现在，假设曲面上有两条相交切线，那么这两条切线可以确定一个切平面，我们来看看这个平面是怎么搞出来的。
Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface. Let's try to see how that works.
这样的2维宇宙模型就像是球体，不可能出现平行的测地线(测地线是曲面上的直线)——两直线必然在某点相交。
A two-dimensional model of such a universe would look like a sphere. It's impossible to have parallel geodesics (straight lines on a curved surface) — the two lines will cross at some point.
接下来，我们的任务就是将平面与拼接曲面的有效部分相交所得截线参数化。
Then our task is to parameterize the intersection of and the valid part of for some fixed .
该算法首先利用结式法计算出两二次曲面相交时交线的投影方程，再对投影方程进行分解等处理。
The algorithm used the resultant method to computing the intersection's projection equation and deal with the projection equation through decomposition and so on.
两个曲面相交得到一条曲线，曲线与第三个曲面的交点既是用户的三维坐标。
Two of them intersect in a curved line which in turn intersects with the third hyperboloid in a point corresponding to the unknown three-dimensional user position.
本文提出了由一条二次曲线和与该二次曲线不共面的两条异面直线为导线，与该三导线均相交的直线轨迹是一个直纹四次曲面，并讨论了二次曲线分别为椭圆、双曲线和抛物线时，形成的曲面的形状特征。
In this paper, it is presented that the locus of a line crossedwith each of two guide lines and a guide conic not being on a commonplane is a ruled surface of fourth order.
两二次曲面相交是工程构件中常遇到的问题。工程图样均用图解法画出它们的交线。
The intersecting of two conicoids is a frequent issue in the engineering components and their intersecting line in the engineering drafts are always drawn by means ofdiagrammatizing method.
本文提出了由一条二次曲线和与该二次曲线不共面的两条异面直线为导线，与该三导线均相交的直线轨迹是一个直纹四次曲面，并讨论了二次曲线分别为椭圆、双曲线和抛物线时，形成的曲面的形状特征。
It is presented that the locus of a line crossed with each of two guide line and a guide conic not being on a common plane is a ruled surface of fourth order.
本文提出了由一条二次曲线和与该二次曲线不共面的两条异面直线为导线，与该三导线均相交的直线轨迹是一个直纹四次曲面，并讨论了二次曲线分别为椭圆、双曲线和抛物线时，形成的曲面的形状特征。
It is presented that the locus of a line crossed with each of two guide line and a guide conic not being on a common plane is a ruled surface of fourth order.
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