ref: 39fb26df70b6d8878953ff18046cdc12817a2e42
dir: /sys/src/libgeometry/arith3.c/
#include <u.h> #include <libc.h> #include <draw.h> #include <geometry.h> /* * Routines whose names end in 3 work on points in Affine 3-space. * They ignore w in all arguments and produce w=1 in all results. * Routines whose names end in 4 work on points in Projective 3-space. */ Point3 add3(Point3 a, Point3 b){ a.x+=b.x; a.y+=b.y; a.z+=b.z; a.w=1.; return a; } Point3 sub3(Point3 a, Point3 b){ a.x-=b.x; a.y-=b.y; a.z-=b.z; a.w=1.; return a; } Point3 neg3(Point3 a){ a.x=-a.x; a.y=-a.y; a.z=-a.z; a.w=1.; return a; } Point3 div3(Point3 a, double b){ a.x/=b; a.y/=b; a.z/=b; a.w=1.; return a; } Point3 mul3(Point3 a, double b){ a.x*=b; a.y*=b; a.z*=b; a.w=1.; return a; } int eqpt3(Point3 p, Point3 q){ return p.x==q.x && p.y==q.y && p.z==q.z; } /* * Are these points closer than eps, in a relative sense */ int closept3(Point3 p, Point3 q, double eps){ return 2.*dist3(p, q)<eps*(len3(p)+len3(q)); } double dot3(Point3 p, Point3 q){ return p.x*q.x+p.y*q.y+p.z*q.z; } Point3 cross3(Point3 p, Point3 q){ Point3 r; r.x=p.y*q.z-p.z*q.y; r.y=p.z*q.x-p.x*q.z; r.z=p.x*q.y-p.y*q.x; r.w=1.; return r; } double len3(Point3 p){ return sqrt(p.x*p.x+p.y*p.y+p.z*p.z); } double dist3(Point3 p, Point3 q){ p.x-=q.x; p.y-=q.y; p.z-=q.z; return sqrt(p.x*p.x+p.y*p.y+p.z*p.z); } Point3 unit3(Point3 p){ double len=sqrt(p.x*p.x+p.y*p.y+p.z*p.z); p.x/=len; p.y/=len; p.z/=len; p.w=1.; return p; } Point3 midpt3(Point3 p, Point3 q){ p.x=.5*(p.x+q.x); p.y=.5*(p.y+q.y); p.z=.5*(p.z+q.z); p.w=1.; return p; } Point3 lerp3(Point3 p, Point3 q, double alpha){ p.x+=(q.x-p.x)*alpha; p.y+=(q.y-p.y)*alpha; p.z+=(q.z-p.z)*alpha; p.w=1.; return p; } /* * Reflect point p in the line joining p0 and p1 */ Point3 reflect3(Point3 p, Point3 p0, Point3 p1){ Point3 a, b; a=sub3(p, p0); b=sub3(p1, p0); return add3(a, mul3(b, 2*dot3(a, b)/dot3(b, b))); } /* * Return the nearest point on segment [p0,p1] to point testp */ Point3 nearseg3(Point3 p0, Point3 p1, Point3 testp){ double num, den; Point3 q, r; q=sub3(p1, p0); r=sub3(testp, p0); num=dot3(q, r);; if(num<=0) return p0; den=dot3(q, q); if(num>=den) return p1; return add3(p0, mul3(q, num/den)); } /* * distance from point p to segment [p0,p1] */ #define SMALL 1e-8 /* what should this value be? */ double pldist3(Point3 p, Point3 p0, Point3 p1){ Point3 d, e; double dd, de, dsq; d=sub3(p1, p0); e=sub3(p, p0); dd=dot3(d, d); de=dot3(d, e); if(dd<SMALL*SMALL) return len3(e); dsq=dot3(e, e)-de*de/dd; if(dsq<SMALL*SMALL) return 0; return sqrt(dsq); } /* * vdiv3(a, b) is the magnitude of the projection of a onto b * measured in units of the length of b. * vrem3(a, b) is the component of a perpendicular to b. */ double vdiv3(Point3 a, Point3 b){ return (a.x*b.x+a.y*b.y+a.z*b.z)/(b.x*b.x+b.y*b.y+b.z*b.z); } Point3 vrem3(Point3 a, Point3 b){ double quo=(a.x*b.x+a.y*b.y+a.z*b.z)/(b.x*b.x+b.y*b.y+b.z*b.z); a.x-=b.x*quo; a.y-=b.y*quo; a.z-=b.z*quo; a.w=1.; return a; } /* * Compute face (plane) with given normal, containing a given point */ Point3 pn2f3(Point3 p, Point3 n){ n.w=-dot3(p, n); return n; } /* * Compute face containing three points */ Point3 ppp2f3(Point3 p0, Point3 p1, Point3 p2){ Point3 p01, p02; p01=sub3(p1, p0); p02=sub3(p2, p0); return pn2f3(p0, cross3(p01, p02)); } /* * Compute point common to three faces. * Cramer's rule, yuk. */ Point3 fff2p3(Point3 f0, Point3 f1, Point3 f2){ double det; Point3 p; det=dot3(f0, cross3(f1, f2)); if(fabs(det)<SMALL){ /* parallel planes, bogus answer */ p.x=0.; p.y=0.; p.z=0.; p.w=0.; return p; } p.x=(f0.w*(f2.y*f1.z-f1.y*f2.z) +f1.w*(f0.y*f2.z-f2.y*f0.z)+f2.w*(f1.y*f0.z-f0.y*f1.z))/det; p.y=(f0.w*(f2.z*f1.x-f1.z*f2.x) +f1.w*(f0.z*f2.x-f2.z*f0.x)+f2.w*(f1.z*f0.x-f0.z*f1.x))/det; p.z=(f0.w*(f2.x*f1.y-f1.x*f2.y) +f1.w*(f0.x*f2.y-f2.x*f0.y)+f2.w*(f1.x*f0.y-f0.x*f1.y))/det; p.w=1.; return p; } /* * pdiv4 does perspective division to convert a projective point to affine coordinates. */ Point3 pdiv4(Point3 a){ if(a.w==0) return a; a.x/=a.w; a.y/=a.w; a.z/=a.w; a.w=1.; return a; } Point3 add4(Point3 a, Point3 b){ a.x+=b.x; a.y+=b.y; a.z+=b.z; a.w+=b.w; return a; } Point3 sub4(Point3 a, Point3 b){ a.x-=b.x; a.y-=b.y; a.z-=b.z; a.w-=b.w; return a; }