 0:
{
if( m_Size.y > 2 * dy )
{
// Don't allow deflate to eat more height than we have,
m_Pos.y -= m_Size.y / 2;
m_Size.y = 0;
}
else
{
// The inflate is valid.
m_Pos.y += dy;
m_Size.y -= 2 * dy; // m_Size.y <0: inflate when dy > 0
}
}
return *this;
}
/**
* Inflate the rectangle horizontally and vertically by \a aDelta. If \a aDelta
* is negative the rectangle is deflated.
*/
BOX2<Vec>& Inflate( int aDelta )
{
Inflate( aDelta, aDelta );
return *this;
}
/**
* Modify the position and size of the rectangle in order to contain \a aRect.
*
* @param aRect is the rectangle to merge with this rectangle.
*/
BOX2<Vec>& Merge( const BOX2<Vec>& aRect )
{
if( !m_init )
{
if( aRect.m_init )
{
m_Pos = aRect.GetPosition();
m_Size = aRect.GetSize();
m_init = true;
}
return *this;
}
Normalize(); // ensure width and height >= 0
BOX2<Vec> rect = aRect;
rect.Normalize(); // ensure width and height >= 0
Vec end = GetEnd();
Vec rect_end = rect.GetEnd();
// Change origin and size in order to contain the given rect
m_Pos.x = std::min( m_Pos.x, rect.m_Pos.x );
m_Pos.y = std::min( m_Pos.y, rect.m_Pos.y );
end.x = std::max( end.x, rect_end.x );
end.y = std::max( end.y, rect_end.y );
SetEnd( end );
return *this;
}
/**
* Modify the position and size of the rectangle in order to contain the given point.
*
* @param aPoint is the point to merge with the rectangle.
*/
BOX2<Vec>& Merge( const Vec& aPoint )
{
if( !m_init )
{
m_Pos = aPoint;
m_Size = VECTOR2I( 0, 0 );
m_init = true;
return *this;
}
Normalize(); // ensure width and height >= 0
Vec end = GetEnd();
// Change origin and size in order to contain the given rectangle.
m_Pos.x = std::min( m_Pos.x, aPoint.x );
m_Pos.y = std::min( m_Pos.y, aPoint.y );
end.x = std::max( end.x, aPoint.x );
end.y = std::max( end.y, aPoint.y );
SetEnd( end );
return *this;
}
/**
* Useful to calculate bounding box of rotated items, when rotation is not cardinal.
*
* @return the bounding box of this, after rotation.
*/
const BOX2<Vec> GetBoundingBoxRotated( const VECTOR2I& aRotCenter,
const EDA_ANGLE& aAngle ) const
{
VECTOR2I corners[4];
// Build the corners list
corners[0] = GetOrigin();
corners[2] = GetEnd();
corners[1].x = corners[0].x;
corners[1].y = corners[2].y;
corners[3].x = corners[2].x;
corners[3].y = corners[0].y;
// Rotate all corners, to find the bounding box
for( int ii = 0; ii < 4; ii++ )
RotatePoint( corners[ii], aRotCenter, aAngle );
// Find the corners bounding box
VECTOR2I start = corners[0];
VECTOR2I end = corners[0];
for( int ii = 1; ii < 4; ii++ )
{
start.x = std::min( start.x, corners[ii].x );
start.y = std::min( start.y, corners[ii].y );
end.x = std::max( end.x, corners[ii].x );
end.y = std::max( end.y, corners[ii].y );
}
BOX2<Vec> bbox;
bbox.SetOrigin( start );
bbox.SetEnd( end );
return bbox;
}
/**
* Mirror the rectangle from the X axis (negate Y pos and size).
*/
void RevertYAxis()
{
m_Pos.y = -m_Pos.y;
m_Size.y = -m_Size.y;
Normalize();
}
/**
* Return the area of the rectangle.
*
* @return The area of the rectangle.
*/
ecoord_type GetArea() const
{
return (ecoord_type) GetWidth() * (ecoord_type) GetHeight();
}
/**
* Return the length of the diagonal of the rectangle.
*
* @return The length of the rectangle diagonal.
*/
ecoord_type Diagonal() const
{
return m_Size.EuclideanNorm();
}
ecoord_type SquaredDistance( const Vec& aP ) const
{
ecoord_type x2 = m_Pos.x + m_Size.x;
ecoord_type y2 = m_Pos.y + m_Size.y;
ecoord_type xdiff = std::max( aP.x < m_Pos.x ? m_Pos.x - aP.x : m_Pos.x - x2,
(ecoord_type) 0 );
ecoord_type ydiff = std::max( aP.y < m_Pos.y ? m_Pos.y - aP.y : m_Pos.y - y2,
(ecoord_type) 0 );
return xdiff * xdiff + ydiff * ydiff;
}
ecoord_type Distance( const Vec& aP ) const
{
return sqrt( SquaredDistance( aP ) );
}
/**
* Return the square of the minimum distance between self and box \a aBox
*
* @param aBox is the other box.
* @return The distance squared from \a aBox.
*/
ecoord_type SquaredDistance( const BOX2<Vec>& aBox ) const
{
ecoord_type s = 0;
if( aBox.m_Pos.x + aBox.m_Size.x < m_Pos.x )
{
ecoord_type d = aBox.m_Pos.x + aBox.m_Size.x - m_Pos.x;
s += d * d;
}
else if( aBox.m_Pos.x > m_Pos.x + m_Size.x )
{
ecoord_type d = aBox.m_Pos.x - m_Size.x - m_Pos.x;
s += d * d;
}
if( aBox.m_Pos.y + aBox.m_Size.y < m_Pos.y )
{
ecoord_type d = aBox.m_Pos.y + aBox.m_Size.y - m_Pos.y;
s += d * d;
}
else if( aBox.m_Pos.y > m_Pos.y + m_Size.y )
{
ecoord_type d = aBox.m_Pos.y - m_Size.y - m_Pos.y;
s += d * d;
}
return s;
}
/**
* Return the minimum distance between self and \a aBox.
*
* @param aBox is the other box to get the distance from.
* @return The distance from \a aBox.
*/
ecoord_type Distance( const BOX2<Vec>& aBox ) const
{
return sqrt( SquaredDistance( aBox ) );
}
/**
* Return the point in this rect that is closest to the provided point
*/
const Vec ClosestPointTo( const Vec& aPoint ) const
{
BOX2<Vec> me( *this );
me.Normalize(); // ensure size is >= 0
// Determine closest point to the circle centre within this rect
coord_type nx = std::max( me.GetLeft(), std::min( aPoint.x, me.GetRight() ) );
coord_type ny = std::max( me.GetTop(), std::min( aPoint.y, me.GetBottom() ) );
return Vec( nx, ny );
}
/**
* Return the point in this rect that is farthest from the provided point
*/
const Vec FarthestPointTo( const Vec& aPoint ) const
{
BOX2<Vec> me( *this );
me.Normalize(); // ensure size is >= 0
coord_type fx;
coord_type fy;
Vec center = me.GetCenter();
if( aPoint.x < center.x )
fx = me.GetRight();
else
fx = me.GetLeft();
if( aPoint.y < center.y )
fy = me.GetBottom();
else
fy = me.GetTop();
return Vec( fx, fy );
}
bool operator==( const BOX2<Vec>& aOther ) const
{
auto t1 ( *this );
auto t2 ( aOther );
t1.Normalize();
t2.Normalize();
return ( t1.m_Pos == t2.m_Pos && t1.m_Size == t2.m_Size );
}
bool operator!=( const BOX2<Vec>& aOther ) const
{
auto t1 ( *this );
auto t2 ( aOther );
t1.Normalize();
t2.Normalize();
return ( t1.m_Pos != t2.m_Pos || t1.m_Size != t2.m_Size );
}
bool IsValid() const
{
return m_init;
}
private:
Vec m_Pos; // Rectangle Origin
Vec m_Size; // Rectangle Size
bool m_init; // Is the rectangle initialized
};
/* Default specializations */
typedef BOX2<VECTOR2I> BOX2I;
typedef BOX2<VECTOR2D> BOX2D;
typedef std::optional<BOX2I> OPT_BOX2I;
#endif
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