Former Projects

Shape Uncertainty and Variability

This project analyzes shape uncertainty and variability in point-sampled geometry. The uncertainty of acquired surface data due to noise and undersampling is measured using a statistical representation based on locally aggregated linear extrapolators computed from weighted least squares fits. Important issues are the effect of noise on this representation, efficiency of computation, and scale-space extensions of the scheme. Potential applications include adaptive re-sampling and merging of multiple scans.

Conformal Alpha Shapes

In this project we extend a classical geometric structure, alpha shapes, to locally adapted scales. Conformal alpha shapes shed new light on the relationship between the two main approaches in Delaunay-based surface reconstruction algorithms. We hope that this new understanding will allow for a new "universal" theory that unifies the two approaches in the near future.

Moving Least Squares Surfaces

Moving least squares (MLS) surfaces are an important tool in sample-based shape modeling. This project introduces adaptive MLS surfaces and an approximate scheme for fast computation of the implicit surface.

Feature Extraction

This project investigates multi-scale techniques for the extraction of line-type features on point-sampled surfaces. Using principal component analysis on local neighborhoods a feature graph is build that serves as input to a constrained smoothing method using active contour models. The extracted features are then used to create line drawings of the model.

Scan Cleaning and Shape Completion

This project addresses the problem of obtaining a complete and consistent 3D model representation from incomplete surface scans. Two different directions are persued. The first approach is based on extensive user interaction and provides a set of suitable shape processing tools to remove noise, fill holes, and adjust the sampling rate. The second approach uses context information retrieved from a 3D shape database as a geometric prior for regions of missing data. This allows shape completion even from highly incomplete surface data without requiring significant manual support.

Interactive Scan Cleaning

Example-Based 3D Scan Completion

Shape Simplification

This project is concerned with the implementation, analysis, and comparison of different surface simplification methods for point-sampled surfaces. We have implemented incremental and hierarchical clustering, iterative simplification, and particle simulation algorithms to create approximations of point-based models with lower sampling density.

Spectral Processing

This project is concerned with the design of spectral filters for advanced surface processing. Using an adaptive tesselation of the model surface into regularly resampled displacement fields, the method computes a set of windowed Fourier transforms to create a spectral decomposition of the model. Direct analysis and manipulation of the spectral coefficients supports effective filtering, resampling, power spectrum analysis and local error control.

Shape Modeling

This project is concerned with the design of algorithms and interactive tools for modifying the shape of a digital 3D model. Novel sampling strategies are devoloped for handling large deformations during free-form editing, as well as resolving complex surface-surface intersections for Boolean shape operators. Additionally, a multi-scale representation for 3D objects is introduced that allows advanced editing operations such es shape filtering and morphing.

Appearance Modeling

This project investigates novel methods for interactively altering the appearance of a surface model. New painting operators are introduced that allow simultaneous modification of color, material properties, and surface microstructure through the use of carving and displacement operations. A constrained minimum distortion parameterization supports interactive texture mapping for point-sampled surfaces.

Meshless Methods for Physically-Based Animation

In this project we investigate meshless methods for the animation of elastic and plastic materials. Novel features include a sample-based representation of both the simulation domain and the boundary surface, a dynamic re-sampling strategy of the solid to handle large plastic deformations and fracture, and a flexible dynamic surface model to handle dynamic changes of topology during the simulation.

Meshless Animation of Fracturing Solids - ACM SIGGRAPH 2005 - [paper] [movie] [slides] [web]
Efficient Raytracing of Deformable Point-Sampled Surfaces - Eurographics 2005 - [paper] [movie1] [movie2] [slides] [web]
Point-Based Animation of Elastic, Plastic, and Melting Objects - Symp. on Comp. Anim. 2004 - [paper] [movie] [slides] [web]

Quasi-Rigid Objects

This project investigates techniques for modeling contact between quasi-rigid objects - solids that undergo modest deformation in the vicinity of a contact, while the overall object still preserves its basic shape. The quasi-rigid model combines the benefits of rigid body models for dynamic simulation and the benefits of deformable models for resolving contacts and producing visible deformations.

Quasi-Rigid Objects in Contact - Symp. on Comp. Anim. 2004 - [paper] [movie] [slides] [web]