Lecture 2 Differential geometry of curves 2.1 Definition of curves 2.1.1 Plane curves Implicit curves f(, y)=0 Example:x2+y2=a2 It is difficult to trace implicit curves It is easy to check if a point lies on the curve Multi-valued and closed curves can be represented

0.1 Overview of intersection problems 10.2 Intersection problem classification 10. 2. 1 Classification by dimension 10.2.2 Classification by type of geometr 10.2.3 Classification by number system 10.3 Point /point\intersection

13 Offsets of Parametric Curves and Surfaces 13.1 Motivation.... 13.2 Parametric offset curves ........... 13.2.1 Differential geometry of parametric offset curves 22556 13.2.2 Singularities of parametric offset curves 13.2.3 Approximations

21 Object Matching 21.1 Various matching methods ..ti 21.2 Methods through localization/registration 21.3 Classification of matching methods 21.4 Problem statement. 21.4.1 Distance metric 21.4.2 Distance between a point and a parametric surface 21.4.3 Distance metric function 21.5 Matching problems: CGWOS, CPWOS, CGWS or CPWS

19.2 Exhaustive enumeration 19.2.1 Definition and construction methods 19. 2.2 Applications 19.2.3 Properties of exhaustive enumeration methods 19.3 Space subdivision 19.3.1 Motivation and definitions 2233356677 19.3.2 Construction of octrees 19.3.3 Algorithms for octrees 19.3.4 Properties of octrees 19.3.5 Binary space subdivision

工程热力学的两大类工质 1、理想气体( ideal gas) 可用简单的式子描述 如汽车发动机和航空发动机以空气为主的燃气、空调中的湿空气等。 2、实际气体( real gas 不能用简单的式子描述,真实工质火力发电的水和水蒸气、制冷空调中制冷工质等

Deployment and Geometry Maintenance Deployable Membranes Used for solar arrays, sunshields, decoys Being researched for apertures starting at RF and eventually going to optical Inflatables First US satellite was inflated (ECHO D) Enables a very large deployment ratio -=deployed over stowed dimension

Why Cost Estimation? Critically important part of system design Too high- lose the contract award Too low-over-run cost plus contracts, company loss on fixed price contracts Trends Design to cost Cost as an independent variable

Autonomy Technologies Fault Detection, Isolation and Recovery Planning & Scheduling Intelligent Data Understanding Path Planning Gradient method

The telemetry, tracking and control subsystem provides vital communication to and from the spacecraft TT&c is the only way to observe and to control the spacecraft's functions and condition from the ground October 29 2003 Massachusetts Institute of Technology