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+/*
+ * This program source code file is part of KiCad, a free EDA CAD application.
+ *
+ * Copyright (C) 2014 Jean-Pierre Charras, jp.charras at wanadoo.fr
+ * Copyright (C) 2014 KiCad Developers, see CHANGELOG.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
+ */
+
+/**
+ * @file trigo.cpp
+ * @brief Trigonometric and geometric basic functions.
+ */
+
+#include <fctsys.h>
+#include <macros.h>
+#include <trigo.h>
+#include <common.h>
+#include <math_for_graphics.h>
+
+// Returns true if the point P is on the segment S.
+// faster than TestSegmentHit() because P should be exactly on S
+// therefore works fine only for H, V and 45 deg segm (suitable for wires in eeschema)
+bool IsPointOnSegment( const wxPoint& aSegStart, const wxPoint& aSegEnd,
+ const wxPoint& aTestPoint )
+{
+ wxPoint vectSeg = aSegEnd - aSegStart; // Vector from S1 to S2
+ wxPoint vectPoint = aTestPoint - aSegStart; // Vector from S1 to P
+
+ // Use long long here to avoid overflow in calculations
+ if( (long long) vectSeg.x * vectPoint.y - (long long) vectSeg.y * vectPoint.x )
+ return false; /* Cross product non-zero, vectors not parallel */
+
+ if( ( (long long) vectSeg.x * vectPoint.x + (long long) vectSeg.y * vectPoint.y ) <
+ ( (long long) vectPoint.x * vectPoint.x + (long long) vectPoint.y * vectPoint.y ) )
+ return false; /* Point not on segment */
+
+ return true;
+}
+
+
+// Returns true if the segment 1 intersectd the segment 2.
+bool SegmentIntersectsSegment( const wxPoint &a_p1_l1, const wxPoint &a_p2_l1,
+ const wxPoint &a_p1_l2, const wxPoint &a_p2_l2 )
+{
+
+ //We are forced to use 64bit ints because the internal units can oveflow 32bit ints when
+ // multiplied with each other, the alternative would be to scale the units down (i.e. divide
+ // by a fixed number).
+ long long dX_a, dY_a, dX_b, dY_b, dX_ab, dY_ab;
+ long long num_a, num_b, den;
+
+ //Test for intersection within the bounds of both line segments using line equations of the
+ // form:
+ // x_k(u_k) = u_k * dX_k + x_k(0)
+ // y_k(u_k) = u_k * dY_k + y_k(0)
+ // with 0 <= u_k <= 1 and k = [ a, b ]
+
+ dX_a = a_p2_l1.x - a_p1_l1.x;
+ dY_a = a_p2_l1.y - a_p1_l1.y;
+ dX_b = a_p2_l2.x - a_p1_l2.x;
+ dY_b = a_p2_l2.y - a_p1_l2.y;
+ dX_ab = a_p1_l2.x - a_p1_l1.x;
+ dY_ab = a_p1_l2.y - a_p1_l1.y;
+
+ den = dY_a * dX_b - dY_b * dX_a ;
+
+ //Check if lines are parallel
+ if( den == 0 )
+ return false;
+
+ num_a = dY_ab * dX_b - dY_b * dX_ab;
+ num_b = dY_ab * dX_a - dY_a * dX_ab;
+
+ //We wont calculate directly the u_k of the intersection point to avoid floating point
+ // division but they could be calculated with:
+ // u_a = (float) num_a / (float) den;
+ // u_b = (float) num_b / (float) den;
+
+ if( den < 0 )
+ {
+ den = -den;
+ num_a = -num_a;
+ num_b = -num_b;
+ }
+
+ //Test sign( u_a ) and return false if negative
+ if( num_a < 0 )
+ return false;
+
+ //Test sign( u_b ) and return false if negative
+ if( num_b < 0 )
+ return false;
+
+ //Test to ensure (u_a <= 1)
+ if( num_a > den )
+ return false;
+
+ //Test to ensure (u_b <= 1)
+ if( num_b > den )
+ return false;
+
+ return true;
+}
+
+
+/* Function TestSegmentHit
+ * test for hit on line segment
+ * i.e. a reference point is within a given distance from segment
+ * aRefPoint = reference point to test
+ * aStart, aEnd are coordinates of end points segment
+ * aDist = maximum distance for hit
+ * Note: for calculation time reasons, the distance between the ref point
+ * and the segment is not always exactly calculated
+ * (we only know if the actual dist is < aDist, not exactly know this dist.
+ * Because many times we have horizontal or vertical segments,
+ * a special calcultaion is made for them
+ * Note: sometimes we need to calculate the distande between 2 points
+ * A square root should be calculated.
+ * However, because we just compare 2 distnaces, to avoid calculating square root,
+ * the square of distances are compared.
+*/
+static inline double square( int x ) // helper function to calculate x*x
+{
+ return (double) x * x;
+}
+bool TestSegmentHit( const wxPoint &aRefPoint, wxPoint aStart,
+ wxPoint aEnd, int aDist )
+{
+ // test for vertical or horizontal segment
+ if( aEnd.x == aStart.x )
+ {
+ // vertical segment
+ int ll = abs( aRefPoint.x - aStart.x );
+
+ if( ll > aDist )
+ return false;
+
+ // To have only one case to examine, ensure aEnd.y > aStart.y
+ if( aEnd.y < aStart.y )
+ std::swap( aStart.y, aEnd.y );
+
+ if( aRefPoint.y <= aEnd.y && aRefPoint.y >= aStart.y )
+ return true;
+
+ // there is a special case: x,y near an end point (distance < dist )
+ // the distance should be carefully calculated
+ if( (aStart.y - aRefPoint.y) < aDist )
+ {
+ double dd = square( aRefPoint.x - aStart.x) +
+ square( aRefPoint.y - aStart.y );
+ if( dd <= square( aDist ) )
+ return true;
+ }
+
+ if( (aRefPoint.y - aEnd.y) < aDist )
+ {
+ double dd = square( aRefPoint.x - aEnd.x ) +
+ square( aRefPoint.y - aEnd.y );
+ if( dd <= square( aDist ) )
+ return true;
+ }
+ }
+ else if( aEnd.y == aStart.y )
+ {
+ // horizontal segment
+ int ll = abs( aRefPoint.y - aStart.y );
+
+ if( ll > aDist )
+ return false;
+
+ // To have only one case to examine, ensure xf > xi
+ if( aEnd.x < aStart.x )
+ std::swap( aStart.x, aEnd.x );
+
+ if( aRefPoint.x <= aEnd.x && aRefPoint.x >= aStart.x )
+ return true;
+
+ // there is a special case: x,y near an end point (distance < dist )
+ // the distance should be carefully calculated
+ if( (aStart.x - aRefPoint.x) <= aDist )
+ {
+ double dd = square( aRefPoint.x - aStart.x ) +
+ square( aRefPoint.y - aStart.y );
+ if( dd <= square( aDist ) )
+ return true;
+ }
+
+ if( (aRefPoint.x - aEnd.x) <= aDist )
+ {
+ double dd = square( aRefPoint.x - aEnd.x ) +
+ square( aRefPoint.y - aEnd.y );
+ if( dd <= square( aDist ) )
+ return true;
+ }
+ }
+ else
+ {
+ // oblique segment:
+ // First, we need to calculate the distance between the point
+ // and the line defined by aStart and aEnd
+ // this dist should be < dist
+ //
+ // find a,slope such that aStart and aEnd lie on y = a + slope*x
+ double slope = (double) (aEnd.y - aStart.y) / (aEnd.x - aStart.x);
+ double a = (double) aStart.y - slope * aStart.x;
+ // find c,orthoslope such that (x,y) lies on y = c + orthoslope*x,
+ // where orthoslope=(-1/slope)
+ // to calculate xp, yp = near point from aRefPoint
+ // which is on the line defined by aStart, aEnd
+ double orthoslope = -1.0 / slope;
+ double c = (double) aRefPoint.y - orthoslope * aRefPoint.x;
+ // find nearest point to (x,y) on line defined by aStart, aEnd
+ double xp = (a - c) / (orthoslope - slope);
+ double yp = a + slope * xp;
+ // find distance to line, in fact the square of dist,
+ // because we just know if it is > or < aDist
+ double dd = square( aRefPoint.x - xp ) + square( aRefPoint.y - yp );
+ double dist = square( aDist );
+
+ if( dd > dist ) // this reference point is not a good candiadte.
+ return false;
+
+ // dd is < dist, therefore we should make a fine test
+ if( fabs( slope ) > 0.7 )
+ {
+ // line segment more vertical than horizontal
+ if( (aEnd.y > aStart.y && yp <= aEnd.y && yp >= aStart.y) ||
+ (aEnd.y < aStart.y && yp >= aEnd.y && yp <= aStart.y) )
+ return true;
+ }
+ else
+ {
+ // line segment more horizontal than vertical
+ if( (aEnd.x > aStart.x && xp <= aEnd.x && xp >= aStart.x) ||
+ (aEnd.x < aStart.x && xp >= aEnd.x && xp <= aStart.x) )
+ return true;
+ }
+
+ // Here, the test point is still a good candidate,
+ // however it is not "between" the end points of the segment.
+ // It is "outside" the segment, but it could be near a segment end point
+ // Therefore, we test the dist from the test point to each segment end point
+ dd = square( aRefPoint.x - aEnd.x ) + square( aRefPoint.y - aEnd.y );
+ if( dd <= dist )
+ return true;
+ dd = square( aRefPoint.x - aStart.x ) + square( aRefPoint.y - aStart.y );
+ if( dd <= dist )
+ return true;
+ }
+
+ return false; // no hit
+}
+
+
+double ArcTangente( int dy, int dx )
+{
+
+ /* gcc is surprisingly smart in optimizing these conditions in
+ a tree! */
+
+ if( dx == 0 && dy == 0 )
+ return 0;
+
+ if( dy == 0 )
+ {
+ if( dx >= 0 )
+ return 0;
+ else
+ return -1800;
+ }
+
+ if( dx == 0 )
+ {
+ if( dy >= 0 )
+ return 900;
+ else
+ return -900;
+ }
+
+ if( dx == dy )
+ {
+ if( dx >= 0 )
+ return 450;
+ else
+ return -1800 + 450;
+ }
+
+ if( dx == -dy )
+ {
+ if( dx >= 0 )
+ return -450;
+ else
+ return 1800 - 450;
+ }
+
+ // Of course dy and dx are treated as double
+ return RAD2DECIDEG( atan2( dy, dx ) );
+}
+
+
+void RotatePoint( int* pX, int* pY, double angle )
+{
+ int tmp;
+
+ NORMALIZE_ANGLE_POS( angle );
+
+ // Cheap and dirty optimizations for 0, 90, 180, and 270 degrees.
+ if( angle == 0 )
+ return;
+
+ if( angle == 900 ) /* sin = 1, cos = 0 */
+ {
+ tmp = *pX;
+ *pX = *pY;
+ *pY = -tmp;
+ }
+ else if( angle == 1800 ) /* sin = 0, cos = -1 */
+ {
+ *pX = -*pX;
+ *pY = -*pY;
+ }
+ else if( angle == 2700 ) /* sin = -1, cos = 0 */
+ {
+ tmp = *pX;
+ *pX = -*pY;
+ *pY = tmp;
+ }
+ else
+ {
+ double fangle = DECIDEG2RAD( angle );
+ double sinus = sin( fangle );
+ double cosinus = cos( fangle );
+ double fpx = (*pY * sinus ) + (*pX * cosinus );
+ double fpy = (*pY * cosinus ) - (*pX * sinus );
+ *pX = KiROUND( fpx );
+ *pY = KiROUND( fpy );
+ }
+}
+
+
+void RotatePoint( int* pX, int* pY, int cx, int cy, double angle )
+{
+ int ox, oy;
+
+ ox = *pX - cx;
+ oy = *pY - cy;
+
+ RotatePoint( &ox, &oy, angle );
+
+ *pX = ox + cx;
+ *pY = oy + cy;
+}
+
+
+void RotatePoint( wxPoint* point, const wxPoint& centre, double angle )
+{
+ int ox, oy;
+
+ ox = point->x - centre.x;
+ oy = point->y - centre.y;
+
+ RotatePoint( &ox, &oy, angle );
+ point->x = ox + centre.x;
+ point->y = oy + centre.y;
+}
+
+
+void RotatePoint( double* pX, double* pY, double cx, double cy, double angle )
+{
+ double ox, oy;
+
+ ox = *pX - cx;
+ oy = *pY - cy;
+
+ RotatePoint( &ox, &oy, angle );
+
+ *pX = ox + cx;
+ *pY = oy + cy;
+}
+
+
+void RotatePoint( double* pX, double* pY, double angle )
+{
+ double tmp;
+
+ NORMALIZE_ANGLE_POS( angle );
+
+ // Cheap and dirty optimizations for 0, 90, 180, and 270 degrees.
+ if( angle == 0 )
+ return;
+
+ if( angle == 900 ) /* sin = 1, cos = 0 */
+ {
+ tmp = *pX;
+ *pX = *pY;
+ *pY = -tmp;
+ }
+ else if( angle == 1800 ) /* sin = 0, cos = -1 */
+ {
+ *pX = -*pX;
+ *pY = -*pY;
+ }
+ else if( angle == 2700 ) /* sin = -1, cos = 0 */
+ {
+ tmp = *pX;
+ *pX = -*pY;
+ *pY = tmp;
+ }
+ else
+ {
+ double fangle = DECIDEG2RAD( angle );
+ double sinus = sin( fangle );
+ double cosinus = cos( fangle );
+
+ double fpx = (*pY * sinus ) + (*pX * cosinus );
+ double fpy = (*pY * cosinus ) - (*pX * sinus );
+ *pX = fpx;
+ *pY = fpy;
+ }
+}
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