A Tool For Teaching Spline Methods In A Computer Graphics Course

The specialized mathematics knowledge covered in a computer graphics course is usually presented to students in an abstract way. Albeit, computer graphics is an application of this (abstract) mathematics, students may find it hard to link them together. In particular one of the most difficult topics to present in a pedagogical manner to junior students in a computer graphics course is spline methods (mathematical method for data smoothing) used for curve/surface modelling. This topic involves mainly the mathematics of parametric functions, piecewise functions, derivatives, matrices, and parametric/geometric continuities. Usually a student has a vague picture of the actual output of the application of this mathematics. Many educators have experienced that students may fully understand splines application, if and when they are assigned a software project to implement splines, and this understanding could still remain vague until the very last stages of the implementation. As an alternative, static pictures may be presented in class to provide an intuitive understanding of splines. This approach is, in effect, similar to viewing a picture in a textbook. A better alternative is for the educator to demonstrate real-time spline generation, since a picture is worth ten thousand words but a moving picture (animation) is worth ten thousand static ones. This paper presents an interactive software program which is used as a tool to introduce important concepts and algorithms of spline methods to computer science and computer engineering students. The software is specially developed for educational purposes, and generates spline curves

Computer Graphics Learning Materials

Selles lõputöös on antud ülevaade Tartu Ülikooli aine Arvutigraafika (MTAT.03.015) jaoks koostatud õppematerjalist ja õppekeskkonnast. Kirjeldatud on aine modulaarset ülesehitust, mis rakendab kombineeritud ülevalt-alla (ing. k. top-down) ja alt-üles (ing. k. bottom-up) lähenemisi. Loodud õppematerjal sisaldab endas interaktiivseid näiteid, mis vastavad hõivatuse taksonoomia 4ndale tasemele. Õppekeskkonna CGLearn spetsifikatsioon ja implementatsiooni detailid on kirjeldatud. Töö lõpus on kursusel osalenud õpilaste hulgas läbi viidud tagasiside küsitluse tulemuste analüüsiga. Lisa fail on lingina kätesaadav serveri probleemide tõttu aadresil : http://comserv.cs.ut.ee/forms/ati_report/files/ComputerGraphicsLearningMaterialsAppendix.zipThis thesis provides an overview of the learning material and a custom learning environment created for the Computer Graphics (MTAT.03.015) course in the University of Tartu. It describes a modular layout, that mixes a top-down and bottom-up approaches, in which the course was organized. The created material also includes interactive examples that satisfy engagement level 4 requirements. The specification and implementation details of the custom learning environment called CGLearn are given. Thesis concludes with the analysis of the feedback questionnaire answered by the students participating in the course and using the material. Due to server problems extras file is in here : http://comserv.cs.ut.ee/forms/ati_report/files/ComputerGraphicsLearningMaterialsAppendix.zi

THE RIGHT PLACE OF CAD-COURSES IN ENGINEERING EDUCATION

An educational conception of teaching CAD for beginners is presented based upon the geometric backgrounds of CAD. Teaching of geometric modelling is proposed as an extension of the fundamental geometry courses

Comparison and Evaluation of Didactic Methods in Numerical Analysis for the Teaching of Cubic Spline Interpolation

In mathematical education it is crucial to have a good teaching plan and to execute it correctly. In particular, this is true in the field of numerical analysis. Every teacher has a different style of teaching. This thesis studies how the basic material of a particular topic in numerical analysis was developed in four different textbooks. We compare and evaluate this process in order to achieve a good teaching strategy. The topic we chose for this research is cubic spline interpolation. Although this topic is a basic one in numerical analysis it may be complicated for students to understand. The aim of the thesis is to analyze the effectiveness of different approaches of teaching cubic spline interpolation and then use this insight to write our own chapter. We intend to channel every-day thinking into a more technical/practical presentation of a topic in numerical analysis. The didactic methodology that we use here can be extended to cover other topics in numerical analysis.Methods of teaching mathematics are different for several reasons, for example, the presentation style of teacher of a particular topic. In several books we can observe a different approach of presentation material of a topic, and at the end we can produce a unique way of teaching but in a different way. In our thesis we study different approaches to teaching in a several numerical analysis books in the topic of cubic spline interpolation. What is cubic spline interpolation? Cubic spline interpolation is a type of interpolation of data points. Interpolation is a method of constructing a curve between some data points. We chose cubic spline interpolation because it is better than other kinds of interpolation. Cubic spline interpolation has a smaller curvature compared with other types of interpolation. Therefore, cubic spline interpolation produces a smooth curve. In this research we study different approaches of teaching cubic spline interpolation to find a good way for presenting the cubic spline interpolation topic, because this topic may be complicated for students to understand. To reach a good process of presentation of cubic spline interpolation we compare each part of different approaches in the books we have studied for teaching cubic spline interpolation by asking questions and then answering those questions. In this way we will show how we can evaluate each answer. Evaluating each answer we will obtain a good result which will prepare us for writing our own chapter in order to present cubic spline interpolation in our way

Computer Animation to teach interpolation

While mathematics courses are a basic topic in engineering studies, they are often considered as a dif- cult subject by students. In this work we present a learning experience based on computer animation and using the perspective of mathematical modelling. Our goal is to provide the students with a context that motivates the study of function interpolation. We present a problem statement that is intended to be solved by means of the Modeling Cycle. The development of the activity and the strategies identi ed during the process are presented and discussed