摘要Abstract：本文簡要說明OpenCascade中幾何曲線的資料，并将這些幾何曲線在OpenSceneGraph中繪制出來。 關鍵字KeyWords：OpenCascade、Geometry Curve、OpenSceneGraph、B-Spline、NURBS

在OpenSceneGraph中繪制OpenCascade的曲線

Render OpenCascade Geometry Curves in OpenSceneGraph

[email protected]

摘要Abstract：本文簡要說明OpenCascade中幾何曲線的資料，并将這些幾何曲線在OpenSceneGraph中繪制出來。 

關鍵字KeyWords：OpenCascade、Geometry Curve、OpenSceneGraph、B-Spline、NURBS 

一、引言 Introduction

結合《BRep Format Description White Paper》對OpenCascade中的幾何資料結構有詳細的介紹。OpenCascade中BRep格式中的曲線總共分為九種，不過有二維三維之分： 

1．直線 Line 

2．圓 Circle 

3．橢圓 Ellipse 

4．抛物線 Parabola 

5．雙曲線 Hyperbola 

6．Bezier曲線 Bezier Curve 

7．B-Spline曲線 B-Spline Curve 

8．裁剪曲線 Trimmed Curve 

9．偏移曲線 Offset Curve 

曲線的幾何資料都有一個抽象基類Geom_Curve，類圖如下所示： 

Figure 1.1 Geometry curve class diagram 

抽象基類Geom_Curve有幾個純虛函數FirstParameter()、LastParameter()、Value()，根據這幾個虛函數，就可以計算曲線上對應參數U的值。類圖如下圖所示： 

Figure 1.2 Geom_Curve Inherited class diagram 

每種曲線都對那些純虛函數進行實作，使計算曲線上點的方式統一。 

二、程式示例 Code Example

根據抽象基類Geom_Curve的幾個純虛函數： 

1．FirstParameter(); 

2．LastParameter(); 

3．Value(u); 

利用多态可将曲線上點都以統一的方式計算出來，并使用GL_LINE_STRIP繪制出來。示例程式如下所示：

/*
*    Copyright (c) 2013 eryar All Rights Reserved.
*
*        File    : Main.cpp
*        Author  : [email protected]
*        Date    : 2013-08-09 18:09
*        Version : 1.0v
*
*    Description : Draw OpenCascade Geometry Curves in OpenSceneGraph.
*                  
*/

// OpenSceneGraph library.
#include <osgDB/ReadFile>
#include <osgViewer/Viewer>
#include <osgViewer/ViewerEventHandlers>
#include <osgGA/StateSetManipulator>

#pragma comment(lib, "osgd.lib")
#pragma comment(lib, "osgDbd.lib")
#pragma comment(lib, "osgGAd.lib")
#pragma comment(lib, "osgViewerd.lib")

// OpenCascade library.
#include <TColgp_Array1OfPnt.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColStd_Array1OfInteger.hxx>

#include <Geom_Circle.hxx>
#include <Geom_Ellipse.hxx>
#include <Geom_Hyperbola.hxx>
#include <Geom_Parabola.hxx>
#include <Geom_BezierCurve.hxx>
#include <Geom_BSplineCurve.hxx>

#pragma comment(lib, "TKernel.lib")
#pragma comment(lib, "TKMath.lib")
#pragma comment(lib, "TKG3d.lib")

// Curve Segment Delta.
const double CURVE_SEGMENT_DELTA = 0.01;

/*
* @brief Build geometry curve of OpenCascade.
*/
osg::Node* buildCurve(const Geom_Curve& curve)
{
    osg::ref_ptr<osg::Geode> geode = new osg::Geode();
    osg::ref_ptr<osg::Geometry> linesGeom = new osg::Geometry();
    osg::ref_ptr<osg::Vec3Array> pointsVec = new osg::Vec3Array();

    gp_Pnt point;
    double dFirst = curve.FirstParameter();
    double dLast = curve.LastParameter();

    Precision::IsNegativeInfinite(dFirst) ? dFirst = -1.0 : dFirst;
    Precision::IsInfinite(dLast) ? dLast = 1.0 : dLast;
    
    for (double u = dFirst; u <= dLast; u += CURVE_SEGMENT_DELTA)
    {
        point = curve.Value(u);

        pointsVec->push_back(osg::Vec3(point.X(), point.Y(), point.Z()));
    }

    // Set the colors.
    osg::ref_ptr<osg::Vec4Array> colors = new osg::Vec4Array;
    colors->push_back(osg::Vec4(1.0f, 1.0f, 0.0f, 0.0f));
    linesGeom->setColorArray(colors.get());
    linesGeom->setColorBinding(osg::Geometry::BIND_OVERALL);

    // Set the normal in the same way of color.
    osg::ref_ptr<osg::Vec3Array> normals = new osg::Vec3Array;
    normals->push_back(osg::Vec3(0.0f, -1.0f, 0.0f));
    linesGeom->setNormalArray(normals.get());
    linesGeom->setNormalBinding(osg::Geometry::BIND_OVERALL);

    // Set vertex array.
    linesGeom->setVertexArray(pointsVec);
    linesGeom->addPrimitiveSet(new osg::DrawArrays(osg::PrimitiveSet::LINE_STRIP, 0, pointsVec->size()));
    
    geode->addDrawable(linesGeom.get());

    return geode.release();
}

/**
* @breif Build geometry curve of OpenCascade.
*/
osg::Node* buildScene()
{
    osg::ref_ptr<osg::Group> root = new osg::Group();

    // 1. Build circle curve.
    Geom_Circle circle(gp::YOZ(), 1.0);

    root->addChild(buildCurve(circle));

    // 2. Build ellipse curve.
    Geom_Ellipse ellipse(gp::ZOX(), 1.0, 0.3);

    root->addChild(buildCurve(ellipse));

    // 3. Build Hyperbola curve.
    Geom_Hyperbola hyperbola(gp::XOY(), 1.0, 0.6);

    root->addChild(buildCurve(hyperbola));

    // 4. Build parabola curve.
    Geom_Parabola parabola(gp::ZOX(), 1.0);

    root->addChild(buildCurve(parabola));

    // 5. Build Bezier curve.
    TColgp_Array1OfPnt poles(1, 4);
    poles.SetValue(1, gp_Pnt(-1, -1, 0));
    poles.SetValue(2, gp_Pnt(1, 2, 0));
    poles.SetValue(3, gp_Pnt(3, 0, 0));
    poles.SetValue(4, gp_Pnt(4, 1, 0));
    Geom_BezierCurve bezierCurve(poles);

    root->addChild(buildCurve(bezierCurve));

    // 6. Build BSpline curve.
    TColgp_Array1OfPnt ctrlPnts(1, 3);
    TColStd_Array1OfReal knots(1, 5);
    TColStd_Array1OfInteger mults(1, 5);
    
    ctrlPnts.SetValue(1, gp_Pnt(0, 1, 0));
    ctrlPnts.SetValue(2, gp_Pnt(1, -2, 0));
    ctrlPnts.SetValue(3, gp_Pnt(2, 3, 0));

    knots.SetValue(1, 0.0);
    knots.SetValue(2, 0.25);
    knots.SetValue(3, 0.5);
    knots.SetValue(4, 0.75);
    knots.SetValue(5, 1.0);

    mults.Init(1);

    Geom_BSplineCurve bsplineCurve(ctrlPnts, knots, mults, 1);

    root->addChild(buildCurve(bsplineCurve));

    return root.release();
}

int main(int argc, char* argv[])
{
    osgViewer::Viewer myViewer;

    myViewer.setSceneData(buildScene());

    myViewer.addEventHandler(new osgGA::StateSetManipulator(myViewer.getCamera()->getOrCreateStateSet()));
    myViewer.addEventHandler(new osgViewer::StatsHandler);
    myViewer.addEventHandler(new osgViewer::WindowSizeHandler);

    return myViewer.run();
}      

因抛物線和雙曲線的FirstParameter()和LastParameter()為負無窮和正無窮，是以對其進行處理，隻輸出了部分曲線。 

程式效果如下圖所示： 

Figure 2.1 OpenCascade Geometry Curves in OpenSceneGraph 

三、結論 Conclusion

OpenCascade的幾何資料使用還是很友善的，隻要将相應的曲線構造出來之後，計算曲線上的點使用函數Value()即可，還可計算相應參數處的微分值等。 

通過了解《BRep Format Description White Paper》，可将BRep檔案中資料導入OpenCascade中與上面實作的程式進行對比，結果正确。如下圖所示： 

Figure 3.1 B-Spline in OpenSceneGraph