NURBS Modeling Sample

Overview

This tutorial provides the basic usage of AMCAX NURBS module to model a pipe model.

Model Preview

This tutorial uses a pipe model to show some of main modeling functionalities in the AMCAX NURBS module. The model is shown in the figure below:

The pipe model

The model consists of three NURBS surfaces:

1. The pipe at the left side.
2. The blend pipe in the middle.
3. The circular section pipe at the right side.

We will introduce the construction methods step-by-step.

Building the pipe at the left side

Creating the ellipse section curve

The first step is to create an ellipse using the AMCAX::Geom3Ellipse class.

std::shared_ptr<AMCAX::Geom3Ellipse> gellipse = std::make_shared<AMCAX::Geom3Ellipse>(AMCAX::Frame3(), 0.7, 0.5);
gellipse->Translate(AMCAX::Vector3(3.0, 0.0, 0.0));

Creating the B-Spline section curve

The second step is to create a B-Spline curve using the AMCAX::NURBSAPIBuildCurve class.

std::vector<AMCAX::Point3> sectionPoles;
sectionPoles.push_back(AMCAX::Point3(0.5, 0.5, 1.5));
sectionPoles.push_back(AMCAX::Point3(0.5, -0.25, 1.5));
sectionPoles.push_back(AMCAX::Point3(0.5, -0.75, 2.0));
sectionPoles.push_back(AMCAX::Point3(0.5, -0.25, 2.5));
sectionPoles.push_back(AMCAX::Point3(0.5, 0.5, 2.5));
sectionPoles.push_back(AMCAX::Point3(0.5, 0.0, 2.0));
std::shared_ptr<AMCAX::Geom3BSplineCurve> endingProfileCurve = AMCAX::NURBSAPIBuildCurve::BuildCurve(sectionPoles, 3, true);

Creating the guide curve

The third step is to create a B-Spline guide curve using the AMCAX::NURBSAPIBuildCurve class.

std::vector<AMCAX::Point3> guidePoles;
guidePoles.push_back(AMCAX::Point3(3.0, 0.5, 0.0));
guidePoles.push_back(AMCAX::Point3(3.0, 0.5, 2.0));
guidePoles.push_back(AMCAX::Point3(0.5, 0.5, 2.0));
std::shared_ptr<AMCAX::Geom3BSplineCurve> guide = AMCAX::NURBSAPIBuildCurve::BuildCurve(guidePoles, 2, false);

Applying the one rail sweeping

Finally, create the swept surface by using the AMCAX::NURBSAPISweep class.

std::vector<std::pair<int, double>> guideCorrParams;
std::vector<AMCAX::NURBSCurveSection> profiles;
profiles.push_back(AMCAX::NURBSCurveSection(gellipse));
profiles.push_back(AMCAX::NURBSCurveSection(endingProfileCurve));
auto sweptSurfaces = AMCAX::NURBSAPISweep::SweepOneRail(profiles, guide, 0.0, guideCorrParams, false, true);
std::shared_ptr<AMCAX::Geom3BSplineSurface> complexPipe = sweptSurfaces.front();

Click here example01 to get the complete source code for the above example, which you can download according to your learning needs.

Building the circular section pipe at the right side

Construct the center curve

The shape of the center curve is similar to a quarter of an ellipse.

std::vector<AMCAX::Point3> centerCurvePoles;
centerCurvePoles.push_back(AMCAX::Point3(-3.0, 0.0, 0.0));
centerCurvePoles.push_back(AMCAX::Point3(-3.0, 0.0, 2.0));
centerCurvePoles.push_back(AMCAX::Point3(-1.0, 0.0, 2.0));
std::shared_ptr<AMCAX::Geom3BSplineCurve> centerCurve = AMCAX::NURBSAPIBuildCurve::BuildCurve(centerCurvePoles, 2, false);

Setting the spine

Here, we simply set the center curve as the spine.

std::shared_ptr<AMCAX::Geom3BSplineCurve> spine = centerCurve;
double spineLeftBound = spine->FirstParameter();
double spineRightBound = spine->LastParameter();

Setting the circular section radius

Here, we simply set the radius of all the circular sections to a fixed value of 0.5.

AMCAX::LawConstant radiusLaw;
radiusLaw.Set(0.5, 0.0, 1.0);

Creating swept surface

Next, we use the AMCAX::NURBSAPICircularSweep class to create the swept surface.

auto [status, circlePipe] = AMCAX::NURBSAPICircularSweep::SweepWithCenterAndRadius(centerCurve, radiusLaw, spine, spineLeftBound, spineRightBound);
if (status != AMCAX::NURBSSweepStatus::Success || !circlePipe)
{
    return;
}

Click here example02 to get the complete source code for the above example, which you can download according to your learning needs.

Creating the blend pipe in the middle

Finally, we build the blend pipe in the middle.

Setting the parameters of the blend surface

std::vector<double> parameters1 = {1.0, 1.0};
std::vector<double> parameters2 = {1.0, 1.0};
std::vector<double> tol = {0.001, 0.1 * M_PI / 180.0, 0.05};

Creating the blend pipe

std::shared_ptr<AMCAX::Geom3BSplineSurface> blendSurface = AMCAX::NURBSAPIBlend::BlendSurfaces(circlePipe, false, false, AMCAX::ContinuityType::G2, parameters1, complexPipe, false, false, AMCAX::ContinuityType::G2, parameters2, true, true, tol);

Click here example03 to get the full source code of the NURBS modeling example, you can download it according to your learning needs.

Appendix

The complete code of this sample is listed here:

#include <memory>
#include <vector>
 
#include <common/PointT.hpp>
#include <geomAlgo/LawConstant.hpp>
#include <geometry/Geom3BSplineCurve.hpp>
#include <geometry/Geom3BSplineSurface.hpp>
#include <geometry/Geom3Circle.hpp>
#include <geometry/Geom3Ellipse.hpp>
#include <nurbs/NURBSAPIBlend.hpp>
#include <nurbs/NURBSAPIBuildCurve.hpp>
#include <nurbs/NURBSAPICircularSweep.hpp>
#include <nurbs/NURBSAPISweep.hpp>
 
void TestPipe()
{
    // build a complex pipe
    // build section curves
    std::shared_ptr<AMCAX::Geom3Ellipse> gellipse = std::make_shared<AMCAX::Geom3Ellipse>(AMCAX::Frame3(), 0.7, 0.5);
    gellipse->Translate(AMCAX::Vector3(3.0, 0.0, 0.0));
 
    std::vector<AMCAX::Point3> sectionPoles;
    sectionPoles.push_back(AMCAX::Point3(0.5, 0.5, 1.5));
    sectionPoles.push_back(AMCAX::Point3(0.5, -0.25, 1.5));
    sectionPoles.push_back(AMCAX::Point3(0.5, -0.75, 2.0));
    sectionPoles.push_back(AMCAX::Point3(0.5, -0.25, 2.5));
    sectionPoles.push_back(AMCAX::Point3(0.5, 0.5, 2.5));
    sectionPoles.push_back(AMCAX::Point3(0.5, 0.0, 2.0));
    std::shared_ptr<AMCAX::Geom3BSplineCurve> endingProfileCurve = AMCAX::NURBSAPIBuildCurve::BuildCurve(sectionPoles, 3, true);
 
    // build guide curves
    std::vector<AMCAX::Point3> guidePoles;
    guidePoles.push_back(AMCAX::Point3(3.0, 0.5, 0.0));
    guidePoles.push_back(AMCAX::Point3(3.0, 0.5, 2.0));
    guidePoles.push_back(AMCAX::Point3(0.5, 0.5, 2.0));
    std::shared_ptr<AMCAX::Geom3BSplineCurve> guide = AMCAX::NURBSAPIBuildCurve::BuildCurve(guidePoles, 2, false);
 
    // sweeping to build surface
    std::vector<std::pair<int, double>> guideCorrParams;
    std::vector<AMCAX::NURBSCurveSection> profiles;
    profiles.push_back(AMCAX::NURBSCurveSection(gellipse));
    profiles.push_back(AMCAX::NURBSCurveSection(endingProfileCurve));
    auto sweptSurfaces = AMCAX::NURBSAPISweep::SweepOneRail(profiles, guide, 0.0, guideCorrParams, false, true);
    std::shared_ptr<AMCAX::Geom3BSplineSurface> complexPipe = sweptSurfaces.front();
 
    // build a circle section pipe
    // build the pipe center curve
    std::vector<AMCAX::Point3> centerCurvePoles;
    centerCurvePoles.push_back(AMCAX::Point3(-3.0, 0.0, 0.0));
    centerCurvePoles.push_back(AMCAX::Point3(-3.0, 0.0, 2.0));
    centerCurvePoles.push_back(AMCAX::Point3(-1.0, 0.0, 2.0));
    std::shared_ptr<AMCAX::Geom3BSplineCurve> centerCurve = AMCAX::NURBSAPIBuildCurve::BuildCurve(centerCurvePoles, 2, false);
    
    // set the center curve as the spine
    std::shared_ptr<AMCAX::Geom3BSplineCurve> spine = centerCurve;
    double spineLeftBound = spine->FirstParameter();
    double spineRightBound = spine->LastParameter();
    
    // set the radius
    AMCAX::LawConstant radiusLaw;
    radiusLaw.Set(0.5, 0.0, 1.0);
    
    // sweep to make the circle section pipe
    auto [status, circlePipe] = AMCAX::NURBSAPICircularSweep::SweepWithCenterAndRadius(centerCurve, radiusLaw, spine, spineLeftBound, spineRightBound);
    if (status != AMCAX::NURBSSweepStatus::Success || !circlePipe)
    {
        return;
    }
 
    // set the parameters
    std::vector<double> parameters1 = {1.0, 1.0};
    std::vector<double> parameters2 = {1.0, 1.0};
    std::vector<double> tol = {0.001, 0.1 * M_PI / 180.0, 0.05};
    std::shared_ptr<AMCAX::Geom3BSplineSurface> blendSurface = AMCAX::NURBSAPIBlend::BlendSurfaces(circlePipe, false, false, AMCAX::ContinuityType::G2, parameters1, complexPipe, false, false, AMCAX::ContinuityType::G2, parameters2, true, true, tol);
}