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/**
* @file
* @brief Plane geometry for shooting rays.
**/
#include "AppHdr.h"
#include "geom2d.h"
#include <cmath>
namespace geom
{
static bool double_is_zero(double d)
{
return abs(d) < 0.00005;
}
// Is v parallel to the kernel of f?
bool parallel(const vector &v, const form &f)
{
return double_is_zero(f(v));
}
vector ray::shoot(double t) const
{
return start + t*dir;
}
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;
}
double lineseq::index(const vector &v) const
{
return (f(v) - offset) / dist;
}
// 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 > 0 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);
if (double_is_zero(k - a))
k += (ls.dist*fd > 0 ? 1 : -1);
double t = (k - a) * ls.dist / fd;
return t;
}
// Move the ray towards the next grid line.
// Half way there if "half" is true, else all the way there
// Returns whether it hit a corner.
bool ray::to_grid(const grid &g, bool half)
{
// ASSERT(!parallel(g.vert, g.horiz));
bool corner = false;
double t = 0;
if (parallel(dir, g.ls1.f))
t = nextintersect(*this, g.ls2);
else if (parallel(dir, g.ls2.f))
t = nextintersect(*this, g.ls1);
else
{
double r = nextintersect(*this, g.ls1);
double s = nextintersect(*this, g.ls2);
t = min(r, s);
corner = double_is_zero(r - s);
}
advance(half ? 0.5 * t : t);
return corner && !half;
}
// Shoot the ray inside the next cell, stopping at corners.
// Returns true if it hit a corner.
bool ray::to_next_cell(const grid &g)
{
if (to_grid(g, false))
return true;
to_grid(g, true);
return false;
}
vector reflect(const vector &v, const form &f)
{
vector normal = vector(f.a, f.b);
return v - 2 * f(v)/f(normal) * normal;
}
//////////////////////////////////////////////////
// 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;
}
vector vector::operator-() const
{
return (-1) * (*this);
}
const vector& vector::operator-=(const vector &v)
{
return *this += -v;
}
vector vector::operator-(const vector &v) const
{
return *this + (-v);
}
vector operator*(double t, const vector &v)
{
return vector(t*v.x, t*v.y);
}
double form::operator()(const vector& v) const
{
return a*v.x + b*v.y;
}
}
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