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/*
* File: geom2d.cc
* Summary: Plane geometry for shooting rays.
*/
#include "AppHdr.h"
#include "debug.h"
#include "geom2d.h"
#include <cmath>
namespace geom {
static bool double_is_zero(double d)
{
return (std::abs(d) < 0.0000001);
}
// Is v parallel to the kernel of f?
static bool parallel(vector v, form f)
{
return (double_is_zero(f(v)));
}
vector ray::shoot(double t) const
{
return (start + dir * t);
}
void ray::advance(double t)
{
start = shoot(t);
}
// Determine the value of t such that
// r.start + t * r.dir lies on the line l.
// r and l must not be parallel.
double intersect(const ray &r, const line &l)
{
ASSERT(!parallel(r.dir, l.f));
double fp = l.f(r.start);
double fd = l.f(r.dir);
double t = (l.val - fp) / fd;
return (t);
}
// Find the next intersection of r with a line in ls.
double nextintersect(const ray &r, const lineseq &ls)
{
// ray must not be parallel to the lines
ASSERT(!parallel(r.dir, ls.f));
double fp = ls.f(r.start);
double fd = ls.f(r.dir);
// want smallest positive t with
// fp + t*fd = ls.offset + k*ls.dist, k integral
double a = (fp - ls.offset) / ls.dist;
double k = (ls.dist*fd) > 0 ? ceil(a) : floor(a);
double t = (k - a) * ls.dist / fd;
return (t);
}
// Line distance in the ray parameter.
// ls.f(r.shoot(tdist)) == ls.f(r.start) +- ls.dist
static double tdist(const ray &r, const lineseq &ls)
{
ASSERT(!parallel(r.dir, ls.f));
return (std::abs(ls.dist / ls.f(r.dir)));
}
// Shoot the ray inside the next cell.
// Returns true if succesfully advanced into a new cell,
// false if it hit a corner.
bool nextcell(ray &r, const grid &g)
{
// ASSERT(!parallel(g.vert, g.horiz));
lineseq ls;
if (parallel(r.dir, g.ls1.f))
ls = g.ls2;
else if (parallel(r.dir, g.ls2.f))
ls = g.ls1;
else
{
double s = nextintersect(r, g.ls1);
double t = nextintersect(r, g.ls2);
double sd = tdist(r, g.ls1);
double td = tdist(r, g.ls2);
if (double_is_zero(s - t))
{
// Move onto the corner. The fact that we're on a corner
// should be tracked externally.
r.advance(s);
return (false);
}
double dmin = std::min(s,t);
double dnext = std::min(std::max(s,t), dmin + std::min(sd, td));
r.advance((dmin + dnext) / 2.0);
return (true);
}
// parallel: just advance an extra half
double s = nextintersect(r, ls);
r.advance(s + 0.5 * tdist(r, ls));
return (true);
}
void movehalfcell(ray &r, const grid &g)
{
// ASSERT(!parallel(g.vert, g.horiz));
lineseq ls;
double t;
if (parallel(r.dir, g.ls1.f))
t = tdist(r, g.ls2);
else if (parallel(r.dir, g.ls2.f))
t = tdist(r, g.ls1);
else
t = std::min(tdist(r, g.ls1), tdist(r, g.ls2));
r.advance(0.5 * t);
}
// vector space implementation
const vector& vector::operator+=(const vector &v)
{
x += v.x;
y += v.y;
return (*this);
}
vector vector::operator+(const vector &v) const
{
vector copy = *this;
copy += v;
return (copy);
}
const vector& vector::operator*=(double t)
{
x *= t;
y *= t;
return (*this);
}
vector vector::operator*(double t) const
{
vector copy = *this;
copy *= t;
return (copy);
}
double form::operator()(const vector& v) const
{
return (a*v.x + b*v.y);
}
}
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