前言：在很多情况下，需要根据点云来拟合球体，本博文主要介绍各种方法的拟合情况及优缺点，希望对各位小伙伴有所帮助！

目录

1. vtkFitImplicitFunction进行球拟合

2. 四点求解球

---

1. vtkFitImplicitFunction进行球拟合

缺点：需要输入待拟合球的半径和结构，即在已知最优解的情况下求解。

vtkMath::RandomSeed(4355412); // for test result consistency

double radius = 1.0;
vtkSmartPointer<vtkBoundedPointSource> points =
    vtkSmartPointer<vtkBoundedPointSource>::New();
points->SetNumberOfPoints(1000000);
points->SetBounds(-2.0, 2.0, -2.0, 2.0, -2.0, 2.0);
points->Update();

vtkSmartPointer<vtkSphere> sphere =
    vtkSmartPointer<vtkSphere>::New();
sphere->SetRadius(radius*2);

vtkSmartPointer<vtkFitImplicitFunction> fit =
    vtkSmartPointer<vtkFitImplicitFunction>::New();
fit->SetInputConnection(points->GetOutputPort());
fit->SetImplicitFunction(sphere);
fit->SetThreshold(.01);
fit->Update();
std::cout << fit->GetOutput()->GetNumberOfPoints() << " out of "
    << points->GetNumberOfPoints() << " points are within "
    << fit->GetThreshold() << " of the implicit function" << std::endl;

vtkSmartPointer<vtkSphereSource> sphereSource =
    vtkSmartPointer<vtkSphereSource>::New();
sphereSource->SetRadius(radius * .05);

vtkSmartPointer<vtkGlyph3D> glyph3D =
    vtkSmartPointer<vtkGlyph3D>::New();
glyph3D->SetInputConnection(fit->GetOutputPort());
glyph3D->SetSourceConnection(sphereSource->GetOutputPort());
glyph3D->ScalingOff();
glyph3D->Update();

vtkSmartPointer<vtkPolyDataMapper> glyph3DMapper =
    vtkSmartPointer<vtkPolyDataMapper>::New();
glyph3DMapper->SetInputConnection(glyph3D->GetOutputPort());

vtkSmartPointer<vtkActor> glyph3DActor =
    vtkSmartPointer<vtkActor>::New();
glyph3DActor->SetMapper(glyph3DMapper);
glyph3DActor->GetProperty()->SetColor(0.8900, 0.8100, 0.3400);

m_viewer->renderWindow()->GetRenderers()->GetFirstRenderer()->AddActor(glyph3DActor);
m_viewer->renderWindow()->Render();

2. 四点求解球

缺点：要求输入的四点为精确球上的点；否则计算错误。

void fitSphere(vtkPoints* points, double center[3], double& radius) {

    double p1[3];
    double p2[3];
    double p3[3];
    double p4[3];
    points->GetPoint(0, p1);
    points->GetPoint(1, p2);
    points->GetPoint(2, p3);
    points->GetPoint(3, p4);

    double a = p1[0] - p2[0], b = p1[1] - p2[1], c = p1[2] - p2[2];
    double a1 = p3[0] - p4[0], b1 = p3[1] - p4[1], c1 = p3[2] - p3[2];
    double a2 = p2[0] - p3[0], b2 = p2[1] - p3[1], c2 = p2[2] - p3[2];
    double D = a * b1 * c2 + a2 * b * c1 + c * a1 * b2 - (a2 * b1 * c + a1 * b * c2 + a * b2 * c1);
    if (D == 0)
    {
        return;
    }

    double A = p1[0] * p1[0] - p2[0] * p2[0];
    double B = p1[1] * p1[1] - p2[1] * p2[1];
    double C = p1[2] * p1[2] - p2[2] * p2[2];
    double A1 = p3[0] * p3[0] - p4[0] * p4[0];
    double B1 = p3[1] * p3[1] - p4[1] * p4[1];
    double C1 = p3[2] * p3[2] - p4[2] * p4[2];
    double A2 = p2[0] * p2[0] - p3[0] * p3[0];
    double B2 = p2[1] * p2[1] - p3[1] * p3[1];
    double C2 = p2[2] * p2[2] - p3[2] * p3[2];
    double P = (A + B + C) / 2;
    double Q = (A1 + B1 + C1) / 2;
    double R = (A2 + B2 + C2) / 2;

    double Dx = P * b1 * c2 + b * c1 * R + c * Q * b2 - (c * b1 * R + P * c1 * b2 + Q * b * c2);
    double Dy = a * Q * c2 + P * c1 * a2 + c * a1 * R - (c * Q * a2 + a * c1 * R + c2 * P * a1);
    double Dz = a * b1 * R + b * Q * a2 + P * a1 * b2 - (a2 * b1 * P + a * Q * b2 + R * b * a1);

    center[0] = Dx / D;
    center[1] = Dy / D;
    center[2] = Dz / D;
    radius = sqrt((p1[0] - center[0]) * (p1[0] - center[0]) +
        (p1[1] - center[1]) * (p1[1] - center[1]) +
        (p1[2] - center[2]) * (p1[2] - center[2]));

}