点群フィッティング球

はじめに: 多くの場合、点群に基づいて球をフィッティングする必要がありますが、このブログ記事では主にフィッティングの状況やさまざまな方法の利点と欠点を紹介します。

目次

1. ボールフィッティングのための vtkFitImplicitFunction

2. 球の四点解法

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1. ボールフィッティングのための vtkFitImplicitFunction

短所: 適合するボールの半径と構造を入力する必要があります。つまり、最適解がわかっている場合に解く必要があります。

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. 球の四点解法

欠点: 入力する必要がある 4 点は正確な球上の点であるため、そうでないと計算が間違ってしまいます。

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]));

}