Algorithm 2 Parallel Resampling of Proposed Method

1:  struct vertex   2:  float x,y,z;   3:  float tx,tx,tz; /* original position */   4:  procedure SampleTetrahedron (Mat4 $\overline{X_0}$, vertex A, B, C, D, Tex3D outGrid, Tex3D inVolume)   5:   aabb boundingBox = outGrid.computeAABB(A, B, C, D);   6:   foreach (voxel in boundingBox)   7:    float4 baryCoords = computeBaryCoords (voxel.center, A, B, C, D);  /* $\mathrm{b}={\overline{X_1}}^{-1}\left(\begin{array}{c}{x}_1\\ 1\end{array}\right)$ in Equation (3) */   8:    if (centerLiesInsideTetrahedron(baryCoords))   9:     float4 inpos = $\overline{X_0}$ * baryCoords; 10:     float4 newValue = tex3D (inVolume, inpos.xyz); 11:    setValue (voxel, newValue); 12:   end if 13:  end foreach 14: end procedure