三次曲线

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。

An image conic can be the projection of either a planar conic or silhouette of a conicoid. We show that at least three images, taken from the same position with different camera orientations, of two planar conics, or two conicoids, or one conic and one conicoid, are needed for the calibration, and a closed-form solution can be obtained. Our new conic based calibration technique requires no knowledge of camera's orientations, and relies solely on image correspondences.

在不同的方位拍摄三幅或三幅以上图像，每幅图像至少包含两个空间平面二次曲线、或两个二次曲面、或一个平面二次曲线与一个二次曲面的投影，利用图像之间的二次曲线对应关系，可以确定摄像机的内参数矩阵，同时可以获得摄像机不同方位之间的旋转矩阵。

Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.

第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。

Degree B-Spline curve is chosen to fit the longitudinal settlement curves, which solves the problem of curvature continuum for joint notes due to its continuous second derivative vector and overcomes the efficiency and accuracy of computing curvature with 3 points by hand.

选取三次B样条方法对隧道纵向累计沉降曲线进行拟合，利用三次B样条曲线二阶导矢连续的特性，解决了拟合曲线在曲线连接点处曲率的连续性问题，克服了以往人工计算隧道曲率半径在效率和准确性方面的缺陷；并在此基础上，推导了隧道纵向变形曲率与纵向螺栓拉应力、相对弯曲与纵向螺栓剪应力之间的关系； 3。

Then, a modifiable cubic polynomial curve is presented based on the basis functions, and the relation between the curve and the classical Bézier curves is discussed.

然后，基于该调配函数生成了一类可调控的三次多项式曲线，并讨论了该曲线与二次Bézier曲线及三次Bézier曲线之间的关系。

Ythagorean hodograph curves enjoy a number of remarkable properties, such as, its offset curves have exact rational representations; the arc length function of a Pythagorean hodograph curve is simply a polynomial function of the curve parameter; and the lower degree Pythagorean hodograph curves have intuitive geometrical interpretation.

H曲线具有诸如有精确的有理 Offset、弧长函数可由多项式函数表示以及几何解释优美等一系列优良性质。基于复分析方法，避免了实分析讨论中出现的复杂表示及繁琐计算，构造了满足给定 C1 Hermite插值条件且以C1拼接连续的三次 PH曲线偶。该曲线偶可灵活处理拐点，从而克服了一般三次 PH曲线因恒凸而无法处理拐点的缺陷。

Furthermore,it can represent the elliptic curves,parabola and other quadratic curves without using rational form.

给出了一种基于三角函数的类三次参数曲线，该曲线不仅具有类似于三次Bézier曲线的诸多性质，而且无需有理形式即可精确地表示椭圆、抛物线等二次曲线。

In order to overcome these weaknesses, we use quartic B-spline structure the yield curve, which indicates the less node cubic B-spline model is better under the situation that do not use the forward rate curve, if need to make use of forward rate curve to carry on the economy analysis, the suggestion use quartic B-spline method.

为克服这些缺点，我们用四次B-样条构造收益率曲线，实证表明能克服三次B-样条曲线上述缺点。因此，在不使用远期利率曲线情况下较少节点的三次样条模型是较好选择，当需要利用远期利率曲线进行经济分析时，建议使用四次B-样条法。

The results showed that it was unsatisfactory for the whole samples to estimate the LAI, with the correlation coefficient being only 0.523. After the total samples were divided into four vegetation types, i.e., meadow vegetation, marsh vegetation, shrub and islanded forest, the correlation coefficients and the estimation accuracy were improved evidently. Cubic equations were found to be the best in the different forms of the regression models for retrieving the LAI of wetland vegetation by using CBERS data, with the R^2 value being 0.723, 0.588, 0.837, and 0.720, respectively.

结果表明，整个研究区样本总体的LAI估算效果不太理想，其NDVI与LAI的相关性仅为0.523；将研究区分为草甸、沼泽、灌丛和岛状林4种湿地植被类型，NDVI与各植被型LAI的相关性和估算效果均有很大程度的提高，所建立的LAI遥感反演模型以三次曲线回归方程拟合精度最高，R^2分别达到0.723、0.588、0.837、0.720。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。