A number of people have supported me during the work which has culminated into this dissertation. First and foremost, I would like to thank my main supervisor Arne Lakså. His deep enthusiasm for the field of research, sharing of knowledge in many aspects, support and guidance during the period of the project have been invaluable. My co-supervisor, Knut Mørken, has taken care of many practical and organizational arrangements at the UiO. He has provided constructive feedback which was very useful in order to compile a final version of this text.Then I would like to thank Børre Bang for his patience in discussions of theoretical and practical matters, sharing of his ideas and for always taking the time to provide constructive feedback and advice. Lubomir Dechevsky has prepared the ground by initiating and developing the theory of expo-rational B-splines and other topics. He has provided valuable feedback at several occasions. Klas Pettersson has been supportive through providing his expertise in mathematical theory and analysis, and by coordinating a series of interesting seminars on the topic of differential geometry. Peter Zanaty has put his mark by performing efficient and thorough work, which undoubtedly has influenced the way I work.My dear friend and colleague Jostein Bratlie has spent what seems like an uncountable number of hours together with me. Together we have been learning, researching, programming, writing, traveling and teaching, just to mention a few, throughout the period of the research project.My friends and colleagues at Narvik University College are always positive and provide a great working atmosphere. They are an interesting group of people with knowledge in many fields. The open door policy is much appreciated. This thesis would not have been realized without the funding from the Verdikt program (project id 201511) by the Research Council of Norway.I would like to thank my friends and family for the understanding and patience during long working hours. My parents, Randi and Magne, and my parents in law, Solveig and Ole, have taken care of my family while I have been away traveling to attend research conferences. My daughters, Evine and Alvilde, have been dragging me out of "deep hack mode" to remind me of the most important aspects of life.Last, but not least, a big warm hug to my wife and best friend Therese for showing patience and for putting up with me during this period. v

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Surface deformation over flexible joints using spline blending techniques AIP Conf.Abstract. Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by C k -smooth basis functions. One way of approximating discrete regular data using GERBS is by partitioning the data set into subsets and fit a local function to each subset. Partitioning and fitting strategies can be devised such that important or interesting data points are interpolated in order to preserve certain features.We present a method for fitting discrete data using a tensor product GERBS construction. The method is based on detection of feature points using differential geometry. Derivatives, which are necessary for feature point detection and used to construct local surface patches, are approximated from the discrete data using finite differences.

We present a concept for representation of motion-capture data where information from the animation data is used to generate a blending-type spline curve using local curves of Hermite type.

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