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#ifndef GEOM2D_H
#define GEOM2D_H
namespace geom {
struct vector
{
double x;
double y;
vector(double _x = 0.0, double _y = 0.0)
: x(_x), y(_y) {}
const vector& operator+=(const vector &v);
vector operator+(const vector &v) const;
vector operator-() const;
const vector& operator-=(const vector &v);
vector operator-(const vector &v) const;
};
vector operator*(double t, const vector &v);
struct form
{
double a;
double b;
form(double _a = 0.0, double _b = 0.0)
: a(_a), b(_b) {}
double operator()(const vector &v) const;
};
// A ray in two-dimensional space given by starting point
// and direction vector.
// The points of R are start + t*dir.
struct grid;
struct ray
{
vector start;
vector dir;
ray() {}
ray(double x0, double y0, double xd, double yd)
: start(x0, y0), dir(xd, yd) {}
vector shoot(double t) const;
void advance(double t);
bool to_grid(const grid& g, bool half);
bool to_next_cell(const grid& g);
};
// A line in two-dimensional space as the preimage of a number
// under a linear form. L = form^{-1}(val).
struct line
{
form f;
double val;
line() {}
line(double a, double b, double v)
: f(a,b), val(v) {}
};
// A sequence of evenly spaced parallel lines, like the
// horizontal or vertical lines in a grid.
// Lines are f^{-1}(offset + k*dist) for integers k.
struct lineseq
{
form f;
double offset;
double dist;
lineseq() {}
lineseq(double a, double b, double o, double d)
: f(a,b), offset(o), dist(d) {}
double index(const vector &v) const;
};
struct grid
{
lineseq ls1;
lineseq ls2;
grid(lineseq l1, lineseq l2) : ls1(l1), ls2(l2) {}
};
double intersect(const ray &r, const line &l);
double nextintersect(const ray &r, const lineseq &ls);
bool parallel(const vector& v, const form &f);
vector reflect(const vector& v, const form &f);
vector degree_to_vector(const double d);
double degrees(const vector &v);
}
#endif
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