C ++ solves common Geometric Problems in plane computing

C ++ solves common Geometric Problems in plane computing

By encapsulating common point and line segment types, and providing calculation of the relationship between points and lines, this provides a basic framework for compiling the ry tool library.

The Code is as follows: (the Code correctness still needs to be tested and used with caution)

 

// Reference // www.bkjia.com/www.bkjia.com/?toolbox: Geometry algorithm toolboxauthor: alaclpemail: alaclp@qq.compublish date: */# include
 
  
# Include
  
   
# Include
   
    
Using namespace std; // predefined # define Min (x, y) (x) <(y )? (X): (y) # define Max (x, y) (x)> (y )? (X): (y) // Point Object typedef struct Point {double x, y; // constructor Point (double x, double y): x (x ), y (y) {}// Point (): x (0), y (0) When no parameter is set) {} // obtain the distance from the pt Point to double distance (const Point & pt) {return sqrt (x-pt. x) * (x-pt. x) + (y-pt. y) * (y-pt. y);} // determine whether two points are at the same Point bool equal (const Point & pt) {return (x-pt. x) = 0) & (y-pt. y = 0) ;}} Point; // line segment object typedef struct PartLine {Point pa, pb; double length; PartLine () {Length = 0;} // constructor PartLine (Point pa, Point pb): pa (pa), pb (pb) {length = sqrt (pa. x-pb. x) * (pa. x-pb. x) + (pa. y-pb. y) * (pa. y-pb. y);} void assign (const PartLine & pl) {pa = pl. pa; pb = pl. pb; length = pl. length;} // calculate the vertical distance from a point to a line segment using the cross product. // note: the distance between the result is positive and negative. // If the pc point is in the counterclockwise direction, the distance is positive; otherwise, the distance is the sub-value double getDistantToPoint (Point pc) {double area = crossProd (pc)/2; return area * 2/length;/* use the Helen formula to calculate PartLine pl1 (This-> pa, pc), pl2 (this-> pb, pc); double l1 = this-> length, l2 = pl1.length, l3 = pl2.length; double s = (l1 + l2 + l3)/2; // Helen formula double area = sqrt (s * (s-l1) * (s-l2) * (s-l3); return area * 2/l1; * // cross product of the vector/* Cross Product of the calculated vector (ABxAC A (x1, y1) B (x2, y2) C (x3, y3) is the result of calculating the deciding factor | x1-x0 y1-y0 | x2-x0 y2-y0 |) * // calculate the cross product of AB and AC --- the absolute value of the cross product is the area of the parallelogram formed by the two vectors double crossProd (Point & pc) {// calculate AB X acret Urn (pb. x-pa. x) * (pc. y-pa. y)-(pb. y-pa. y) * (pc. x-pa. x) ;}// determine whether the two line segments overlap bool isIntersected (PartLine & pl) {double d1, d2, d3, d4, d5, d6; d1 = pl. crossProd (pb); d2 = pl. crossProd (pa); d3 = crossProd (pl. pa); d4 = crossProd (pl. pb); d5 = crossProd (pl. pa); d6 = crossProd (pl. pb); // printf (% f, d1, d2, d3, d4, d5, d6 ); bool cond1 = d1 * d2 <= 0, // cond2 = d3 * d4 <= 0 for pb and pa on both sides of pl or on the extension line of a line segment or line segment, // Pl. pa and pl. pb are on both sides of this or on the extension line of a line segment or line segment. cond3 = d5! = 0, // pl. pa is not on the line segment and extension line. cond4 = d6! = 0; // pl. pb does not return cond1 & cond2 & cond3 & cond4;} // determines whether the two parts are parallel to bool isParallel (PartLine & pl) {double v1 = crossProd (pl. pa), v2 = crossProd (pl. pb); return (v1 = v2) & (v1! = 0);} // rotate thetaPartLine rotateA (double theta) {float nx = pa. x + (pb. x-pa. x) * cos (theta)-(pb. y-pa. y) * sin (theta), ny = pa. y + (pb. x-pa. x) * sin (theta) + (pb. y-pa. y) * cos (theta); return PartLine (pa, Point (nx, ny);} // rotate thetaPartLine rotateB (double theta) {float nx = pb. x + (pa. x-pb. x) * cos (theta)-(pa. y-pb. y) * sin (theta), ny = pb. y + (pa. x-pb. x) * sin (theta) + (pa. y-pb. y) * Cos (theta); return PartLine (Point (nx, ny), pb);} // determine whether two line segments overlap or are collocated bool inSameLine (PartLine & pl) {double v1 = crossProd (pl. pa), v2 = crossProd (pl. pb); if (v1! = V2) return false; if (v1! = 0) return false; return true;} // get the intersection of two line segments --- if there is no intersection, return valid = false // If there are multiple intersections, warning Point getCrossPoint (PartLine & pl, bool & valid) {valid = false; if (! IsIntersected (pl) {// returns Point ();} if (inSameLine (pl) {// returns if (pa. equal (pl. pa) {valid = true; return pa;} if (pa. equal (pl. pb) {valid = true; return pa;} if (pb. equal (pl. pa) {valid = true; return pb;} if (pb. equal (pl. pb) {valid = true; return pb;} // multiple focus cout <error: the number of intersection result calculation results is infinite <endl; valid = false; return Point ();} // Intersection Point pt1, pt2, pt3, result; pt1 = pa; pt2 = p B; pt3.x = (pt1.x + pt2.x)/2; pt3.y = (pt1.y + pt2.y)/2; double L1 = pl. crossProd (pt1), L2 = pl. crossProd (pt2), L3 = pl. crossProd (pt3); printf (% f = % f, L1, L2, L3, L1 + L2); while (fabs (L1)> 1e-7 | fabs (L2)> 1e-7) {valid = true; if (fabs (L1) <fabs (L2) pt2 = pt3; else pt1 = pt3; pt3.x = (pt1.x + pt2.x)/2; pt3.y = (pt1.y + pt2.y)/2; result = pt3; L1 = pl. crossProd (pt1), L2 = pl. crossProd (pt2 ), L3 = pl. crossProd (pt3); printf (% f = % f, L1, L2, L3, L1-L2);} return pt3 ;} // obtain the Point getNearestPointToPoint (Point & pt) {Point pt1, pt2, pt3, result; pt1 = pa; pt2 = pb on the line segment; pt3.x = (pt1.x + pt2.x)/2; pt3.y = (pt1.y + pt2.y)/2; double L1 = pt1.distance (pt), L2 = pt2.distance (pt ), l3 = pt3.distance (pt); if (L1 = L2) return pt3; while (fabs (L1-L2)> 1e-7) {if (L1 <L2) pt2 = pt3; else pt1 = pt 3; pt3.x = (pt1.x + pt2.x)/2; pt3.y = (pt1.y + pt2.y)/2; result = pt3; L1 = pt1.distance (pt); L2 = pt2.distance (pt ); l3 = pt3.distance (pt); // printf (% f = % f, L1, L2, L3, L1-L2);} return result ;} // obtain the image Point getaskpoint (Point & pc) {}} PartLine on a Point online segment; int main (void) {Point p1 (0, 0 ), p2 (1, 1), p3 (0, 1.1), p4 (0.5, 0.5 + 1e-10), p5 (0.5, 0.5-1e-10), np; PartLine pl1 (p1, p2), pl2 (p3, p4), pl3 (p3, p5 ); Cout <pl1.getDistantToPoint (p3) <endl; cout <intersection of line segments 1 and 2? <Pl1.isIntersected (pl2) <endl; np = pl1.getNearestPointToPoint (p5); cout <closest point: <np. x <, <np. y <endl; bool isvalid; np = pl1.getCrossPoint (pl3, isvalid); cout <intersection of two line segments: <(isvalid? Valid: Invalid) <= <np. x <, <np. y <endl; PartLine plx = pl1.rotateA (M_PI/2); printf (after 90 degrees rotation: % f, plx. pa. x, plx. pa. y, plx. pb. x, plx. pb. y); return 0 ;}