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# END-3607 Geometric Modelling - 5 stp

## The course is administrated by

Institutt for datateknologi og beregningsorienterte ingeniørfag

## Type of course

The course can be taken as a single course.

## Course contents

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.

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

A relevant undergraduate Bachelor Engineering program with minimum 25 credits mathematics, 5 credits statistics, 7,5 credits physics

Application code: 9371

## 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 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)

## Date for examination

Off campus exam hand out date 06.03.2023 hand in date 06.03.2023

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