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SAGA project:

Post-doc position

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AGGM, COMPASS

Nearest event:

Oslo 2012

Post-Doc Position

One full-time post-doc position for 7 months (should end by October 30, 2012) is available at Faculty of Mathematics and Informatics, Vilnius University (Lithuania) in the framework of Marie Curie Network SAGA (ShApes, Geometry, and Algebra).

General Topic: Rational surfaces with rational offsets and applications to geometric modeling

Possible Project Description

Current CAD technology is essentially based on NURBS. Therefore it is desirable that CAD constructions would generate rational surfaces, which finally can be represented in NURBS form. For example, offsets are very natural tools in CAD with a wide applicability for defining either safe (i.e. collision free) regions or trajectories in numerical control machining. Unfortunately their use in CAD relies on approximation techniques since generically the offset of a rational surface is no longer rational. About 15 years ago a special class of surfaces with rational offsets, so-called PN-surfaces, was introduced. PN-surfaces are important for CAD. The simplest primitive surfaces - natural quadrics, torus and other Dupin cyclides, and arbitrary rational canal surfaces are PN-surfaces. During last few years new results on parametrization and implicitization of rational canal surfaces were obtained, and new non-canal PN-surface constructions were proposed for branching blend between circular cylinders, cones or Dupin cyclides. The challenge is to understand several phenomena of these PN-surface constructions in order to invent new low-degree constructions useful for CAD. For example, the branching blend between cylinders has unexpected parametrization degree drop (during conversion from dual to point representation) and relatively low implicit degree. Recently a new promising approach to PN-surfaces in terms of Lie sphere geometry and geometric algebra appeared that should help to translate the associated CAD problems into the language of algebraic geometry.

Background

The Experienced Researcher candidate is expected to have a strong background in geometry, surface modeling, or related fields. The experience in computational algebraic geometry, e.g. in parametrization and implicitization of surfaces would be an advantage.

Qualifications

Degree: More than 4 years research experience or PhD, and less than 5 years research experience (after PhD) in Mathematics, Computer Science, or related field is required.
Nationality: The candidate cannot be of Lithuanian nationality, and cannot have resided or worked in Lithuania for more than a year during the 3 years before the start date of employment.
Languages: Fluency in English is required. Other languages would be an advantage.

Financial support

Gross salary of about 3111 Euro per month (~1800 Euro net) plus living allowance 359 Euro (~205 Euro net) without family or 574 Euro (~330 Euro netto) with family (family not necessary comes together).
Total net: ~ 2005 / 2130 EUR depending on family status.

Dates and application procedure

Start date: preferably in February, 2012; End date: till October 30, 2012.
Application deadline: the earlier the better.
Application procedure: email your complete CV to
rimvydas (DOT) krasauskas (ETA) mif.vu.lt,
including relevant courses with grades, your Master's/PhD thesis, any academic publications, and names/addresses of professors who may provide recommendations.

3D Gallery

Viewing VRML

Surfaces:

Algebraic surfaces

Patchworks

Canal surfaces

PN surfaces

Web 3D graphics:

Architecture