曲线

By invoking a suitable measure of shape, e.g., the absolute rotation index or elastic bending energy, a "good" interpolant is selected. A new means to differentiate among the solutions is introduced here, namely, the winding number of the closed loopformed by a union of the hodographs of the couple of PH cubic and of the unique "ordinary" cubic interpolant.

已有的插值算法都是依赖于构造出所有四个解，利用绝对旋转数或弹性弯曲能量来找出这条"好"的插值曲线，本文介绍一种新的方法来区分这些解，即用由三次PH曲线偶和惟一传统三次插值曲线的速端曲线形成的闭环的弯曲数来区分。

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。

Algebraic curve is commonly used in CAGD. Traditional curve interpolation is in various forms of spline fuction. Although better result can be obtained by spline curve, the former two of elliptic, hyperbolic and parabolic shapes can not be represented by spline curve. An exploring research in this aspect is made in this thesis.

代数曲线是CAGD中经常用到的曲线，以往的曲线插值基本上是采用样条函数的形式，采用这种形式虽然能够获得很好的效果，但样条函数所能表达的形状都是抛物线型，对椭圆型与双曲线型曲线的表示是无能为力的。

The cubic algebraic curves (the Bezier curve and B style curve, etc belong to the parameter curve) is apter to realize the curve transition and fitting to dispersed data than the cubic parametric curves.

比如参数曲面与平面的交线就是一条平面代数曲线；平面参数曲线的等距曲线也是一条代数曲线。

For a general parametric curve/surface, we usually cannot compute its exact implicit form. Even though its exact implicit form can be computed, the curve/surface implicitization involves relatively complicated computation and the degree is higher. Moreover, it may have unexpected components and self-intersections. All these unsatisfied properties limit the applications of the exact implicitization. So finding curve/surface approximate implicitization has become a practical problem. In this paper, we present an algorithm to solve the approximate implicitization of a given parametric curve by using a quadratic algebraic spline curve.

由于精确隐式化过程不一定可以实现，即使可以实现隐式曲线曲面的阶数高计算复杂，并且具有不希望的自交点和奇异分支，从而限制了隐式化的运用，所以寻求参数曲线曲面的近似隐式化问题成为很实际又重要的问题，提出利用二次代数样条曲线来实现一般平面参数曲线近似隐式化的一种算法。

The unsaturated and compacted soil triaxial test result under constant suction describes the unsaturated soil critical state surface in p-q-s three dimensional space: in p - q plane, the slope M of critical state line is independent of suction; the cross line of LC yield surface and critical state surface is a curve with extremum in three dimensional stress space, and its projection in p-s plane is located in quadrant 1 in triaxial compression state; its projection in q-s plane has asymptote, and there should also be asymptote in respect of the curve that stands for the function relationship between cohesive and suction.

基于局部变形测量的常吸力非饱和压实土三轴剪切试验结果，全面描述了非饱和土p—g—s三维应力空间中临界状态面的合理形态：在p—q平面，临界状态线斜率M是与吸力无关的物理量；临界状态面与LC屈服面交线在三维应力空间中是一条存在极值的曲线；该交线在p—s平面的投影曲线在三轴压缩应力状态下应位于第一象限；该交线在q—s平面的投影曲线应存在渐近线；反映凝聚力与吸力关系的函数曲线也应存在渐近线。

These curves contain a shape parameter which can adjust the softness of curve and have the same continuity with the original B-spline. In succession, using the positive conditions of Bernstein polynomial to find a range in which the shape parameter takes its value so as to make the corresponding interpolating curves monotonicity-preserving and C~2 continuous.

利用奇异混合的思想构造出一类带有形状参数的多项式样条曲线，即均匀α-B样条曲线，在无需反求方程组、迭代过程和最值求解的情况下就能轻松做到插值给定的点列；它含有形状参数α，这就增加了曲线的柔性，同时又和原B样条曲线具有相同的参数连续性。

In this paper,the author obtains some features of Bertrand curves such as that necessary and sufficient conditions for a Bertrand curve is curve,discusses the distance from a point of a Bertrand curve to the corresponding point of the mate of Γ,the angle of the two tangent lines and so on.

讨论了Bertrand曲线的特征，得出了诸如曲线是Bertrand曲线的充要条件，Bertrand曲线Γ上的点与其偶线上对应点的距离，以及两点切线交角等结论。

Discusses algebraically and geometrically the properties of the ruled surfaces in the Euclidean three-space, especially, the principal normal surfaces on which there are some special curves, such as Mannheim curves, Bertrand curves and general helices.

在三维欧氏空间中，作为特殊曲线，Mannheim曲线、Bertrand曲线以及一般螺线具有良好的几何和代数性质。讨论了三维欧氏空间中特殊曲线的主法线曲面。

For the regular curves, we find two Killing fields for the purpose of integrating the structural equations of the p-elastic curves and express the p-elastica by quadratures in a syste...

对于正则曲线的情形，我们发现了两个用于求解p-弹性曲线的结构方程的Killing向量场并用积分将p-弹性曲线在一个柱面坐标系中表示出来，而对仿射星形曲线的情形，我们用积分方法解出了欧拉-拉格朗日方程，利用Killing向量场及线性李代数s1(2，R)、s1(3，R)和s1(4，R)的分类将高阶结构方程降为一阶线性方程，因此我们用积分完全解出了中心仿射p-弹性曲线。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。