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 <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
PDF Version: Draw OpenCascade Geometry Curves in OpenSceneGraph
