Preetham Sky Model

Preetham Sky Model

The Preetham sky model simulates sky color for a given time (year, day of year and time of day) and location (latitude, longitude). The main idea is to compute the color at zenith and use a clever distribution technique to approximate the rest of the hemisphere. This leads to a cheap, closed-form solution that is reasonably close to meteorological measurements and relatively easy to implement. However, this model is not perfect, and a rigorous criticism was made recently. In spite of this, the Preetham sky model provides nice backgrounds to CG scenes, especially when compared to many of the simpler alternatives, such as single colors or gradients. The main alternative is to go out and acquire panoramic photographs of real skies, a task that requires expensive hardware and is time-consuming. Also, photographs cannot be animated over time, providing only static snapshots of lighting conditions. Finally, this implementation could be improved by adding physically based glare and some form of tone mapping.

Animations

Download day-cycle [.mov]

Images

KlickKlacker 2 Solver

KlickKlacker 2 Solver

The general idea of this game is that areas that are connected by having the same color are removable, and the objective is to remove areas in a strategic way until no further moves are possible. Cells will fall down if there is empty space below them and will be pushed together if there are empty columns. The game ends if there are no possible moves or if all the cells are gone.

My idea was to write a solver that builds a game tree where each leaf contains the final score from making a particular sequence of moves. As one quickly realizes there is a huge number of possible solutions. In order to speed things up, pruning of the game tree can be deployed. However, it is very likely (although unproven for this particular problem, but proven for similar but simpler problems) that the problem of optimally solving this game is NP-complete. This means that pruning won’t really help, because all leaves have to be visited in order to guarantee an optimal solution. However, a few obviously strategically flawed paths can be skipped. As with most pruning, evaluation functions must trade greediness and speed for optimal solutions.

A more failsafe optimization would be to implement a transposition table, because it is likely that by following different sequences of moves (in some cases simply changing the order of the moves) we arrive at the same game position, albeit with a different score. However, this involves checking for existens of a game position before solving at each node. This requires a fast hash-function for computing unique ID’s for game positions, which is non-trivial to design. In these cases we can terminate the paths where the same position was achieved with a lower score.

Currently, I can solve small grids (5×5) using a brute force approach. I also have a playable version of the game, for verifying the suggested moves (and for fun). The solver and the game are built on the same core-library developed by me.

Images

Hough/Radon Transform

Hough/Radon Transform

The Hough transform is a feature extraction technique used to detect objects or shapes in images. Features are represented in a suitable parameter space. The transform then casts votes into this space based on processing of the pixels in the input image. Local maxima in parameter space then correspond to the parameterised features.

The Hough transform operates on binary images, and as such often requires a thresholding of the original image. For greyscale images an alternative is to use the Radon transform. The Radon transform is roughly equivalent to a continuous formulation of the Hough transform.

The images to the right show the respective parameter spaces of a Hough and Radon transform applied to an image (not shown here). At first glance we seem to get better contrast in the Hough image. This is often desirable because it makes the task of finding robust local maxima easier. However, the price we pay for this is the constraint of having to input a binary image. Although it is more difficult to find robust local maxima in the Radon image, this method may sometimes be preferrable. One such case would be when the task of finding robust local maxima is easier than finding a suitable threshold for the original image.

Images

Obamafication

Obamafication

First, please note that this project does not express any political views whatsoever. Posterization is an art-form with the power to transform images into aesthetic renderings geared towards a particular message, often using few colors for printing purposes. I have taken the impressive style used in the 2008 Obama-campaign and applied it to a picture of myself. The procedure is well described in this tutorial. A lot of manual work is required and it is non-trivial to achieve the professional look produced for the presidential campaign. Also, some of the procedures described in the abovementioned tutorial are needlessly complicated. For instance, I have found that using a combination of blurring and median-filtering on the different threshold levels, followed by manual tweaking, is an intuitive way of shaping the final product. Also, this allows much more efficient use of the live-tracing capabilities of Adobe Illustrator, which eliminates the most time-consuming part of the process, namely the path-tracing. Adobe Photoshop and Illustrator were used to create the different image levels and the following path tracing.

Documents

Download vectorized version [.pdf]

Images

Level Set Ray Tracer

Level Set Ray Tracer

This application ray traces level sets by using the signed distance function to determine safe distances for rays to “leap” into the data grid. Snow is applied by letting particles fall downward in a 4D simplex noise field and applying a union operation where particles collide with the level set. The build-up of snow is rather slow for small particles, but smaller particles yield a finer grained build-up where individual unions are not visible after a while.

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Room Acoustics

Room Acoustics

A pressure source in a room will cause pressure changes to propagate. Our method of solution uses the Transmission Line Matrix (TLM) approach. Pressure is scattered in four directions at each node (i.e. each pixel in the visualization) and is partially absorbed by walls.

Documents

Download report [.pdf]

Images

PLY Reader

PLY Reader

Together with a friend I developed this application for an assignment at school. The application reads PLY-files and is capable of displaying normals, rendering {polygons | wireframe | points}, smooth or flat shading, and cel shading with edge detection (including interior edges). For efficient geometric queries a partial adjacency list was used.

Images