在VTK TCL脚本教程中，经常看到这样的系数设置：
quadric->SetCoefficients( .5, 1, .2, 0, .1, 0, 0, .2, 0, 0 );
我们需要知道，三元二次方程代表了空间中的曲面：
可以看出，这里有10个系数，他们对应着Coefficients。
#include <vtkActor.h>
#include <vtkCamera.h>
#include <vtkContourFilter.h>
#include <vtkNamedColors.h>
#include <vtkOutlineFilter.h>
#include <vtkPolyDataMapper.h>
#include <vtkProperty.h>
#include <vtkQuadric.h>
#include <vtkRenderWindow.h>
#include <vtkRenderWindowInteractor.h>
#include <vtkRenderer.h>
#include <vtkSampleFunction.h>
int main( int, char *[] )
{
vtkSmartPointer<vtkNamedColors> colors =
vtkSmartPointer<vtkNamedColors>::New();
vtkSmartPointer<vtkRenderer> aren =
vtkSmartPointer<vtkRenderer>::New();
vtkSmartPointer<vtkRenderWindow> renWin =
vtkSmartPointer<vtkRenderWindow>::New();
renWin->AddRenderer(aren);
vtkSmartPointer<vtkRenderWindowInteractor> iren =
vtkSmartPointer<vtkRenderWindowInteractor>::New();
iren->SetRenderWindow(renWin);
//
// Create surfaces F(x,y,z) = constant
//
// Sample quadric function
vtkSmartPointer<vtkQuadric> quadric =
vtkSmartPointer<vtkQuadric>::New();
// 0.5 * x^2 + 1 * y^2 + 0.2 * z^2 + 0 * xy + 0.1 * yz + 0 * zx + 0 * x + 0.2 * y + 0 * z + 0 = 0
quadric->SetCoefficients( .5, 1, .2, 0, .1, 0, 0, .2, 0, 0 );
vtkSmartPointer<vtkSampleFunction> sample =
vtkSmartPointer<vtkSampleFunction>::New();
sample->SetSampleDimensions( 50, 50, 50 );
sample->SetImplicitFunction( quadric );
vtkSmartPointer<vtkContourFilter> contour =
vtkSmartPointer<vtkContourFilter>::New();
contour->SetInputConnection( sample->GetOutputPort() );
contour->GenerateValues( 6, 0, 2 );
vtkSmartPointer<vtkPolyDataMapper> contourMapper =
vtkSmartPointer<vtkPolyDataMapper>::New();
contourMapper->SetInputConnection(contour->GetOutputPort());
contourMapper->SetScalarRange( 0, 2 );
vtkSmartPointer<vtkActor> contourActor =
vtkSmartPointer<vtkActor>::New();
contourActor->SetMapper(contourMapper);
// Create outline
// vtkSmartPointer<vtkOutlineFilter> outline =
// vtkSmartPointer<vtkOutlineFilter>::New();
// outline->SetInputConnection( sample->GetOutputPort() );
// vtkSmartPointer<vtkPolyDataMapper> outlineMapper =
// vtkSmartPointer<vtkPolyDataMapper>::New();
// outlineMapper->SetInputConnection(outline->GetOutputPort());
// vtkSmartPointer<vtkActor> outlineActor =
// vtkSmartPointer<vtkActor>::New();
// outlineActor->SetMapper( outlineMapper );
// outlineActor->GetProperty()->SetColor(colors->GetColor3d("Brown").GetData());
// outlineActor->GetProperty()->SetLineWidth(3.0);
//
// Rendering stuff
//
aren->SetBackground(colors->GetColor3d("SlateGray").GetData());
aren->AddActor(contourActor);
//aren->AddActor(outlineActor);
aren->ResetCamera();
aren->GetActiveCamera()->Azimuth(30);
aren->GetActiveCamera()->Elevation(30);
renWin->SetSize(640, 512);
renWin->Render();
// interact with data
iren->Start();
return EXIT_SUCCESS;
} 上面例子中的系数对应的方程是：
ContourPlot3D[0.5 * x^2 + 1 * y^2 + 0.2 * z^2 + 0 * x*y + 0.1 * y*z + 0 * z*x + 0 * x + 0.2 * y + 0 * z + 0 == 0, {x, 0, 50}, {y, 0, 50}, {z, 0, 50}]
但为什么是空呢？
(在mathematics上绘图而成)
使用采样的方法研究这个三元二次函数，得到的图像是这样的：
Here is code:
package require vtk
package require vtkinteraction
vtkQuadric quadric
quadric SetCoefficients .5 1 .2 0 .1 0 0 .2 0 0
vtkSampleFunction sample
sample SetSampleDimensions 50 50 50
sample SetImplicitFunction quadric
sample ComputeNormalsOff
vtkDataSetMapper dataMapper
dataMapper SetInputConnection [sample GetOutputPort]
vtkActor dataActor
dataActor SetMapper dataMapper
# The outline gives context to the original data.
vtkOutlineFilter outline
outline SetInputConnection [sample GetOutputPort]
vtkPolyDataMapper outlineMapper
outlineMapper SetInputConnection [outline GetOutputPort]
vtkActor outlineActor
outlineActor SetMapper outlineMapper
set outlineProp [outlineActor GetProperty]
eval $outlineProp SetColor 0 0 0
vtkRenderer ren1
vtkRenderWindow renWin
renWin AddRenderer ren1
vtkRenderWindowInteractor iren
iren SetRenderWindow renWin
#ren1 AddActor outlineActor
ren1 AddActor dataActor
ren1 SetBackground 1 1 1
renWin SetSize 500 500
ren1 ResetCamera
[ren1 GetActiveCamera] Zoom 1.5
iren Initialize
iren AddObserver UserEvent {wm deiconify .vtkInteract}
# prevent the tk window from showing up then start the event loop
wm withdraw .
iren Start
