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Vår 2020
STE6238 Geometric Modelling  5 stp
The course is administrated by
Type of course
Course contents
Application deadline
Admission requirements
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
Objective 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 wellsystematized 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, Bsplines, rational forms, NURBS, relevant special function families, algorithms for interpolation and approximation, aspects of graph theory related to partitions and covers, closestneighbour manifolds, intersections, tensorproduct 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, computeraided 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
Teaching methods
Classroom lectures
Classroom exercises
Computersession lectures using SageMath
Computersession 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 selfstudy week, for the purpose of the students' selfassessment 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 3hour written examination (assessment grades AF), F is Fail.
There will not be arranged a resit exam for this course
Date for examination
The date for the exam can be changed. The final date will be announced at your faculty early in May and early in November.
Course overlap
Lectures Spring 2020 

Forelensing 
prof. Lubomir Todorov Dechevsky 