曲面

The judging speed is accelerated To assure generating correct tool paths in 3-axis NC machining, the processing plans of undercut and overcut situations for whole tool trajectories are discussed Sometimes certain of complex problems can be simplified using an approximating surface offset strategy presented The surface reconstruction technology in reverse engineering is studied deeply.

讨论了三轴数控加工球头铣刀关于整个刀轨路径的漏切与过切的检查和处理方法，保证最终生成正确的刀具路径。研究了曲面偏距问题，提出了一种曲面近似偏距新策略，在保证正确结果的前提下，将复杂问题简单化。深入研究了逆向工程中散乱数据点的曲面重构技术。

Feature parameters are achieved by comparing the coefficient of standard representation and general representation. As for cone, parameter of general representation has no explicit geometric meaning and can not reflect design intent.

基于二次曲面的统一表示方程，采用最小二乘法进行参数拟合，通过对比其标准形式和二次曲面的统一表示方程，确定圆柱曲面特征带有明显几何意义的参数圆柱轴线法矢量、圆柱的中心和半径。

The error compensation is introduced in the interpolation algorithm to increase the interpolation point's solution precision in the cutting direction of the parametric curved surface. The reasonable simplification of the computed result of the interpolation point's parameter value is carried in the operation process by focusing on the character that curvature of slow-varying parametric curved surface changed slowly and the feature that the scanned profile of translational scanned curved surface is parallel along the scanned line.

通过引入误差补偿值以提高参数曲面在走刀方向上插补点的计算精度，针对缓变参数曲面曲率缓变和平移扫描曲面扫描轮廓沿扫描线平行的特点在运算过程中对插补点参数值的计算结果进行合理简化。

In computer-aided manufacturing, the processed parametric curve and surface should be regular, so the parametric curve and surface generated by computer-aided design should be regular first.

在计算机辅助制造过程中，要求所处理的参数曲线曲面是正则的，前提是计算机辅助设计得到的参数曲线曲面是正则曲线曲面。

With regard to CAD modeling in reverse engineering, some key techniques, including feature extraction from point cloud and parametric representation, are studied.

本文针对反求工程CAD建模路线：从点云提取特征曲面，再进行曲面参数化CAD造型过程中非常关键的步骤——特征提取进行了深入研究，着重研究了二次曲面特征的提取，并对点云中的全局特征约束优化技术进行了有益的探索。

Simultaneously, we study the existence problem of a special Weingarten rotation surface s in H_1~3(-1) and give all spacelike and timelike Weingarten rotation surface sin H_1~3(-1) using the parametric representation of rotation surfaces.

同时研究了H_1~3(-1)中一类特殊的Weingarten 旋转曲面的存在性问题，并利用曲面的参数表示，给出了H_1~3(-1)中所有的类空和类时Weingarten 旋转曲面的表示。

Simultaneously, we study the existence problem of a special Weingarten rotation surfaces in H_1~3(-1) and give all spacelike and timelike Weingarten rotation surfacesin H_1~3(-1) using the parametric representation of rotation surfaces.

同时研究了H_1~3(-1)中一类特殊的Weingarten旋转曲面的存在性问题，并利用曲面的参数表示，给出了H_1~3(-1)中所有的类空和类时Weingarten旋转曲面的表示。

A new technique of free-form deformation about parametric surface through so-called extension factor is presented in this article.

提出一种新的参数曲面自由变形方法：构造出特殊的伸缩因子函数，用它去作用待变形曲面，从而使曲面发生形变。

The vertex within control mesh of fitting subdivision surface was located by iterative modification and local adaptive subdivision. This method makes it feasible to avoid the solution of linear equation system. The size of control mesh, which is corresponding to the fitting Loop subdivision surface, is smaller. The surface is reconstructed according to the given precision. It can represent detail characteristics of original model, and is piecewise smooth (C^2 continuous everywhere except at extraordinary vertices where they are C^1 continuous).

系统通过对控制网格顶点的循环修正和局部自适应细分来求解最终拟合细分曲面控制网格，避免了求解线性方程组，提高了拟合曲面的质量，实现了在给定精度下用较少的控制网格反映物体细节特征的分片光滑（片内除奇异点C^1，外其余C^2连续）的Loop细分曲面重建。

A better plane is the so-called maximum area plane, i.e. the plane on which the convex hull of the projection forms a maximum area.

一种更好的曲面被称为最大面积曲面，就是曲面所在的投影凸起外壳构成最大面积。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。