在OpenSceneGraph中绘制OpenCascade的曲线

Draw OpenCascade Geometry Curves in OpenSceneGraph

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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：

  1 /*
  2 *    Copyright (c) 2013 eryar All Rights Reserved.
  3 *
  4 *        File    : Main.cpp
  5 *        Author  : [email protected]
  6 *        Date    : 2013-08-09 18:09
  7 *        Version : 1.0v
  8 *
  9 *    Description : Draw OpenCascade Geometry Curves in OpenSceneGraph.
10 *
11 */
12
13 // OpenSceneGraph library.
14 #include < osgDB / ReadFile >
15 #include < osgViewer / Viewer >
16 #include < osgViewer / ViewerEventHandlers >
17 #include < osgGA / StateSetManipulator >
18
19 #pragma comment(lib, " osgd.lib " )
20 #pragma comment(lib, " osgDbd.lib " )
21 #pragma comment(lib, " osgGAd.lib " )
22 #pragma comment(lib, " osgViewerd.lib " )
23
24 // OpenCascade library.
25 #include < TColgp_Array1OfPnt.hxx >
26 #include < TColStd_Array1OfReal.hxx >
27 #include < TColStd_Array1OfInteger.hxx >
28
29 #include < Geom_Circle.hxx >
30 #include < Geom_Ellipse.hxx >
31 #include < Geom_Hyperbola.hxx >
32 #include < Geom_Parabola.hxx >
33 #include < Geom_BezierCurve.hxx >
34 #include < Geom_BSplineCurve.hxx >
35
36 #pragma comment(lib, " TKernel.lib " )
37 #pragma comment(lib, " TKMath.lib " )
38 #pragma comment(lib, " TKG3d.lib " )
39
40 // Curve Segment Delta.
41 const double CURVE_SEGMENT_DELTA = 0.01 ;
42
43 /*
44 * @brief Build geometry curve of OpenCascade.
45 */
46 osg::Node * buildCurve( const Geom_Curve & curve)
47 {
48     osg::ref_ptr < osg::Geode > geode = new osg::Geode();
49     osg::ref_ptr < osg::Geometry > linesGeom = new osg::Geometry();
50     osg::ref_ptr < osg::Vec3Array > pointsVec = new osg::Vec3Array();
51
52     gp_Pnt point;
53      double dFirst = curve.FirstParameter();
54      double dLast = curve.LastParameter();
55
56     Precision::IsNegativeInfinite(dFirst) ? dFirst = - 1.0 : dFirst;
57     Precision::IsInfinite(dLast) ? dLast = 1.0 : dLast;
58
59      for ( double u = dFirst; u <= dLast; u += CURVE_SEGMENT_DELTA)
60     {
61         point = curve.Value(u);
62
63         pointsVec -> push_back(osg::Vec3(point.X(), point.Y(), point.Z()));
64     }
65
66      // Set the colors.
67     osg::ref_ptr < osg::Vec4Array > colors = new osg::Vec4Array;
68     colors -> push_back(osg::Vec4( 1.0f , 1.0f , 0.0f , 0.0f ));
69     linesGeom -> setColorArray(colors. get ());
70     linesGeom -> setColorBinding(osg::Geometry::BIND_OVERALL);
71
72      // Set the normal in the same way of color.
73     osg::ref_ptr < osg::Vec3Array > normals = new osg::Vec3Array;
74     normals -> push_back(osg::Vec3( 0.0f , - 1.0f , 0.0f ));
75     linesGeom -> setNormalArray(normals. get ());
76     linesGeom -> setNormalBinding(osg::Geometry::BIND_OVERALL);
77
78      // Set vertex array.
79     linesGeom -> setVertexArray(pointsVec);
80     linesGeom -> addPrimitiveSet( new osg::DrawArrays(osg::PrimitiveSet::LINE_STRIP, 0 , pointsVec -> size()));
81
82     geode -> addDrawable(linesGeom. get ());
83
84      return geode.release();
85 }
86
87 /* *
88 * @breif Build geometry curve of OpenCascade.
89 */
90 osg::Node * buildScene()
91 {
92     osg::ref_ptr < osg::Group > root = new osg::Group();
93
94      // 1. Build circle curve.
95     Geom_Circle circle(gp::YOZ(), 1.0 );
96
97     root -> addChild(buildCurve(circle));
98
99      // 2. Build ellipse curve.
100     Geom_Ellipse ellipse(gp::ZOX(), 1.0 , 0.3 );
101
102     root -> addChild(buildCurve(ellipse));
103
104      // 3. Build Hyperbola curve.
105     Geom_Hyperbola hyperbola(gp::XOY(), 1.0 , 0.6 );
106
107     root -> addChild(buildCurve(hyperbola));
108
109      // 4. Build parabola curve.
110     Geom_Parabola parabola(gp::ZOX(), 1.0 );
111
112     root -> addChild(buildCurve(parabola));
113
114      // 5. Build Bezier curve.
115     TColgp_Array1OfPnt poles( 1 , 4 );
116     poles.SetValue( 1 , gp_Pnt( - 1 , - 1 , 0 ));
117     poles.SetValue( 2 , gp_Pnt( 1 , 2 , 0 ));
118     poles.SetValue( 3 , gp_Pnt( 3 , 0 , 0 ));
119     poles.SetValue( 4 , gp_Pnt( 4 , 1 , 0 ));
120     Geom_BezierCurve bezierCurve(poles);
121
122     root -> addChild(buildCurve(bezierCurve));
123
124      // 6. Build BSpline curve.
125     TColgp_Array1OfPnt ctrlPnts( 1 , 3 );
126     TColStd_Array1OfReal knots( 1 , 5 );
127     TColStd_Array1OfInteger mults( 1 , 5 );
128
129     ctrlPnts.SetValue( 1 , gp_Pnt( 0 , 1 , 0 ));
130     ctrlPnts.SetValue( 2 , gp_Pnt( 1 , - 2 , 0 ));
131     ctrlPnts.SetValue( 3 , gp_Pnt( 2 , 3 , 0 ));
132
133     knots.SetValue( 1 , 0.0 );
134     knots.SetValue( 2 , 0.25 );
135     knots.SetValue( 3 , 0.5 );
136     knots.SetValue( 4 , 0.75 );
137     knots.SetValue( 5 , 1.0 );
138
139     mults.Init( 1 );
140
141     Geom_BSplineCurve bsplineCurve(ctrlPnts, knots, mults, 1 );
142
143     root -> addChild(buildCurve(bsplineCurve));
144
145      return root.release();
146 }
147
148 int main( int argc, char * argv[])
149 {
150     osgViewer::Viewer myViewer;
151
152     myViewer.setSceneData(buildScene());
153
154     myViewer.addEventHandler( new osgGA::StateSetManipulator(myViewer.getCamera() -> getOrCreateStateSet()));
155     myViewer.addEventHandler( new osgViewer::StatsHandler);
156     myViewer.addEventHandler( new osgViewer::WindowSizeHandler);
157
158      return myViewer.run();
159 }

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：