spring 2017
STE6238 Geometric Modelling - 5 ECTS

Application deadline

Applicants from Nordic countries: 1 June for the autumn semester and 1 December for the spring semester. Exchange students and Fulbright students: 1 October for the spring semester and 15 April for the autumn semester.

Type of course

The course may be taken as a single subject.

Admission requirements

A relevant undergraduate bachelor Engineering programme with minimum 30 credits Mathematics/statistics topics.

Prerequisite(s)

SMN6191 Numerical methods

SMN6190 Linear algebra 2

Application code: 9371


Course content

Geometrical representations- exact and approximate, aspects of differential geometry and parametrization of differentiable manifolds, geometric modelling approaches, methods of computational geometry, efficiency and complexity of geometric algorithms.

Recommended prerequisites

SMN6190 Linear Algebra 2, SMN6191 Numerical Methods

Objectives of the course

Learning outcomes, skills and attitudes
On completion of the course, the successful student is expected to have achieved the following:

Knowledge
Sound and well-systematized knowledge of the fundamentals of theoretical and computational aspects of advanced geometry relevant to mathematical modelling with curves, surfaces and volume deformations. Key words and phrases: cartesian, hyperspherical and projective coordinates, implicitization, parametrization and differential geometry of curves, surfaces and volume deformations, curve length, curvature and torsion, surface area and curvature, volume, geodesics, intrinsic geometric invariants, symmetries and conservation in geometry, polynomials, splines, B-splines, rational forms, NURBS, relevant special function families, algorithms for interpolation and approximation, aspects of graph theory related to partitions and covers, closest-neighbour manifolds, intersections, tensor-product and simplicial surfaces and volume deformations.

Skills
Inventiveness and resourcefulness in applying methods of geometric modelling in new engineering contexts, in particular, within scientific visualization, computer graphics, virtual reality, animation, geometrical constructions and representations and their manipulation and tuning, development of mathematical models and their numerical simulations, assessing model and algorithm efficiency,  CAD/CAM, computer-aided geometric design (CAGD), finite and boundary element methods (FEM/BEM), etc..

Acquiring sufficient programming skills in Python via an easy introduction to SageMath (http://www.sagemath.org/) with the purpose of simulation and verification of geometric models.

General competence
A holistic understanding of the interrelations between geometric fundamentals and invariants in space - form, position, orientation, degrees of freedom, size, complexity of geometric representations.

Versatility in cooperation in joint projects of research and development teams.

Ability to formulate new problems and define new concepts relevant to applications of geometry in engineering projects.

Versatility in communication of concepts, ideas and methods of geometric modelling. Some of the best students in this course, who later choose a topic in geometric modelling for their master diploma thesis project, will be expected to communicate their results at international conferences.


Language of instruction and examination

English

Teaching methods

Classroom lectures

Classroom exercises

Computer-session lectures using SageMath

Computer-session exercises using SageMath, without and with parallelization, and an interactive tutorial (http://i33www.ira.uka.de/applets/mocca/html/noplugin/inhalt.html)


Assessment

A set of "model exam" problems, several days prior to the actual exam, is posted at the course website at the end of the second self-study week, for the purpose of the students' self-assessment of their level of preparedness (the solution of the "model exam" is posted on the course website 24 hours after the posting of the formulations of the model problems).

Actual exam: a 3-hour written examination (assessment grades A-F), F is Fail. A re-sit exam will be arranged for this course.


Recommended reading/syllabus

Detailed curriculum/syllabus with time schedule - announced by the lecturer at the beginning of the course lectures.

A comprehensive, self-consistent, stand-alone course website which serves as an online compendium. The uniform resource locator (URL) of the course's main web page is announced by the lecturer at the beginning of the course lectures.

A structured collection of optional materials for further reading on the different topic in the course-posted on the course website.

A detailed, topically oriented and structured, list of references for further reading and self-improvement in the course's topics - posted on the course website.

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  • About the course
  • Campus: Narvik |
  • ECTS: 5
  • Course code: STE6238
  • Tidligere år og semester for dette emnet