在OpenSceneGraph中繪制OpenCascade的曲線
Draw OpenCascade Geometry Curves in OpenSceneGraph
eryar@163.com
摘要Abstract：本文簡要說明OpenCascade中幾何曲線的數據，并將這些幾何曲線在OpenSceneGraph中繪制出來。
關鍵字KeyWords：OpenCascade、Geometry Curve、OpenSceneGraph、B-Spline、NURBS
一、引言 Introduction
結合《BRep Format Description White Paper》對OpenCascade中的幾何數據結構有詳細的介紹。OpenCascade中BRep格式中的曲線總共分為九種，不過有二維三維之分：
1．直線 Line
2．圓 Circle
3．橢圓 Ellipse
4．拋物線 Parabola
5．雙曲線 Hyperbola
6．Bezier曲線 Bezier Curve
7．B-Spline曲線 B-Spline Curve
8．裁剪曲線 Trimmed Curve
9．偏移曲線 Offset Curve
曲線的幾何數據都有一個抽象基類Geom_Curve，類圖如下所示：
Figure 1.1 Geometry curve class diagram
抽象基類Geom_Curve有幾個純虛函數FirstParameter()、LastParameter()、Value()，根據這幾個虛函數，就可以計算曲線上對應參數U的值。類圖如下圖所示：
Figure 1.2 Geom_Curve Inherited class diagram
每種曲線都對那些純虛函數進行實現，使計算曲線上點的方式統一。
二、程序示例 Code Example
根據抽象基類Geom_Curve的幾個純虛函數：
1．FirstParameter();
2．LastParameter();
3．Value(u);
利用多態可將曲線上點都以統一的方式計算出來，并使用GL_LINE_STRIP繪制出來。示例程序如下所示：
1 /*
2 * Copyright (c) 2013 eryar All Rights Reserved.
3 *
4 * File : Main.cpp
5 * Author : eryar@163.com
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 }
因拋物線和雙曲線的FirstParameter()和LastParameter()為負無窮和正無窮，所以對其進行處理，只輸出了部分曲線。
程序效果如下圖所示：
Figure 2.1 OpenCascade Geometry Curves in OpenSceneGraph
三、結論 Conclusion
OpenCascade的幾何數據使用還是很方便的，只要將相應的曲線構造出來之后，計算曲線上的點使用函數Value()即可，還可計算相應參數處的微分值等。
通過理解《BRep Format Description White Paper》，可將BRep文件中數據導入OpenCascade中與上面實現的程序進行對比，結果正確。如下圖所示：
Figure 3.1 B-Spline in OpenSceneGraph
Figure 3.2 B-Spline in OpenCascade Draw