Research and Software

The newest research results appear under Publications .

iPASS using OpenGL 4

An OpenGL 4 implementation of the interactive Pixel-Accurate Shading of Surfaces (iPASS) algorithm.

Blender free-form modeling

Semi-structure splines

Toolkit for Illustration of Procedures in Surgery

Polyhedral Splines

Swarm-NG: Discovery of extra-solar planets using CUDA

Project documentation | Source Code
Publication: Dindar, S., E.B. Ford, M. Juric, Y.I. Yeo, J. Gao, A.C. Boley, B. Nelson, J. Peters Swarm-NG: A CUDA Library for Parallel n-body Integrations with focus on Simulations of Planetary Systems , New Astronomy, Volumes 23-24, October 2013, Pages 6-18 DOI: 10.1016/j.newast.2013.01.002 arXiv:1208.1157 [astro-ph.EP].

Box-splines and applications

M. Kim

Constraint Solving and Configuration Spaces

M. Sitharam video

Tri/Quad/Pent Surface Patch Construction and Rendering on the GPU

As an alternative to mesh refinement, a quad-dominant control mesh is converted directly to polynomial patches that join smoothly. Our two-pass GPU algorithm addresses meshes with adjacent extraordinary vertices, triangles, pentagons, and polar configurations. The first pass constructs the Bezier patches of the final surface using the vertex and geometry shader, and the second pass evaluates and renders these patches after sending in a pre-tessellated domain. The source code is freely available for educational purposes and has been tested on the following.
  • Windows Vista Professional 32- and 64-bit
  • Visual Studio 2005
  • November 2007 DirectX 10 SDK (June 2008 SDK's shader compiler crashes)
  • CGAL 3.3.1
  • GeForce 8800GTX, 8800GT (used for the paper), and ATI Radeon HD 4870 X2
Questions go to Ashish Myles (, and if that doesn't work, then to Jorg Peters (
(pdf) (movie 9.2MB) (source code, updated 2009-02-24)

A Realtime GPU Subdivision Kernel

By organizing the control mesh of subdivision in texture memory so that irregularities occur strictly inside independently refinable fragment mesh, all major features of subdivision algorithms can be realized in the framework of highly parallel stream processing. Our implementation of Catmull-Clark subdivision as a GPU kernel in programmable graphics hardware can model features like semi-smooth creases and global boundaries; and a simplified version achieves near-realtime depth-five re-evaluation of moderate-sized subdivision meshes. The approach is easily adapted to other refinement patterns, such as Loop, Doo-Sabin or sqrt3 and it allows for postprocessing with additional shaders. (pdf) (quicktime movie)

4-3 Direction Subdivision

4-3 subdivision is an alternative to Catmull-Clark subdivision on quadrilateral nets and a modification of Loop's scheme for triangulations, plus a simple transition rule. In regular mesh regions, 4-3 surfaces are C2 (otherwise C1) and generalize two closely-related quartic box-splines. The quad-component of 4-3 has a smaller stencil than Catmull-Clark and is the unique scheme with a 3 x 3 stencil that can model constant features, aligned with the quad grid or diagonal to it, without ripples. (pdf)

Subdividable Linear Maximum-norm Enclosure (SubLiME)

Subdividable linear efficient function enclosures (Slefes) provide, at low cost, a piecewise linear pair of upper and lower bounds f^+, f^-, that sandwich a function f on a given interval: f^- <= f <= f^+. These bounds are observed to be very tight. See papers: [Univariate B\'ezier], [Multivariate], [uniform B-Spline], [Optimality] and download the SubLiME package for [Linux/Unix], [Windows] (Version 1.1, updated June 22th 2003)

Mesh Mutation in Programmable Graphics Hardware

We show how a future graphics or visual processor unit, enhanced with random read and write to video memory, can represent, refine and adjust complex meshes arising in modeling, simulation and animation. To leverage SIMD parallelism, a general model based on the mesh atlas is developed and a particular implementation without pointers is proposed in which primal, binary refinement of, possibly mixed, quadrilateral and triangular meshes of arbitrary topological genus, as well as their traversal is supported by user-transparent programmable graphics hardware. Adjustment, such as subdivision smoothing rules, is realized as user-programmable mesh shader routines. Attributes are generic and can be defined in the graphics application by binding them to one of several general addressing mechanisms. (pdf)

Patching Catmull-Clark Meshes

PCCM  transformation creates maximally large, smoothly joining Nurbs patches of order 4 from Catmull-Clark subdivision meshes. It can be applied after any of the first subdivision steps and creates patches that are maximally large in the sense that one patch corresponds to one quadrilateral facet of the initial, coarsest quadrilateral mesh before subdivision. The patches join $C^2$ almost everywhere and with tangent continuity in the immediate neighborhood of extraordinary mesh nodes, matching the global smoothness of Catmull-Clark limit surfaces.  More...

Surface Splines

Twisted Cubes C1 surface splines represent smooth manifolds that can be embedded smoothly or non-smoothly into Rn. The connectivity allows for arbitrary patch layout and the blend ratios for local control over the distribution of curvature. In particular, sharp features can be modeled in the same framework by local, intuitive choice of these blend ratios. 
The GMOD title page shows a surface spline.

We implemented a minimal, portable C-implementation of Surface splines without major data structure overhead (Read the papers in particular Pcp2Nurb): OpenGL code and VRML output

Box-Spline Based CSG Blends

Blend Surface To blend implicitly defined constructive solid geometry surfaces, we are using the zero set of a spline in three variables. The resulting blend surface is generically curvature continuous, of algebraic degree four independent of the number of surfaces joined, and supports both point classification and efficient rendering. 

The Artesano immediate modeler

Pacho Artesano provides an intuitive interface to modeling complex surfaces. It is based on deforming surfaces with virtual tools rather than by modifying mathematical quantities such as control points or blend ratios. The virtual tools mimic the tools a designer uses for modeling in clay. It is primarily intended for the first steps in a design process, where creativity is more important than exactness in the mathematical sense. Even though, the models produced are guaranteed to be smooth and can be easily exported into general CAD-packages. 
It uses the SurfLab's geometry library using an Open Inventor frontend. A port to WIN32 platforms exists. 
Objects and images created with Artesano

Real time moment computations

Grippers with moments Efficient and exact calculation of the moments of objects enclosed by a free-form surface for animation or design. Since the moments, like the volume, can be computed rapidly, it is possible to solve inverse problems as, for example, determining the fill-height of a given volume of liquid in a container in real-time. 

Show me the movie QuickTime movie (260k bytes)

The Topological House

topohouse   Homotopy illustrating a piecewise linear immersion of the sphere in 3-space such that its complement is connected. The representation interpolating the sphere and the final house has to be capable of continuously increasing the curvature, resulting in sharp edges in the limit.

topohouse Semi-transparent (Draft version, QuickTime 3 Mb)  Bing's house with two rooms see wiki
topohouse Semi-transparent (AVI 219 kb)  youtube
topohouse Half house is visible (AVI 9 Mb)  youtube   sphere collapse   water fill   water conservation   exact volume computation   rocket frog fast parallel 2008   Siggraph 2005 realtime GPU subdivision kernel

SurfLab's geometry library

The library consists of a collection of data structures, routines, and programs to define and manipulate  the geometry of Surface Splines and other parametric representations. 
The geometry library is composed of several modules of C++, Maple, and Matlab code. 
The C++ modules work for SGI IRIX 5.3 and Windows NT. 

BezierView A small program to visualize Bezier patches and their curvatures.

Last modified 06:54:44 PM, Fri Mar 31, 2023