kicad/libs/kimath/include/trigo.h

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/*
* This program source code file is part of KiCad, a free EDA CAD application.
*
* Copyright (C) 2018-2021 KiCad Developers, see AUTHORS.txt for contributors.
*
* 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 TRIGO_H
#define TRIGO_H
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#include <cmath>
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#include <math/vector2d.h>
#include <geometry/eda_angle.h>
/**
* Test if \a aTestPoint is on line defined by \a aSegStart and \a aSegEnd.
*
* This function is faster than #TestSegmentHit() because \a aTestPoint should be exactly on
* the line. This works fine only for H, V and 45 degree line segments.
*
* @param aSegStart The first point of the line segment.
* @param aSegEnd The second point of the line segment.
* @param aTestPoint The point to test.
*
* @return true if the point is on the line segment.
*/
bool IsPointOnSegment( const VECTOR2I& aSegStart, const VECTOR2I& aSegEnd,
const VECTOR2I& aTestPoint );
/**
* Test if two lines intersect.
*
* @param a_p1_l1 The first point of the first line.
* @param a_p2_l1 The second point of the first line.
* @param a_p1_l2 The first point of the second line.
* @param a_p2_l2 The second point of the second line.
* @param aIntersectionPoint is filled with the intersection point if it exists
* @return bool - true if the two segments defined by four points intersect.
* (i.e. if the 2 segments have at least a common point)
*/
bool SegmentIntersectsSegment( const VECTOR2I& a_p1_l1, const VECTOR2I& a_p2_l1,
const VECTOR2I& a_p1_l2, const VECTOR2I& a_p2_l2,
VECTOR2I* aIntersectionPoint = nullptr );
/*
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* Calculate the new point of coord coord pX, pY, for a rotation center 0, 0
*/
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void RotatePoint( int *pX, int *pY, const EDA_ANGLE& aAngle );
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inline void RotatePoint( VECTOR2I& point, const EDA_ANGLE& aAngle )
{
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RotatePoint( &point.x, &point.y, aAngle );
}
/*
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* Calculate the new point of coord coord pX, pY, for a rotation center cx, cy
*/
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void RotatePoint( int *pX, int *pY, int cx, int cy, const EDA_ANGLE& aAngle );
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inline void RotatePoint( VECTOR2I& point, const VECTOR2I& centre, const EDA_ANGLE& aAngle )
{
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RotatePoint( &point.x, &point.y, centre.x, centre.y, aAngle );
}
/*
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* Calculate the new coord point point for a rotation center 0, 0
*/
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void RotatePoint( double* pX, double* pY, const EDA_ANGLE& aAngle );
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inline void RotatePoint( VECTOR2D& point, const EDA_ANGLE& aAngle )
{
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RotatePoint( &point.x, &point.y, aAngle );
}
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void RotatePoint( double* pX, double* pY, double cx, double cy, const EDA_ANGLE& aAngle );
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inline void RotatePoint( VECTOR2D& point, const VECTOR2D& aCenter, const EDA_ANGLE& aAngle )
{
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RotatePoint( &point.x, &point.y, aCenter.x, aCenter.y, aAngle );
}
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/**
* Determine the center of an arc or circle given three points on its circumference.
*
* @param aStart The starting point of the circle (equivalent to aEnd)
* @param aMid The point on the arc, half-way between aStart and aEnd
* @param aEnd The ending point of the circle (equivalent to aStart)
* @return The center of the circle
*/
const VECTOR2I CalcArcCenter( const VECTOR2I& aStart, const VECTOR2I& aMid, const VECTOR2I& aEnd );
const VECTOR2D CalcArcCenter( const VECTOR2D& aStart, const VECTOR2D& aMid, const VECTOR2D& aEnd );
const VECTOR2D CalcArcCenter( const VECTOR2D& aStart, const VECTOR2D& aEnd,
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const EDA_ANGLE& aAngle );
/**
* Return the middle point of an arc, half-way between aStart and aEnd. There are two possible
* solutions which can be found by toggling aMinArcAngle. The behaviour is undefined for
* semicircles (i.e. 180 degree arcs).
*
* @param aStart The starting point of the arc (for calculating the radius)
* @param aEnd The end point of the arc (for determining the arc angle)
* @param aCenter The center point of the arc
* @param aMinArcAngle If true, returns the point that results in the smallest arc angle.
* @return The middle point of the arc
*/
const VECTOR2I CalcArcMid( const VECTOR2I& aStart, const VECTOR2I& aEnd, const VECTOR2I& aCenter,
bool aMinArcAngle = true );
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inline double EuclideanNorm( const VECTOR2I& vector )
{
// this is working with doubles
return hypot( vector.x, vector.y );
}
//! @brief Compute the distance between a line and a reference point
//! Reference: http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
//! @param linePointA Point on line
//! @param linePointB Point on line
//! @param referencePoint Reference point
inline double DistanceLinePoint( const VECTOR2I& linePointA, const VECTOR2I& linePointB,
const VECTOR2I& referencePoint )
{
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// Some of the multiple double casts are redundant. However in the previous definition
// the cast was (implicitly) done too late, just before the division (EuclideanNorm gives
// a double so from int it would be promoted); that means that the whole expression were
// vulnerable to overflow during int multiplications
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return fabs( ( static_cast<double>( linePointB.x - linePointA.x ) *
static_cast<double>( linePointA.y - referencePoint.y ) -
static_cast<double>( linePointA.x - referencePoint.x ) *
static_cast<double>( linePointB.y - linePointA.y) )
/ EuclideanNorm( linePointB - linePointA ) );
}
//! @brief Test, if two points are near each other
//! @param pointA First point
//! @param pointB Second point
//! @param threshold The maximum distance
//! @return True or false
inline bool HitTestPoints( const VECTOR2I& pointA, const VECTOR2I& pointB, double threshold )
{
VECTOR2I vectorAB = pointB - pointA;
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// Compare the distances squared. The double is needed to avoid overflow during int
// multiplication
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double sqdistance = (double)vectorAB.x * vectorAB.x + (double)vectorAB.y * vectorAB.y;
return sqdistance < threshold * threshold;
}
/**
* Test if \a aRefPoint is with \a aDistance on the line defined by \a aStart and \a aEnd..
*
* @param aRefPoint = reference point to test
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* @param aStart is the first end-point of the line segment
* @param aEnd is the second end-point of the line segment
* @param aDist = maximum distance for hit
*/
bool TestSegmentHit( const VECTOR2I& aRefPoint, const VECTOR2I& aStart, const VECTOR2I& aEnd,
int aDist );
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/**
* Return the length of a line segment defined by \a aPointA and \a aPointB.
*
* See also EuclideanNorm and Distance for the single vector or four scalar versions.
*
* @return Length of a line (as double)
*/
inline double GetLineLength( const VECTOR2I& aPointA, const VECTOR2I& aPointB )
{
// Implicitly casted to double
return hypot( aPointA.x - aPointB.x, aPointA.y - aPointB.y );
}
// These are the usual degrees <-> radians conversion routines
inline double DEG2RAD( double deg ) { return deg * M_PI / 180.0; }
inline double RAD2DEG( double rad ) { return rad * 180.0 / M_PI; }
// These are the same *but* work with the internal 'decidegrees' unit
inline double RAD2DECIDEG( double rad ) { return rad * 1800.0 / M_PI; }
/* These are templated over T (and not simply double) because Eeschema
is still using int for angles in some place */
/// Normalize angle to be in the 0.0 .. 360.0 range: angle is in 1/10 degrees.
template <class T> inline T NormalizeAnglePos( T Angle )
{
while( Angle < 0 )
Angle += 3600;
while( Angle >= 3600 )
Angle -= 3600;
return Angle;
}
template <class T> inline void NORMALIZE_ANGLE_POS( T& Angle )
{
Angle = NormalizeAnglePos( Angle );
}
/// Normalize angle to be in the -180.0 .. 180.0 range
template <class T> inline T NormalizeAngle180( T Angle )
{
while( Angle <= -1800 )
Angle += 3600;
while( Angle > 1800 )
Angle -= 3600;
return Angle;
}
/**
* Test if an arc from \a aStartAngle to \a aEndAngle crosses the positive X axis (0 degrees).
*
* Testing is performed in the quadrant 1 to quadrant 4 direction (counter-clockwise).
*
* @param aStartAngle The arc start angle in degrees.
* @param aEndAngle The arc end angle in degrees.
*/
inline bool InterceptsPositiveX( double aStartAngle, double aEndAngle )
{
double end = aEndAngle;
if( aStartAngle > aEndAngle )
end += 360.0;
return aStartAngle < 360.0 && end > 360.0;
}
/**
* Test if an arc from \a aStartAngle to \a aEndAngle crosses the negative X axis (180 degrees).
*
* Testing is performed in the quadrant 1 to quadrant 4 direction (counter-clockwise).
*
* @param aStartAngle The arc start angle in degrees.
* @param aEndAngle The arc end angle in degrees.
*/
inline bool InterceptsNegativeX( double aStartAngle, double aEndAngle )
{
double end = aEndAngle;
if( aStartAngle > aEndAngle )
end += 360.0;
return aStartAngle < 180.0 && end > 180.0;
}
#endif