概述

本教程提供了 AMCAX NURBS模组对管道模型进行建模的基本用法。

模型预览

本教程使用管道模型来展示 AMCAX NURBS模组中的一些主要建模功能。模型如下图所示：

管道模型

该模型由三个NURBS曲面组成：

左侧的管道。
中间过渡管道。
右侧圆形截面管道。

我们将逐步介绍这些结构，并尽可能详细地提供解释。

构建左侧管道

创建椭圆截面曲线

第一步是使用 AMCAX::Geom3Ellipse 类创建一个椭圆。

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));

AMCAX::Vector3

VectorT< double, 3 > Vector3

三维向量

定义 VectorT.hpp:707

AMCAX::Frame3

FrameT< double, 3 > Frame3

三维标架

定义 FrameT.hpp:885

创建B样条截面曲线

第二步是使用 AMCAX::NURBSAPIBuildCurve 类创建一个B样条曲线。

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);

创建引导曲线

第三步是使用 AMCAX::NURBSAPIBuildCurve 类创建两个B样条曲线作为引导曲线。

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);

应用单轨扫掠

然后，使用 AMCAX::NURBSAPISweep 类创建扫掠曲面。

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();

点击这里example01可获得以上示例完整源码，大家根据学习需要自行下载。

构建右侧圆形截面管道

构建扫掠路径

扫掠路径是一个形状接近于四分之一椭圆的路径。

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);

设置扫掠脊线

这里我们将脊线简单地设置为扫掠路径。

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

构建圆形截面半径

这里我们将圆形截面的半径简单地设置为固定值0.5。

AMCAX::LawConstant radiusLaw;

radiusLaw.Set(0.5, 0.0, 1.0);

AMCAX::LawConstant

常值法则函数的类

定义 LawConstant.hpp:12

AMCAX::LawConstant::Set

AMCAX_API void Set(double r, double pf, double pl)

设置参数

创建扫掠面

接下来，我们使用 AMCAX::NURBSAPICircularSweep 类生成扫掠面。

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

点击这里example02可获得以上示例完整源码，大家根据学习需要自行下载。

构建中间过渡曲面

最后，我们中间的过渡曲面。

设置过渡曲面参数

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};

构建过渡曲面

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);

AMCAX::NURBSAPIBlend::BlendSurfaces

static AMCAX_API std::shared_ptr< Geom3BSplineSurface > BlendSurfaces(const std::shared_ptr< Geom3BSplineSurface > &surf1, bool isUIso1, bool isFront1, ContinuityType cont1, std::vector< double > &parameters1, const std::shared_ptr< Geom3BSplineSurface > &surf2, bool isUIso2, bool isFront2, ContinuityType cont2, std::vector< double > &parameters2, bool autoReverse, bool isPrecise, const std::vector< double > &tol)

给定两个曲面，构造两个曲面的混接曲面

点击这里example03可获得NURBS建模示例完整源码，大家根据学习需要自行下载。

附录

下面列出了此示例的完整代码：

#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);
}

概述