代数曲线

An algebraic B-spline curve fitting algorithm based on the signed distance field is proposed in this paper.

提出了一种以代数B-样条曲线为表达形式、基于有向距离场的隐式曲线重建方法。

Regularity is an important algebraic property of parametric curve and surface, which depends on the parameterization of parametric curve and surface.

正则性是参数曲线曲面的重要代数性质，是由参数曲线曲面的参数化决定的。

Plane analytic geometry is a important content in the mathematics curriculum of high school, which embodies powerful function of analytic method and algebraic method in the depicting curve. It reflects important idea of the combination of number and figure. Learning the course is very important for students to improve mathematics thought ability. Teachers and students are engaged in teaching and learning by the textbook, so it is necessary to analyse plane analytic geometry textbook.

平面解析几何是高中数学课程中的重要内容之一，它体现了解析方法和代数方法在刻画平面曲线方面的强大作用，反映了数形结合的重要思想，学习这部分内容对提高学生的数学思维能力具有十分重要的价值，师生正是通过教材这一载体从事教学和学习活动的，因此，很有必要对平面解析几何教材进行分析。

The constructed algebraic spline curve not only possesses unwanted components and unexpected singular points but also satisfies C^2 continuity.

该算法得到的通近曲线二次代数样条曲线既不会产生多余的分支和不希望的奇异点，又达到整体C^2连续。

An implicit Curve reconstruction method is proposed which represents the curve with all algebraic tensor-product B-spline,and minimizes the tension ofthe B-spline and the approximate geometric distance between the curve and the point set.

提出一种以代数张量积样条曲线作为几何表示形式，基于近似几何误差和薄板能量极小化的隐式重构模型。

The procedure of transform the parametric form into algebraic form is calledimplicitization.

将参数形式的曲线曲面转化为代数形式的曲线曲面的过程称为隐式化。

In this paper, we have made a systemic theoretic research on modelling and reshaping several types of spline curves/surfaces in CAGD. And some creative productions are given as follows. At first, the uniform C-B-spline basis is proved to be a normalized totally positive basis, and can be extended to a normalized B-basis. C-B-spline and C-Bézier basis, similar to B-spline basis and Bézier basis in algebraic space, are two bases in algebraic trigonometric space.

本文围绕着CAGD中常用的几种曲线曲面造型和形状调整进行了深入的研究，主要获得了以下一些成果：首先，证明了代数三角空间中的n次均匀C-B-spline基是一组标准全正基，并进一步扩充为一组标准B基。C-B-spline基与C-Bézier基是多项式与三角混合空间中的两组基，是适应工程实践中设计特殊曲线曲面的需要而产生的，类似于多项式空间中的B-spline基与Bézier基，是CAGD中重要的造型工具。

We shall first apply the technique ofμ-bases and local cohomology to study the minimal generators for the moving surface ideals of rational cubic space curves and rational quartic space curves,and then study the implicit equations of rational space curves under different definitions of implicit equations.

在第五章中，我们将同调代数理论与μ基理论相结合，详细分析三次及四次空间有理曲线的动曲面理想生成元，为一般空间有理曲线的动曲面理想生成元的(来源：A21B12ceC论文网www.abclunwen.com)研究开辟可能的道路。

Projective transformation of curved surface and plane intersecting line are completed based on vector algebra,adopting space coordinate transforming method.

方法基于向量代数，采用空间坐标变换方法，建立了圆锥面与平面相交中截交曲线的形成特点，讨论了二次曲线的构成的数学原理。

High School: Algebra, Geometry, Advanced Algebra, Trigonometry, Pre-Calculus conics and limits

高中：代数，几何，高等代数，三角学，微积分先修课二次曲线论和极限

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。