spring 2019

## STE6238 Geometric Modelling - 5 ECTS

Sist endret: 30.08.2019

## The course is provided by

Faculty of Engineering Science and Technology

## Location

Narvik |

Applicants from Nordic countries: 1. December
Exchange students and Fulbright students: 1. October

## Type of course

The course may be taken as a single subject.

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

Application code: 9371

Recommended Prerequisite(s):
SMN6191 Numerical methods
SMN6190 Linear algebra 2

## 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.

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.

There will not be arranged a re-sit exam for this course

## Date for examination

Written 08.03.2019

The date for the exam can be changed. The final date will be announced in the StudentWeb early in May and early in November.

## Course overlap

STE6238 Geometric modeling 1 5 stp