Blending spline constructions are generated by blending local geometry using a smooth basis function. Compared with de facto industry standards used within CAGD, blending spline constructions are structurally complex. However, they enjoy a combined set of unique properties that are exploitable in real-world applications.

The ph.d. thesis investigates some of the construction's curve and surface applications in interactive geometric modeling (IGM). In particular, in the thesis's main contribution, the basis's property of vanishing derivatives is exploited to enable a patchwork interpretation for surface constructions. Together with a salient API feature of modern graphics hardware, this enables cost-consistent evaluation schemes.

Moreover, the patchwork interpretation itself enables polygonal surface constructions with constant parameter lines that are non-dependent on the local surface type.

Software prototypes are utilized to develop and verify the thesis results. An in-house library built on a set of salient features of modern C++ is used for this purpose. With the thesis, a minimal feature version of this library is provided, and the feature utilization is argued.

The thesis defense was held on June 11, 2021, at 12:00, consisting of a trial lecture followed by a public thesis defense. Due to COVID-19, the trial lecture was submitted in advance as a video lecture, and the defense was conducted via Zoom.

Trial lecture

Methods for interpolation of scattered 3D data by smooth surfaces
(with a focus on different type of splines, their advantages and disadvantages)

• Trial lecture slides

Defence

Applications of blending splines in interactive geometric modeling

• The thesis [pdf]
• Defence lecture slides

Adjudication committee

• Associate Professor Krassimira Vlachkova, Sofia University, Bulgaria
• Research manager Jon Mikkelsen Hjelmervik, Sintef, Norway
• Professor Xing Cai, Department of Informatics, University of Oslo, Norway

Chair of defence

• Associate Professor Petter Nielsen, Department of Informatics, UiO

Supervisors

• Professor Arne Lakså, Department of Computer Science and Computational Engineering, UiT The Arctic University of Norway, Norway
• Professor Knut Mørken, Department of Mathematics, University of Oslo Norway

Procedures

Trial Lecture

The trial lecture is held in English and is organized by the unit, which is also responsible for publicizing it. The trial lecture will last 45 minutes. The purpose of the trial lecture is to test the PhD candidate's ability to convey research-based knowledge outside of his/her specialist field. The assigned topic must not therefore be taken from key areas of the PhD work. The assigned topic will be determined by the committee.

The committee’s report on the trial lecture must be written on a special form. The following elements must be included in the assessment:

• the PhD candidate’s choice of material
• structure/organization of the trial lecture
• understanding and academic maturity
• presentation technique, including the use of visual aids

At least two weeks before the trial lecture, the unit will publically announce the trial lecture and public defence. The candidate will be informed of the topic by the unit ten working days before the trial lecture.

Defence

The public defence is an open event where a PhD candidate publicly presents and defends his/her completed doctoral thesis to two critical opponents from the expert adjudication committee. The public defence is normally chaired by one person from the department management or a representative. Once the PhD candidate has passed both the trial lecture and public defence, the doctoral degree is awarded.

The public defence is held in English.

The chair of the public defence will briefly explain the submission and assessment of the thesis, and give a brief formal introduction of the candidate. The candidate will then spend a maximum of 30 minutes explaining the purpose and findings of the scientific investigation.

Two of the committee members serve as opponents. The first opponent will put the candidate's work into an international academic context, for a maximum of ten minutes. When both opponents have concluded their arguments, the chair of the public defence will invite others present to participate in the discussions.

Finally, the candidate will take the floor to extend his/her thanks, before the chair of the public defence declares the public defence concluded.

Following a brief meeting of the committee after the conclusion of the public defence, the chair will announce the committee’s decision on the candidate’s public defence.

The public defence must be held on UiO premises.