Fast and Accurate Visibility Preprocessing

Visibility culling is a means of accelerating the graphical rendering of geometric models. Invisible objects are efficiently culled to prevent their submission to the standard graphics pipeline. It is advantageous to preprocess scenes in order to determine invisible objects from all possible camera views. This information is typically saved to disk and may then be reused until the model geometry changes. Such preprocessing algorithms are therefore used for scenes that are primarily static. Currently, the standard approach to visibility preprocessing algorithms is to use a form of approximate solution, known as conservative culling. Such algorithms over-estimate the set of visible polygons. This compromise has been considered necessary in order to perform visibility preprocessing quickly. These algorithms attempt to satisfy the goals of both rapid preprocessing and rapid run-time rendering. We observe, however, that there is a need for algorithms with superior performance in preprocessing, as well as for algorithms that are more accurate. For most applications these features are not required simultaneously. In this thesis we present two novel visibility preprocessing algorithms, each of which is strongly biased toward one of these requirements. The first algorithm has the advantage of performance. It executes quickly by exploiting graphics hardware. The algorithm also has the features of output sensitivity (to what is visible), and a logarithmic dependency in the size of the camera space partition. These advantages come at the cost of image error. We present a heuristic guided adaptive sampling methodology that minimises this error. We further show how this algorithm may be parallelised and also present a natural extension of the algorithm to five dimensions for accelerating generalised ray shooting. The second algorithm has the advantage of accuracy. No over-estimation is performed, nor are any sacrifices made in terms of image quality. The cost is primarily that of time. Despite the relatively long computation, the algorithm is still tractable and on average scales slightly superlinearly with the input size. This algorithm also has the advantage of output sensitivity. This is the first known tractable exact solution to the general 3D from-region visibility problem. In order to solve the exact from-region visibility problem, we had to first solve a more general form of the standard stabbing problem. An efficient solution to this problem is presented independently

Lazy visibility evaluation for exact soft shadows

International audienceThis report presents a novel approach to compute high quality and alias-free soft shadows using exact visibility computations. This work relies on a theoritical framework allowing to group lines according to the geometry they intersect. From this study, we derive a new algorithm encoding lazily the visibility from a polygon. Contrary to previous works on from-polygon visibility, our approach is very robust and straightforward to implement. We apply this algorithm to solve exactly and efficiently the visibility of an area light source from any point in a scene. As a consequence, results are not sensitive to noise, contrary to soft shadows methods based on area light source sampling. We demonstrate the reliability of our approach on different scenes and configurations

Lazy visibility evaluation for exact soft shadows

Présentation invitée de l'article du même nom publié en 2012 dans la revue Computer Graphics Forum.International audienceThis paper presents a novel approach to compute high quality and noise-free soft shadows using exact visibility computations. This work relies on a theoretical framework allowing to group lines according to the geometry they intersect. From this study, we derive a new algorithm encoding lazily the visibility from a polygon. Contrary to previous works on from-polygon visibility, our approach is very robust and straightforward to implement. We apply this algorithm to solve exactly and efficiently the visibility of an area light source from any point in a scene. As a consequence, results are not sensitive to noise, contrary to soft shadows methods based on area light source sampling. We demonstrate the reliability of our approach on different scenes and configurations

Indirect Image Registration with Large Diffeomorphic Deformations

The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.Comment: 43 pages, 4 figures, 1 table; revise

Warping geometric structures and abelianizing SL(2,R) local systems

The abelianization process of Gaiotto, Hollands, Moore, and Neitzke parameterizes SL(K,C) local systems on a punctured surface by turning them into C^\times local systems, which have a much simpler moduli space. When applied to an SL(2,R) local system describing a hyperbolic structure, abelianization produces an R^\times local system whose holonomies encode the shear parameters of the hyperbolic structure. This dissertation extends abelianization to SL(2,R) local systems on a compact surface, using tools from dynamics to overcome the technical challenges that arise in the compact setting. Thurston's shear parameterization of hyperbolic structures, which has its own technical subtleties on a compact surface, once again emerges as a special case.Mathematic

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential

We derive generalizations of McShane's identity for higher ranked surface group representations by studying a family of mapping class group invariant functions introduced by Goncharov and Shen which generalize the notion of horocycle lengths. In particular, we obtain McShane-type identities for finite-area cusped convex real projective surfaces by generalizing the Birman--Series geodesic scarcity theorem. More generally, we establish McShane-type identities for positive surface group representations with loxodromic boundary monodromy, as well as McShane-type inequalities for general rank positive representations with unipotent boundary monodromy. Our identities are systematically expressed in terms of projective invariants, and we study these invariants: we establish boundedness and Fuchsian rigidity results for triple and cross ratios. We apply our identities to derive the simple spectral discreteness of unipotent-bordered positive representations, collar lemmas, and generalizations of the Thurston metric