comments

algoim/bernstein.hpp

@@ -581,7 +581,7 @@ namespace algoim::bernstein
     // Methods to compute, and cache, the SVD for Bernstein interpolation based on modified Chebysev nodes
     struct BernsteinVandermondeSVD
     {
-        struct SVD
+        struct SVD  // 将矩阵A分解为U * diag(sigma) * Vt，其中U和Vt是正交矩阵，sigma是对角矩阵
         {
             real *U;
             real *Vt;
@@ -619,6 +619,8 @@ namespace algoim::bernstein
     }; 
 
     // Interpolate tensor-product data f, assumed to be nodal values at the same nodes returned by modifiedChebyshevNode()
+    // ？
+    // out: control points ?
     template<int N, bool B = false>
     void bernsteinInterpolate(const xarray<real,N>& f, real tol, xarray<real,N>& out)
     {

algoim/quadrature_multipoly.hpp

@@ -497,7 +497,7 @@ namespace algoim
         PolySet<N,ALGOIM_M> phi;                                                // Given N-dimensional polynomials
         int k;                                                                  // Elimination axis/height direction; k = N if there are no interfaces
         ImplicitPolyQuadrature<N-1> base;                                       // Base polynomials corresponding to removal of axis k
-        bool auto_apply_TS;                                                     // If quad method is auto chosen, indicates whether TS is applied
+        bool auto_apply_TS;                                                     // If quad method is auto chosen, indicates whether TS is applied  // what is ts ? 
         IntegralType type;                                                      // Whether an inner integral, or outer of two kinds
         std::array<std::tuple<int,ImplicitPolyQuadrature<N-1>>,N-1> base_other; // Stores other base cases, besides k, when in aggregate mode
 
@@ -611,6 +611,7 @@ namespace algoim
             assert(0 <= k && k <= N);
 
             // If there are no interfaces, apply rectangular tensor-product Gauss-Legendre quadrature
+            // 所以这个是积分域包裹了整个box时的做法？
             if (k == N)
             {
                 assert(!auto_apply_TS);
@@ -620,7 +621,7 @@ namespace algoim
                     real w = 1.0;
                     for (int dim = 0; dim < N; ++dim)
                     {
-                        x(dim) = GaussQuad::x(q, i(dim));
+                        x(dim) = GaussQuad::x(q, i(dim));   // 0 <= i(dim) < q
                         w *= GaussQuad::w(q, i(dim));
                     }
                     f(x, w);
@@ -629,6 +630,7 @@ namespace algoim
             }
 
             // Determine maximum possible number of roots; used to allocate a small buffer
+            // ???
             int max_count = 2;
             for (size_t i = 0; i < phi.count(); ++i)
                 max_count += phi.poly(i).ext(k) - 1;

compile_output.txt

@@ -0,0 +1,3 @@
+C:\Users\Dtouch\AppData\Local\Temp\ccH8XvNG.s:37:2: error: unknown directive
+        .ident  "GCC: (GNU) 13.1.0"
+        ^

exampleA-phase0.vtp

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exampleA-phase1.vtp

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+<?xml version="1.0"?>
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exampleA-surf.vtp

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exampleB-phase0.vtp

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exampleB-phase1.vtp

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exampleB-surf.vtp

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exampleC-surf.vtp

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+</Points>
+<Verts>
+  <DataArray type="Int32" Name="connectivity" format="ascii">0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 </DataArray>
+  <DataArray type="Int32" Name="offsets" format="ascii">1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 </DataArray>
+</Verts>
+<PointData Scalars="w">
+  <DataArray type="Float32" Name="w" NumberOfComponents="1" format="ascii">0.12536 0.122026 0.220307 0.214732 0.15198 0.144566 0.14338 0.131986 0.263692 0.21508 0.275384 0.138375 0.0514321 0.0844645 0.0547052 </DataArray>
+</PointData>
+</Piece>
+</PolyData>
+</VTKFile>

exampleC-vol.vtp

@@ -0,0 +1,17 @@
+<?xml version="1.0"?>
+<VTKFile type="PolyData" version="0.1" byte_order="LittleEndian">
+<PolyData>
+<Piece NumberOfPoints="81" NumberOfVerts="81" NumberOfLines="0" NumberOfStrips="0" NumberOfPolys="0">
+<Points>
+  <DataArray type="Float32" Name="Points" NumberOfComponents="3" format="ascii">0.047469 0.0394771 0 0.047469 0.17514 0 0.047469 0.310802 0 0.047469 0.401433 0 0.047469 0.577223 0 0.047469 0.753013 0 0.047469 0.826238 0 0.047469 0.902083 0 0.047469 0.977929 0 0.210596 0.0474188 0 0.210596 0.210373 0 0.210596 0.373328 0 0.210596 0.454733 0 0.210596 0.571526 0 0.210596 0.688319 0 0.210596 0.753602 0 0.210596 0.861153 0 0.210596 0.968703 0 0.373722 0.0594714 0 0.373722 0.263844 0 0.373722 0.468217 0 0.373722 0.536219 0 0.373722 0.565532 0 0.373722 0.594845 0 0.373722 0.648076 0 0.373722 0.801688 0 0.373722 0.9553 0 0.463715 0.0590711 0 0.463715 0.262068 0 0.463715 0.465066 0 0.463715 0.53212 0 0.463715 0.559555 0 0.463715 0.586989 0 0.463715 0.64062 0 0.463715 0.797486 0 0.463715 0.954353 0 0.60985 0.0417514 0 0.60985 0.18523 0 0.60985 0.328708 0 0.60985 0.408688 0 0.60985 0.540059 0 0.60985 0.67143 0 0.60985 0.742381 0 0.60985 0.854829 0 0.60985 0.967278 0 0.755984 0.0148467 0 0.755984 0.0658671 0 0.755984 0.116888 0 0.755984 0.210513 0 0.755984 0.481237 0 0.755984 0.751961 0 0.755984 0.849816 0 0.755984 0.91537 0 0.755984 0.980924 0 0.813994 0.0993885 0 0.813994 0.440936 0 0.813994 0.782484 0 0.813994 0.895186 0 0.813994 0.940936 0 0.813994 0.986687 0 0.86721 0.104954 0 0.86721 0.46563 0 0.86721 0.826305 0 0.86721 0.939006 0 0.86721 0.96563 0 0.86721 0.992253 0 0.920426 0.110888 0 0.920426 0.491953 0 0.920426 0.873019 0 0.920426 0.98572 0 0.920426 0.991953 0 0.920426 0.998186 0 0.943135 0.112702 0 0.943135 0.5 0 0.943135 0.887298 0 0.967956 0.112702 0 0.967956 0.5 0 0.967956 0.887298 0 0.992777 0.112702 0 0.992777 0.5 0 0.992777 0.887298 0 </DataArray>
+</Points>
+<Verts>
+  <DataArray type="Int32" Name="connectivity" format="ascii">0 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 </DataArray>
+  <DataArray type="Int32" Name="offsets" format="ascii">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 </DataArray>
+</Verts>
+<PointData Scalars="w">
+  <DataArray type="Float32" Name="w" NumberOfComponents="1" format="ascii">0.0113838 0.0182142 0.0113838 0.014751 0.0236016 0.014751 0.00636445 0.0101831 0.00636445 0.0218784 0.0350054 0.0218784 0.0156807 0.0250892 0.0156807 0.0144398 0.0231037 0.0144398 0.0171495 0.0274392 0.0171495 0.00245976 0.00393562 0.00245976 0.01289 0.0206241 0.01289 0.0152597 0.0244155 0.0152597 0.0020623 0.00329969 0.0020623 0.011792 0.0188671 0.011792 0.0172569 0.027611 0.0172569 0.0158007 0.0252811 0.0158007 0.0135248 0.0216396 0.0135248 0.00383531 0.00613649 0.00383531 0.0203508 0.0325613 0.0203508 0.00492783 0.00788452 0.00492783 0.00934972 0.0149596 0.00934972 0.0012524 0.00200384 0.0012524 0.0157973 0.0252757 0.0157973 0.00116608 0.00186572 0.00116608 0.0104315 0.0166904 0.0104315 0.000170626 0.000273002 0.000170626 0.00494509 0.00791214 0.00494509 0.00791214 0.0126594 0.00791214 0.00494509 0.00791214 0.00494509 </DataArray>
+</PointData>
+</Piece>
+</PolyData>
+</VTKFile>

test.cpp

@@ -0,0 +1,9 @@
+#include <iostream>
+#include <cstdio>
+
+using namespace std;
+
+int main() {
+    cout << "Hello, World!" << endl;
+    return 0;
+}