OSG 球体参数方程绘制

球面参数方程

球面的参数曲线可以用球坐标表示，引入参数u,v，其中v是球面点与原点的连线与z轴正向的夹角，u表示连线在xy平面的投影与x轴正向的夹角

球面法向量

已知球面的参数方程以后，很容易求得给定点的法向量，分别对u和v方向求偏导数
，然后对两个所得向量进行叉积即可：

 

 

osg::Vec3 getPoint(double u, double v)
{
	double x = sin(osg::PI*v)*cos(osg::PI*2*u);
	double y = sin(osg::PI*v)*sin(osg::PI * 2 *u);
	double z =  cos(osg::PI*v);
	return osg::Vec3(x, y, z);
}

//主函数
    osg::ref_ptr geode = new osg::Geode();
	osg::ref_ptr vertices = new osg::Vec3Array();
	osg::ref_ptr triGeom = new osg::Geometry();
	geode->addDrawable(triGeom);

	int uStepsNum = 50, vStepNum = 50;
	double ustep = 1 / (double)uStepsNum, vstep = 1 / (double)vStepNum;
	double u = -0, v = -0;

	int count = 0;
	for (int i = 0; i < uStepsNum; i++)
	{
		osg::Vec3 a = getPoint(0, 0);
		osg::Vec3 b = getPoint(u, vstep);
		osg::Vec3 c = getPoint(u + ustep, vstep);
		vertices->push_back(a);
		vertices->push_back(b);
		vertices->push_back(c);
		triGeom->addPrimitiveSet(new osg::DrawArrays(osg::PrimitiveSet::LINE_LOOP, count, 3));
		count += 3;
		u += ustep;
	}
	//绘制中间四边形组
	u = 0, v = vstep;
	for (int i = 1; i < vStepNum - 1; i++)
	{
		for (int j = 0; j < uStepsNum; j++)
		{
			osg::Vec3  a = getPoint(u, v);
			osg::Vec3  b = getPoint(u + ustep, v);
			osg::Vec3  c = getPoint(u + ustep, v + vstep);
			osg::Vec3  d = getPoint(u, v + vstep);
			vertices->push_back(a);
			vertices->push_back(b);
			vertices->push_back(c);
			vertices->push_back(d);
			triGeom->addPrimitiveSet(new osg::DrawArrays(osg::PrimitiveSet::LINE_LOOP, count, 4));
			count += 4;
			u += ustep;
		}
		v += vstep;
	}
	//绘制下端三角形组
	u = 0;
	for (int i = 0; i < uStepsNum; i++)
	{
		osg::Vec3  a = getPoint(0, 1);
		osg::Vec3  b = getPoint(u, 1 - vstep);
		osg::Vec3 c = getPoint(u + ustep, 1 - vstep);
		vertices->push_back(a);
		vertices->push_back(b);
		vertices->push_back(c);
		triGeom->addPrimitiveSet(new osg::DrawArrays(osg::PrimitiveSet::LINE_LOOP, count, 3));
		count += 3;
		u += ustep;
	}
	triGeom->setVertexArray(vertices);

	m_root->addChild(geode);

 参考：

opengl：绘制球体_溪水流不停的博客-CSDN博客_opengl 球体