1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
|
/**
* @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) < 0.0000001;
}
// 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 = 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;
}
}
|
