304 lines
11 KiB
C++
304 lines
11 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) 2018-2023 KiCad Developers, see AUTHORS.txt for contributors.
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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 TRIGO_H
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#define TRIGO_H
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#include <cmath>
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#include <math/vector2d.h>
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#include <geometry/eda_angle.h>
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/**
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* Test if \a aTestPoint is on line defined by \a aSegStart and \a aSegEnd.
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*
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* This function is faster than #TestSegmentHit() because \a aTestPoint should be exactly on
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* the line. This only works for horizontal, vertical, and 45 degree line segments.
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*
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* @param aSegStart The first point of the line segment.
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* @param aSegEnd The second point of the line segment.
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* @param aTestPoint The point to test.
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*
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* @return true if the point is on the line segment.
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*/
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bool IsPointOnSegment( const VECTOR2I& aSegStart, const VECTOR2I& aSegEnd,
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const VECTOR2I& aTestPoint );
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/**
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* Test if two lines intersect.
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*
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* @param a_p1_l1 The first point of the first line.
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* @param a_p2_l1 The second point of the first line.
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* @param a_p1_l2 The first point of the second line.
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* @param a_p2_l2 The second point of the second line.
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* @param aIntersectionPoint is filled with the intersection point if it exists
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* @return bool true if the two segments defined by four points intersect.
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* (i.e. if the 2 segments have at least a common point)
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*/
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bool SegmentIntersectsSegment( const VECTOR2I& a_p1_l1, const VECTOR2I& a_p2_l1,
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const VECTOR2I& a_p1_l2, const VECTOR2I& a_p2_l2,
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VECTOR2I* aIntersectionPoint = nullptr );
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/**
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* Calculate the new point of coord coord pX, pY, for a rotation center 0, 0.
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*/
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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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{
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RotatePoint( &point.x, &point.y, aAngle );
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}
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/**
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* Calculate the new point of coord coord pX, pY, for a rotation center cx, cy.
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*/
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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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{
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RotatePoint( &point.x, &point.y, centre.x, centre.y, aAngle );
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}
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/**
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* Calculate the new coord point point for a rotation center 0, 0.
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*/
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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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{
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RotatePoint( &point.x, &point.y, aAngle );
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}
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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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{
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RotatePoint( &point.x, &point.y, aCenter.x, aCenter.y, aAngle );
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}
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/**
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* Determine the center of an arc or circle given three points on its circumference.
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*
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* @param aStart The starting point of the circle (equivalent to aEnd).
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* @param aMid The point on the arc, half-way between aStart and aEnd.
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* @param aEnd The ending point of the circle (equivalent to aStart).
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* @return The center of the circle.
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*/
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const VECTOR2I CalcArcCenter( const VECTOR2I& aStart, const VECTOR2I& aMid, const VECTOR2I& aEnd );
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const VECTOR2D CalcArcCenter( const VECTOR2D& aStart, const VECTOR2D& aMid, const VECTOR2D& aEnd );
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const VECTOR2D CalcArcCenter( const VECTOR2D& aStart, const VECTOR2D& aEnd,
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const EDA_ANGLE& aAngle );
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/**
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* Return the middle point of an arc, half-way between aStart and aEnd.
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*
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* There are two possible solutions which can be found by toggling aMinArcAngle. The behavior
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* is undefined for semicircles (i.e. 180 degree arcs).
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*
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* @param aStart The starting point of the arc (for calculating the radius).
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* @param aEnd The end point of the arc (for determining the arc angle).
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* @param aCenter The center point of the arc.
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* @param aMinArcAngle If true, returns the point that results in the smallest arc angle.
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* @return The middle point of the arc.
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*/
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const VECTOR2I CalcArcMid( const VECTOR2I& aStart, const VECTOR2I& aEnd, const VECTOR2I& aCenter,
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bool aMinArcAngle = true );
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inline double EuclideanNorm( const VECTOR2I& vector )
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{
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// this is working with doubles
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return hypot( vector.x, vector.y );
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}
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/**
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* Compute the distance between a line and a reference point.
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*
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* Reference: http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
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*
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* @param linePointA Point on line.
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* @param linePointB Point on line.
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* @param referencePoint Reference point.
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*/
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inline double DistanceLinePoint( const VECTOR2I& linePointA, const VECTOR2I& linePointB,
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const VECTOR2I& referencePoint )
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{
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// Some of the multiple double casts are redundant. However in the previous definition
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// the cast was (implicitly) done too late, just before the division (EuclideanNorm gives
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// a double so from int it would be promoted); that means that the whole expression were
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// vulnerable to overflow during int multiplications
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return fabs( ( static_cast<double>( linePointB.x - linePointA.x ) *
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static_cast<double>( linePointA.y - referencePoint.y ) -
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static_cast<double>( linePointA.x - referencePoint.x ) *
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static_cast<double>( linePointB.y - linePointA.y) )
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/ EuclideanNorm( linePointB - linePointA ) );
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}
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/**
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* Test if two points are near each other.
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*
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* @param pointA First point.
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* @param pointB Second point.
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* @param threshold The maximum distance.
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* @return true if \a pointA is within \a threshold of \a pointB otherwise false.
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*/
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inline bool HitTestPoints( const VECTOR2I& pointA, const VECTOR2I& pointB, double threshold )
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{
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VECTOR2I vectorAB = pointB - pointA;
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// Compare the distances squared. The double is needed to avoid overflow during int
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// multiplication
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double sqdistance = (double)vectorAB.x * vectorAB.x + (double)vectorAB.y * vectorAB.y;
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return sqdistance < threshold * threshold;
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}
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/**
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* Test if \a aRefPoint is with \a aDistance on the line defined by \a aStart and \a aEnd..
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*
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* @param aRefPoint = reference point to test
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* @param aStart is the first end-point of the line segment
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* @param aEnd is the second end-point of the line segment
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* @param aDist = maximum distance for hit
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*/
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bool TestSegmentHit( const VECTOR2I& aRefPoint, const VECTOR2I& aStart, const VECTOR2I& aEnd,
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int aDist );
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/**
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* Return the length of a line segment defined by \a aPointA and \a aPointB.
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*
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* See also EuclideanNorm and Distance for the single vector or four scalar versions.
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*
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* @return Length of a line (as double)
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*/
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inline double GetLineLength( const VECTOR2I& aPointA, const VECTOR2I& aPointB )
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{
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return hypot( (double) aPointA.x - aPointB.x, (double) aPointA.y - aPointB.y );
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}
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// These are the usual degrees <-> radians conversion routines
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inline double DEG2RAD( double deg ) { return deg * M_PI / 180.0; }
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inline double RAD2DEG( double rad ) { return rad * 180.0 / M_PI; }
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// These are the same *but* work with the internal 'decidegrees' unit
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inline double RAD2DECIDEG( double rad ) { return rad * 1800.0 / M_PI; }
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/* These are templated over T (and not simply double) because Eeschema
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is still using int for angles in some place */
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/**
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* Normalize angle to be in the 0.0 .. 360.0 range: angle is in 1/10 degrees.
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*/
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template <class T> inline T NormalizeAnglePos( T Angle )
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{
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while( Angle < 0 )
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Angle += 3600;
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while( Angle >= 3600 )
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Angle -= 3600;
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return Angle;
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}
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template <class T> inline void NORMALIZE_ANGLE_POS( T& Angle )
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{
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Angle = NormalizeAnglePos( Angle );
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}
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/**
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* Normalize angle to be in the -180.0 .. 180.0 range.
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*/
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template <class T> inline T NormalizeAngle180( T Angle )
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{
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while( Angle <= -1800 )
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Angle += 3600;
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while( Angle > 1800 )
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Angle -= 3600;
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return Angle;
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}
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/**
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* Test if an arc from \a aStartAngle to \a aEndAngle crosses the positive X axis (0 degrees).
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*
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* Testing is performed in the quadrant 1 to quadrant 4 direction (counter-clockwise).
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*
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* @param aStartAngle The arc start angle in degrees.
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* @param aEndAngle The arc end angle in degrees.
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*/
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inline bool InterceptsPositiveX( double aStartAngle, double aEndAngle )
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{
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double end = aEndAngle;
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if( aStartAngle > aEndAngle )
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end += 360.0;
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return aStartAngle < 360.0 && end > 360.0;
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}
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/**
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* Test if an arc from \a aStartAngle to \a aEndAngle crosses the negative X axis (180 degrees).
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*
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* Testing is performed in the quadrant 1 to quadrant 4 direction (counter-clockwise).
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*
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* @param aStartAngle The arc start angle in degrees.
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* @param aEndAngle The arc end angle in degrees.
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*/
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inline bool InterceptsNegativeX( double aStartAngle, double aEndAngle )
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{
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double end = aEndAngle;
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if( aStartAngle > aEndAngle )
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end += 360.0;
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return aStartAngle < 180.0 && end > 180.0;
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}
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/**
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* Calculate the area of a parallelogram defined by \a aPointA, \a aPointB, and \a aPointC.
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* B ______________________
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* / /
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* / /
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* /______________________/
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* A C
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* The area of a parallelogram is the cross product of the vectors A->B and A->C.
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* The order of the vertices is not important, the result will be the same (modulo sign).
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*/
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template <class T>
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inline typename VECTOR2<T>::extended_type
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ParallelogramArea( const VECTOR2<T>& aPointA, const VECTOR2<T>& aPointB, const VECTOR2<T>& aPointC )
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{
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VECTOR2<T> v1 = aPointB - aPointA;
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VECTOR2<T> v2 = aPointC - aPointA;
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return v1.Cross( v2 );
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}
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/**
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* Test if a point hits a line segment within a given distance. This is a faster version of
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* TestSegmentHit() that does not calculate the distance.
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*/
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bool TestSegmentHitFast( const VECTOR2I& aRefPoint, const VECTOR2I& aStart, const VECTOR2I& aEnd,
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int aDist );
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#endif
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