Render OpenCascade Geometry Curves in OpenSceneGraph

在OpenSceneGraph中绘制OpenCascade的曲线

Render OpenCascade Geometry Curves in OpenSceneGraph

eryar@163.com

摘要Abstract：本文简要说明OpenCascade中几何曲线的数据，并将这些几何曲线在OpenSceneGraph中绘制出来。

关键字KeyWords：OpenCascade、Geometry Curve、OpenSceneGraph、B-Spline、NURBS

一、引言 Introduction

结合《BRep Format Description White Paper》对OpenCascade中的几何数据结构有详细的介绍。OpenCascade中BRep格式中的曲线总共分为九种，不过有二维三维之分：

1．直线 Line

2．圆 Circle

3．椭圆 Ellipse

4．抛物线 Parabola

5．双曲线 Hyperbola

6．Bezier曲线 Bezier Curve

7．B-Spline曲线 B-Spline Curve

8．裁剪曲线 Trimmed Curve

9．偏移曲线 Offset Curve

曲线的几何数据都有一个抽象基类Geom_Curve，类图如下所示：

Figure 1.1 Geometry curve class diagram

抽象基类Geom_Curve有几个纯虚函数FirstParameter()、LastParameter()、Value()，根据这几个虚函数，就可以计算曲线上对应参数U的值。类图如下图所示：

Figure 1.2 Geom_Curve Inherited class diagram

每种曲线都对那些纯虚函数进行实现，使计算曲线上点的方式统一。

二、程序示例 Code Example

根据抽象基类Geom_Curve的几个纯虚函数：

1．FirstParameter();

2．LastParameter();

3．Value(u);

利用多态可将曲线上点都以统一的方式计算出来，并使用GL_LINE_STRIP绘制出来。示例程序如下所示：

/*
*    Copyright (c) 2013 eryar All Rights Reserved.
*
*        File    : Main.cpp
*        Author  : eryar@163.com
*        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, , 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(, );
    poles.SetValue(, gp_Pnt(-, -, ));
    poles.SetValue(, gp_Pnt(, , ));
    poles.SetValue(, gp_Pnt(, , ));
    poles.SetValue(, gp_Pnt(, , ));
    Geom_BezierCurve bezierCurve(poles);
 
    root->addChild(buildCurve(bezierCurve));
 
    // 6. Build BSpline curve.
    TColgp_Array1OfPnt ctrlPnts(, );
    TColStd_Array1OfReal knots(, );
    TColStd_Array1OfInteger mults(, );
 
    ctrlPnts.SetValue(, gp_Pnt(, , ));
    ctrlPnts.SetValue(, gp_Pnt(, -, ));
    ctrlPnts.SetValue(, gp_Pnt(, , ));
 
    knots.SetValue(, 0.0);
    knots.SetValue(, 0.25);
    knots.SetValue(, 0.5);
    knots.SetValue(, 0.75);
    knots.SetValue(, 1.0);
 
    mults.Init();
 
    Geom_BSplineCurve bsplineCurve(ctrlPnts, knots, mults, );
 
    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();
}

因抛物线和双曲线的FirstParameter()和LastParameter()为负无穷和正无穷，所以对其进行处理，只输出了部分曲线。

程序效果如下图所示：

Figure 2.1 OpenCascade Geometry Curves in OpenSceneGraph

三、结论 Conclusion

OpenCascade的几何数据使用还是很方便的，只要将相应的曲线构造出来之后，计算曲线上的点使用函数Value()即可，还可计算相应参数处的微分值等。

通过理解《BRep Format Description White Paper》，可将BRep文件中数据导入OpenCascade中与上面实现的程序进行对比，结果正确。如下图所示：

Figure 3.1 B-Spline in OpenSceneGraph

Figure 3.2 B-Spline in OpenCascade Draw

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