#ifndef __2d_h #define __2d_h #include #include "danStuff.h" /******************************* all angles are in rads less polar, which is in degs for cartesian, X is amplitude, and Y is the angle in degrees *******************************/ #define pt2 pt #define pt(X,Y) ((point2d_t){X,Y}) #define l2d(A,B) ((line2d_t){A,B}) #define rotCos(A) cos(deg2rad(A)) #define rotSin(A) sin(deg2rad(A)) #define point2dDistSquared(A,B) (SQR(A.x-B.x)+SQR(A.y-B.y)) #define geom2dOriginDistP(A) (sqrt(SQR(A.x)+SQR(A.y)) ) // the dot product will tell you if the two vectors are on the same major heading or not #define dot2d(A,B) ((A.x*B.x)+(A.y*B.y)) #define vectDotPoint(A,B,P) ( (P.x - B.x) * (B.x - A.x) + (P.y - B.y) * (B.y - A.y) ) // the cross product will tell you if the other vector is to your left or right #define cross2d(A,B) ((A.x*B.y)-(A.y*B.x)) #define vectCrossPoint(A,B,P) ( (P.x - B.x) * (B.y - A.y) - (P.y - B.y) * (B.x - A.x) ) // positive for clockwise triangles #define signedTriArea(A,B,C) (A.x*(C.y - B.y) + B.x*(A.y - C.y) + C.x*(B.y - A.y))/2 //#define geom2dOriginAngleP(A) #define colinearIsBetween(P,L) (vectDotPoint(L.p1, P, L.p2)>0?1:0) #define colinear(A,B,C) (vectCrossPoint(A, B, C)==0?1:0) /* the following should jsut be macros: set, scale, offset */ typedef struct point2d_s { // point double x, y; } point2d_t; typedef struct line2d_s { // line point2d_t p1; point2d_t p2; } line2d_t; typedef struct arc2d_s { // arc point2d_t c; // centre overlaps with point and first point on line. double r; // primary / circle radius double r2; // secondary radius for elliptical arc double start; // start angle double end; // end angle double zrot; // elliptical arc, offset angle. } arc2d_t; typedef struct vect2d_s { // vector double t; double r; } vect2d_t; typedef struct line2dGF_s { // general form line double A, B, C; } line2dGF_t; typedef struct line2dHV_s { // hybrid vector, used for chopping/extending lines point2d_t origin; vect2d_t stroke; } line2dHV_t; // --- math support --- double posatan2(point2d_t p); // --- points and point things --- point2d_t * point2dSet (point2d_t *p, point2d_t to); point2d_t * point2dTranslate (point2d_t *p, point2d_t by) ; point2d_t * point2dRotateZ (point2d_t *p, double by) ; point2d_t * point2dRotateZAround (point2d_t *p, point2d_t around, double by) ; point2d_t * point2dScale (point2d_t *p, point2d_t by) ; point2d_t * point2dScaleAround (point2d_t *p, point2d_t around, point2d_t by); char * point2d2s (char *s, int bl, point2d_t this) ; void point2dShow (point2d_t p, char * pre, char * post); point2d_t * point2dCart2Polar (point2d_t *p, point2d_t cart); point2d_t * point2dPolar2Cart (point2d_t *p, point2d_t polar); //vect2d_t * point2Vect (vect2d_t *v, point2d_t this); //point2d_t * vect2Point (point2d_t *p, vect2d_t v); // --- lines and line things --- line2d_t * line2dInit (line2d_t *l) ; line2d_t * line2dSet (line2d_t *l, double x1, double y1, double x2, double y2) ; line2d_t * line2dSetPts (line2d_t *l, point2d_t this, point2d_t that); line2d_t * line2dSetLine (line2d_t *l, line2d_t to); line2d_t * line2dTrans (line2d_t *l, point2d_t by) ; line2d_t * line2dRot (line2d_t *l, double by) ; line2d_t * line2dRotAround (line2d_t *l, point2d_t around, double by) ; line2d_t * line2dScale (line2d_t *l, point2d_t by) ; line2d_t * line2dSetLen (line2d_t *l, double to); line2d_t * line2dOffset (line2d_t *l, double by); char * line2d2s (char *s, int bl, line2d_t this) ; // joinLines // line2dGF_t * line2dLine2General (line2dGF_t *g1, line2d_t this); // --- arcs and arc things --- arc2d_t * arc2dInit (arc2d_t *a) ; arc2d_t * arc2dSet (arc2d_t *a, double x1, double y1, double r, double start, double end) ; arc2d_t * arc2dSetPR (arc2d_t *a, point2d_t c, double r, double start, double end); arc2d_t * arc2dSetArc (arc2d_t *a, arc2d_t to); arc2d_t * arc2dTrans (arc2d_t *a, point2d_t by); arc2d_t * arc2dRot (arc2d_t *a, point2d_t around, double by); arc2d_t * arc2dRotAround (arc2d_t *a, point2d_t around, double by); arc2d_t * arc2dScale (arc2d_t *a, point2d_t by);// !!!???!!! arc2d_t * arc2dScaleAround (arc2d_t *a, point2d_t around, point2d_t by); // !!!???!!! arc2d_t * arc2dGetArcOn (arc2d_t * a, point2d_t this, point2d_t that, point2d_t other); char * arc2d2s (char *s, int bl, arc2d_t this); // ------ geometry stuff ---- #define geom2dDistPP(PA,PB) (sqrt(point2dDistSquared(PA, PB))) //double geom2dDistPP (point2d_t this, point2d_t that); double geom2dAcute (point2d_t this, point2d_t that, point2d_t other); point2d_t * geom2dCentroid (point2d_t *c, point2d_t this, point2d_t that, point2d_t other); point2d_t * geom2dGetOffset (point2d_t *result, point2d_t this, point2d_t that); double geom2dGetAngleBetween (point2d_t this, point2d_t that); double geom2dTriArea (point2d_t this, point2d_t that, point2d_t other) ; unsigned int geom2dIsPtInTri (point2d_t P, point2d_t A, point2d_t B, point2d_t C) ; point2d_t * geom2dGetMidPoint (point2d_t *mp, line2d_t l); point2d_t * geom2dGetSegmentIntersection (point2d_t * is, line2d_t this, line2d_t that); unsigned char geom2dIsLineTouchingLine (line2d_t this, line2d_t that); point2d_t * geom2dGetIntersection (point2d_t * is, line2d_t this, line2d_t that); point2d_t * geom2dGetIntersectionGF (point2d_t * is, line2dGF_t g1, line2dGF_t g2); point2d_t * geom2dGetClosestPointLine (point2d_t *is, point2d_t this, line2d_t that); double geom2dGetClosestDistLine (point2d_t this, line2d_t that); unsigned char geom2dIsPointCloseToLine (point2d_t p, line2d_t l, double t) ; unsigned char geom2dIsPointOnLine (point2d_t p, line2d_t l); unsigned char geom2dIsPointPerp (line2d_t base, point2d_t this); char geom2dPointDir (point2d_t A, point2d_t B, point2d_t P); // inclusive // P is point, A is circle (arc) #define geom2dIsPointInCircle(P,A) ((point2dDistSquared(P, A.c) <= SQR(A.r))?1:0) #define geom2dDoCirclesTouch(AA,AB) ((geom2dDistPP(AA.c,AB.c) <= (AA.r+AB.r))?1:0) // R is line (kittycorner straight rect) #define geom2dIsPointInRect(P,R) ((WITHINI(R.p1.x, R.p2.x, P.x) & WITHINI(R.p1.y, R.p2.y, P.y))?1:0) // T is threshold //#define geom2dIsPointOnLine(P,L,T) (ABS((L.p1.y - L.p2.y)*(L.p1.x - P.x) -( (L.p1.x - L.p2.x)*(L.p1.y - P.y))) <= T)?1:0 #endif /* closest point on line line segment a -> b, point c, projection of point onto line segment is (c-a).(b-a)/||b-a|| + a, unless the closest point is a or b (c-a).(b-a)/||b-a||^2 * (b-a) + a (b-a)/||b-a|| is a vector in the direction going from a to b, of unit length. (c-a) is a vector going from a to c. dot them together to find how much of the vector going from a to c, is in the direction of a to b. then multiply that magnitude by (b-a)/||b-a|| to get a directional vector, and add it to a */