几何的

Immanuel Kant argued that there is only one, absolute , geometry, which is known to be true a priori by an inner faculty of mind: Euclidean geometry was synthetic a priori .

康德认为，只有一个，绝对的，几何，这是众所周知的事实的先验的内在系铭记：欧几里德几何是合成先验。

This paper first summarizes recent researches on this topic, and then proposes some methods for curve modeling with cubic algebraic curve based on pure geometric constraints that involve control points, tangent directions and curvatures.

然后提出了一种基于几何约束的三次代数曲线的插值方法，该方法完全通过几何量如控制顶点、切线和曲率来控制三次代数曲线的形状，使得对三次代数曲线的编辑与对三次 B-样条曲线的编辑一样灵活方便。

The paper applies algebraic geometry, computational geometry, approximation theory to study the following problems: the Nother type theory and the Riemann-Roch type theory of the piecewise algebraic curve; the number of real intersection points of piecewise algebraic curves; the real piecewise algebraic variety and the B-net resultant of polynomials.

本文应用代数几何，计算几何，函数逼近论等学科的基本理论，分别就分片代数曲线的Nother型与Riemann-Roch型定理；分片代数曲线的实交点数；实分片代数簇以及多项式的B-网结式进行研究。

The meaningful regions obtained by range image segmentation correspond to the surface patches of 3D object.The 3D surface patches are then reconstructed by the algebraic surface fitting method;the surface parameters are estimated by solving generalized eigenvector problem. The geometric model of 3D object is constructed from reconstructed surface patches by using CAD geometric modeling tool GEOMOD.

首先通过编码光栅方法获取三维物体的深度图象，并采用数学形态学的方法加以分割，然后利用代数曲面拟合手段对分割后的三维曲面片进行重建，并使用CAD几何建模工具由重建的曲面片构成物体的几何模型。

Based on the spherical and plane triangular relationships of the spacecraft, the center of the earth, the projected-cloud and the true-cloud, several error analyses were done when one pixel was incorrectly matched with different intersection angle of crafts and the same cloud height.

利用卫星、真云、投影云和球心的平面球面几何关系，在几何反演方法的基础上，分析了在固定云高、不同卫星间隔和固定卫星间隔、不同云高这两种情况下，错误对比1个像素导致的可能的反演误差。

Results:The 3-dimensional finite element models of the minimum distal occlusal structure defect with restoration were created, which included metal crown with exterior anatomic morphology of the mandibular first molar, tooth preparation, filling material and the structure of periodontal membrane.

本研究采用逆向工程技术，通过先进的三维激光扫描技术，三维造型设计技术建立几何模型，将几何数据导入有限元分析软件中，建立了右下颌第一磨牙具有根管和远中面(distal occlusal，DO)最小缺损的全冠修复牙体预备体、充填体、金属冠、牙周膜的三维有限元模型。

This paper chooses some simple knowledge in the transformation of surface figures and the concept of group, sphere geometry.

但是我们现行的几何教材中，却没有安排现代数学的内容，也没有安排具实际意义的球面几何内容。

Support for all modern per-pixel lighting and rendering techniques including normal mapped, parameterized Phong lighting; virtual displacement mapping; light attenuation functions; pre-computed shadow masks; and pre-computed bump-granularity self-shadowing using spherical harmonic maps.

虚拟位移可以在平面上模拟3D几何曲面效果，与凸凹映射是通过光照实现不同，该技术实际上可以随意创造几何曲面。UE 3.0支持 ragdoll物理特性，被击中的物体会翻转，而有重量的物体会互相碰撞，倾斜等等极为真实和互动的物理效果

Based on the limitations of OBB, this thesis proposes an optimizing overlap test algorithm of bounding box and primitive. This method eliminates the bounding boxes of leaf nodes and streamlines the OBB hierarchical layer. This method also introduces a separating axis theory in the overlapping test between the primitives in order to accelerate the velocity.

针对基于OBB碰撞检测算法存在的缺陷，研究利用包围盒与基本几何元素相交测试的优化方法，消除叶子结点包围盒，精简OBB层次结构；同时在基本几何元素相交测试中引入类似分离轴的方法，加快检测速度。

The number of support, vectors is decreased by 28%. Then, the structure of the Riemannian geometry is introduced in the input space, and using the Riemannian geometric modifies the kernel function of the classifier and gets less improved support vectors at the second training.

在第一次训练后产生的支持向量的基础上，将黎曼几何结构引入到输入空间，利用黎曼几何结构将分类器中的核函数进行修改，在第二次训练中再次减少了支持向量数目。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。