在OpenSceneGraph中绘制OpenCascade的曲面
Render OpenCascade Geometry Surfaces in OpenSceneGraph
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
