Type of course

This course might be canceled under certain conditions, i.e. less than five people. This will be considered before the start of the course. For other information, contact the director of studies.

Deadline for application: June 1st for the autumn semester.

Who has to apply for admission?

• PhD students at UiT that wishes to take a PhD level course which is not going to be a part of the PhD degree they study for at UiT.

• PhD students from other institutions than UiT.

• Applicants that has achieved a master’s degree (five year master or three year bachelor degree + two year master degree), but isn’t a PhD student.

Admission requirements

Obligatory prerequisites

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 of curves and surfaces, with emphasis on both the mathematical theory and practical methods.

Key-words include, but is not limited to, divided differences, Hermite splines, cubic spline interpolation, B-splines, knots and junctions, the Cox-deBoor algorithm, matrix notation, knot insertion and -removal, degree raising, interpolation, approximation, data fitting, B-spline curves and surfaces, and NURBS.

The course focuses on constructions of surfaces in engineering.

Recommended prerequisites

Objectives of the course

Knowledge:

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

• Demonstrate understanding of what 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.

General competence:

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

• Combine the information in the course with other courses and use it 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