Point closest_pt_seg(Point a, Point b, Point p) {
double along;
if (lng2(b-a) < EPS) return a;
along = dot(b-a,p-a)/lng2(b-a);
if (along < 0) along = 0;
if (along > 1) along = 1;
return (b-a)*along + a;
}
/* given two lines in 3D space, find distance of closest approach */
double line_line_dist(Point a, Point b, Point c, Point d) {
Point perp = cross(b-a,d-c);
if (lng2(perp) < EPS) /* parallel */
perp = cross(b-a,cross(b-a,c-a));
if (lng2(perp) < EPS) return 0; /* coincident */
return fabs(dot(a-c,perp))/lng(perp);
}
int sphere_iline_isect(Point c, double r, Point a, Point b,
Point *p, Point *q) {
Point vec, mid = closest_pt_iline(a,b,c);
if (lng2(c-mid) > r*r) return 0;
vec = (a-b)*sqrt((r*r - lng2(c-mid))/lng2(a-b));
*p = mid + vec;
*q = mid - vec;
return 1;
}
int bounce(Point ori, Point dir, Point a, Point b,
Point *np, Point *ndir) {
Point tmp;
int res;
res = intersect_iline(ori, ori+dir, a, b, &tmp);
if (res == -1) return -1;
if (res != 1 || dot(tmp-ori,dir) < 0 ||
fabs(lng(a-tmp) + lng(b-tmp) - lng(a-b)) > EPS)
return 0;
*np = tmp;
if (lng2(a-tmp) < EPS || lng2(b-tmp) < EPS) return -2;
*ndir = reflect(a,b,tmp+dir) - tmp;
return 1;
}
Point closest_pt_plane(Point a, Point b, Point c, Point p) {
Point norm;
norm = cross(b-a,c-a);
assert(lng2(norm) > EPS); // collinearity
return closest_pt_plane(norm,a,p);
}
/* this is the same as line_line_dist, but it also returns
the points of closest approach */
double closest_approach(Point a, Point b, Point c, Point d,
Point *p, Point *q) {
double s = dot(d-c,b-a), t = dot(a-c,d-c);
double num, den, tmp;
den = lng2(b-a)*lng2(d-c) - s*s;
num = t*s - dot(a-c,b-a)*lng2(d-c);
if (fabs(den) < EPS) { /* parallel */
*p = a;
*q = (d-c)*t/lng2(d-c) + c;
if (fabs(s) < EPS) *q = a; /* coincident */
} else { /* skew */
tmp = num/den;
*p = a + (b-a)*tmp;
*q = c + (d-c)*(t + s*tmp)/lng2(d-c);
}
return lng(*p-*q);
}
Point to_plane(Point a, Point b, Point c, Point p) {
Point norm, ydir, xdir, res;
norm = cross(b-a,c-a);
assert(lng2(norm) > EPS); // collinearity
xdir = (b-a)/lng(b-a); // create orthonormal vectors
ydir = cross(norm,xdir);
ydir = ydir/lng(ydir);
res.x = dot(p-a,xdir);
res.y = dot(p-a,ydir);
res.z = 0;
return res;
}
void main()
{
FCPartitionDesc dbl("dbl","dbl");
FCPartitionDesc lng("lng","lng");
FCPartitionDesc charp("charp","charp");
FCPartitionDesc date("date","date");
FCPartitionDesc dblx("dblx","dblx");
FCPartitionDesc lngx("lngx","lngx");
FCPartitionDesc charpx("charpx","charpx");
FCPartitionDesc datex("datex","datex");
PDFriend::MakeADouble(dbl);
PDFriend::MakeACharPtr(charp);
PDFriend::MakeALong(lng);
PDFriend::MakeAColDate(date);
// test copy constructor..
FCPartitionDesc dbl2(dbl);
FCPartitionDesc lng2(lng);
FCPartitionDesc charp2(charp);
FCPartitionDesc date2(date);
dblx = dbl;
lngx = lng;
charpx = charp;
datex = date;
cout << "dbl----" << endl << dbl ;
cout << "lng----" << endl << lng ;
cout << "charp--" << endl << charp ;
cout << "date---" << endl << date << endl;
cout << "dbl2----" << endl << dbl2 ;
cout << "lng2----" << endl << lng2 ;
cout << "charp2--" << endl << charp2 ;
cout << "date2---" << endl << date2 << endl;
cout << "dblx----" << endl << dblx ;
cout << "lngx----" << endl << lngx ;
cout << "charpx--" << endl << charpx ;
cout << "date2x--" << endl << datex << endl;
cout << dbl.GetDouble() << endl;
cout << charp.GetCharPtr() << endl;
cout << lng.GetLong() << endl;
cout << date.GetColDate().nMonth << "/"
<< date.GetColDate().nDay << "/"
<< date.GetColDate().nYear << endl;
}
/* Given a plane and a line ab, determine if the two intersect,
and if so, find the single point of intersection */
int plane_iline_isect(Point norm, Point ori, Point a, Point b, Point *p) {
double along, den = dot(norm,b-a);
if (fabs(den) < EPS) { /* parallel */
if (lng2(cross(ori-a,b-a)) < EPS) return -1; /* coincident */
return 0; /* non-intersecting */
}
along = dot(norm,ori-a)/den;
/* if you want to intersect a plane with a finite segment,
check that (along <= 1 && along => 0) */
*p = a + along*(b-a);
return 1;
}
Point closest_pt_iline(Point a, Point b, Point p) {
double along = dot(b-a,p-a)/lng2(b-a);
return (b-a)*along + a;
}
/* is the point p on the infinite line ab? */
int on_iline(Point a, Point b, Point p) {
return (lng2(p-closest_pt_iline(a,b,p)) < EPS);
}
Point closest_pt_plane(Point norm, Point a, Point p) {
Point res = cross(cross(norm,p-a),norm);
if (lng2(res) < EPS) return a;
return res*dot(res,p-a)/lng2(res);
}