Application deadline

1 June for the autumn semester and 1 December for the spring semester. Exchange students and Fulbright students: 1 October for the spring semester and 15 April for the autumn semester.

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.

Type of course

The subject can be taken as a singular course.

• The PhD course is primarily open to UiT's PhD students (Category 1).

One or more of these categories of course students may also

be admitted:

• Category 2: Participants in the Associate Professor programme that fulfil the educational requirements.
• Category 3: Doctoral students from other universities.
• Category 4: People with a minimum of a master's degree (or equivalent), who have not been admitted to a doctoral programme.

Admission requirements

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.

Recommended reading/syllabus