/** * @file trigo.cpp * @brief Trigonometric and geometric basic functions. */ #include #include #include #include #include /* 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( 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 ) EXCHG( 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 ) EXCHG( 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 } int ArcTangente( int dy, int dx ) { double fangle; 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; } fangle = atan2( (double) dy, (double) dx ) / M_PI * 1800; return KiROUND( fangle ); } void RotatePoint( int* pX, int* pY, double angle ) { int tmp; while( angle < 0 ) angle += 3600; while( angle >= 3600 ) angle -= 3600; // 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 = DEG2RAD( angle / 10.0 ); 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; while( angle < 0 ) angle += 3600; while( angle >= 3600 ) angle -= 3600; // 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 = DEG2RAD( angle / 10.0 ); double sinus = sin( fangle ); double cosinus = cos( fangle ); double fpx = (*pY * sinus ) + (*pX * cosinus ); double fpy = (*pY * cosinus ) - (*pX * sinus ); *pX = fpx; *pY = fpy; } } double EuclideanNorm( wxPoint vector ) { return hypot( (double) vector.x, (double) vector.y ); } double DistanceLinePoint( wxPoint linePointA, wxPoint linePointB, wxPoint referencePoint ) { return fabs( (double) ( (linePointB.x - linePointA.x) * (linePointA.y - referencePoint.y) - (linePointA.x - referencePoint.x ) * (linePointB.y - linePointA.y) ) / EuclideanNorm( linePointB - linePointA ) ); } bool HitTestPoints( wxPoint pointA, wxPoint pointB, double threshold ) { wxPoint vectorAB = pointB - pointA; double distance = EuclideanNorm( vectorAB ); return distance < threshold; } double CrossProduct( wxPoint vectorA, wxPoint vectorB ) { return (double)vectorA.x * vectorB.y - (double)vectorA.y * vectorB.x; } double GetLineLength( const wxPoint& aPointA, const wxPoint& aPointB ) { return hypot( (double) aPointA.x - (double) aPointB.x, (double) aPointA.y - (double) aPointB.y ); }