Gaël Guennebaud

Algebraic point set surfaces

In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar MLS include significantly improved stability of the projection under low sampling rates and in the presence of high curvature. The method can approximate or interpolate the input point set and naturally handles planar point clouds. In addition, our approach provides a reliable estimate of the mean curvature of the surface at no additional cost and allows for the robust handling of sharp features and boundaries. It processes a simple point set as input, but can also take significant advantage of surface normals to improve robustness, quality and performance. We also present an novel normal estimation procedure which exploits the properties of the spherical fit for both direction estimation and orientation propagation. Very efficient computational procedures enable us to compute the algebraic sphere fitting with up to 40 million points per second on latest generation GPUs.

Robust iso-surface tracking for interactive character skinning

We present a novel approach to interactive character skinning, which is robust to extreme character movements, handles skin contacts and produces the effect of skin elasticity (sliding). Our approach builds on the idea of implicit skinning in which the character is approximated by a 3D scalar field and mesh-vertices are appropriately re-projected. Instead of being bound by an initial skinning solution used to initialize the shape at each time step, we use the skin mesh to directly track iso-surfaces of the field over time. Technical problems are two-fold: firstly, all contact surfaces generated between skin parts should be captured as iso-surfaces of the implicit field; secondly, the tracking method should capture elastic skin effects when the joints bend, and as the character returns to its rest shape, so the skin must follow. Our solutions include: new composition operators enabling blending effects and local self-contact between implicit surfaces, as well as a tangential relaxation scheme derived from the as-rigid-as possible energy to solve the tracking problem.

Dynamic Sampling and Rendering of Algebraic Point Set Surfaces

Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving least‐squares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature control of the fitted spheres. As a second contribution we present a novel real‐time rendering system of such surfaces using a dynamic up‐sampling strategy combined with a conventional splatting algorithm for high quality rendering. Our approach also includes a new view dependent geometric error tailored to efficient and adaptive up‐sampling of the surface. One of the key features of our system is its high degree of flexibility that enables us to achieve high performance even for highly dynamic data or complex models by exploiting temporal coherence at the primitive level. We also address the issue of efficient spatial search data structures with respect to construction, access and GPU friendliness. Finally, we present an efficient parallel GPU implementation of the algorithms and search structures.

Implicit skinning: real-time skin deformation with contact modeling

Geometric skinning techniques, such as smooth blending or dual-quaternions, are very popular in the industry for their high performances, but fail to mimic realistic deformations. Other methods make use of physical simulation or control volume to better capture the skin behavior, yet they cannot deliver real-time feedback. In this paper, we present the first purely geometric method handling skin contact effects and muscular bulges in real-time. The insight is to exploit the advanced composition mechanism of volumetric, implicit representations for correcting the results of geometric skinning techniques. The mesh is first approximated by a set of implicit surfaces. At each animation step, these surfaces are combined in real-time and used to adjust the position of mesh vertices, starting from their smooth skinning position. This deformation step is done without any loss of detail and seamlessly handles contacts between skin parts. As it acts as a post-process, our method fits well into the standard animation pipeline. Moreover, it requires no intensive computation step such as collision detection, and therefore provides real-time performances.

A Survey of Surface Reconstruction from Point Clouds

The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contain a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece‐wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations—not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques and provide directions for future work in surface reconstruction.

High-Quality Adaptive Soft Shadow Mapping

The recent soft shadow mapping technique [ GBP06] allows the rendering in real‐time of convincing soft shadows on complex and dynamic scenes using a single shadow map. While attractive, this method suffers from shadow overestimation and becomes both expensive and approximate when dealing with large penumbrae. This paper proposes new solutions removing these limitations and hence providing an efficient and practical technique for soft shadow generation. First, we propose a new visibility computation procedure based on the detection of occluder contours, that is more accurate and faster while reducing aliasing. Secondly, we present a shadow map multi‐resolution strategy keeping the computation complexity almost independent on the light size while maintaining high‐quality rendering. Finally, we propose a view‐dependent adaptive strategy, that automatically reduces the screen resolution in the region of large penumbrae, thus allowing us to keep very high frame rates in any situation.

Growing Least Squares for the Analysis of Manifolds in Scale-Space

We present a novel approach to the multi‐scale analysis of point‐sampled manifolds of co‐dimension 1. It is based on a variant of Moving Least Squares, whereby the evolution of a geometric descriptor at increasing scales is used to locate pertinent locations in scale‐space, hence the name “Growing Least Squares”. Compared to existing scale‐space analysis methods, our approach is the first to provide a continuous solution in space and scale dimensions, without requiring any parametrization, connectivity or uniform sampling. An important implication is that we identify multiple pertinent scales for any point on a manifold, a property that had not yet been demonstrated in the literature. In practice, our approach exhibits an improved robustness to change of input, and is easily implemented in a parallel fashion on the GPU. We compare our method to state‐of‐the‐art scale‐space analysis techniques and illustrate its practical relevance in a few application scenarios.

Packet-based hierarchal soft shadow mapping

Recent soft shadow mapping techniques based on back‐projection can render high quality soft shadows in real time. However, real time high quality rendering of large penumbrae is still challenging, especially when multilayer shadow maps are used to reduce single light sample silhouette artifact. In this paper, we present an efficient algorithm to attack this problem. We first present a GPU‐friendly packet‐based approach rendering a packet of neighboring pixels together to amortize the cost of computing visibility factors. Then, we propose a hierarchical technique to quickly locate the contour edges, further reducing the computation cost. At last, we suggest a multi‐view shadow map approach to reduce the single light sample artifact. We also demonstrate its higher image quality and higher efficiency compared to the existing depth peeling approaches.

A vectorial solver for free-form vector gradients

The creation of free-form vector drawings has been greatly improved in recent years with techniques based on (bi)-harmonic interpolation. Such methods offer the best trade-off between sparsity (keeping the number of control points small) and expressivity (achieving complex shapes and gradients). In this paper, we introduce a vectorial solver for the computation of free-form vector gradients. Based on Finite Element Methods (FEM), its key feature is to output a low-level vector representation suitable for very fast GPU accelerated rasterization and close-form evaluation. This intermediate representation is hidden from the user: it is dynamically updated using FEM during drawing when control points are edited. Since it is output-insensitive, our approach enables novel possibilities for (bi)-harmonic vector drawings such as instancing, layering, deformation, texture and environment mapping. Finally, in this paper we also generalize and extend the set of drawing possibilities. In particular, we show how to locally control vector gradients.

Least Squares Subdivision Surfaces

The usual approach to design subdivision schemes for curves and surfaces basically consists in combining proper rules for regular configurations, with some specific heuristics to handle extraordinary vertices. In this paper, we introduce an alternative approach, called Least Squares Subdivision Surfaces (LS), where the key idea is to iteratively project each vertex onto a local approximation of the current polygonal mesh. While the resulting procedure haves the same complexity as simpler subdivision schemes, our method offers much higher visual quality, especially in the vicinity of extraordinary vertices. Moreover, we show it can be easily generalized to support boundaries and creases. The fitting procedure allows for a local control of the surface from the normals, making LS3 very well suited for interactive freeform modeling applications. We demonstrate our approach on diadic triangular and quadrangular refinement schemes, though it can be applied to any splitting strategies.