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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?
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 = std::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 normal(const form &f)
{
return (vector(f.a, f.b));
}
vector reflect(const vector &v, const form &f)
{
vector n = normal(f);
return (v - 2 * f(v)/f(n) * n);
}
//////////////////////////////////////////////////
// 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);
}
double degrees(const vector &v)
{
if (v.x == 0)
return (v.y > 0 ? 90.0 : -90.0);
double rad = v.x > 0 ? atan(v.y/v.x) : M_PI + atan(v.y/v.x);
return (180.0 / M_PI * rad);
}
vector degree_to_vector(double d)
{
double rad = d / 180.0 * M_PI;
return (vector(cos(rad), sin(rad)));
}
}
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