在OpenSceneGraph中绘制OpenCascade的曲线

Render OpenCascade Geometry Curves in OpenSceneGraph

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 
     
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         #pragma comment(lib, "osgd.lib")#pragma comment(lib, "osgDbd.lib")#pragma comment(lib, "osgGAd.lib")#pragma comment(lib, "osgViewerd.lib")// OpenCascade library.#include 
         
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                  #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
                  
                    geode = new osg::Geode(); osg::ref_ptr
                   
                     linesGeom = new osg::Geometry(); osg::ref_ptr
                    
                      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
                     
                       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
                      
                        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
                       
                         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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