在加工具有大型复杂曲面的工件或对这些工件进行加工误差的检测时，都需要对曲面上的点进行测量。
When machining good-side workpiece or measuring its machining error, the points of these workpiece surface must be measured.
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.
文摘：给出了一种基于等高线求解坡度约束下曲面上两点间最短路径的搜索算法。
Abstract: a path searching algorithm using contour is presented to obtain the shortest path between two points on a curved surface under the slope constraint.
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。
It is proved that geodesics can be produced by stretch elastic strings along a smooth surface.
只要已知被加工曲面的参数表达式，就可运用点涉法在该曲面上生成非球面刀的数控加工轨迹。
As soon as the parametric representation of the sculptured surface is known, the NC machining path on it is determined for the nonspherical cutters.
给出了求解代数曲面上两点之间测地线的一种算法。
An algorithm for computing the geodesic line between the two points of an algebraic surface was presented.
本文提出一种直接在点采样曲面上计算曲面的高斯曲率、平均曲率及主曲率等局部微分性质的方法。
An approach is proposed to estimate several differential properties, including Gaussian curvature, mean curvature and main curvature on point-sampled surfaces in presence of noise.
给出了一种基于等高线求解坡度约束下曲面上两点间最短路径的搜索算法。
A path searching algorithm using contour is presented to obtain the shortest path between two points on a curved surface under the slope constraint.
NURBS方法在实际应用中遇到的一个重要问题就是已知曲线曲面上的型值点而求解控制点。
An important problem which is brought about by the method of NURBS in practice is that calculating control points based on the curve or surfaces data points.
为了支持并行设计与制造，本文研究提取曲面上一点的可行接近方向集合的方法。
In order to support concurrent design and manufacturing, the research focus on sculptured surface interrogation method for visibility direction information in design procedure.
当压力、包围角和滚筒半径在某一范围内变化时，以临界曲面的方法寻找曲面上与坐标原点距离最小的点，以此点作为理论上的防滑移设计最优方案。
When these factors vary in some range, the method of the critical curved surface can be used to find the critical point which has the shortest…
然后，从背景曲面的边界到内部逐个地搜索定义于背景曲面上某物理量的等值点，并按一定的规则将其连成等值线；
We searched each grid for picking up the 3D point position on which the quantity was equal to the designated contour level. Then these special points were connected in some contours according …
然后，从背景曲面的边界到内部逐个地搜索定义于背景曲面上某物理量的等值点，并按一定的规则将其连成等值线；
We searched each grid for picking up the 3D point position on which the quantity was equal to the designated contour level. Then these special points were connected in some contours according …
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