Research Ideas

Mark Grundland



Computational Geometry Tools for Decorative Architectural Design
for Sheldon Bakos at Integrale Architects, Johannesburg, South Africa (2010)

Voronoi diagram editor with DXF export to AutoCAD

Architectural sketch with Voronoi shaped windows, by Sheldon Bakos



Automated Non-photorealistic Rendering for Image Compression
supervised by Dr. Neil Dodgson at the Rainbow Group of the Computer Laboratory, University of Cambridge (2001)

Summary: For use in progressive image compression, these techniques generate a wide variety of image rendering styles, ranging from a hand-painted look to an inlay mosaic, by applying geometric subdivision as well as parametric procedural textures to Voronoi spatial partitions. This approach of image reconstruction from scattered color samples provides for an efficient multiresolution image representation.

Seminar: Automated Artistic Image Rendering

Paper: Stylized Rendering For Multiresolution Image Representation

Play: Progressive Image Rendering QuickTime Movies: "Adaptive Voronoi Diagram", "Lighthouse", "Autumn", and "Lena"



Computer Visualization of Quasicrystals
for Dr. Jiri Patera at the Centre de Recherches Mathématiques, Université de Montréal (2000)

Seminar: Generating Aperiodic Tilings Using Quasicrystals

Paper: Image Sampling with Quasicrystals

View: Quasicrystals Experiments

Delaunay triangulation and Delaunay graph of the quasicrystal point set defined by the H2 Coxeter Group.



Genetic Algorithms for Geometric Primitive Detection
with Youenn Fablet for the Pattern Recognition Course at the School of Computer Science, McGill University (1999)



Visualization in Number Theory
for the Number Theory Course at the Department of Mathematics and Statistics, McGill University (1999)

Source: Luc Devroye's Random Trees

Binary tree of a sequence of random numbers.

Binary tree of the sequence of fractional parts of n*Sqrt(2).



VoronoImage: A Virtual Stained Glass Workshop
with for the Computational Geometry Course at the School of Computer Science, McGill University (1998)

Summary: VoronoImage is a program for the Macintosh which demonstrates an application of computational geometry to rendering a picture into an image resembling a stained glass panel. The technique works through generating a partition tree representing a fractal arrangement of discreet Voronoi diagrams, where each Voronoi polygon is recursively subdivided into a Voronoi diagram. The Voronoi diagrams are calculated using a fast Euclidean distance mapping algorithm.

Visit: The VoronoImage Website: Technique and Results

View: Godfried Toussaint's VoronoImage Gallery



Visual Simulation of Fire
with Andrew Sacamano for the Computer Graphics Course at the School of Computer Science, McGill University (1997)

Real-time candle flame animation running on a 25MHz Mac.



Image Processing for the Imagination



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