在OpenSceneGraph中繪制OpenCascade的曲面
Render?OpenCascade Geometry Surfaces in OpenSceneGraph
摘要Abstract：本文對OpenCascade中的幾何曲面數(shù)據(jù)進行簡要說明，并結(jié)合OpenSceneGraph將這些曲面顯示。?
關(guān)鍵字Key Words：OpenCascade、OpenSceneGraph、Geometry Surface、NURBS?
一、引言 Introduction
《BRep Format Description White Paper》中對OpenCascade的幾何數(shù)據(jù)結(jié)構(gòu)進行了詳細說明。BRep文件中用到的曲面總共有11種：?
1．Plane 平面；?
2．Cylinder 圓柱面；?
3．Cone 圓錐面；?
4．Sphere 球面；?
5．Torus 圓環(huán)面；?
6．Linear Extrusion 線性拉伸面；?
7．Revolution Surface 旋轉(zhuǎn)曲面；?
8．Bezier Surface 貝塞爾面；?
9．B-Spline Surface B樣條曲面；?
10．Rectangle Trim Surface 矩形裁剪曲面；?
11．Offset Surface 偏移曲面；?
曲面的幾何數(shù)據(jù)類都有一個共同的基類Geom_Surface，類圖如下所示：?
Figure 1.1 Geometry Surface class diagram?
抽象基類Geom_Surface有幾個純虛函數(shù)Bounds()、Value()等，可用來計算曲面上的點。類圖如下所示：?
Figure 1.2 Geom_Surface class diagram?
與另一幾何內(nèi)核sgCore中的幾何的概念一致，幾何（geometry）是用參數(shù)方程對曲線曲面精確表示的。?
每種曲面都對純虛函數(shù)進行實現(xiàn)，使計算曲面上點的方式統(tǒng)一。?
曲線C（u）是單參數(shù)的矢值函數(shù)，它是由直線段到三維歐幾里得空間的映射。曲面是關(guān)于兩個參數(shù)u和v的矢值函數(shù)，它表示由uv平面上的二維區(qū)域R到三維歐幾里得空間的映射。把曲面表示成雙參數(shù)的形式為：?
它的參數(shù)方程為：?
u，v參數(shù)形成了一個參數(shù)平面，參數(shù)的變化區(qū)間在參數(shù)平面上構(gòu)成一個矩形區(qū)域。正常情況下，參數(shù)域內(nèi)的點（u,v）與曲面上的點r（u,v）是一一對應(yīng)的映射關(guān)系。?
給定一個具體的曲面方程，稱之為給定了一個曲面的參數(shù)化。它既決定了所表示的曲面的形狀，也決定了該曲面上的點與其參數(shù)域內(nèi)的點的一種對應(yīng)關(guān)系。同樣地，曲面的參數(shù)化不是唯一的。?
曲面雙參數(shù)u，v的變化范圍往往取為單位正方形，即u∈[0，1]，v∈[0，1]。這樣討論曲面方程時，即簡單、方便，又不失一般性。?
二、程序示例 Code Example
使用函數(shù)Value(u, v)根據(jù)參數(shù)計算出曲面上的點，將點分u，v方向連成線，可以繪制出曲面的線框模型。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();
}
程序效果如下圖所示：?
Figure 2.1 OpenCascade Geometry Surfaces in OpenSceneGraph?
三、結(jié)論 Conclusion?
根據(jù)OpenCascade中的幾何曲面的函數(shù)Value(u, v)可以計算出曲面上的點。分u方向和v方向分別繪制曲面上的點，并將之連接成線，即可以表示出曲面的線框模型。因為這樣的模型沒有面的信息，所以不能有光照效果、材質(zhì)效果等。要有光照、材質(zhì)的信息，必須將曲面進行三角剖分。相關(guān)的剖分算法有Delaunay三角剖分等。?
?
PDF Version: Draw OpenCascade Geometry Surfaces in OpenSceneGraph
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