An analytic geometry-variant approach to line ratio enhancement above the optically thin limit

We describe a simple theoretical model to investigate the anomalous effects of opacity on spectral line ratios, as previously studied in elements such as Fe XV and Fe XVII. The model developed is general: it is not specific to a particular atomic system, thus giving applicability to a number of coronal and chromospheric plasmas; furthermore, it may be applied to a variety of astrophysically relevant geometries. The analysis is underpinned by geometrical arguments, and we outline a technique for it to be used as a tool for the explicit diagnosis of plasma geometry in distant astrophysical objects.

An elementary treatise on analytic geometry, embracing plane geometry and an introduction to geometry of threee dimensions with numerous examples.

UANL

The basic concepts of mathematics; a companion to current textbooks on algebra and analytic geometry.

pt.1. Algebra.

Analytic geometry,

"Answers to odd-numbered problems": p. 375-393.

Calculus and analytic geometry

Mode of access: Internet.

Calculus, with analytic geometry.

Includes index.

Historical development of some ideas in analytic geometry of space.

Thesis (A.M.)--Cornell Univ., June 1913.

Elements of analytic geometry.

Mode of access: Internet.

Practical analytic geometry with applications to aircraft /

"Answers": p. 273-277.

Analytic geometry.

Mode of access: Internet.

Projective and analytical geometry.

Mode of access: Internet.

A school course in geometry, including the elements of trigonometry and mensuration and an introduction to the methods of co-ordinate geometry,

Mode of access: Internet.

Notes on elements of (analytical) solid geometry /

Spine title: Venable's notes on solid geometry.

Notes and problems on solid geometry : [Text of C. Smith] /

Author's autograph on fly-leaf.

装配机器人系统快速碰撞检测算法

提出一种面向操作手装配系统的快速碰撞检测算法。该算法以机器人运动学和空间解析几何为基础 ,将判断机械手手臂与障碍物是否发生碰撞问题转化为直线段与有界平面是否存在公共点的简单解析几何问题 ,并以 PU MA5 6 0操作手为例对算法加以说明。该算法不仅适用于静态的障碍物已知的环境 ,而且适用于障碍物运动规律已知的动态环境 ,减少了碰撞检测占用的时间 ,提高了路径规划的效率