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LoopDetector
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  1. 36
      .gitignore
  2. 9
      CMakeLists.txt
  3. 3
      README.md
  4. 64
      include/loop_detector.h
  5. 77
      main.cpp
  6. 170
      src/loop_detector.cpp

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.gitignore
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# ---> C++
# Prerequisites
*.d
# Compiled Object files
*.slo
*.lo
*.o
*.obj
# Precompiled Headers
*.gch
*.pch
# Compiled Dynamic libraries
*.so
*.dylib
*.dll
# Fortran module files
*.mod
*.smod
# Compiled Static libraries
*.lai
*.la
*.a
*.lib
# Executables
*.exe
*.out
*.app
cmake-build-debug/
.idea/

9
CMakeLists.txt
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cmake_minimum_required(VERSION 3.21)
project(LoopDetector)
set(CMAKE_CXX_STANDARD 14)
add_executable(LoopDetector main.cpp src/loop_detector.cpp include/loop_detector.h)
include_directories(E:/CLib/tinynurbs/include E:/CLib/glm)
include_directories(include)

3
README.md
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# GaussMap
A Gauss mapping tool for Nurbs surfaces on CPUs.

64
include/loop_detector.h
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#ifndef LOOPDETECTOR_LOOP_DETECTOR_H
#define LOOPDETECTOR_LOOP_DETECTOR_H
#include "tinynurbs/tinynurbs.h"
#include "glm/glm.hpp"
using namespace std;
class LoopDetector {
public:
// 两个曲面
tinynurbs::RationalSurface<float> s;
tinynurbs::RationalSurface<float> f;
// 细分采样的总层数（最高与BVH的总层数相等）。从第二层开始，每一层都表示把原来的一个小sub patch分成了更小的四份
int maxSplitLayer;
// 采样点的求值和求切向量先设为public，因为这些因该是算好的，LoopDetector不用重复计算
// 曲面s和f的采样点。
vector<vector<glm::vec3>> s_evaluation;
vector<vector<glm::vec3>> f_evaluation;
// 曲面s和f的切向量。
vector<vector<glm::vec3>> s_tangent_u;
vector<vector<glm::vec3>> s_tangent_v;
vector<vector<glm::vec3>> f_tangent_u;
vector<vector<glm::vec3>> f_tangent_v;
// int subPatchEdgeSampleCnt; // 在一个sub patch的采样网格中，边上的采样点个数
// void init(tinynurbs::RationalSurface<float> _s, tinynurbs::RationalSurface<float> _f, int _maxSplitLayer);
vector<pair<int, int>> detect(pair<int, int> _s_subPatchIdxRange_u, pair<int, int> _s_subPatchIdxRange_v,
pair<int, int> _f_subPatchIdxRange_u, pair<int, int> _f_subPatchIdxRange_v);
private:
// 需要做Loop检测的sub patch在最后一层上的下标的范围(每个范围都真包含于[0, 2^(maxSplitLayer-1)-1])
pair<int, int> s_subPatchIdxRange_u;
pair<int, int> s_subPatchIdxRange_v;
pair<int, int> f_subPatchIdxRange_u;
pair<int, int> f_subPatchIdxRange_v;
// subPatch每条边上的采样点个数
// 这四个值根据subPatchRange的范围得到，不可被外部修改
int s_subPatchEdgeSampleCnt_u;
int s_subPatchEdgeSampleCnt_v;
int f_subPatchEdgeSampleCnt_u;
int f_subPatchEdgeSampleCnt_v;
// 整个曲面一条边上的采样点个数
int edgeSampleCnt;
// 有向距离计算结果。有向距离通过采样的方式计算，其结果与s曲面sub patch中的采样网格规模相同，即与s_evaluation大小一致
// vector<vector<glm::vec3>> distance;
// 确定有向距离后，对应的f曲面上的最短距离点的位置
vector<vector<pair<int, int>>> selectedPointsIdx;
// vector fields, 即有向距离关于u、v的导数
vector<vector<glm::vec2>> vectorFields;
void initEvaluation();
void initOrientedDistance();
void initVectorField();
void getRotationNumber();
};
#endif //LOOPDETECTOR_LOOP_DETECTOR_H

77
main.cpp
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#include <iostream>
#include "loop_detector.h"
int main() {
LoopDetector loopDetector;
tinynurbs::RationalSurface<float> s;
tinynurbs::RationalSurface<float> f;
s.degree_u = 3;
s.degree_v = 3;
s.knots_u = {0, 0, 0, 0, 1, 1, 1, 1};
s.knots_v = {0, 0, 0, 0, 1, 1, 1, 1};
s.control_points = {4, 4, {
glm::vec3(0, 0.3, 0.9), glm::vec3(0, 0.6, 1), glm::vec3(0, 0.9, 1.1), glm::vec3(0, 1.2, 1),
glm::vec3(0.33, 0.3, 0.12), glm::vec3(0.33, 0.6, 0.12), glm::vec3(0.33, 0.9, 0.12),
glm::vec3(0.33, 1.2, 0.12),
glm::vec3(0.66, 0.3, 0.12), glm::vec3(0.66, 0.6, 0.12), glm::vec3(0.66, 0.9, 0.12),
glm::vec3(0.66, 1.2, 0.12),
glm::vec3(1, 0.3, 0.8), glm::vec3(1, 0.6, 1), glm::vec3(1, 0.9, 1.1), glm::vec3(1, 1.2, 1)
}};
s.weights = {4, 4,
{
1, 1, 1, 1,
1, 1, 1, 1,
1, 1, 1, 1,
1, 1, 1, 1,
}
};
f.degree_u = 3;
f.degree_v = 3;
f.knots_u = {0, 0, 0, 0, 1, 1, 1, 1};
f.knots_v = {0, 0, 0, 0, 1, 1, 1, 1};
f.control_points = {4, 4, {
glm::vec3(0, 0.2, 0.9), glm::vec3(0, 0.5, 1.8), glm::vec3(0, 0.8, 1.1), glm::vec3(0, 1.2, 1),
glm::vec3(0.33, 0.2, 0.12), glm::vec3(0.33, 0.5, 0.42), glm::vec3(0.33, 0.9, -0.62),
glm::vec3(0.33, 1.1, -1.756),
glm::vec3(0.66, 0.2, 0.12), glm::vec3(0.66, 0.5, 0.42), glm::vec3(0.66, 0.9, -0.62),
glm::vec3(0.66, 1.0, -1.756),
glm::vec3(1, 0.2, 0.8), glm::vec3(1, 0.5, 1), glm::vec3(1, 0.9, 1.1), glm::vec3(1, 1.2, 1)
}};
f.weights = {4, 4,
{
1, 1, 1, 1,
1, 1, 1, 1,
1, 1, 1, 1,
1, 1, 1, 1,
}
};
loopDetector.s = s;
loopDetector.f = f;
loopDetector.maxSplitLayer = 6;
// 需要做Loop检测的sub patch在最后一层上的下标的范围(每个范围都真包含于[0, 2^(maxSplitLayer-1)-1])
// 这里范围真包含于[0, 31]
loopDetector.detect({3, 11}, {4, 11}, {2, 7}, {6, 15});
glm::vec3 a(2, 3, 4);
glm::vec3 b(3, 7, 1);
auto nab = glm::normalize(a - b);
auto res = nab * (a - b);
auto ab = a * b;
cout << res.x << ", " << res.y << ", " << res.z << endl;
cout << nab.x << ", " << nab.y << ", " << nab.z << endl;
cout << ab.x << ", " << ab.y << ", " << ab.z << endl;
std::cout << "Hello, World!" << std::endl;
auto m = glm::mat2x2(1, 2, 3, 4);
cout << m[0][0] << " " << m[0][1] << endl;
auto dotRes = glm::dot(a, b);
cout << dotRes << endl;
cout<<isnan(glm::normalize(glm::vec3(0, 0, 0)).x)<<endl;
cout<<isnan(1.)<<endl;
// auto m1 = glm::mat2(1., 2.);
cout<<round(3.7)<<" "<<round(3.5657567658)<<" "<<round(3.2)<<" "<<round(3.0)<<endl;
return 0;
}

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src/loop_detector.cpp
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#include "loop_detector.h"
#include <utility>
const float PI = 3.1415927;
void LoopDetector::initEvaluation() {
// 初始化subPatch上所有采样点的值，以及它们的切向量，并存储
// 当该工具集成到系统中后，这一部分应该是可以直接全部去掉的
// 因为在GPU上已经做过对每个点的最细粒度的evaluation了，只需要从整个曲面把需要的subPatch找出来即可
// subPatch每条边上的采样点个数。边上的格子个数=range.second-range.first+1，采样点个数=格子个数+1
s_subPatchEdgeSampleCnt_u = s_subPatchIdxRange_u.second - s_subPatchIdxRange_u.first + 2;
s_subPatchEdgeSampleCnt_v = s_subPatchIdxRange_v.second - s_subPatchIdxRange_v.first + 2;
f_subPatchEdgeSampleCnt_u = f_subPatchIdxRange_u.second - f_subPatchIdxRange_u.first + 2;
f_subPatchEdgeSampleCnt_v = f_subPatchIdxRange_v.second - f_subPatchIdxRange_v.first + 2;
edgeSampleCnt = int(pow(2, maxSplitLayer - 1)) + 1;
s_evaluation = vector<vector<glm::vec3>>(s_subPatchEdgeSampleCnt_u, vector<glm::vec3>(s_subPatchEdgeSampleCnt_v));
f_evaluation = vector<vector<glm::vec3>>(f_subPatchEdgeSampleCnt_u, vector<glm::vec3>(f_subPatchEdgeSampleCnt_v));
// 曲面s和f的切向量。
s_tangent_u = vector<vector<glm::vec3>>(s_subPatchEdgeSampleCnt_u, vector<glm::vec3>(s_subPatchEdgeSampleCnt_v));
s_tangent_v = vector<vector<glm::vec3>>(s_subPatchEdgeSampleCnt_u, vector<glm::vec3>(s_subPatchEdgeSampleCnt_v));
f_tangent_u = vector<vector<glm::vec3>>(f_subPatchEdgeSampleCnt_u, vector<glm::vec3>(f_subPatchEdgeSampleCnt_v));
f_tangent_v = vector<vector<glm::vec3>>(f_subPatchEdgeSampleCnt_u, vector<glm::vec3>(f_subPatchEdgeSampleCnt_v));
auto s_first_u = *(s.knots_u.begin());
auto s_first_v = *(s.knots_v.begin());
auto s_step_u = (*(s.knots_u.end() - 1) - s_first_u) / float(edgeSampleCnt - 1);
auto s_step_v = (*(s.knots_v.end() - 1) - s_first_v) / float(edgeSampleCnt - 1);
auto f_first_u = *(f.knots_u.begin());
auto f_first_v = *(f.knots_v.begin());
auto f_step_u = (*(f.knots_u.end() - 1) - f_first_u) / float(edgeSampleCnt - 1);
auto f_step_v = (*(f.knots_v.end() - 1) - f_first_v) / float(edgeSampleCnt - 1);
for (int i = 0; i < s_subPatchEdgeSampleCnt_u; i++) {
auto u = s_first_u + s_step_u * float(s_subPatchIdxRange_u.first + i);
for (int j = 0; j < s_subPatchEdgeSampleCnt_v; j++) {
auto v = s_first_v + s_step_v * float(s_subPatchIdxRange_v.first + j);
s_evaluation[i][j] = tinynurbs::surfacePoint(s, u, v);
auto der = tinynurbs::surfaceDerivatives(s, 1, u, v);
s_tangent_u[i][j] = der(1, 0);
s_tangent_v[i][j] = der(0, 1);
}
}
for (int i = 0; i < f_subPatchEdgeSampleCnt_u; i++) {
auto u = f_first_u + f_step_u * float(f_subPatchIdxRange_u.first + i);
for (int j = 0; j < f_subPatchEdgeSampleCnt_v; j++) {
auto v = f_first_v + f_step_v * float(f_subPatchIdxRange_v.first + j);
f_evaluation[i][j] = tinynurbs::surfacePoint(f, u, v);
auto der = tinynurbs::surfaceDerivatives(f, 1, u, v);
f_tangent_u[i][j] = der(1, 0);
f_tangent_v[i][j] = der(0, 1);
}
}
}
void LoopDetector::initOrientedDistance() {
selectedPointsIdx = vector<vector<pair<int, int>>>(s_subPatchEdgeSampleCnt_u,
vector<pair<int, int>>(s_subPatchEdgeSampleCnt_v));
// distance = vector<vector<glm::vec3>>(s_subPatchEdgeSampleCnt_u, vector<glm::vec3>(s_subPatchEdgeSampleCnt_v));
for (int i = 0; i < s_subPatchEdgeSampleCnt_u; i++) {
for (int j = 0; j < s_subPatchEdgeSampleCnt_v; j++) {
float minDis = FLT_MAX;
int minDisFIdx_u = -1, minDisFIdx_v = -1;
for (int k = 0; k < f_subPatchEdgeSampleCnt_u; k++) {
for (int l = 0; l < f_subPatchEdgeSampleCnt_v; l++) {
auto dis = glm::distance(s_evaluation[i][j], f_evaluation[k][l]);
// 确定f上的对应点时，依据的最小欧氏距离，而不是有向距离
if (dis < minDis) {
minDis = dis;
minDisFIdx_u = k;
minDisFIdx_v = l;
}
}
}
// auto N = glm::normalize(s_evaluation[i][j] - f_evaluation[minDisFIdx_u][minDisFIdx_v]);
// // 直接normalize得到的单位向量总是与SF同向，但实际上N应当总是与f的一侧法向量成锐角
// auto testAngle = N * glm::cross(f_tangent_u[minDisFIdx_u][minDisFIdx_v], f_tangent_v[minDisFIdx_u][minDisFIdx_v]);
// N = testAngle.x + testAngle.y + testAngle.z > 0 ? N : -N;
// distance[i][j] = N * (s_evaluation[i][j] - f_evaluation[minDisFIdx_u][minDisFIdx_v]);
selectedPointsIdx[i][j] = {minDisFIdx_u, minDisFIdx_v};
}
}
}
void LoopDetector::initVectorField() {
vectorFields = vector<vector<glm::vec2>>(s_subPatchEdgeSampleCnt_u, vector<glm::vec2>(s_subPatchEdgeSampleCnt_v));
for (int i = 0; i < s_subPatchEdgeSampleCnt_u; i++) {
for (int j = 0; j < s_subPatchEdgeSampleCnt_v; j++) {
auto fPointIdx = selectedPointsIdx[i][j];
auto N = glm::normalize(s_evaluation[i][j] - f_evaluation[fPointIdx.first][fPointIdx.second]);
if (isnan(N.x) || isnan(N.y) || isnan(N.z)) {
// 绝了，曲面s和f的交线正好经过采样点，此时就无法定义向量N
// 这里取两个曲面在交点的法向量的平均做近似
auto tmp1 = glm::cross(s_tangent_u[i][j], s_tangent_v[i][j]);
auto tmp2 = glm::cross(f_tangent_u[fPointIdx.first][fPointIdx.second],
f_tangent_v[fPointIdx.first][fPointIdx.second]);
N = glm::normalize(glm::cross(s_tangent_u[i][j], s_tangent_v[i][j]) +
glm::cross(f_tangent_u[fPointIdx.first][fPointIdx.second],
f_tangent_v[fPointIdx.first][fPointIdx.second]));
}
// u1、u2两个向量构成和N垂直的曲面
glm::vec3 u1(1, 1, 1);
if (N.z != 0)u1.z = (-N.x - N.y) / N.z;
else if (N.y != 0)u1.y = (-N.x - N.z) / N.y;
else u1.x = (-N.y - N.z) / N.x;
u1 = glm::normalize(u1);
auto u2 = glm::normalize(glm::cross(N, u1));
// s，f曲面在两个方向上的偏导
auto ps_pu = s_tangent_u[i][j], ps_pv = s_tangent_v[i][j];
auto pf_pp = f_tangent_u[fPointIdx.first][fPointIdx.second], pf_pq = f_tangent_v[fPointIdx.first][fPointIdx.second];
// 构造Aij矩阵，见<Detection of loops and singularities of surface intersections> APPENDIX (A7)
auto inverseAij = glm::inverse(
glm::mat2x2(glm::dot(u1, pf_pp), glm::dot(u1, pf_pq), glm::dot(u2, pf_pp), glm::dot(u2, pf_pq))
);
auto mBmn = glm::mat2x2(glm::dot(u1, ps_pu), glm::dot(u1, ps_pv), glm::dot(u2, ps_pu), glm::dot(u2, ps_pv));
auto tmp = glm::vec2(glm::dot(N, pf_pp), glm::dot(N, pf_pq));
auto vNfpNfq_inverseAij = glm::vec2(glm::dot(N, pf_pp), glm::dot(N, pf_pq)) * inverseAij;
auto pd_pu = glm::dot(N, ps_pu) -
glm::dot(vNfpNfq_inverseAij, glm::vec2(glm::dot(u1, ps_pu), glm::dot(u2, ps_pu)));
auto pd_pv = glm::dot(N, ps_pv) -
glm::dot(vNfpNfq_inverseAij, glm::vec2(glm::dot(u1, ps_pv), glm::dot(u2, ps_pv)));
vectorFields[i][j] = glm::vec2(pd_pu, pd_pv);
}
}
int a = 1;
int b = 2;
}
void LoopDetector::getRotationNumber() {
// 以小格子为单位遍历
for (int i = 0; i < s_subPatchEdgeSampleCnt_u - 1; i++) {
for (int j = 0; j < s_subPatchEdgeSampleCnt_v - 1; j++) {
auto rotationNumber = 0.;
for (int biasI = 0; biasI < 2; biasI++) {
for (int biasJ = 0; biasJ < 2; biasJ++) {
auto v = vectorFields[i + biasI][j + biasJ];
rotationNumber += atan(double(v.x / v.y));
}
}
auto v00 = vectorFields[i][j];
auto v01 = vectorFields[i][j + 1];
auto v11 = vectorFields[i + 1][j + 1];
auto v10 = vectorFields[i + 1][j];
rotationNumber = 2 * atan(double (v11.x/v11.y)) - 2 * atan(double(v00.x/v00.y));
rotationNumber /= (2 * PI);
printf("rotationNumber: %lf\n", rotationNumber);
}
}
}
vector<pair<int, int>> LoopDetector::detect(pair<int, int> _s_subPatchIdxRange_u, pair<int, int> _s_subPatchIdxRange_v,
pair<int, int> _f_subPatchIdxRange_u,
pair<int, int> _f_subPatchIdxRange_v) {
s_subPatchIdxRange_u = _s_subPatchIdxRange_u;
s_subPatchIdxRange_v = _s_subPatchIdxRange_v;
f_subPatchIdxRange_u = _f_subPatchIdxRange_u;
f_subPatchIdxRange_v = _f_subPatchIdxRange_v;
initEvaluation(); // 当evaluation已经完成，这一步就不用了，直接传入两个evaluation矩阵和四个tangent矩阵的值即可
initOrientedDistance();
initVectorField();
getRotationNumber();
return {};
}
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