vtk中实现网格细化的累有vtkLinearSubdivisionFilter、vtkLoopsubdivisionFilter、vtkButterflySubdivisionFilter。这三个类都继承自vtkInterpolatingSubdivisionFilter。具体的类的继承关系图如下图所示：

vtkInterpolatingSunvisionFilter内部提供了SetNumberOfSubvisions()函数来设置细化的次数，其中每次细化后模型的三角面片的个数将是细化前的四倍。因此，在对网格模型进行n次细化后，该模型的面片个数将是原始模型面片数目的4*n倍。

1.1 vtkLinearSubdivisionFilter

该类实现了一种线性细分算法，每次细分将每个三角形面片生成四个新的面片，该算法比较简单，速度快，但是细分后不能产生光滑的模型。

1.2 vtkLoopSubdivisionFilter

该类实现的是Loop细分算法，每次细分会将一个三角面片生成4个三角面片，具体算法思想可以参考文献[1]；该方法可以生成光滑的连续曲面，应用比较广泛。

1.3 vtkButterflySubdivisionFilter

该类实现了蝶形细分算法，具体的算法思想可以参考文献[2].

2.网格模型细化实验

#include <vtkAutoInit.h>
VTK_MODULE_INIT(vtkRenderingOpenGL);
VTK_MODULE_INIT(vtkRenderingFreeType);
VTK_MODULE_INIT(vtkInteractionStyle);#include <vtkSmartPointer.h>
#include <vtkPolyDataReader.h>
#include <vtkPolyData.h>
#include <vtkLinearSubdivisionFilter.h>
#include <vtkLoopSubdivisionFilter.h>
#include <vtkButterflySubdivisionFilter.h>
#include <vtkPolyDataMapper.h>
#include <vtkActor.h>
#include <vtkRenderer.h>
#include <vtkRenderWindow.h>
#include <vtkCamera.h>
#include <vtkRenderWindowInteractor.h>int main()
{//读数据vtkSmartPointer<vtkPolyDataReader> reader =vtkSmartPointer<vtkPolyDataReader>::New();reader->SetFileName("fran_cut.vtk");reader->Update();vtkSmartPointer<vtkPolyData> orig = reader->GetOutput();std::cout << "original" << "-----------------------" << std::endl;std::cout << "模型点数为： " << orig->GetNumberOfPoints() << std::endl;std::cout << "模型面数为： " << orig->GetNumberOfPolys() << std::endl;//线性网格细分滤波器vtkSmartPointer<vtkLinearSubdivisionFilter> linear =vtkSmartPointer<vtkLinearSubdivisionFilter>::New();linear->SetInputData(orig);linear->SetNumberOfSubdivisions(4);linear->Update();vtkSmartPointer<vtkPolyData> linearInfo = linear->GetOutput();std::cout << "linear" << "-----------------------" << std::endl;std::cout << "模型点数为： " << linearInfo->GetNumberOfPoints() << std::endl;std::cout << "模型面数为： " << linearInfo->GetNumberOfPolys() << std::endl;//Loop网格细分滤波器vtkSmartPointer<vtkLoopSubdivisionFilter> loop =vtkSmartPointer<vtkLoopSubdivisionFilter>::New();loop->SetInputData(orig);loop->SetNumberOfSubdivisions(4);loop->Update();vtkSmartPointer<vtkPolyData> loopInfo = loop->GetOutput();std::cout << "loop" << "-----------------------" << std::endl;std::cout << "模型点数为： " << loopInfo->GetNumberOfPoints() << std::endl;std::cout << "模型面数为： " << loopInfo->GetNumberOfPolys() << std::endl;//butterfly网格细分滤波器vtkSmartPointer<vtkButterflySubdivisionFilter> butterfly =vtkSmartPointer<vtkButterflySubdivisionFilter>::New();butterfly->SetInputData(orig);butterfly->SetNumberOfSubdivisions(4);butterfly->Update();vtkSmartPointer<vtkPolyData> butterflyInfo = butterfly->GetOutput();std::cout << "butterfly" << "-----------------------" << std::endl;std::cout << "模型点数为： " << butterflyInfo->GetNumberOfPoints() << std::endl;std::cout << "模型面数为： " << butterflyInfo->GetNumberOfPolys() << std::endl;vtkSmartPointer<vtkPolyDataMapper> origMapper =vtkSmartPointer<vtkPolyDataMapper>::New();origMapper->SetInputData(orig);vtkSmartPointer<vtkActor> origActor =vtkSmartPointer<vtkActor>::New();origActor->SetMapper(origMapper);vtkSmartPointer<vtkPolyDataMapper> linearMapper =vtkSmartPointer<vtkPolyDataMapper>::New();linearMapper->SetInputData(linear->GetOutput());vtkSmartPointer<vtkActor> linearActor =vtkSmartPointer<vtkActor>::New();linearActor->SetMapper(linearMapper);vtkSmartPointer<vtkPolyDataMapper> loopMapper =vtkSmartPointer<vtkPolyDataMapper>::New();loopMapper->SetInputData(loop->GetOutput());vtkSmartPointer<vtkActor> loopActor =vtkSmartPointer<vtkActor>::New();loopActor->SetMapper(loopMapper);vtkSmartPointer<vtkPolyDataMapper> butterflyMapper =vtkSmartPointer<vtkPolyDataMapper>::New();butterflyMapper->SetInputData(butterfly->GetOutput());vtkSmartPointer<vtkActor> butterflyActor =vtkSmartPointer<vtkActor>::New();butterflyActor->SetMapper(butterflyMapper);//double ltView[4] = { 0, 0, 0.5, 0.5 };double rtView[4] = { 0.5, 0, 1, 0.5 };double lbView[4] = { 0, 0.5, 0.5, 1 };double rbView[4] = { 0.5, 0.5, 1, 1 };vtkSmartPointer<vtkRenderer> origRender =vtkSmartPointer<vtkRenderer>::New();origRender->SetViewport(ltView);origRender->AddActor(origActor);origRender->SetBackground(1, 0, 0);vtkSmartPointer<vtkRenderer> linearRender =vtkSmartPointer<vtkRenderer>::New();linearRender->SetViewport(rtView);linearRender->AddActor(linearActor);linearRender->SetBackground(0, 1, 0);vtkSmartPointer<vtkRenderer> loopRender =vtkSmartPointer<vtkRenderer>::New();loopRender->SetViewport(lbView);loopRender->AddActor(loopActor);loopRender->SetBackground(0, 0, 1);vtkSmartPointer<vtkRenderer> butterflyRender =vtkSmartPointer<vtkRenderer>::New();butterflyRender->SetViewport(rbView);butterflyRender->AddActor(butterflyActor);butterflyRender->SetBackground(0, 0, 0);//vtkSmartPointer<vtkRenderWindow> rw =vtkSmartPointer<vtkRenderWindow>::New();rw->AddRenderer(origRender);rw->AddRenderer(linearRender);rw->AddRenderer(loopRender);rw->AddRenderer(butterflyRender);rw->SetSize(640, 640);rw->SetWindowName("PolyData Subdivision");origRender->GetActiveCamera()->SetPosition(0, -1, 0);origRender->GetActiveCamera()->SetFocalPoint(0, 0, 0);origRender->GetActiveCamera()->SetViewUp(0, 0, 1);origRender->GetActiveCamera()->Azimuth(30);origRender->GetActiveCamera()->Elevation(30);origRender->ResetCamera();//刷新照相机  linearRender->SetActiveCamera(origRender->GetActiveCamera());loopRender->SetActiveCamera(origRender->GetActiveCamera());butterflyRender->SetActiveCamera(origRender->GetActiveCamera());vtkSmartPointer<vtkRenderWindowInteractor> rwi =vtkSmartPointer<vtkRenderWindowInteractor>::New();rwi->SetRenderWindow(rw);rwi->Start();rw->Render();return 0;
}

输出结果：

红色视窗为原始三角网格模型，绿色视窗采用了线性细分算法；蓝色视窗采用Loop细分算法；黑色视窗采用了Butterfly细分算法。

鼻子部位的细节图：

从上面结果上看，我们可以看出：线性细分效果似乎没有起到多大作用？？！Loop细分结果得到了很光滑的曲面，Butterfly细分在细节部分处理的并不很理想。

注意事项：

所有模型细化算子仅对三角网格数据有效，因此在处理多边形数据时，需要通过VTKTriangleFilter将多边形网格转换为三角网格才能处理。

3.参考文献

[1] Loop C T. Smooth Subdivision Surfaces Based on Triangles[J]. Department of Mathematics the University of Utah Masters Thesis, 1987.

[2] Zorin D, Der P, Sweldens W. Interpolating Subdivision for meshes with arbitrary topology[C]// Conference on Computer Graphics and Interactive Techniques. ACM, 1996:189-192.

4.参看资料

1.《C++ primer》
2.《The VTK User’s Guide – 11thEdition》
3.  张晓东, 罗火灵. VTK图形图像开发进阶[M]. 机械工业出版社, 2015.