443 lines
13 KiB
C++
443 lines
13 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) 2018-2021 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 <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 works fine only for H, V 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,
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* for a rotation center 0, 0, and angle in (1/10 degree)
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*/
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void RotatePoint( int *pX, int *pY, double angle );
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inline void RotatePoint( int *pX, int *pY, EDA_ANGLE angle )
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{
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RotatePoint( pX, pY, angle.AsTenthsOfADegree() );
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}
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/*
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* Calculate the new point of coord coord pX, pY,
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* for a rotation center cx, cy, and angle in (1/10 degree)
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*/
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void RotatePoint( int *pX, int *pY, int cx, int cy, double angle );
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/*
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* Calculate the new coord point point for a rotation angle in (1/10 degree).
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*/
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inline void RotatePoint( VECTOR2I& point, double angle )
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{
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RotatePoint( &point.x, &point.y, angle );
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}
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inline void RotatePoint( VECTOR2I& point, EDA_ANGLE angle )
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{
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RotatePoint( &point.x, &point.y, angle.AsTenthsOfADegree() );
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}
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void RotatePoint( VECTOR2I& point, const VECTOR2I& centre, double angle );
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inline void RotatePoint( VECTOR2I& point, const VECTOR2I& centre, EDA_ANGLE angle )
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{
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RotatePoint( point, centre, angle.AsTenthsOfADegree() );
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}
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/*
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* Calculate the new coord point point for a center rotation center and angle in (1/10 degree).
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*/
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void RotatePoint( double *pX, double *pY, double angle );
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void RotatePoint( double *pX, double *pY, double cx, double cy, double angle );
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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 VECTOR2I CalcArcCenter( const VECTOR2I& aStart, const VECTOR2I& aEnd, double aAngle );
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/**
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* Return the subtended angle for a given arc.
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*/
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double CalcArcAngle( const VECTOR2I& aStart, const VECTOR2I& aMid, const VECTOR2I& aEnd );
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/**
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* Return the middle point of an arc, half-way between aStart and aEnd. There are two possible
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* solutions which can be found by toggling aMinArcAngle. The behaviour is undefined for
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* 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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/* Return the arc tangent of 0.1 degrees coord vector dx, dy
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* between -1800 and 1800
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* Equivalent to atan2 (but faster for calculations if
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* the angle is 0 to -1800, or + - 900)
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* Lorenzo: In fact usually atan2 already has to do these optimizations
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* (due to the discontinuity in tan) but this function also returns
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* in decidegrees instead of radians, so it's handier
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*/
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double ArcTangente( int dy, int dx );
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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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//! @brief Compute the distance between a line and a reference point
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//! Reference: http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
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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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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
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// definition the cast was (implicitly) done too late, just before
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// the division (EuclideanNorm gives a double so from int it would
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// 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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//! @brief Test, if two points are near each other
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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 or false
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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
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// overflow during int 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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// Implicitly casted to double
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return hypot( aPointA.x - aPointB.x, 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 DECIDEG2RAD( double deg ) { return deg * M_PI / 1800.0; }
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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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/// Normalize angle to be >=-360.0 and <= 360.0
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/// Angle can be equal to -360 or +360
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template <class T> inline T NormalizeAngle360Max( T Angle )
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{
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while( Angle < -3600 )
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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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/// Normalize angle to be > -360.0 and < 360.0
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/// Angle equal to -360 or +360 are set to 0
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template <class T> inline T NormalizeAngle360Min( T Angle )
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{
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while( Angle <= -3600 )
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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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/// Normalize angle to be in the 0.0 .. -360.0 range: angle is in 1/10 degrees.
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template <class T>
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inline T NormalizeAngleNeg( T Angle )
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{
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while( Angle <= -3600 )
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Angle += 3600;
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while( Angle > 0 )
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Angle -= 3600;
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return Angle;
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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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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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/// Normalize angle to be in the 0.0 .. 360.0 range: angle is in degrees.
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inline double NormalizeAngleDegreesPos( double Angle )
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{
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while( Angle < 0 )
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Angle += 360.0;
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while( Angle >= 360.0 )
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Angle -= 360.0;
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return Angle;
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}
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inline void NORMALIZE_ANGLE_DEGREES_POS( double& Angle )
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{
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Angle = NormalizeAngleDegreesPos( Angle );
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}
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inline double NormalizeAngleRadiansPos( double Angle )
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{
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while( Angle < 0 )
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Angle += (2 * M_PI );
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while( Angle >= ( 2 * M_PI ) )
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Angle -= ( 2 * M_PI );
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return Angle;
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}
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/// Normalize angle to be aMin < angle <= aMax angle is in degrees.
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inline double NormalizeAngleDegrees( double Angle, double aMin, double aMax )
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{
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while( Angle < aMin )
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Angle += 360.0;
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while( Angle >= aMax )
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Angle -= 360.0;
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return Angle;
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}
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/// Add two angles (keeping the result normalized). T2 is here
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// because most of the time it's an int (and templates don't promote in
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// that way)
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template <class T, class T2> inline T AddAngles( T a1, T2 a2 )
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{
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a1 += a2;
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NORMALIZE_ANGLE_POS( a1 );
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return a1;
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}
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template <class T> inline T NegateAndNormalizeAnglePos( T Angle )
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{
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Angle = -Angle;
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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 NEGATE_AND_NORMALIZE_ANGLE_POS( T& Angle )
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{
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Angle = NegateAndNormalizeAnglePos( Angle );
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}
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/// Normalize angle to be in the -90.0 .. 90.0 range
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template <class T> inline T NormalizeAngle90( T Angle )
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{
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while( Angle < -900 )
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Angle += 1800;
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while( Angle > 900 )
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Angle -= 1800;
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return Angle;
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}
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template <class T> inline void NORMALIZE_ANGLE_90( T& Angle )
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{
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Angle = NormalizeAngle90( Angle );
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}
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/// Normalize angle to be in the -180.0 .. 180.0 range
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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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template <class T> inline void NORMALIZE_ANGLE_180( T& Angle )
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{
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Angle = NormalizeAngle180( 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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* Circle generation utility: computes r * sin(a)
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* Where a is in decidegrees, not in radians.
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*/
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inline double sindecideg( double r, double a )
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{
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return r * sin( DECIDEG2RAD( a ) );
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}
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/**
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* Circle generation utility: computes r * cos(a)
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* Where a is in decidegrees, not in radians.
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*/
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inline double cosdecideg( double r, double a )
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{
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return r * cos( DECIDEG2RAD( a ) );
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}
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#endif
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