Freeform curve design has existed in various forms for at least two millennia, and is important throughout computer-aided design and manufacture. With the increasing importance of animation and robotics, coupled with the increasing power of computers, there is now interest in freeform motion design, which, in part, extends techniques from curve design, as well as introducing some entirely distinct challenges. There are several approaches to freeform motion construction, and the first step in designing freeform motions is to choose a representation. Unlike for curves, there is no "standard" way of representing freeform motions, and the different tools available each have different properties. A motion can be viewed as a continuously-varying pose, where a pose is a position and an orientation. This immediately presents a problem; the dimensions of rotations and translations are different, and it is not clear how the two can be compared, such as to define distance along a motion. One solution is to treat the rotational and translational components of a motion separately, but this is inelegant and clumsy. The philosophy of this thesis is that a motion is not defined purely by rotations and translations, but that the body following a motion is a part of that motion. Specifically, the part of the body that is accounted for is its inertia tensor. The significance of the inertia tensor is that it allows the rotational and translational parts of a motion to be, in some sense, compared in a dimensionally- consistent way. Using the inertia tensor, this thesis finds the form of kinetic energy in <;1'4, and also discusses extensions of the concepts of arc length and curvature to the space of motions, allowing techniques from curve fairing to be applied to motion fairing. Two measures of motion fairness are constructed, and motion fairing is the process of minimizing the measure of a motion by adjusting degrees of freedom present in the motion's construction. This thesis uses the geometric algebra <;1'4 in the generation offreeform motions, and the fairing of such motions. <;1'4 is chosen for its particular elegance in representing rigid-body transforms, coupled with an equivalence relation between elements representing transforms more general than for ordinary homogeneous coordinates. The properties of the algebra germane to freeform motion design and improvement are given, and two distinct frameworks for freeform motion construction and modification are studied in detail.

Det här arbetet har gått ut på att jämföra två algoritmer för bildbaserad rendering. Båda algoritmerna använder två bilder som spelats in med formatet MultiView plus depth för att rendera nya mellanliggande vyer av en tredimensionell scen. De tvådimensionella bilderna är kompletterade med djupvärden för varje bildpunkt. Renderingen kan då utföras genom perspektivriktiga transformationer där alla bildpunkters nya positioner projiceras individuellt. I samband med renderingen behöver bland annat mätfel i de ursprungliga bilderna samt skymda partier hanteras. Algoritm I gör det delvis genom utjämning av skarvararna mellan bildernas bidrag till den nya vyn. Algoritm II bygger på att bilderna delas upp i lager där de lager som ansetts vara säkra prioriteras framför lager som har bedömts vara mer riskabla. Algoritmerna har implementerats i Matlab och algoritm II har modifierats genom kompletteringar av dess regler för prioriteringen av lagren till mer komplicerade scener. Algoritm II har visat sig vara bättre på att bevara detaljer i de renderade vyerna och håller en jämnare hastighet vid renderingarna. Den ger även högre och jämnare resultat vid jämförelse med kvalitetsmåttet PSNR men vid jämförelser med MSSIM har den däremot fått något lägre värden. De ytterligare stegen vid renderingen har även ökat renderingstiderna med upp till 40 % jämfört med algoritm I. Författaren ger förslag på områden för fortsatt utveckling av algoritm II. Till exempel bör algoritmen testas vidare för att avgöra om de använda gränsvärdena är generella eller om de måste anpassas till olika scener. / This thesis has been aimed at comparing two algorithms for image-based renderings. Both algorithms uses two images recorded with the MultiView plus depth format, to render new intermediate views of a three-dimensional scene. The two-dimensional images extensions with depth values for each pixel, makes it possible to perform the image warping as perspective projections of all individually pixels to their new positions. During rendering, such as measurement error in the original images and occlusions has to be handled. Algorithm I is partly based on smoothening the joints between the contributions from the two images to the novel view. Algorithm II divides the images into layers, in which layers consid-ered safe has priority over layers that have been defined as more risky. The algorithms have been implemented in Matlab and algorithm II has been modified through additions to the priority rules for the layers to more complex scenes. Algorithm II has proven to be better at preserving the details in the rendered views, and maintains a less varying speed when rendering. It also provides higher and more consistent PSNR values, but in comparison using MSSIM the values are slightly lower. The additional steps have also increased the rendering times by up to 40 % compared to algorithm I. The author suggests areas for further development of algorithm II. For example, the algorithm should be tested further to determine if the used thresholds are general or whether they must be adapted to different scenes.

The main goal of this project was to familiarize readers with the techniques used in real-time animation of 3D characters. This work is focused on two types of animation: keyframe animation and skeletal animation. There are described algorithms for software and hardware accelerated model deformations, keyframe interpolations, animation blending, inverse kinematics and ragdoll. The result of this project is a framework, which consists of an animation library, examples demonstrating library functions and tools for export animations from 3D Studio Max and MilkShape 3D.

Since the introduction of high end graphical workstations, computer animation has quickly replaced the traditional means of animation. Nowadays computer animation has many applications e.g. video games, motion picture industry, media, weather forecasting and many others. This master thesis discusses various techniques used to created animations using computers. Keyframing, is the most common approach in computer animation. Borrowing its name from the concept of traditional hand animation, the workflow process remained the same. Basic principles of animation using key-frames are explained and an Interactive Animation Editor solution based on keyframing is proposed and the implementation of this editor is described. Editor uses the Kochanek-Bartels interpolation of values between each key-frame.