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
|
#define RADIUS $radius
#define N_PARTICLES $n_particles
#define DELTA_T $delta_t
#if $dimension == 3
#define ENABLE_3D
#endif
typedef float scalar_t;
#ifdef ENABLE_3D
typedef float3 vec_t;
typedef float4 data_vec_t;
#define N_WALLS 6
#else
typedef float2 vec_t;
typedef float2 data_vec_t;
#define N_WALLS 4
#endif
#define SCALAR_MAX FLT_MAX
__constant float4 wall_normals[N_WALLS] = {
(float4)(-1., 0., 0., 0.),
(float4)( 1., 0., 0., 0.),
(float4)( 0., 1., 0., 0.),
(float4)( 0.,-1., 0., 0.),
(float4)( 0., 0.,-1., 0.),
(float4)( 0., 0., 1., 0.),
};
__constant scalar_t wall_loc[N_WALLS] = {
-RADIUS, 1.-RADIUS, 1.-RADIUS, -RADIUS, -RADIUS, 1.-RADIUS
};
vec_t wall_normal(unsigned int iWall) {
#ifdef ENABLE_3D
return wall_normals[iWall].xyz;
#else
return wall_normals[iWall].xy;
#endif
}
scalar_t solve_wall_collision(vec_t n, scalar_t loc, vec_t p, vec_t v) {
if (dot(n,v) > 0.) {
vec_t wall_v = dot(n,v) * n;
return (loc - dot(p,n)) / dot(wall_v,n);
} else {
return SCALAR_MAX;
}
}
scalar_t pos_min_or_infty(scalar_t t0, scalar_t t1) {
if (t0 >= 0.) {
if (t1 >= 0.) {
return min(min(t0, t1), SCALAR_MAX);
} else {
return min(t0, SCALAR_MAX);
}
} else {
if (t1 >= 0.) {
return min(t1, SCALAR_MAX);
} else {
return SCALAR_MAX;
}
}
}
scalar_t solve_collision(vec_t p, vec_t v, vec_t p_, vec_t v_) {
scalar_t a = dot(v-v_, v-v_);
scalar_t b = 2.*dot(p-p_, v-v_);
scalar_t c = dot(p-p_, p-p_) - 4.*RADIUS*RADIUS;
scalar_t d = b*b - 4.*a*c;
if (d >= 0.) {
scalar_t t0 = (-b + sqrt(d))/(2.*a);
scalar_t t1 = (-b - sqrt(d))/(2.*a);
return pos_min_or_infty(t0, t1);
} else {
return SCALAR_MAX;
}
}
vec_t getPosition(__global data_vec_t* pos,
unsigned int iParticle)
{
#ifdef ENABLE_3D
return pos[iParticle].xyz;
#else
return pos[iParticle];
#endif
}
vec_t getVelocity(__global data_vec_t* vel,
unsigned int iParticle)
{
#ifdef ENABLE_3D
return vel[iParticle].xyz;
#else
return vel[iParticle];
#endif
}
void set(__global data_vec_t* pos,
__global data_vec_t* vel,
unsigned int iParticle,
vec_t p,
vec_t v)
{
#ifdef ENABLE_3D
pos[iParticle].xyz = p;
vel[iParticle].xyz = v;
#else
pos[iParticle] = p;
vel[iParticle] = v;
#endif
}
__kernel void evolve(__global data_vec_t* pos_a,
__global data_vec_t* vel_a,
__global data_vec_t* pos_b,
__global data_vec_t* vel_b,
__global volatile unsigned int* last_collide)
{
unsigned int i = get_global_id(0);
vec_t p = getPosition(pos_a, i);
vec_t v = getVelocity(vel_a, i);
unsigned int jParticle = N_PARTICLES;
scalar_t min2intersect = SCALAR_MAX;
for (unsigned int iParticle=0; iParticle < N_PARTICLES; ++iParticle) {
if (iParticle != i && !(last_collide[i] == iParticle && last_collide[iParticle] == i)) {
vec_t p_ = getPosition(pos_a, iParticle);
vec_t v_ = getVelocity(vel_a, iParticle);
scalar_t time2intersect = solve_collision(p, v, p_, v_);
if (time2intersect < min2intersect) {
min2intersect = time2intersect;
jParticle = iParticle;
}
}
}
unsigned int jWall = N_PARTICLES;
scalar_t min2wall = SCALAR_MAX;
for (unsigned int iWall=0; iWall < N_WALLS; ++iWall) {
scalar_t time2wall = solve_wall_collision(wall_normal(iWall), wall_loc[iWall], p, v);
if (time2wall < min2wall) {
min2wall = time2wall;
jWall = iWall;
}
}
if (min2intersect < DELTA_T) {
if (min2wall < min2intersect) {
p += min2wall * v;
v -= 2*dot(v,wall_normal(jWall)) * wall_normal(jWall);
p += (DELTA_T - min2wall) * v;
last_collide[i] = N_PARTICLES;
set(pos_b, vel_b, i, p, v);
} else {
if (i < jParticle) {
vec_t p_ = getPosition(pos_a, jParticle);
vec_t v_ = getVelocity(vel_a, jParticle);
p += min2intersect * v;
p_ += min2intersect * v_;
vec_t omega = normalize(p - p_);
v -= dot(getVelocity(vel_a, i) - getVelocity(vel_a, jParticle), omega) * omega;
v_ -= dot(getVelocity(vel_a, jParticle) - getVelocity(vel_a, i), omega) * omega;
p += (DELTA_T - min2intersect) * v;
p_ += (DELTA_T - min2intersect) * v_;
set(pos_b, vel_b, i, p, v);
set(pos_b, vel_b, jParticle, p_, v_);
last_collide[i] = jParticle;
last_collide[jParticle] = i;
}
}
} else {
if (min2wall < DELTA_T) {
p += min2wall * v;
v -= 2*dot(v,wall_normal(jWall)) * wall_normal(jWall);
p += (DELTA_T - min2wall) * v;
last_collide[i] = N_PARTICLES;
} else {
p += DELTA_T * v;
}
set(pos_b, vel_b, i, p, v);
}
}
__kernel void get_velocity_norms(__global data_vec_t* velocities, __global scalar_t* norms)
{
unsigned int i = get_global_id(0);
norms[i] = length(getVelocity(velocities, i));
}
|
