ACloudViewer  3.9.4
A Modern Library for 3D Data Processing
GeometryMacros.h
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1 // ----------------------------------------------------------------------------
2 // - CloudViewer: www.cloudViewer.org -
3 // ----------------------------------------------------------------------------
4 // Copyright (c) 2018-2024 www.cloudViewer.org
5 // SPDX-License-Identifier: MIT
6 // ----------------------------------------------------------------------------
7 
8 #pragma once
9 
10 #include <cmath>
11 
13 
14 #if defined(__CUDACC__)
15 
16 #if defined(__CUDA_ARCH__)
17 #if __CUDA_ARCH__ < 600
18 __device__ double atomicAdd(double *address, double val) {
19  unsigned long long int *address_as_ull = (unsigned long long int *)address;
20  unsigned long long int old = *address_as_ull, assumed;
21 
22  do {
23  assumed = old;
24  old = atomicCAS(
25  address_as_ull, assumed,
26  __double_as_longlong(val + __longlong_as_double(assumed)));
27 
28  // Note: uses integer comparison to avoid hang in case of NaN (since NaN
29  // != NaN)
30  } while (assumed != old);
31 
32  return __longlong_as_double(old);
33 }
34 #endif
35 #endif
36 
37 #define OPEN3D_ATOMIC_ADD(X, Y) atomicAdd(X, Y)
38 #else
39 #define OPEN3D_ATOMIC_ADD(X, Y) (*X).fetch_add(Y)
40 #endif
41 
42 // Compatibility: map CloudViewer atomic macro to CloudViewer's
43 #ifndef CLOUDVIEWER_ATOMIC_ADD
44 #define CLOUDVIEWER_ATOMIC_ADD(X, Y) OPEN3D_ATOMIC_ADD(X, Y)
45 #endif
46 
47 namespace cloudViewer {
48 template <typename scalar_t, typename T>
49 CLOUDVIEWER_HOST_DEVICE bool IsClose(const scalar_t &x,
50  const T &y,
51  const double rtol = 1e-4) {
52  return ((x > (1.0 - rtol) * y) && (x < (1.0 + rtol) * y));
53 }
54 
55 template <typename scalar_t>
56 CLOUDVIEWER_HOST_DEVICE scalar_t Square(const scalar_t &x) {
57  return x * x;
58 }
59 } // namespace cloudViewer
60 
61 // https://stackoverflow.com/a/51549250
62 #ifdef __CUDACC__
63 __device__ inline float atomicMinf(float *addr, float value) {
64  float old;
65  old = (value >= 0) ? __int_as_float(
66  atomicMin((int *)addr, __float_as_int(value)))
67  : __uint_as_float(atomicMax((unsigned int *)addr,
68  __float_as_uint(value)));
69  return old;
70 }
71 
72 __device__ inline float atomicMaxf(float *addr, float value) {
73  float old;
74  old = (value >= 0) ? __int_as_float(
75  atomicMax((int *)addr, __float_as_int(value)))
76  : __uint_as_float(atomicMin((unsigned int *)addr,
77  __float_as_uint(value)));
78  return old;
79 }
80 #endif
81 
82 CLOUDVIEWER_HOST_DEVICE inline int Sign(int x) {
83  return (x > 0) ? 1 : ((x < 0) ? -1 : 0);
84 }
85 
86 namespace {
88 const int edge_table[256] = {
89  0x0, 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c, 0x80c, 0x905,
90  0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00, 0x190, 0x99, 0x393, 0x29a,
91  0x596, 0x49f, 0x795, 0x69c, 0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93,
92  0xf99, 0xe90, 0x230, 0x339, 0x33, 0x13a, 0x636, 0x73f, 0x435, 0x53c,
93  0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30, 0x3a0, 0x2a9,
94  0x1a3, 0xaa, 0x7a6, 0x6af, 0x5a5, 0x4ac, 0xbac, 0xaa5, 0x9af, 0x8a6,
95  0xfaa, 0xea3, 0xda9, 0xca0, 0x460, 0x569, 0x663, 0x76a, 0x66, 0x16f,
96  0x265, 0x36c, 0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
97  0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff, 0x3f5, 0x2fc, 0xdfc, 0xcf5,
98  0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0, 0x650, 0x759, 0x453, 0x55a,
99  0x256, 0x35f, 0x55, 0x15c, 0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53,
100  0x859, 0x950, 0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc,
101  0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0, 0x8c0, 0x9c9,
102  0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc, 0xcc, 0x1c5, 0x2cf, 0x3c6,
103  0x4ca, 0x5c3, 0x6c9, 0x7c0, 0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f,
104  0xf55, 0xe5c, 0x15c, 0x55, 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
105  0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc, 0x2fc, 0x3f5,
106  0xff, 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0, 0xb60, 0xa69, 0x963, 0x86a,
107  0xf66, 0xe6f, 0xd65, 0xc6c, 0x36c, 0x265, 0x16f, 0x66, 0x76a, 0x663,
108  0x569, 0x460, 0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
109  0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa, 0x1a3, 0x2a9, 0x3a0, 0xd30, 0xc39,
110  0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c, 0x53c, 0x435, 0x73f, 0x636,
111  0x13a, 0x33, 0x339, 0x230, 0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f,
112  0x895, 0x99c, 0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99, 0x190,
113  0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c, 0x70c, 0x605,
114  0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0};
115 
117 const int tri_table[256][16] = {
118  {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
119  {0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
120  {0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
121  {1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
122  {1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
123  {0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
124  {9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
125  {2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1},
126  {3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
127  {0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
128  {1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
129  {1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1},
130  {3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
131  {0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1},
132  {3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1},
133  {9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
134  {4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
135  {4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
136  {0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
137  {4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1},
138  {1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
139  {3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1},
140  {9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
141  {2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1},
142  {8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
143  {11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1},
144  {9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
145  {4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1},
146  {3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1},
147  {1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1},
148  {4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1},
149  {4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1},
150  {9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
151  {9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
152  {0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
153  {8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1},
154  {1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
155  {3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
156  {5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1},
157  {2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1},
158  {9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
159  {0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1},
160  {0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1},
161  {2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1},
162  {10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1},
163  {4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1},
164  {5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1},
165  {5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1},
166  {9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
167  {9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1},
168  {0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1},
169  {1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
170  {9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1},
171  {10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1},
172  {8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1},
173  {2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1},
174  {7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1},
175  {9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1},
176  {2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1},
177  {11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1},
178  {9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1},
179  {5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1},
180  {11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1},
181  {11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
182  {10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
183  {0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
184  {9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
185  {1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
186  {1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
187  {1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1},
188  {9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1},
189  {5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1},
190  {2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
191  {11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
192  {0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1},
193  {5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1},
194  {6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1},
195  {0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1},
196  {3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1},
197  {6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1},
198  {5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
199  {4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1},
200  {1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1},
201  {10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1},
202  {6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1},
203  {1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1},
204  {8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1},
205  {7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1},
206  {3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1},
207  {5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1},
208  {0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1},
209  {9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1},
210  {8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1},
211  {5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1},
212  {0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1},
213  {6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1},
214  {10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
215  {4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1},
216  {10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1},
217  {8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1},
218  {1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1},
219  {3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1},
220  {0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
221  {8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1},
222  {10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1},
223  {0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1},
224  {3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1},
225  {6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1},
226  {9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1},
227  {8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1},
228  {3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1},
229  {6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
230  {7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1},
231  {0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1},
232  {10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1},
233  {10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1},
234  {1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1},
235  {2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1},
236  {7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1},
237  {7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
238  {2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1},
239  {2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1},
240  {1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1},
241  {11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1},
242  {8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1},
243  {0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
244  {7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1},
245  {7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
246  {7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
247  {3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
248  {0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
249  {8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
250  {10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
251  {1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
252  {2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1},
253  {6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1},
254  {7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
255  {7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1},
256  {2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1},
257  {1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1},
258  {10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1},
259  {10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1},
260  {0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1},
261  {7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1},
262  {6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
263  {3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1},
264  {8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1},
265  {9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1},
266  {6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1},
267  {1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1},
268  {4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1},
269  {10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1},
270  {8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1},
271  {0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
272  {1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1},
273  {1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1},
274  {8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1},
275  {10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1},
276  {4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1},
277  {10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
278  {4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
279  {0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1},
280  {5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
281  {11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1},
282  {9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
283  {6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1},
284  {7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1},
285  {3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1},
286  {7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1},
287  {9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1},
288  {3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1},
289  {6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1},
290  {9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1},
291  {1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1},
292  {4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1},
293  {7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1},
294  {6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1},
295  {3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1},
296  {0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1},
297  {6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1},
298  {1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1},
299  {0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1},
300  {11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1},
301  {6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1},
302  {5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1},
303  {9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1},
304  {1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1},
305  {1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
306  {1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1},
307  {10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1},
308  {0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
309  {10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
310  {11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
311  {11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1},
312  {5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1},
313  {10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1},
314  {11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1},
315  {0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1},
316  {9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1},
317  {7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1},
318  {2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1},
319  {8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1},
320  {9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1},
321  {9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1},
322  {1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
323  {0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1},
324  {9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1},
325  {9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
326  {5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1},
327  {5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1},
328  {0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1},
329  {10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1},
330  {2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1},
331  {0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1},
332  {0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1},
333  {9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
334  {2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1},
335  {5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1},
336  {3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1},
337  {5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1},
338  {8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1},
339  {0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
340  {8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1},
341  {9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
342  {4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1},
343  {0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1},
344  {1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1},
345  {3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1},
346  {4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1},
347  {9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1},
348  {11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1},
349  {11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1},
350  {2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1},
351  {9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1},
352  {3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1},
353  {1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
354  {4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1},
355  {4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1},
356  {4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
357  {4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
358  {9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
359  {3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1},
360  {0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1},
361  {3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
362  {1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1},
363  {3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1},
364  {0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
365  {3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
366  {2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1},
367  {9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
368  {2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1},
369  {1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
370  {1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
371  {0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
372  {0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
373  {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}};
374 
375 CLOUDVIEWER_DEVICE const int tri_count[256] = {
376  0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 2, 3, 3, 4,
377  2, 3, 3, 4, 3, 4, 4, 3, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3,
378  2, 3, 3, 2, 3, 4, 4, 3, 3, 4, 4, 3, 4, 5, 5, 2, 1, 2, 2, 3, 2, 3, 3, 4,
379  2, 3, 3, 4, 3, 4, 4, 3, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 4,
380  2, 3, 3, 4, 3, 4, 2, 3, 3, 4, 4, 5, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 3, 2,
381  4, 5, 5, 4, 5, 2, 4, 1, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3,
382  2, 3, 3, 4, 3, 4, 4, 5, 3, 2, 4, 3, 4, 3, 5, 2, 2, 3, 3, 4, 3, 4, 4, 5,
383  3, 4, 4, 5, 4, 5, 5, 4, 3, 4, 4, 3, 4, 5, 5, 4, 4, 3, 5, 2, 5, 4, 2, 1,
384  2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 2, 3, 3, 2, 3, 4, 4, 5, 4, 5, 5, 2,
385  4, 3, 5, 4, 3, 2, 4, 1, 3, 4, 4, 5, 4, 5, 3, 4, 4, 5, 5, 2, 3, 4, 2, 1,
386  2, 3, 3, 2, 3, 4, 2, 1, 3, 2, 4, 1, 2, 1, 1, 0,
387 };
388 
389 CLOUDVIEWER_DEVICE const int vtx_shifts[8][3] = {
390  {0, 0, 0}, {1, 0, 0}, {1, 1, 0}, {0, 1, 0},
391  {0, 0, 1}, {1, 0, 1}, {1, 1, 1}, {0, 1, 1},
392 };
393 
394 // First 3 elements: edge start vertex coordinate (assume origin at (0, 0, 0))
395 // The last element: edge direction {0: x, 1: y, 2: z}
396 CLOUDVIEWER_DEVICE const int edge_shifts[12][4] = {
397  {0, 0, 0, 0}, // Edge 0: {0, 1}
398  {1, 0, 0, 1}, // Edge 1: {1, 2}
399  {0, 1, 0, 0}, // Edge 2: {3, 2}
400  {0, 0, 0, 1}, // Edge 3: {0, 3}
401  {0, 0, 1, 0}, // Edge 4: {4, 5}
402  {1, 0, 1, 1}, // Edge 5: {5, 6}
403  {0, 1, 1, 0}, // Edge 6: {7, 6}
404  {0, 0, 1, 1}, // Edge 7: {4, 7}
405  {0, 0, 0, 2}, // Edge 8: {0, 4}
406  {1, 0, 0, 2}, // Edge 9: {1, 5}
407  {1, 1, 0, 2}, // Edge 10: {2, 6}
408  {0, 1, 0, 2}, // Edge 11: {3, 7}
409 };
410 
411 CLOUDVIEWER_DEVICE const int edge_to_vert[12][2] = {
412  {0, 1}, {1, 2}, {3, 2}, {0, 3}, {4, 5}, {5, 6},
413  {7, 6}, {4, 7}, {0, 4}, {1, 5}, {2, 6}, {3, 7},
414 };
415 
416 // Turbo colormap
417 // https://ai.googleblog.com/2019/08/turbo-improved-rainbow-colormap-for.html
418 CLOUDVIEWER_DEVICE const unsigned char turbo_srgb_bytes[256][3] = {
419  {48, 18, 59}, {50, 21, 67}, {51, 24, 74}, {52, 27, 81},
420  {53, 30, 88}, {54, 33, 95}, {55, 36, 102}, {56, 39, 109},
421  {57, 42, 115}, {58, 45, 121}, {59, 47, 128}, {60, 50, 134},
422  {61, 53, 139}, {62, 56, 145}, {63, 59, 151}, {63, 62, 156},
423  {64, 64, 162}, {65, 67, 167}, {65, 70, 172}, {66, 73, 177},
424  {66, 75, 181}, {67, 78, 186}, {68, 81, 191}, {68, 84, 195},
425  {68, 86, 199}, {69, 89, 203}, {69, 92, 207}, {69, 94, 211},
426  {70, 97, 214}, {70, 100, 218}, {70, 102, 221}, {70, 105, 224},
427  {70, 107, 227}, {71, 110, 230}, {71, 113, 233}, {71, 115, 235},
428  {71, 118, 238}, {71, 120, 240}, {71, 123, 242}, {70, 125, 244},
429  {70, 128, 246}, {70, 130, 248}, {70, 133, 250}, {70, 135, 251},
430  {69, 138, 252}, {69, 140, 253}, {68, 143, 254}, {67, 145, 254},
431  {66, 148, 255}, {65, 150, 255}, {64, 153, 255}, {62, 155, 254},
432  {61, 158, 254}, {59, 160, 253}, {58, 163, 252}, {56, 165, 251},
433  {55, 168, 250}, {53, 171, 248}, {51, 173, 247}, {49, 175, 245},
434  {47, 178, 244}, {46, 180, 242}, {44, 183, 240}, {42, 185, 238},
435  {40, 188, 235}, {39, 190, 233}, {37, 192, 231}, {35, 195, 228},
436  {34, 197, 226}, {32, 199, 223}, {31, 201, 221}, {30, 203, 218},
437  {28, 205, 216}, {27, 208, 213}, {26, 210, 210}, {26, 212, 208},
438  {25, 213, 205}, {24, 215, 202}, {24, 217, 200}, {24, 219, 197},
439  {24, 221, 194}, {24, 222, 192}, {24, 224, 189}, {25, 226, 187},
440  {25, 227, 185}, {26, 228, 182}, {28, 230, 180}, {29, 231, 178},
441  {31, 233, 175}, {32, 234, 172}, {34, 235, 170}, {37, 236, 167},
442  {39, 238, 164}, {42, 239, 161}, {44, 240, 158}, {47, 241, 155},
443  {50, 242, 152}, {53, 243, 148}, {56, 244, 145}, {60, 245, 142},
444  {63, 246, 138}, {67, 247, 135}, {70, 248, 132}, {74, 248, 128},
445  {78, 249, 125}, {82, 250, 122}, {85, 250, 118}, {89, 251, 115},
446  {93, 252, 111}, {97, 252, 108}, {101, 253, 105}, {105, 253, 102},
447  {109, 254, 98}, {113, 254, 95}, {117, 254, 92}, {121, 254, 89},
448  {125, 255, 86}, {128, 255, 83}, {132, 255, 81}, {136, 255, 78},
449  {139, 255, 75}, {143, 255, 73}, {146, 255, 71}, {150, 254, 68},
450  {153, 254, 66}, {156, 254, 64}, {159, 253, 63}, {161, 253, 61},
451  {164, 252, 60}, {167, 252, 58}, {169, 251, 57}, {172, 251, 56},
452  {175, 250, 55}, {177, 249, 54}, {180, 248, 54}, {183, 247, 53},
453  {185, 246, 53}, {188, 245, 52}, {190, 244, 52}, {193, 243, 52},
454  {195, 241, 52}, {198, 240, 52}, {200, 239, 52}, {203, 237, 52},
455  {205, 236, 52}, {208, 234, 52}, {210, 233, 53}, {212, 231, 53},
456  {215, 229, 53}, {217, 228, 54}, {219, 226, 54}, {221, 224, 55},
457  {223, 223, 55}, {225, 221, 55}, {227, 219, 56}, {229, 217, 56},
458  {231, 215, 57}, {233, 213, 57}, {235, 211, 57}, {236, 209, 58},
459  {238, 207, 58}, {239, 205, 58}, {241, 203, 58}, {242, 201, 58},
460  {244, 199, 58}, {245, 197, 58}, {246, 195, 58}, {247, 193, 58},
461  {248, 190, 57}, {249, 188, 57}, {250, 186, 57}, {251, 184, 56},
462  {251, 182, 55}, {252, 179, 54}, {252, 177, 54}, {253, 174, 53},
463  {253, 172, 52}, {254, 169, 51}, {254, 167, 50}, {254, 164, 49},
464  {254, 161, 48}, {254, 158, 47}, {254, 155, 45}, {254, 153, 44},
465  {254, 150, 43}, {254, 147, 42}, {254, 144, 41}, {253, 141, 39},
466  {253, 138, 38}, {252, 135, 37}, {252, 132, 35}, {251, 129, 34},
467  {251, 126, 33}, {250, 123, 31}, {249, 120, 30}, {249, 117, 29},
468  {248, 114, 28}, {247, 111, 26}, {246, 108, 25}, {245, 105, 24},
469  {244, 102, 23}, {243, 99, 21}, {242, 96, 20}, {241, 93, 19},
470  {240, 91, 18}, {239, 88, 17}, {237, 85, 16}, {236, 83, 15},
471  {235, 80, 14}, {234, 78, 13}, {232, 75, 12}, {231, 73, 12},
472  {229, 71, 11}, {228, 69, 10}, {226, 67, 10}, {225, 65, 9},
473  {223, 63, 8}, {221, 61, 8}, {220, 59, 7}, {218, 57, 7},
474  {216, 55, 6}, {214, 53, 6}, {212, 51, 5}, {210, 49, 5},
475  {208, 47, 5}, {206, 45, 4}, {204, 43, 4}, {202, 42, 4},
476  {200, 40, 3}, {197, 38, 3}, {195, 37, 3}, {193, 35, 2},
477  {190, 33, 2}, {188, 32, 2}, {185, 30, 2}, {183, 29, 2},
478  {180, 27, 1}, {178, 26, 1}, {175, 24, 1}, {172, 23, 1},
479  {169, 22, 1}, {167, 20, 1}, {164, 19, 1}, {161, 18, 1},
480  {158, 16, 1}, {155, 15, 1}, {152, 14, 1}, {149, 13, 1},
481  {146, 11, 1}, {142, 10, 1}, {139, 9, 2}, {136, 8, 2},
482  {133, 7, 2}, {129, 6, 2}, {126, 5, 2}, {122, 4, 3}};
483 } // unnamed namespace
Common CUDA utilities.
#define CLOUDVIEWER_HOST_DEVICE
Definition: CUDAUtils.h:44
#define CLOUDVIEWER_DEVICE
Definition: CUDAUtils.h:45
CLOUDVIEWER_HOST_DEVICE int Sign(int x)
Generic file read and write utility for python interface.
CLOUDVIEWER_HOST_DEVICE bool IsClose(const scalar_t &x, const T &y, const double rtol=1e-4)
CLOUDVIEWER_HOST_DEVICE scalar_t Square(const scalar_t &x)