Invited Speakers

Invited Speaker 1: Bert Juettler, Johannes Kepler Universität Linz, Austria

Title: Exact geometry description as a key technology for numerical simulation

Abstract: Choosing the "right" representation of geometric objects can provide tremendous advantages for subsequent computations, e.g., for numerical simulation. The talk will illustrate this observation by two case studies. First, we will report about the use of arc splines for computing medial axes and Voronoi diagrams for planar domains with free-form boundaries.  Compared to existing methods, which are based on point samples or piecewise linear representations, the use of splines eliminates the need for pruning and leads to more efficient algorithms. Second, we will describe our recent experiences with Isogeometric Analysis (IGA). IGA, which was proposed by T. Hughes et al. (2005) provides a new aproach to bridge the gap between numerical simulation and geometric design of engineering objects. We will focus on  the challenges for the geometric design community that arise from using this approach and demonstrate the potential gains.


Invited Speaker 2: Charles Loop, Microsoft Research

Title: Analytic Displacement and GPU Rendering of Catmull-Clark Subdivision Surfaces

Abstract: We present a novel method for high-performance GPU based rendering of Catmull-Clark subdivision surfaces called feature adaptive subdivision. Unlike previous methods, our algorithm computes the true limit surface up to machine precision, and is capable of rendering surfaces that conform to the full RenderMan specification for Catmull-Clark surfaces. Specifically, our algorithm can accommodate base meshes (possibly with boundary) consisting of arbitrary valence vertices and faces, and the surface can contain any number and arrangement of semi-sharp creases. Though considerably more general, the performance of our algorithm is comparable to the best approximating method, and is considerably faster than Stam's exact method.

Displacement mapping is ideal for modern GPUs since it enables high-frequency geometric detail on surfaces with low memory I/O. However, problems such as texture seams, normal re-computation, and under-sampling artifacts have limited its adoption. To tackle these problems, we introduce a GPU-friendly tile based texture format, store the coefficients of a smooth displacement function in these tiles, and form a multi-resolution hierarchy of this function. Using a scalar valued biquadratic B-spline with Doo-Sabin connectivity, we displace the Catmull-Clark base limit surface in its normal direction. We accurately compute surface normal variation at the pixel level; obviating the need for pre-computed normal maps while allowing correct shading under animation. Additionally, we propose a smooth level of detail scheme where we compute per vertex adaptive tessellation factors and select appropriate pre-filtered mip levels of the displacement function to prevent under-sampling.


Invited Speaker 3: Wenping Wang, University of Hong Kong

Title: Free-form Shape Modeling Using Cyclides Splines

Abstract: Dupin cyclides are classical surfaces discovered by the French mathematician Charles Dupin in the early 19th century. These surfaces have been extensively studied for surface representation for about three decades since Ralph Martin introduced them to surface modeling in early 1980s. Cyclides have several remarkable properties; for instance, they are low-degree algebraic surfaces (degree 4 or less) and have rational bi-quadratic parameterization. Furthermore, the offsets of a cyclide are again cyclides. However, despite all these advantages cyclide could potentially offer for shape modeling, all previous attempts at using cyclides to model free-form surfaces have been unsuccessful because of the relative inflexibility of cyclide patches. Therefore, it is widely believed that cyclides do not have enough freedom to represent free-form shapes. The applications of cyclides are currently limited to modeling blend surfaces or canal surfaces.

I shall propose an effective approach to modeling free-form shapes using fair, smooth cyclide splines. The key ideas behind the approach are vertex relaxation and global optimization. Specifically, the inflexibility of cyclides is overcome by relaxing the vertices of cyclide patches in a constrained optimization framework. I shall present results on using cyclide splines for free-form surface fitting and general free-form shape modeling, thus proposing cyclide splines as the first practical free-form surface representation with the exact offset property.

GMP 2012: Geometric Modeling and Processing June, 18-24, 2012, Huangshan, China