11、VTK重要数学知识：平面和法向量

走好每一步2026-06-15 10:51

法向量的定义蛮简单，就是任意平面上的向量都与法向量垂直

根据2个向量点积为0垂直特性，那就很容易从定义得到点法式方程，再由点法式展开得到一般式方程

cpp 复制代码

#include "MainWindow.h"

#include <QApplication>
#include <vtkPolyDataMapper.h>
#include <vtkActor.h>
#include <vtkRenderWindow.h>
#include <vtkRenderer.h>
#include <vtkRenderWindowInteractor.h>
#include <vtkCamera.h>
#include <vtkProperty.h>
#include <vtkAxesActor.h>
#include <vtkPlaneSource.h>

#include <vtkAutoInit.h>
VTK_MODULE_INIT(vtkRenderingOpenGL2)
VTK_MODULE_INIT(vtkInteractionStyle)
VTK_MODULE_INIT(vtkRenderingFreeType)

int main(int argc, char *argv[])
{
    auto plane = vtkSmartPointer<vtkPlaneSource>::New();
    plane->SetNormal(0, 1, 0);
    plane->SetCenter(0, 0, 0);


    auto mapper = vtkSmartPointer<vtkPolyDataMapper>::New();
    mapper->SetInputConnection(plane->GetOutputPort());

    auto actor = vtkSmartPointer<vtkActor>::New();
    actor->SetMapper(mapper);
    actor->GetProperty()->SetColor(1, 0, 0);

    auto actorAxes = vtkSmartPointer<vtkAxesActor>::New();

    auto render = vtkSmartPointer<vtkRenderer>::New();
    render->SetBackground(0.1, 0.2, 0.3);
    render->AddActor(actor);
    render->AddActor(actorAxes);

    render->GetActiveCamera()->SetFocalPoint(0, 0, 0);
    render->GetActiveCamera()->SetPosition(5, 3, 5);

    auto wd = vtkSmartPointer<vtkRenderWindow>::New();
    wd->AddRenderer(render);

    auto interator = vtkSmartPointer<vtkRenderWindowInteractor>::New();
    wd->SetInteractor(interator);
    wd->SetSize(800, 600);
    wd->SetPosition(200, 200);

    wd->Render();
    interator->Start();

    return 0;
}