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

Lecture 6 B-splines(Uniform and Non-uniform) 6.1 Introduction The formulation of uniform B-splines can be generalized to accomplish certain objectives These include Non-uniform parameterization Greater general flexibility Change of one polygon vertex in a Bezier curve or of one data point in a cardinal(or interpolatory) spline curve changes entire curve(global schemes) Remove necessity to increase degree of Bezier curves or construct composite Bezier curves

Lecture 1 Introduction and classification of geometric modeling forms 1.1 Motivation Geometric modeling deals with the mathematical representation of curves, surfaces, and solids necessary in the definition of complex physical or engineering objects. The associated field of computational geometry is concerned with the development, analysis, and computer implemen tation of algorithms encountered in geometric modeling. The objects we are concerned with in engineering range from the simple

I. Choose the Correct Answer 1. Which of the following quantities are independent of the choice of inertial frame? (There may be more than one correct answer) (A)Velocity (B)Acceleration (C)Force (D)Work Solution: In all the inertial frame, the forces acted on a body are same,=ma=F'=ma', therefore the force and acceleration are independent of the choice of inertial frame

I. Choose the Correct Answer 1. The magnitude of the force of gravity between two identical objects is given by Fo. If the mass of each object is doubled but the distance between them is halved, then the new force of between the objects will be

一、解释下列术语:(本题5小题,每题3分,共15分) 1、 Life Form:生活型是生物对外界环境适应的外部表现形式,同一生活型的物种,不但体态相似,而且其适应特点也是相似的。生活型是不同生物对相同环境趋同适应的结果。 2、 Ecological Relationship:生态关系;指生物与生境间的相互作用而建立起的相互关系。 3、 Polymorphism:多态现象;一种群中有一种以上表现型的现象

一、名词解释(本题共5小题,每题3分,共15分) 1. Metapopulation:复合种群;由经常局部性绝灭,但又重新定居而再生的种群所组成的种群。复合种群是由空间上相互隔离但又有功能联系(繁殖体或生物个体的交流)的两个或两个以上的亚种群组成的种群斑块系统。 2. Ecosystem:生态系统;是指在一定的时间和空间内,由生物群落与其环境组成的一个整体,各组成要素间藉助物种流动、能量流动物质循环、信息传递和价值流动,而相互联系、相互制约,并形成具有自调节功能的复合体

一、解释下列术语:(本题5小题,每题3分,共15分) 1、 Adaptive suites 2、 Plant Community 3、Fitness 4、 Ecological Balance 5、 Predation 二、比较分析以下各组术语:(本题3小题,每题5分,共15分) 1.优势种和建群种 2.原生裸地和次生裸地 3.总初级生产量和净初级生产量

一、解释下例术语(本题5小题,每题3分,共15分) 1、 Ecological Amplitude:生态幅,每一种生物对每一种生态因子都有耐受一个范围,其范围就称为生态辐。 2、 Dominant Species:优势种,指群落中对群落的结构和群落环境的形成有明显控制作用的物种。 3、 Niche:生态位,指生物在群落或生态系统中的地位和角色,是物种所有生态特征的总和。 4、Biodiversity:生物多样性。生物多样性是指生命有机体及其赖以生存的生态综合体的多样性和变异性。生物多样性可以从三个层次上描述,即遗传多样性、物种多样性、生态系统与景观多样性。 5、 Biosphere:生物圈;地球上的全部生物和一切适合生物栖息的场所,包括岩石圈的上层、全部水圈和大气圈的下层

一、解释下列术语:(本题5小题,每题3分,共15分) 1、Siccocolous Plants 2、 Population Size 3、Coo-evolution- 4、Climax 5. Biogeochemical cycle 二、比较分析以下各组术语:(本题2小题,每题5分,共10分) 1、生态型与生活性 2、生态幅与生态位