CAGD考点总结
巴西高考知识点总结
巴西高考知识点总结一、语文语文是巴西高考的一项重要科目，考察学生的语言表达能力、阅读理解能力和写作能力。
语文的考试内容包括语法、词汇、阅读理解和写作等方面。
1. 语法：巴西高考的语法考试主要考察学生对语法知识的掌握程度，包括名词、动词、形容词、副词、代词等的用法和句法结构。
学生需要熟练掌握各种语法知识，并能够准确使用这些知识进行语言表达。
2. 词汇：词汇是语言的基本组成部分，学生需要掌握丰富的词汇量，包括常用词汇、专业词汇和生词等。
考试内容涉及词义辨析、词语搭配、词语拼写等方面。
3. 阅读理解：阅读理解是语文考试的重要环节，考察学生的阅读理解能力和分析能力。
学生需要通过阅读文章，理解文章的主旨、作者的观点和论据等内容，并能够用自己的语言表达出来。
4. 写作：写作是语文考试的另一个重要内容，考察学生的写作能力和表达能力。
学生需要能够根据所给的主题、素材或提示，进行文章的构思、组织和写作，形成连贯、清楚、有逻辑的文章。
二、数学数学是巴西高考的另一项重要科目，考察学生的数学思维能力、解决问题能力和运算能力。
数学的考试内容包括代数、几何、概率统计等方面。
1. 代数：代数是数学的重要分支，考试内容包括方程、不等式、函数、数列等内容。
学生需要掌握代数运算的基本规则和方法，能够解决代数方程和不等式，求解函数的性质和图像，分析数列的性质等。
2. 几何：几何是数学的另一重要分支，考试内容包括几何图形、三角形、圆、相似与全等等内容。
学生需要掌握几何图形的性质、计算几何图形的面积和周长，解决几何问题等。
3. 概率统计：概率统计是数学的另一个重要内容，考试内容包括随机事件、概率、统计图表等。
学生需要掌握概率和统计的基本概念和方法，能够进行概率计算和统计分析。
三、自然科学自然科学是巴西高考的另一项重要科目，考察学生对物理、化学、生物等方面的知识掌握程度。
1. 物理：物理是自然科学的一个重要分支，考试内容包括力学、光学、热学、电磁学等方面。
2024年8月联考GCT数学考查知识点总结（2篇）
2024年8月联考GCT数学考查知识点总结注：以下总结的数学考查知识点仅为参考，具体以考试要求和试题为准。
一、函数与方程1. 函数的概念和性质：定义域、值域、奇偶性、单调性等。
2. 函数的图像：平移、伸缩、反射等变换。
3. 一次函数：函数表示、性质及其应用。
4. 二次函数：函数表示、性质、图像、最值、解析式及其应用。
5. 反函数：函数与反函数的关系、求反函数等。
6. 线性方程组：解线性方程组的方法、解的唯一性及其应用。
7. 二次方程：解二次方程的方法、判别式、根的性质、应用。
二、数列与数列的极限1. 等差数列和等差数列的前n项和：通项公式、前n项和公式、等差数列的求和等。
2. 等比数列和等比数列的前n项和：通项公式、前n项和公式、等比数列的求和等。
3. 递推数列：递推数列的通项公式、前n项和公式、递推数列的求和等。
4. 数列的极限：数列收敛的概念、极限的性质及其应用。
三、三角函数与三角恒等式1. 三角函数的定义与性质：正弦、余弦、正切函数的定义、周期性、对称性等性质。
2. 三角函数的图像：正弦、余弦、正切函数的图像及性质。
3. 三角恒等式：同角三角函数的基本关系式、三角函数的和差化积、积化和差等。
四、数与集合1. 实数与复数：实数的性质、复数的定义、复数的运算及其性质。
2. 集合与集合的运算：集合的基本概念、集合的相等、子集、交集、并集等运算。
五、图形与几何1. 点、线、面、平面图形的基本概念及性质。
2. 直线与圆的性质：直线的倾斜、截距表示法、两直线关系等。
3. 三角形的性质：角的性质、边的性质、面积计算等。
4. 圆的性质：圆心角、弧长、切线与弦的关系等。
5. 几何变换与相似三角形：平移、旋转、翻转等变换，相似三角形的性质与判定等。
六、概率与统计1. 随机事件的概念与性质：随机事件的基本概念、事件的运算等。
2. 概率的计算：基本概率原理、独立事件的概率、互斥事件的概率等。
3. 条件概率与贝叶斯定理：条件概率的定义、条件概率的计算等。
王老师英语单词知识点总结
王老师英语单词知识点总结Importance of Vocabulary AcquisitionVocabulary acquisition is a fundamental aspect of language learning. Without a good grasp of vocabulary, it is difficult for students to understand and communicate effectively in a new language. English has a rich and diverse vocabulary, with over a million words, making it essential for students to continually expand their word knowledge. Research has shown that vocabulary knowledge is strongly correlated with reading comprehension, writing ability, and overall language proficiency.It is important for teachers to recognize the significance of vocabulary acquisition and to prioritize it in their language teaching. By helping students to build a strong foundation of English words, teachers can support their language development in all areas, from speaking and listening to reading and writing.Strategies for Teaching VocabularyThere are several different strategies that teachers can use to teach English vocabulary effectively. One common approach is to use the direct method, where teachers explicitly introduce new words and their meanings to students. This may involve providing definitions, examples, and usage in context. It is important to make sure that students understand the meaning and usage of the words before moving on to the next set of vocabulary.Another effective strategy is to use context to teach vocabulary. This involves presenting new words in meaningful contexts, such as in a reading passage or a dialogue, so that students can understand how the word is used in real-life situations. Contextual learning helps students to grasp the meaning of words and how they are used in different contexts. Teachers can also use mnemonic devices, such as word associations, pictures, or stories, to help students remember new words. By creating connections between new words and existing knowledge, students can retain vocabulary more effectively. Additionally, teachers can encourage students to use the new words in their speaking and writing, which reinforces their understanding and retention of the vocabulary.Role of Context in Understanding and Using WordsUnderstanding the role of context is crucial in language learning, especially when it comes to vocabulary. Context provides important clues for understanding the meaning and usage of words. When students encounter new words in meaningful contexts, they are better able to make inferences about the word's meaning and how it is used.Teachers should provide a variety of contexts for students to encounter and practice new words. This may include reading passages, listening activities, and real-life situations where students can use the words in context. By exposing students to a range of contexts, teacherscan help them to develop a deeper understanding of how words are used in different settings.Practical Tips for TeachersHere are some practical tips for teachers to help their students improve their English vocabulary:1. Integrate vocabulary instruction into all areas of language learning, including speaking, listening, reading, and writing.2. Use a variety of teaching strategies, such as the direct method, contextual learning, and mnemonic devices, to help students acquire and retain new words.3. Provide ample opportunities for students to practice using new words in context, such as through conversations, writing exercises, and real-life situations.4. Encourage students to engage with English outside of the classroom, such as by reading, watching English-language media, and using language learning apps.5. Regularly review and reinforce previously learned vocabulary to ensure retention and mastery.By following these tips, teachers can support their students in building a strong and extensive English vocabulary.ConclusionTeaching English vocabulary is a critical component of language instruction, and it requires careful consideration and thoughtful planning. By recognizing the importance of vocabulary acquisition, using effective teaching strategies, understanding the role of context in word understanding, and implementing practical tips for teaching vocabulary, teachers can help their students develop a strong and comprehensive grasp of English words.It is important for language teachers to be intentional in their vocabulary instruction and to create a supportive and engaging learning environment for students. By prioritizing vocabulary acquisition and providing ample opportunities for practice and reinforcement, teachers can help their students to become confident and proficient English language users.。
2024年8月联考GCT数学考查知识点总结范文
2024年8月联考GCT数学考查知识点总结范文____年8月联考GCT数学考查知识点总结1. 集合与运算：- 集合的概念及表示方法- 集合的运算：交集、并集、补集、差集等- 集合的包含关系和等价关系2. 数与式：- 整数、有理数、无理数、实数、复数的概念及性质- 数轴的表示方法和作图方法- 代数式的定义和运算法则- 同类项、合并同类项、提取公因式等化简技巧3. 方程与不等式：- 方程的基本概念、性质和解的方法- 一次方程组及二元一次方程组的解法- 二次方程的解法和性质- 不等式的基本概念、性质和解的方法4. 函数与图像：- 函数的定义、性质和表示方法- 常用函数的图像和性质：线性函数、一次函数、二次函数、指数函数和对数函数等- 函数的运算：四则运算、复合运算、反函数等- 函数的最值、增减性、奇偶性等5. 三角函数与解三角形：- 弧度制与角度制的相互转换- 常用三角函数的定义和性质- 三角函数的图像、周期性和奇偶性- 解三角形的基本原理与方法：正弦定理、余弦定理、正切定理等6. 数列与数列极限：- 数列的概念和表示方法- 等差数列和等比数列的性质和求和公式- 数列极限的定义和性质- 数列极限的判断方法：夹逼定理、单调有界原理等7. 排列与组合：- 排列和组合的定义和计算公式- 乘法原理和加法原理的应用- 二项式定理的应用- 置换与循环排列的计算技巧8. 平面与空间几何：- 点、线、面的基本概念及性质- 平行线、垂直线、相交线的判定方法- 圆的概念和性质- 空间几何体的表面积和体积计算9. 概率与统计：- 随机试验、样本空间、事件的概念- 概率的定义及计算方法- 事件的独立性和互斥性- 统计数据的整理和分析方法：频数、频率、平均数、中位数等10. 数学推理与证明：- 数学推理的基本规则和方法- 数学证明的基本要素和思路- 数学问题的建模和解决方法- 数学思维的培养和发展策略以上是____年8月联考GCT数学考查的主要知识点总结。
国际经济学基础考试重点总结
国际经济学基础考试重点总结名词解释Pattern of tradeThe commodities exported and imported by each nation.Laissez-faireThe policy of minimum government interference in or regulation of economic activity, advocated by Adam Smith and other classical economists.Opportunity cost theoryThe theory that the cost of a commodity is the amount of a second commodity that must be given up to release just enough resources to produce one more unit of the first commodity.Complete specializationThe utilization of all of a nation’s resources in the production of only one commodity with trade. This usually occurs under constant costs.Increasing opportunity costsThe increasing amounts of one commodity that a nation must give up to release just enough resources to produce each additional unit of another commodity. This is reflected in a production frontier that is concave from the origin.AutarkyThe absence of trade ,or isolation.Incomplete specializationThe continued production of both commodities in both nations with increasing costs, even in a small nation with trade.Terms of tradeThe ratio of the index prince of a nation’s export to its import commodities.DeindustrializationThe decline in the relative importance of manufacturing and in the share of manufacturing employment.Factor-price equalization (H-O) theoremThe part of the H-O theory that predicts, under highly restrictive assumption, that international trade will bring about equalization in relative and absolute returns to homogeneous factors across nations.Stolper-Samuelson theoremIt postulates that free international trade reduces the real income of the nation’s relatively scarce factor and increases the real income of the nation’s relatively abundant factor.Specific-factors modelThe model to analyze the effect of a charge in commodity price on the returns of factors in a nation when at least one factor is not mobile between industriesIncreasing returns to scaleThe production situation where output grows proportionately more than the increase in inputs or factors of production. For example, doubling all inputs more than doubles outputInternational economies of scaleThe increased productivity resulting from the firm’s integration of its entire system of manufacturing operations around the worldDifferentiated productsSomewhat different products (such as automobiles, cigarettes, and soaps) produced by different manufactures in the same industry or general product groupIntra-industry tradeInternational trade in the differentiated products of the same industry or broad product groupAd valorem tariffA tariff expressed as fixed percentage of the value of a traded commodityConsumer surplusThe difference between what consumers are willing to pay for a specific amount of a commodity and what they actually pay for itTerms of trade effect of a tariffThe reduction in the price of the import the commodity that results when a large nation imposes an import tariffOptimum tariffThe rate of tariff that maximizes the benefits resulting from improvement in the nation’s terms of trade against the negative effect resulting from reduction in the volume of tradeRate of effective protectionThe tariff calculated on the domestic value added in the production of a commodityQuotaA direct quantitative restriction on tradeV oluntary export restrains (VERs)Refer to an importing country inducing another country to “voluntarily” reduce its exports of a commodity to the importing nation under the threat of higher all-around trade restrictionsInternational cartelAn organization of suppliers of a commodity located in different nations (or a group of governments ) that agrees to restrict output and exports of the commodity with the aim of maximizing or increasing the total profits of the organization. An international cartel that behaves as a monopolist is called a centralized cartel.DumpingThe export of a commodity at below cast or at a lower price than sold domesticallyPersistent dumpingThe continuous tendency of a domestic monopolist to maximize total profits by selling the commodity at a lower price abroad than domestically ; also called international price discriminationPredatory dumpingThe temporary sale of commodity at a lower price abroad in order to drive foreign producers out of business, after which prices are raised to take advantage of the newly acquired monopoly power abroadSporadic dumpingThe occasional sale of a commodity at a lower price abroad than domestically in order to sell an unforeseen and temporary surplus of the commodity abroad without having to reduce domestic prices.Countervailing duties (CVDs)Tariffs imposed on imports to offset subsidies by foreign governmentsScientific tariffThe tariff rate that would make the price of imports equal to domestic prices so as to allow domestic producers to meet foreign competitionStrategic trade policyA relatively recent development advanced in favor of an activist trade policy and protectionismCustoms unionRemoves all barriers on trade among members and harmonizes trade policies toward the rest of the world . The best example is the European Union.Trade creationOccurs when some domestic production in a member of the customs union is replaced by lower-cost imports from another member nation. This increases welfareTrade diversionOccurs when lower-cost imports from outside the union are replaced by high-cost imports from another union member. By itself this reduces welfareTariff factoriesDirect investments made in a nation or other economic unit (such as a customs union ) to avoid import tariffsTransfer pricingThe overpricing or underpricing of products in the intrafirm trade of multinational corporations in an attempt to shift income and profits from high-to low-tax nationsBrain drainThe migration of highly skilled and trained people from developing to developed nations and from other industrial nations to the United States判断题MercantilismThe body of writing prevailing during the 17th and 18th centuries that postulated that the way for a nation to become richer was to restrict imports and stimulate exports. Thus, one nation could gain only at the expense of other nations.解答题Law of comparative advantage(解答)Explains how mutually beneficial trade can take place even when one nation is less efficient than, or has an absolute disadvantage with respect to, another nation in the production of all commodities. The less efficient nation should specialize in and export the commodity in which its absolute disadvantage is smaller( this is the commodity of its comparative advantage ), and should import the other commodity.Heckscher-Ohlin (H-O) theory (大题)The theory that postulates that⑴ a nation exports commodities intensive in its relatively abundant and cheap factor and⑵international trade brings about equalization in returns to homogeneous factors across countries.Heckscher-Ohlin (H-O) theorem （大题）The part of the Heckscher-Ohlin theory that postulates that a nation will export the commodity intensive in its relatively abundant and cheap factor and import the commodity intensive in its relatively scarce and expensive factor.。
西亚高考知识点总结
西亚高考知识点总结第一部分经济学1、宏观经济学宏观经济学研究总体经济现象，主要包括国民收入、国内生产总值、物价水平、经济增长率、失业率等指标。
西亚高考中，宏观经济学的考点主要包括：宏观经济的基本概念、国民收入的构成及分配、国内生产总值的计算方法、通货膨胀与通货紧缩、经济增长的原因和机制、失业的类型和影响、财政政策与货币政策等。
2、微观经济学微观经济学研究单位经济行为，主要包括生产者、消费者、市场等。
微观经济学的考点主要包括：供求关系、市场均衡价格、价格弹性、边际效用和边际成本、企业生产成本、市场结构与产业生产组织、不完全竞争市场、市场失灵等。
3、国际经济学国际经济学研究国际经济关系，主要包括国际贸易与国际金融。
国际经济学的考点主要包括：绝对优势与比较优势理论、关税与非关税壁垒、外汇市场与汇率体系、国际收支平衡与国际收支失衡、跨国公司与国际直接投资、经济全球化与全球经济治理等。
第二部分政治学1、政治理论政治理论研究政治制度、政治权力、政治文化等方面的理论问题。
西亚高考中，政治理论的考点主要包括：政治学的基本概念、政治权力与政治权威、政治制度的功能与结构、政治文化的特征与作用、政治参与与政治行为等。
2、国际关系国际关系研究国家间的政治、经济、军事、文化等方面的关系，主要包括国际政治理论、国际政治实践、国际政治组织等。
西亚高考中，国际关系的考点主要包括：国际政治的基本概念、国际政治体系与国际政治格局、国际安全与国际冲突、国际合作与国际发展、国际组织与国际制度等。
3、行政管理行政管理研究政府机构的组织、管理和运作，主要包括政府管理、行政管理、公共管理等。
西亚高考中，行政管理的考点主要包括：行政管理学的基本概念、行政管理的职能与原则、公共政策的制定与执行、行政改革与行政效率、公共管理的新趋势与新挑战等。
第三部分历史学1、世界史世界史是研究世界各国历史及其相互联系的学科。
西亚高考中，世界史的考点主要包括：人类社会的起源与演变、古代世界文明、中世纪世界文明、近代世界文明、现代世界文明等。
高中化学合格考知识点总结
Summary of Key Points for the High School Chemistry Qualification Exam1. Atomic Structure and Elements:Atomic number: The number of protons in an atom, which determines the element's identity. Electron configuration: How electrons are arranged in atomic orbitals.Periodic table: Organization of elements based on atomic number and chemical properties. Groups and periods: Categories of elements with similar chemical properties.2. Chemical Bonding and Molecular Structure:Ionic bonding: Electron transfer between atoms, forming positively and negatively charged ions.Covalent bonding: Electron sharing between atoms, forming stable molecules.Molecular geometry: Shape and arrangement of atoms in a molecule.Bond polarity and dipole moments: Distribution of charge within a molecule.3. Chemical Reactions:Types of reactions: Synthesis, decomposition, single displacement, double displacement, and combustion.Balancing chemical equations: Ensuring the conservation of mass and charge. Stoichiometry: Quantitative relationships between reactants and products in chemical reactions.4. Organic Chemistry:Carbon's unique properties: Ability to form four bonds and create a wide variety of compounds.Functional groups: Specific atomic arrangements that determine the chemical properties of organic molecules.Types of organic compounds: Alkanes, alkenes, alkynes, alcohols, ketones, carboxylic acids, etc.5. Solutions and Chemical Quantities:Solutions: Mixtures of two or more substances, usually a solvent and a solute. Concentration: Amount of solute per unit volume of solution.Molarity: Concentration expressed as the number of moles of solute per liter of solution.6. Thermodynamics:Energy and entropy: Measures of system disorder and energy transfer.Endothermic and exothermic reactions: Processes that absorb or release heat.Laws of thermodynamics: Basic principles governing energy transformation and entropy changes.7. Kinetics:Rate of reaction: Speed at which a chemical reaction proceeds.Activation energy: Minimum energy required for a reaction to occur.Order of reaction: Degree to which reactant concentrations affect the reaction rate.This summary covers the key points typically included in a high school chemistry qualification exam. However, it is important to note that the specific content and focus of these exams can vary depending on the region or educational system. Therefore, it is recommended to consult the official exam guidelines or syllabus for a more detailed and accurate list of exam requirements.。
英国竞赛知识点总结
英国竞赛知识点总结IntroductionCompetition is an essential part of our society. It helps to drive innovation, improve efficiency, and promote economic growth. In the United Kingdom, there are various competitions that cover a wide range of fields, including sports, academics, arts, and more. To excel in these competitions, participants must have a good understanding of the knowledge and skills required for success. In this article, we will summarize the key knowledge points for some of the most popular competitions in the UK.Academic Competitions1. The National Mathematics and Science ContestThe National Mathematics and Science Contest is a highly prestigious competition in the UK. It tests students' knowledge and problem-solving skills in mathematics and science. To excel in this competition, participants must have a strong understanding of concepts such as algebra, geometry, calculus, and physics, as well as the ability to apply these concepts to solve complex problems. In addition, participants must also possess excellent analytical and critical thinking skills.2. The UK Linguistics OlympiadThe UK Linguistics Olympiad is an annual competition that challenges students to solve linguistic puzzles and problems. Participants must have a good understanding of the structure and function of language, as well as the ability to analyze and interpret linguistic data. They should be familiar with concepts such as phonetics, phonology, morphology, syntax, and semantics, and be able to apply these concepts to solve problems related to language and communication.3. The British Informatics OlympiadThe British Informatics Olympiad is a programming competition that requires participants to solve complex algorithmic problems. To excel in this competition, participants must have a strong understanding of programming languages, data structures, algorithms, and computational complexity. They should also be capable of writing efficient and well-structured code, and possess excellent problem-solving and logical reasoning skills.4. The National Science and Engineering CompetitionThe National Science and Engineering Competition is a platform for young scientists and engineers to showcase their projects and research. Participants must have a strong understanding of scientific principles and methodologies, as well as the ability to design and conduct experiments, analyze data, and draw meaningful conclusions. They should also be able to communicate their findings effectively and present their work in a clear and engaging manner.Sports Competitions1. The Football Association Challenge Cup (FA Cup)The FA Cup is the oldest football competition in the UK, and one of the most prestigious in the world. To excel in this competition, footballers must have a high level of technical skill, physical fitness, tactical awareness, and mental toughness. They must also possess good teamwork and communication skills, and be able to perform under pressure in high-stakes matches.2. The Wimbledon ChampionshipsThe Wimbledon Championships is the most prestigious tennis tournament in the world. To excel in this competition, tennis players must have excellent racket skills, physical fitness, speed, agility, and mental fortitude. They must also be able to adapt to different playing surfaces and styles of play, and possess good strategic thinking and decision-making abilities.3. The Six Nations ChampionshipThe Six Nations Championship is an annual rugby competition that pits the national teams of England, Scotland, Wales, Ireland, France, and Italy against each other. To excel in this competition, rugby players must have superior physical strength, endurance, and tackling ability. They must also possess good passing, kicking, and running skills, as well as the ability to read and react to the game quickly and effectively.Arts Competitions1. The Turner PrizeThe Turner Prize is an annual award for contemporary art. To excel in this competition, artists must demonstrate a high level of creativity, originality, and technical skill in their work. They should also be able to articulate their ideas and concepts clearly and convincingly, and engage with contemporary issues and debates in the art world.2. The Royal Academy of Dance (RAD) Genée International Ballet CompetitionThe RAD Genée International Ballet Competition is a prestigious event that showcases the talent and skill of young ballet dancers from around the world. To excel in this competition, dancers must possess exceptional technique, artistry, and musicality. They should also be able to perform a wide range of dance styles and techniques, and express emotion and narrative through their movements.3. The BBC Cardiff Singer of the World CompetitionThe BBC Cardiff Singer of the World Competition is a renowned event that celebrates the art of opera singing. To excel in this competition, singers must have outstanding vocaltechnique, range, and control. They should also be able to interpret and express the meaning and emotions of the music, and possess good stage presence and acting ability.General Knowledge Competitions1. The University ChallengeThe University Challenge is a popular quiz competition that tests participants' general knowledge across a wide range of topics. To excel in this competition, participants must have a broad and deep understanding of subjects such as history, literature, science, geography, and the arts. They should also be able to think quickly and critically, and possess excellent memory and recall abilities.2. The Great British Bake OffThe Great British Bake Off is a popular television competition that tests amateur bakers' skills in making a wide variety of sweet and savory dishes. To excel in this competition, bakers must have a good understanding of baking techniques, ingredients, and flavors. They should also be able to work well under time pressure, and possess creativity, innovation, and attention to detail in their baking.3. The X FactorThe X Factor is a popular singing competition that provides a platform for aspiring singers to showcase their talent. To excel in this competition, singers must have exceptional vocal ability, range, and stage presence. They should also be able to interpret and perform a wide range of musical genres and styles, and engage with the audience and judges.ConclusionParticipating in competitions can be a rewarding and challenging experience. Whether it is in academia, sports, arts, or general knowledge, excelling in competitions requires a deep understanding of the subject or skill being tested, as well as the ability to perform under pressure and in front of an audience or judges. By mastering the key knowledge points and skills outlined in this article, participants can increase their chances of success and achieve their goals in the competitive world of the United Kingdom.。
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Ferguson曲线的优缺点
•优点： 1)结构简单
• 2）可以矩阵实现
•缺点： 1 ）端点切矢量用户不易给出
• 2）二阶及二阶以上的光滑拼接不易
实现
• 3） Ferguson曲面片在四个角点处过
于平坦，形状不易控制
Bezier造型方法的优缺点
•实质： Bernstein多项式的参数形式
•优点：灵活、方便控制、仿射不变
性、保凸等等
•缺点：对大量数据进行插值运算较
复杂，缺乏局部修改性。
不能精确
表示圆锥曲线曲面。
孔斯（ Coons）曲面
•实质：利用了超限插值和布尔和的
思想。
•优点： 1 ）给定边界，自动生成曲面
• 2）逼近性能较好
•缺点： 1 ）形状不易控制和修改
• 2）角点处较平坦
• 3）高阶光滑拼接较困难
B样条造型方法的优缺点
•优点：次数低、计算量少、稳定
•便于控制形状和进行局部修改，光
滑性好。
•缺点：与Bezier方法相比，插值
性差，不能精确表示圆锥曲线曲面。
5、NURBS
• Non-Uniform Rational B-Spline 的简称
• 1980s， Piegl/Tiller
•优点：
1 ）对标准的解析形状和自由曲线、曲面提供了统一的数学表示；
2）可通过控制顶点和权因子来灵活地改变形状；
3）对插入节点、修改、分割、几何变换等的
处理工具有利；
4）具有透视投影变换和仿射变换的不变性；5）非有理B样条、有理及非有理Bezier曲线、曲面是NURBS的特例；
被ISO确定为定义几何形状的唯一数学方法。
缺点：需要更大的存储空间
参数连续性和曲线曲面的光滑性没有必然联系
曲线曲面在满足参数连续性的同时，往往也失去了对形状的修改能力
不满足参数连续性的曲线也可以具有较好的光滑性
1、两条曲线在拼接点处只能是C0连续。
2、尽管切矢不连续，但切矢方向是连续的。
3、尽管不是C2连续，但曲率是连续的，两条曲线在拼接点处有公共的曲率圆，曲线具有较好的光滑性。
两条曲线达到n阶几何连续<=>两条曲线弧长参数化后，在连接点处达到Cn连续。
n阶几何连续记作Gn
从B样条曲线的方程可以看出，曲线的次数与控制顶点的个数无关，这是与Bezier曲线的不同之处。
B样条曲线的局部支承性
1）当u∈[ui,ui+1] 时， k次B样条曲线至多与dj,j=i-k,...,i这 k＋1个顶点有关，而与其它控制顶点无关，这是与Bezier曲线不同的地方。
2）移动控制顶点di它仅影响定义在区间 [ui,ui+k+1]上的k+1段曲线，而不会影响其它曲线段的形状。
3）在不含重节点的情况下，样条曲线共有 n－k＋1段，增加或减少一个控制顶点，也相应的增加或减少一段曲线段。
1、不同之处
B样条曲线是一种多项式样条曲线，而Bezier曲线是一种参数多项式曲线。
B样条曲线的控制顶点个数与曲线次数无关，而Bezier曲线的控制顶点个数比曲线次数多 1。
B样条曲线具有比Bezier曲线更强的凸包性。
如果k次B样条曲线的端节点重复度没有达到 k+1, 曲线端点的几何性质与Bezier曲线端点的几何性质不同。
2、联系
若干段k次Bezier曲线按照Ck－ 1的连续度首尾相连，可以表示成B样条曲线。
B样条曲线中的每一段可以通过反复插入节点得到每段曲线的Bezier点。
如果选取特殊的节点矢量， B样条曲线就是一段Bezier曲线，所以， B样条曲线是Bezier曲线的一种推广。
3、相同之处
Bezier曲线和B样条曲线都具有变差缩减性和仿射不变性。