Render OpenCascade Geometry Surfaces in OpenSceneGraph-卡核

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

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OCC源码学习几何造型器
# opencascade code study