Render OpenCascade Geometry Surfaces in OpenSceneGraph

在OpenSceneGraph中绘制OpenCascade的曲面

Render OpenCascade Geometry Surfaces in OpenSceneGraph

eryar@163.com

摘要Abstract：本文对OpenCascade中的几何曲面数据进行简要说明，并结合OpenSceneGraph将这些曲面显示。 

关键字Key Words：OpenCascade、OpenSceneGraph、Geometry Surface、NURBS 

一、引言 Introduction

《BRep Format Description White Paper》中对OpenCascade的几何数据结构进行了详细说明。BRep文件中用到的曲面总共有11种： 

1．Plane 平面； 

2．Cylinder 圆柱面； 

3．Cone 圆锥面； 

4．Sphere 球面； 

5．Torus 圆环面； 

6．Linear Extrusion 线性拉伸面； 

7．Revolution Surface 旋转曲面； 

8．Bezier Surface 贝塞尔面； 

9．B-Spline Surface B样条曲面； 

10．Rectangle Trim Surface 矩形裁剪曲面； 

11．Offset Surface 偏移曲面； 

曲面的几何数据类都有一个共同的基类Geom_Surface，类图如下所示： 

Figure 1.1 Geometry Surface class diagram 

抽象基类Geom_Surface有几个纯虚函数Bounds()、Value()等，可用来计算曲面上的点。类图如下所示： 

Figure 1.2 Geom_Surface class diagram 

与另一几何内核sgCore中的几何的概念一致，几何（geometry）是用参数方程对曲线曲面精确表示的。 

每种曲面都对纯虚函数进行实现，使计算曲面上点的方式统一。 

曲线C（u）是单参数的矢值函数，它是由直线段到三维欧几里得空间的映射。曲面是关于两个参数u和v的矢值函数，它表示由uv平面上的二维区域R到三维欧几里得空间的映射。把曲面表示成双参数的形式为： 

它的参数方程为： 

u，v参数形成了一个参数平面，参数的变化区间在参数平面上构成一个矩形区域。正常情况下，参数域内的点（u,v）与曲面上的点r（u,v）是一一对应的映射关系。 

给定一个具体的曲面方程，称之为给定了一个曲面的参数化。它既决定了所表示的曲面的形状，也决定了该曲面上的点与其参数域内的点的一种对应关系。同样地，曲面的参数化不是唯一的。 

曲面双参数u，v的变化范围往往取为单位正方形，即u∈[0，1]，v∈[0，1]。这样讨论曲面方程时，即简单、方便，又不失一般性。 

二、程序示例 Code Example

使用函数Value(u, v)根据参数计算出曲面上的点，将点分u，v方向连成线，可以绘制出曲面的线框模型。程序如下所示： 

 

/*

*    Copyright (c) 2013 eryar All Rights Reserved.

*

*        File    : Main.cpp

*        Author  : eryar@163.com

*        Date    : 2013-08-11 10:36

*        Version : V1.0

*

*    Description : Draw OpenCascade Geometry Surfaces in OpenSceneGraph.

*

*/



// OpenSceneGraph

#include <osgDB/ReadFile>

#include <osgViewer/Viewer>

#include <osgGA/StateSetManipulator>

#include <osgViewer/ViewerEventHandlers>



#pragma comment(lib, "osgd.lib")

#pragma comment(lib, "osgDBd.lib")

#pragma comment(lib, "osgGAd.lib")

#pragma comment(lib, "osgViewerd.lib")



// OpenCascade

#define WNT

#include <TColgp_Array2OfPnt.hxx>

#include <TColStd_HArray1OfInteger.hxx>

#include <TColGeom_Array2OfBezierSurface.hxx>

#include <GeomConvert_CompBezierSurfacesToBSplineSurface.hxx>



#include <Geom_Surface.hxx>

#include <Geom_BezierSurface.hxx>

#include <Geom_BSplineSurface.hxx>

#include <Geom_ConicalSurface.hxx>

#include <Geom_CylindricalSurface.hxx>

#include <Geom_Plane.hxx>

#include <Geom_ToroidalSurface.hxx>

#include <Geom_SphericalSurface.hxx>



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

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

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

#pragma comment(lib, "TKGeomBase.lib")



// Approximation Delta.

const double APPROXIMATION_DELTA = 0.1;



/**

* @breif Build geometry surface.

*/

osg::Node* buildSurface(const Geom_Surface& surface)

{

    osg::ref_ptr<osg::Geode> geode = new osg::Geode();



    gp_Pnt point;

    Standard_Real uFirst = 0.0;

    Standard_Real vFirst = 0.0;

    Standard_Real uLast = 0.0;

    Standard_Real vLast = 0.0;



    surface.Bounds(uFirst, uLast, vFirst, vLast);



    Precision::IsNegativeInfinite(uFirst) ? uFirst = -1.0 : uFirst;

    Precision::IsInfinite(uLast) ? uLast = 1.0 : uLast;



    Precision::IsNegativeInfinite(vFirst) ? vFirst = -1.0 : vFirst;

    Precision::IsInfinite(vLast) ? vLast = 1.0 : vLast;



    // Approximation in v direction.

    for (Standard_Real u = uFirst; u <= uLast; u += APPROXIMATION_DELTA)

    {

        osg::ref_ptr<osg::Geometry> linesGeom = new osg::Geometry();

        osg::ref_ptr<osg::Vec3Array> pointsVec = new osg::Vec3Array();



        for (Standard_Real v = vFirst; v <= vLast; v += APPROXIMATION_DELTA)

        {

            point = surface.Value(u, v);



            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());

    }



    // Approximation in u direction.

    for (Standard_Real v = vFirst; v <= vLast; v += APPROXIMATION_DELTA)

    {

        osg::ref_ptr<osg::Geometry> linesGeom = new osg::Geometry();

        osg::ref_ptr<osg::Vec3Array> pointsVec = new osg::Vec3Array();



        for (Standard_Real u = vFirst; u <= uLast; u += APPROXIMATION_DELTA)

        {

            point = surface.Value(u, v);



            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 Test geometry surfaces of OpenCascade.

*/

osg::Node* buildScene(void)

{

    osg::ref_ptr<osg::Group> root = new osg::Group();



    // Test Plane.

    Geom_Plane plane(gp::XOY());

    root->addChild(buildSurface(plane));



    // Test Bezier Surface and B-Spline Surface.

    TColgp_Array2OfPnt array1(1,3,1,3);

    TColgp_Array2OfPnt array2(1,3,1,3);

    TColgp_Array2OfPnt array3(1,3,1,3);

    TColgp_Array2OfPnt array4(1,3,1,3);



    array1.SetValue(1,1,gp_Pnt(1,1,1));

    array1.SetValue(1,2,gp_Pnt(2,1,2));

    array1.SetValue(1,3,gp_Pnt(3,1,1));

    array1.SetValue(2,1,gp_Pnt(1,2,1));

    array1.SetValue(2,2,gp_Pnt(2,2,2));

    array1.SetValue(2,3,gp_Pnt(3,2,0));

    array1.SetValue(3,1,gp_Pnt(1,3,2));

    array1.SetValue(3,2,gp_Pnt(2,3,1));

    array1.SetValue(3,3,gp_Pnt(3,3,0));



    array2.SetValue(1,1,gp_Pnt(3,1,1));

    array2.SetValue(1,2,gp_Pnt(4,1,1));

    array2.SetValue(1,3,gp_Pnt(5,1,2));

    array2.SetValue(2,1,gp_Pnt(3,2,0));

    array2.SetValue(2,2,gp_Pnt(4,2,1));

    array2.SetValue(2,3,gp_Pnt(5,2,2));

    array2.SetValue(3,1,gp_Pnt(3,3,0));

    array2.SetValue(3,2,gp_Pnt(4,3,0));

    array2.SetValue(3,3,gp_Pnt(5,3,1));



    array3.SetValue(1,1,gp_Pnt(1,3,2));

    array3.SetValue(1,2,gp_Pnt(2,3,1));

    array3.SetValue(1,3,gp_Pnt(3,3,0));

    array3.SetValue(2,1,gp_Pnt(1,4,1));

    array3.SetValue(2,2,gp_Pnt(2,4,0));

    array3.SetValue(2,3,gp_Pnt(3,4,1));

    array3.SetValue(3,1,gp_Pnt(1,5,1));

    array3.SetValue(3,2,gp_Pnt(2,5,1));

    array3.SetValue(3,3,gp_Pnt(3,5,2));



    array4.SetValue(1,1,gp_Pnt(3,3,0));

    array4.SetValue(1,2,gp_Pnt(4,3,0));

    array4.SetValue(1,3,gp_Pnt(5,3,1));

    array4.SetValue(2,1,gp_Pnt(3,4,1));

    array4.SetValue(2,2,gp_Pnt(4,4,1));

    array4.SetValue(2,3,gp_Pnt(5,4,1));

    array4.SetValue(3,1,gp_Pnt(3,5,2));

    array4.SetValue(3,2,gp_Pnt(4,5,2));

    array4.SetValue(3,3,gp_Pnt(5,5,1));



    Geom_BezierSurface BZ1(array1);

    Geom_BezierSurface BZ2(array2);

    Geom_BezierSurface BZ3(array3);

    Geom_BezierSurface BZ4(array4);

    root->addChild(buildSurface(BZ1));

    root->addChild(buildSurface(BZ2));

    root->addChild(buildSurface(BZ3));

    root->addChild(buildSurface(BZ4));



    Handle_Geom_BezierSurface BS1 = new Geom_BezierSurface(array1);

    Handle_Geom_BezierSurface BS2 = new Geom_BezierSurface(array2);

    Handle_Geom_BezierSurface BS3 = new Geom_BezierSurface(array3);

    Handle_Geom_BezierSurface BS4 = new Geom_BezierSurface(array4);

    TColGeom_Array2OfBezierSurface bezierarray(1,2,1,2);

    bezierarray.SetValue(1,1,BS1);

    bezierarray.SetValue(1,2,BS2);

    bezierarray.SetValue(2,1,BS3);

    bezierarray.SetValue(2,2,BS4);



    GeomConvert_CompBezierSurfacesToBSplineSurface BB (bezierarray);



    if (BB.IsDone())

    {

        Geom_BSplineSurface BSPLSURF(

            BB.Poles()->Array2(),

            BB.UKnots()->Array1(),

            BB.VKnots()->Array1(),

            BB.UMultiplicities()->Array1(),

            BB.VMultiplicities()->Array1(),

            BB.UDegree(),

            BB.VDegree() );



        BSPLSURF.Translate(gp_Vec(0,0,2));



        root->addChild(buildSurface(BSPLSURF));

    }



    // Test Spherical Surface.

    Geom_SphericalSurface sphericalSurface(gp::XOY(), 1.0);

    sphericalSurface.Translate(gp_Vec(2.5, 0.0, 0.0));

    root->addChild(buildSurface(sphericalSurface));



    // Test Conical Surface.

    Geom_ConicalSurface conicalSurface(gp::XOY(), M_PI/8, 1.0);

    conicalSurface.Translate(gp_Vec(5.0, 0.0, 0.0));

    root->addChild(buildSurface(conicalSurface));



    // Test Cylindrical Surface.

    Geom_CylindricalSurface cylindricalSurface(gp::XOY(), 1.0);

    cylindricalSurface.Translate(gp_Vec(8.0, 0.0, 0.0));

    root->addChild(buildSurface(cylindricalSurface));



    // Test Toroidal Surface.

    Geom_ToroidalSurface toroidalSurface(gp::XOY(), 1.0, 0.2);

    toroidalSurface.Translate(gp_Vec(11.0, 0.0, 0.0));

    root->addChild(buildSurface(toroidalSurface));



    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();

}

程序效果如下图所示： 

Figure 2.1 OpenCascade Geometry Surfaces in OpenSceneGraph 

三、结论 Conclusion 

根据OpenCascade中的几何曲面的函数Value(u, v)可以计算出曲面上的点。分u方向和v方向分别绘制曲面上的点，并将之连接成线，即可以表示出曲面的线框模型。因为这样的模型没有面的信息，所以不能有光照效果、材质效果等。要有光照、材质的信息，必须将曲面进行三角剖分。相关的剖分算法有Delaunay三角剖分等。 

 

PDF Version: Draw OpenCascade Geometry Surfaces in OpenSceneGraph