kicad/libs/kimath/include/trigo.h

443 lines
13 KiB
C++

/*
* 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
#include <cmath>
#include <math/vector2d.h>
#include <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 );
/*
* Calculate the new point of coord coord pX, pY,
* for a rotation center 0, 0, and angle in (1/10 degree)
*/
void RotatePoint( int *pX, int *pY, double angle );
inline void RotatePoint( int *pX, int *pY, EDA_ANGLE angle )
{
RotatePoint( pX, pY, angle.AsTenthsOfADegree() );
}
/*
* Calculate the new point of coord coord pX, pY,
* for a rotation center cx, cy, and angle in (1/10 degree)
*/
void RotatePoint( int *pX, int *pY, int cx, int cy, double angle );
/*
* Calculate the new coord point point for a rotation angle in (1/10 degree).
*/
inline void RotatePoint( VECTOR2I& point, double angle )
{
RotatePoint( &point.x, &point.y, angle );
}
inline void RotatePoint( VECTOR2I& point, EDA_ANGLE angle )
{
RotatePoint( &point.x, &point.y, angle.AsTenthsOfADegree() );
}
void RotatePoint( VECTOR2I& point, const VECTOR2I& centre, double angle );
inline void RotatePoint( VECTOR2I& point, const VECTOR2I& centre, EDA_ANGLE angle )
{
RotatePoint( point, centre, angle.AsTenthsOfADegree() );
}
/*
* Calculate the new coord point point for a center rotation center and angle in (1/10 degree).
*/
void RotatePoint( double *pX, double *pY, double angle );
void RotatePoint( double *pX, double *pY, double cx, double cy, double angle );
/**
* 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 VECTOR2I CalcArcCenter( const VECTOR2I& aStart, const VECTOR2I& aEnd, double aAngle );
/**
* Return the subtended angle for a given arc.
*/
double CalcArcAngle( const VECTOR2I& aStart, const VECTOR2I& aMid, const VECTOR2I& aEnd );
/**
* 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 );
/* Return the arc tangent of 0.1 degrees coord vector dx, dy
* between -1800 and 1800
* Equivalent to atan2 (but faster for calculations if
* the angle is 0 to -1800, or + - 900)
* Lorenzo: In fact usually atan2 already has to do these optimizations
* (due to the discontinuity in tan) but this function also returns
* in decidegrees instead of radians, so it's handier
*/
double ArcTangente( int dy, int dx );
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 )
{
// 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
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;
// Compare the distances squared. The double is needed to avoid
// overflow during int multiplication
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
* @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 );
/**
* 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 DECIDEG2RAD( double deg ) { return deg * M_PI / 1800.0; }
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 >=-360.0 and <= 360.0
/// Angle can be equal to -360 or +360
template <class T> inline T NormalizeAngle360Max( T Angle )
{
while( Angle < -3600 )
Angle += 3600;
while( Angle > 3600 )
Angle -= 3600;
return Angle;
}
/// Normalize angle to be > -360.0 and < 360.0
/// Angle equal to -360 or +360 are set to 0
template <class T> inline T NormalizeAngle360Min( T Angle )
{
while( Angle <= -3600 )
Angle += 3600;
while( Angle >= 3600 )
Angle -= 3600;
return Angle;
}
/// Normalize angle to be in the 0.0 .. -360.0 range: angle is in 1/10 degrees.
template <class T>
inline T NormalizeAngleNeg( T Angle )
{
while( Angle <= -3600 )
Angle += 3600;
while( Angle > 0 )
Angle -= 3600;
return Angle;
}
/// 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 0.0 .. 360.0 range: angle is in degrees.
inline double NormalizeAngleDegreesPos( double Angle )
{
while( Angle < 0 )
Angle += 360.0;
while( Angle >= 360.0 )
Angle -= 360.0;
return Angle;
}
inline void NORMALIZE_ANGLE_DEGREES_POS( double& Angle )
{
Angle = NormalizeAngleDegreesPos( Angle );
}
inline double NormalizeAngleRadiansPos( double Angle )
{
while( Angle < 0 )
Angle += (2 * M_PI );
while( Angle >= ( 2 * M_PI ) )
Angle -= ( 2 * M_PI );
return Angle;
}
/// Normalize angle to be aMin < angle <= aMax angle is in degrees.
inline double NormalizeAngleDegrees( double Angle, double aMin, double aMax )
{
while( Angle < aMin )
Angle += 360.0;
while( Angle >= aMax )
Angle -= 360.0;
return Angle;
}
/// Add two angles (keeping the result normalized). T2 is here
// because most of the time it's an int (and templates don't promote in
// that way)
template <class T, class T2> inline T AddAngles( T a1, T2 a2 )
{
a1 += a2;
NORMALIZE_ANGLE_POS( a1 );
return a1;
}
template <class T> inline T NegateAndNormalizeAnglePos( T Angle )
{
Angle = -Angle;
while( Angle < 0 )
Angle += 3600;
while( Angle >= 3600 )
Angle -= 3600;
return Angle;
}
template <class T> inline void NEGATE_AND_NORMALIZE_ANGLE_POS( T& Angle )
{
Angle = NegateAndNormalizeAnglePos( Angle );
}
/// Normalize angle to be in the -90.0 .. 90.0 range
template <class T> inline T NormalizeAngle90( T Angle )
{
while( Angle < -900 )
Angle += 1800;
while( Angle > 900 )
Angle -= 1800;
return Angle;
}
template <class T> inline void NORMALIZE_ANGLE_90( T& Angle )
{
Angle = NormalizeAngle90( 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;
}
template <class T> inline void NORMALIZE_ANGLE_180( T& Angle )
{
Angle = NormalizeAngle180( 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;
}
/**
* Circle generation utility: computes r * sin(a)
* Where a is in decidegrees, not in radians.
*/
inline double sindecideg( double r, double a )
{
return r * sin( DECIDEG2RAD( a ) );
}
/**
* Circle generation utility: computes r * cos(a)
* Where a is in decidegrees, not in radians.
*/
inline double cosdecideg( double r, double a )
{
return r * cos( DECIDEG2RAD( a ) );
}
#endif