plane.h
3.96 KB
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
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
#ifndef TIRA_PLANE_H
#define TIRA_PLANE_H
#include <iostream>
#include <stim/math/vec3.h>
#include <stim/cuda/cudatools/callable.h>
#include <stim/math/quaternion.h>
namespace tira
{
template<typename T> class plane;
}
template<typename T>
CUDA_CALLABLE tira::plane<T> operator-(tira::plane<T> v);
namespace tira
{
template <typename T>
class plane
{
protected:
vec3<T> P;
vec3<T> N;
vec3<T> U;
///Initializes the plane with standard coordinates.
///
CUDA_CALLABLE void init()
{
P = vec3<T>(0, 0, 0);
N = vec3<T>(0, 0, 1);
U = vec3<T>(1, 0, 0);
}
public:
CUDA_CALLABLE plane()
{
init();
}
CUDA_CALLABLE plane(vec3<T> n, vec3<T> p = vec3<T>(0, 0, 0))
{
init();
P = p;
rotate(n.norm());
}
CUDA_CALLABLE plane(T z_pos)
{
init();
P[2] = z_pos;
}
//create a plane from three points (a triangle)
CUDA_CALLABLE plane(vec3<T> a, vec3<T> b, vec3<T> c)
{
init();
P = c;
vec3<T> n = (c - a).cross(b - a);
try
{
if(n.len() != 0)
{
rotate(n.norm());
} else {
throw 42;
}
}
catch(int i)
{
std::cerr << "No plane can be creates as all points a,b,c lie on a straight line" << std::endl;
}
}
template< typename U >
CUDA_CALLABLE operator plane<U>()
{
plane<U> result(N, P);
return result;
}
CUDA_CALLABLE vec3<T> n()
{
return N;
}
CUDA_CALLABLE vec3<T> p()
{
return P;
}
CUDA_CALLABLE vec3<T> u()
{
return U;
}
///flip the plane front-to-back
CUDA_CALLABLE plane<T> flip(){
plane<T> result = *this;
result.N = -result.N;
return result;
}
//determines how a vector v intersects the plane (1 = intersects front, 0 = within plane, -1 = intersects back)
CUDA_CALLABLE int face(vec3<T> v){
T dprod = v.dot(N); //get the dot product between v and N
//conditional returns the appropriate value
if(dprod < 0)
return 1;
else if(dprod > 0)
return -1;
else
return 0;
}
//determine on which side of the plane a point lies (1 = front, 0 = on the plane, -1 = bac k)
CUDA_CALLABLE int side(vec3<T> p){
vec3<T> v = p - P; //get the vector from P to the query point p
return face(v);
}
//compute the component of v that is perpendicular to the plane
CUDA_CALLABLE vec3<T> perpendicular(vec3<T> v){
return N * v.dot(N);
}
//compute the projection of v in the plane
CUDA_CALLABLE vec3<T> parallel(vec3<T> v){
return v - perpendicular(v);
}
CUDA_CALLABLE void setU(vec3<T> v)
{
U = (parallel(v.norm())).norm();
}
CUDA_CALLABLE void decompose(vec3<T> v, vec3<T>& para, vec3<T>& perp){
perp = N * v.dot(N);
para = v - perp;
}
//get both the parallel and perpendicular components of a vector v w.r.t. the plane
CUDA_CALLABLE void project(vec3<T> v, vec3<T> &v_par, vec3<T> &v_perp){
v_perp = v.dot(N);
v_par = v - v_perp;
}
//compute the reflection of v off of the plane
CUDA_CALLABLE vec3<T> reflect(vec3<T> v){
//compute the reflection using N_prime as the plane normal
vec3<T> par = parallel(v);
vec3<T> r = (-v) + par * 2;
return r;
}
CUDA_CALLABLE plane<T> operator-()
{
plane<T> p = *this;
//negate the normal vector
p.N = -p.N;
return p;
}
//output a string
std::string str(){
std::stringstream ss;
ss<<"P: "<<P<<std::endl;
ss<<"N: "<<N<<std::endl;
ss<<"U: "<<U;
return ss.str();
}
CUDA_CALLABLE void rotate(vec3<T> n)
{
quaternion<T> q;
q.CreateRotation(N, n);
matrix_sq<T, 3> M = q.toMatrix3();
N = M * N;
U = M * U;
}
CUDA_CALLABLE void rotate(vec3<T> n, vec3<T> &Y)
{
quaternion<T> q;
q.CreateRotation(N, n);
N = q.toMatrix3() * N;
U = q.toMatrix3() * U;
Y = q.toMatrix3() * Y;
}
CUDA_CALLABLE void rotate(vec3<T> n, vec3<T> &X, vec3<T> &Y)
{
quaternion<T> q;
q.CreateRotation(N, n);
N = q.toMatrix3() * N;
U = q.toMatrix3() * U;
X = q.toMatrix3() * X;
Y = q.toMatrix3() * Y;
}
};
}
#endif