Comparing Isosurface With and Without Scatter Classes

We have recently added scatter classes to VTK-m, which allows building worklets that have a variable amount of output rather than a 1:1 relationship. This is particularly important for algorithms like isosurface that require specifying some amount of output depending on values of the input. Before these scatter classes were introduced, algorithms like isosurface had to build their own indices and then perform their own cross lookup. In addition to being inconvenient and difficult to read, it also meant that the algorithm could not take advantage of other VTK-m features available in the dispatcher/transport/fetch location.

This document compares the implementation of isosurface just before moving to scatter and just after.

The Code

The classify cell part of the isosurface algorithm has remained essentially the same, so we'll ignore that part. The implementation of the generate part of the algorithm has changed significantly in this transformation. We will look at the code in parts and compare the implementations directly.

Worklet State

Because the original implementation had to build its own indices and perform its own data lookups, it had to store array portals in the state of the worklet as well as auxiliary metadata so that the data could be reconstructed in the body of the worklet. In contrast, the new implementation can leverage VTK-m's built in ability to perform these data lookups. All that needs to be specified in the state is the Scatter class being used.

const FieldType Isovalue; vtkm::Id xdim, ydim, zdim; const float xmin, ymin, zmin, xmax, ymax, zmax; typedef typename vtkm::cont::ArrayHandle<FieldType>:: template ExecutionTypes<DeviceAdapter>::PortalConst FieldPortalType; FieldPortalType Field, Source; typedef typename vtkm::cont::ArrayHandle<vtkm::Vec<FieldType, 3> >:: template ExecutionTypes<DeviceAdapter>::Portal VectorPortalType; VectorPortalType Vertices; VectorPortalType Normals; typedef typename vtkm::cont::ArrayHandle<FieldType>:: template ExecutionTypes<DeviceAdapter>::Portal OutputPortalType; OutputPortalType Scalars; typedef typename vtkm::cont::ArrayHandle<vtkm::Id> IdArrayHandle; typedef typename IdArrayHandle::ExecutionTypes<DeviceAdapter>::PortalConst IdPortalType; IdPortalType TriTable; const vtkm::Id cellsPerLayer, pointsPerLayer;

const FieldType Isovalue; ScatterType Scatter;

Original Implementation

New implementation

As the amount of state has dramatically reduced, so has the the complexity of the constructor.

template<typename U, typename W, typename X> VTKM_CONT_EXPORT IsoSurfaceGenerate(FieldType ivalue, const vtkm::Id3 cdims, IdPortalType triTablePortal, const U & field, const U & source, const W & vertices, const W & normals, const X & scalars) : Isovalue(ivalue), xdim(cdims[0]), ydim(cdims[1]), zdim(cdims[2]), xmin(-1), ymin(-1), zmin(-1), xmax(1), ymax(1), zmax(1), Field( field.PrepareForInput( DeviceAdapter() ) ), Source( source.PrepareForInput( DeviceAdapter() ) ), Vertices(vertices), Normals(normals), Scalars(scalars), TriTable(triTablePortal), cellsPerLayer(xdim * ydim), pointsPerLayer ((xdim+1)*(ydim+1)) { }

template<typename CountArrayType, typename Device> VTKM_CONT_EXPORT IsoSurfaceGenerate(FieldType isovalue, const CountArrayType &countArray, Device) : Isovalue(isovalue), Scatter(countArray, Device()) { }

Original Implementation

New implementation

Signatures

Because the new implementation passes data through the dispatcher's invoke interface rather than as array state. Consequently, the interface of the ControlSignature and ExecutionSignature are much longer in the new interface, but they also specify more features of the transport/fetch.

typedef void ControlSignature(FieldIn<IdType> inputCellId, FieldIn<IdType> inputIteration); typedef void ExecutionSignature(WorkIndex, _1, _2);

typedef void ControlSignature( TopologyIn topology, // Cell set FieldInPoint<> fieldIn, // Input point field defining the contour FieldInPoint<Vec3> pcoordIn, // Input point coordinates FieldOutCell<> vertexOut, // Vertices for output triangles // TODO: Have a better way to iterate over and interpolate fields FieldInPoint<Scalar> scalarsIn, // Scalars to interpolate FieldOutCell<> scalarsOut, // Interpolated scalars (one per tri vertex) FieldOutCell<> normalsOut, // Estimated normals (one per tri vertex) ExecObject TriTable // An array portal with the triangle table ); typedef void ExecutionSignature( CellShape, _2, _3, _4, _5, _6, _7, _8, VisitIndex);

Original Implementation

New implementation

Likewise, the interface to the parentheses operator has grown commensurately.

VTKM_EXEC_EXPORT void operator()(vtkm::Id outputCellId, vtkm::Id inputCellId, vtkm::Id inputLowerBounds) const

template<typename CellShapeTag, typename FieldInType, // Vec-like, one per input point typename CoordType, // Vec-like (one per input point) of Vec-3 typename VertexOutType, // Vec-3 of Vec-3 coordinates (for triangle) typename ScalarInType, // Vec-like, one per input point typename ScalarOutType, // Vec-3 (one value per tri vertex) typename NormalOutType, // Vec-3 of Vec-3 typename TriTablePortalType> // Array portal VTKM_EXEC_EXPORT void operator()( CellShapeTag shape, const FieldInType &fieldIn, // Input point field defining the contour const CoordType &coords, // Input point coordinates VertexOutType &vertexOut, // Vertices for output triangles // TODO: Have a better way to iterate over and interpolate fields const ScalarInType &scalarsIn, // Scalars to interpolate ScalarOutType &scalarsOut, // Interpolated scalars (one per tri vertex) NormalOutType &normalsOut, // Estimated normals (one per tri vertex) const TriTablePortalType &triTable, // An array portal with the triangle table vtkm::IdComponent visitIndex ) const

Original Implementation

New implementation

The Meat

Of course, the meat of the worklet algorithm is the code inside the parentheses operator. The new implementation of this code is quite simplified because the operations to compute indices and load data are completely removed. Likewise the point coordinates do not have to be directly computed either. The only data not directly provided is the Marching Cubes case.

// Get data for this cell const int verticesForEdge[] = { 0, 1, 1, 2, 3, 2, 0, 3, 4, 5, 5, 6, 7, 6, 4, 7, 0, 4, 1, 5, 2, 6, 3, 7 }; const vtkm::Id x = inputCellId % xdim; const vtkm::Id y = (inputCellId / xdim) % ydim; const vtkm::Id z = inputCellId / cellsPerLayer; // Compute indices for the eight vertices of this cell const vtkm::Id i0 = x + y*(xdim+1) + z * pointsPerLayer; const vtkm::Id i1 = i0 + 1; const vtkm::Id i2 = i0 + 1 + (xdim + 1); //xdim is cell dim const vtkm::Id i3 = i0 + (xdim + 1); //xdim is cell dim const vtkm::Id i4 = i0 + pointsPerLayer; const vtkm::Id i5 = i1 + pointsPerLayer; const vtkm::Id i6 = i2 + pointsPerLayer; const vtkm::Id i7 = i3 + pointsPerLayer; // Get the field values at these eight vertices FieldType f[8]; f[0] = this->Field.Get(i0); f[1] = this->Field.Get(i1); f[2] = this->Field.Get(i2); f[3] = this->Field.Get(i3); f[4] = this->Field.Get(i4); f[5] = this->Field.Get(i5); f[6] = this->Field.Get(i6); f[7] = this->Field.Get(i7); // Compute the Marching Cubes case number for this cell unsigned int cubeindex = 0; cubeindex += (f[0] > this->Isovalue); cubeindex += (f[1] > this->Isovalue)*2; cubeindex += (f[2] > this->Isovalue)*4; cubeindex += (f[3] > this->Isovalue)*8; cubeindex += (f[4] > this->Isovalue)*16; cubeindex += (f[5] > this->Isovalue)*32; cubeindex += (f[6] > this->Isovalue)*64; cubeindex += (f[7] > this->Isovalue)*128; // printf("inputCellId: %i \n",inputCellId); // printf("x: %i, y: %i, z: %i \n",x, y, z); // printf("i0: %i \n",i0); // printf("f0 %F\n", f[0]); // printf("cubeindex: %i \n",cubeindex); // printf("numCells: %i \n",(vtkm::worklet::internal::numVerticesTable[cubeindex]/3) ); // Compute the coordinates of the uniform regular grid at each of the cell's eight vertices vtkm::Vec<FieldType, 3> p[8]; // If we have offset and spacing, can we simplify this computation { vtkm::Vec<FieldType, 3> offset = vtkm::make_Vec(xmin+(xmax-xmin), ymin+(ymax-ymin), zmin+(zmax-zmin) ); vtkm::Vec<FieldType, 3> spacing = vtkm::make_Vec( 1.0f /((float)(xdim-1)), 1.0f /((float)(ydim-1)), 1.0f /((float)(zdim-1))); vtkm::Vec<FieldType, 3> firstPoint = offset * spacing * vtkm::make_Vec( x, y, z ); vtkm::Vec<FieldType, 3> secondPoint = offset * spacing * vtkm::make_Vec( x+1, y+1, z+1 ); p[0] = vtkm::make_Vec( firstPoint[0], firstPoint[1], firstPoint[2]); p[1] = vtkm::make_Vec( secondPoint[0], firstPoint[1], firstPoint[2]); p[2] = vtkm::make_Vec( secondPoint[0], secondPoint[1], firstPoint[2]); p[3] = vtkm::make_Vec( firstPoint[0], secondPoint[1], firstPoint[2]); p[4] = vtkm::make_Vec( firstPoint[0], firstPoint[1], secondPoint[2]); p[5] = vtkm::make_Vec( secondPoint[0], firstPoint[1], secondPoint[2]); p[6] = vtkm::make_Vec( secondPoint[0], secondPoint[1], secondPoint[2]); p[7] = vtkm::make_Vec( firstPoint[0], secondPoint[1], secondPoint[2]); } // Get the scalar source values at the eight vertices FieldType s[8]; s[0] = this->Source.Get(i0); s[1] = this->Source.Get(i1); s[2] = this->Source.Get(i2); s[3] = this->Source.Get(i3); s[4] = this->Source.Get(i4); s[5] = this->Source.Get(i5); s[6] = this->Source.Get(i6); s[7] = this->Source.Get(i7);

// Get data for this cell const vtkm::IdComponent verticesForEdge[] = { 0, 1, 1, 2, 3, 2, 0, 3, 4, 5, 5, 6, 7, 6, 4, 7, 0, 4, 1, 5, 2, 6, 3, 7 }; // Compute the Marching Cubes case number for this cell vtkm::IdComponent cubeindex = 0; cubeindex += (fieldIn[0] > this->Isovalue); cubeindex += (fieldIn[1] > this->Isovalue)*2; cubeindex += (fieldIn[2] > this->Isovalue)*4; cubeindex += (fieldIn[3] > this->Isovalue)*8; cubeindex += (fieldIn[4] > this->Isovalue)*16; cubeindex += (fieldIn[5] > this->Isovalue)*32; cubeindex += (fieldIn[6] > this->Isovalue)*64; cubeindex += (fieldIn[7] > this->Isovalue)*128;

Original Implementation

New implementation

Note that although the new code is significantly smaller, it corrects a major bug in the original implementation where the point coordinates were not being computed correctly. This is because we are using the shared code in the VTK-m library that we know is consistent and correct.

The remainder of the code is interpolating values on the edges. This code is largely the same. Note, however, that I have changed most of the variable names to be more expressive (for code readability), which makes the code extend a few more lines. Also note that I changed the normal computation. The original code used the normal for the triangle generated whereas the new code uses to gradient of the 3D field. The gradient is a bit more accurate.

// Interpolate for vertex positions and associated scalar values const vtkm::Id inputIteration = (outputCellId - inputLowerBounds); const vtkm::Id outputVertId = outputCellId * 3; const vtkm::Id cellOffset = static_cast<vtkm::Id>(cubeindex*16) + (inputIteration * 3); for (int v = 0; v < 3; v++) { const vtkm::Id edge = this->TriTable.Get(cellOffset + v); const int v0 = verticesForEdge[2*edge]; const int v1 = verticesForEdge[2*edge + 1]; const FieldType t = (this->Isovalue - f[v0]) / (f[v1] - f[v0]); this->Vertices.Set(outputVertId + v, vtkm::Lerp(p[v0], p[v1], t)); this->Scalars.Set(outputVertId + v, vtkm::Lerp(s[v0], s[v1], t)); } vtkm::Vec<FieldType, 3> vertex0 = this->Vertices.Get(outputVertId + 0); vtkm::Vec<FieldType, 3> vertex1 = this->Vertices.Get(outputVertId + 1); vtkm::Vec<FieldType, 3> vertex2 = this->Vertices.Get(outputVertId + 2); vtkm::Vec<FieldType, 3> curNorm = vtkm::Cross(vertex1-vertex0, vertex2-vertex0); vtkm::Normalize(curNorm); this->Normals.Set(outputVertId + 0, curNorm); this->Normals.Set(outputVertId + 1, curNorm); this->Normals.Set(outputVertId + 2, curNorm); }

// Interpolate for vertex positions and associated scalar values const vtkm::Id triTableOffset = static_cast<vtkm::Id>(cubeindex*16 + visitIndex*3); for (vtkm::IdComponent triVertex = 0; triVertex < 3; triVertex++) { const vtkm::IdComponent edgeIndex = triTable.Get(triTableOffset + triVertex); const vtkm::IdComponent edgeVertex0 = verticesForEdge[2*edgeIndex + 0]; const vtkm::IdComponent edgeVertex1 = verticesForEdge[2*edgeIndex + 1]; const FieldType fieldValue0 = fieldIn[edgeVertex0]; const FieldType fieldValue1 = fieldIn[edgeVertex1]; const FieldType interpolant = (this->Isovalue - fieldValue0) / (fieldValue1 - fieldValue0); vertexOut[triVertex] = vtkm::Lerp(coords[edgeVertex0], coords[edgeVertex1], interpolant); scalarsOut[triVertex] = vtkm::Lerp(scalarsIn[edgeVertex0], scalarsIn[edgeVertex1], interpolant); const vtkm::Vec<vtkm::FloatDefault,3> edgePCoord0 = vtkm::exec::ParametricCoordinatesPoint( fieldIn.GetNumberOfComponents(), edgeVertex0, shape, *this); const vtkm::Vec<vtkm::FloatDefault,3> edgePCoord1 = vtkm::exec::ParametricCoordinatesPoint( fieldIn.GetNumberOfComponents(), edgeVertex1, shape, *this); const vtkm::Vec<vtkm::FloatDefault,3> interpPCoord = vtkm::Lerp(edgePCoord0, edgePCoord1, interpolant); normalsOut[triVertex] = vtkm::Normal(vtkm::exec::CellDerivative( fieldIn, coords, interpPCoord, shape, *this)); }

Original Implementation

New implementation

Original Implementation	New implementation