Application deadline

Type of course

Admission requirements

PhD students or holders of a Norwegian master´s degree of five years or 3+ 2 years (or equivalent) may be admitted (categories 3 and 4 above). PhD students must upload a document from their university stating that they are registered PhD students. This group of applicants does not have to prove English proficiency and are exempt from semester fee.

Holders of a Master´s degree must upload a Master´s Diploma with Diploma Supplement / English translation of the diploma. Applicants from listed countries must document proficiency in English. To find out if this applies to you see the following list:

Proficiency in English must be documented - list of countries.

For more information on accepted English proficiency tests and scores, as well as exemptions from the English proficiency tests, please see the following document: Proficiency in English - PhD level studies.

The course will be cancelled if less than five participants.

Offered irregularly. The course will be cancelled if less than five participants.

The course will only be available if there are students at the  IVT-faculty who have  the course in their PhD-plans for that particular term, and there are resources available for lecturing the course.

This course is organized as an  intensive course with concentrated  teaching.

Course content

The objective of the course is to give candidates a thorough understanding of splines, physical background, implementations, properties and how to use splines. The students will get a thorough introduction to spline methods for modelling curves and surfaces, with emphasis on both the mathematical theory and practical methods.

Divided differences, Hermite splines, cubic spline interpolation, B-splines, knots and junctions, Cox-deBoor algorithm, matrix notation, knot insertion and removal, degree raising, interpolation, approximation, B-spline curves and surfaces, NURBS.

The course will focus on constructions of surfaces in engineering (geometric modeling applied to wind- and snow simulation and design of aerodynamical surfaces).

Objectives of the course

Knowledge:

After passing the course, the student is expected to be able to

• Demonstrate understanding of the forefront of knowledge within spline theory is.
• Evaluate the expediency and application of methods for modelling spline curves and surfaces, and using splines in general, in research and scholarly development projects.
• Contribute to the development of new knowledge, new theories, methods, interpretations and forms of documentation in research fields where splines and use of splines can be of importance.

Skills:

After passing the course, the student is expected to be able to

• Formulate problems, plan and carry out research and scholarly development work connected to modelling spline curves and surfaces.
• Carry out research and scholarly research work connected to splines (theory and implementations) of high international standard.
• Handle complex academic issues and challenge established knowledge and practice in the field of computer aided geometric design.

Habits of mind:

After passing the course, the student is expected to be able to

• Combine the information in the course with other courses and use this to manage complex interdisciplinary assignments and projects.
• Communicate research and development work through recognized international channels.
• Present research results orally.
• Participate in debates concerning spline theory in international forums.
• Assess the need for, initiate, and practice innovation connected to modelling curves and surfaces.

Language of instruction and examination

Teaching methods

Assessment

Mandatory tasks: Lectures and assignment.

Exam: Oral examination. The grades will be Passed/Not passed.

A re-sit exam will be arranged for this course.