Designing and Animating a Character Sprite with Modern Techniques

High-quality 2D animation for video game production is both strenuous and time consuming. Traditionally, 2D game animation consisted of drawing each frame by hand and processing it into a bitmap for use in-game. As every frame was individually drawn, it was difficult to create enough drawings for smooth animation as well as keep form consistent between frames. Although, this technique usually resulted in a strong sense of 3D volume and realism when well executed. Current technology allows for faster 2D animation workflows using interpolation and bone systems as well as greater consistency, smoothness, and efficiency, but oftentimes the results lose the sense of depth and quality found in traditional animation. This thesis explores efficiently creating, and animating a 2D sprite by utilizing a composite of traditional animation techniques and computer animation practices. Using Adobe Photoshop, Adobe Flash, and the Unity3D game engine, a short game was created to demonstrate this process in a finished work

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

Uniform Interpolation for Coalgebraic Fixpoint Logic

We use the connection between automata and logic to prove that a wide class of coalgebraic fixpoint logics enjoys uniform interpolation. To this aim, first we generalize one of the central results in coalgebraic automata theory, namely closure under projection, which is known to hold for weak-pullback preserving functors, to a more general class of functors, i.e.; functors with quasi-functorial lax extensions. Then we will show that closure under projection implies definability of the bisimulation quantifier in the language of coalgebraic fixpoint logic, and finally we prove the uniform interpolation theorem

A semi-Lagrangian scheme for the game pp-Laplacian via pp-averaging

We present and analyze an approximation scheme for the two-dimensional game $p$-Laplacian in the framework of viscosity solutions. The approximation is based on a semi-Lagrangian scheme which exploits the idea of $p$-averages. We study the properties of the scheme and prove that it converges, in particular cases, to the viscosity solution of the game $p$-Laplacian. We also present a numerical implementation of the scheme for different values of $p$; the numerical tests show that the scheme is accurate.Comment: 34 pages, 3 figures. To appear on Applied Numerical Mathematic

Quiz Games as a model for Information Hiding

We present a general computation model inspired in the notion of information hiding in software engineering. This model has the form of a game which we call quiz game. It allows in a uniform way to prove exponential lower bounds for several complexity problems of elimination theory.Comment: 46 pages, to appear in Journal of Complexit

Decidability of higher-order matching

We show that the higher-order matching problem is decidable using a game-theoretic argument.Comment: appears in LMCS (Logical Methods in Computer Science