In 1728 Euler gave differential equations for geodesics on surfaces.
1728年，奥伊勒绘出了曲面上测地线的微方程。
It is proved that geodesics can be produced by stretch elastic strings along a smooth surface.
可以证明，连接平滑曲面上任意两点的弹性细丝当拉紧时具有测地线的形状。
Adopting geodesics as dividing lines, space surfaces were developed by minimal extremum method.
采用测地线划分曲面，应用最小极值法进行曲面的展开。
Also, the paper discuss the existence of the infinite closed geodesics of a compact no-simply connected Riemannian manifold.
并由此讨论了紧致的非单连通黎曼流形上无穷多的闭测地线存在性问题。
Straightest geodesics are with intact differential definition and theory system, but related study and application in graphics is very few now.
最直测地线有更完整的微分几何定义和理论系统，在图形学领域内，对它的研究和应用还比较少。
Geodesics on smooth surface have many good geometric properties and there are equivalent partial differential equations and analytical methods solving it.
测地线在光滑曲面上有很好的几何性质，也有相应的测地线偏微分方程表达以及一些解析的方法来求解。
We present two practical linear methods computing straightest geodesics starting from a given point and going along a special tangent direction on triangle mesh.
我们提出了两个个实际的线性时间的算法求解三角网格上一点开始沿给定切方向的最直测地线。
Because arc length of trajectory is regarded as the variant in geodesics based method, it possesses the advantages of non-time based trajectory planning at the same time.
本文的基于测地线的轨迹规划是以轨迹弧长作为参考变量的，因此它还具有非时间参考的机器人轨迹规划的优点。
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.
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.
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。
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