Ray-Traced Collision Detection : Interpenetration Control and Multi-GPU Performance

International audienceWe proposed [LGA13] an iterative ray-traced collision detection algorithm (IRTCD) that exploits spatial and temporal coherency and proved to be computationally efficient but at the price of some geometrical approximations that allow more interpenetration than needed. In this paper, we present two methods to efficiently control and reduce the interpenetration without noticeable computation overhead. The first method predicts the next potentially colliding vertices. These predictions are used to make our IRTCD algorithm more robust to the above-mentioned approximations, therefore reducing the errors up to 91%. We also present a ray re-projection algorithm that improves the physical response of ray-traced collision detection algorithm. This algorithm also reduces, up to 52%, the interpenetration between objects in a virtual environment. Our last contribution shows that our algorithm, when implemented on multi-GPUs architectures, is far faster

Robust interactive simulation of deformable solids with detailed geometry using corotational FEM

This thesis focuses on the interactive simulation of highly detailed deformable solids modelled with the Corotational Finite Element Method. Starting from continuum mechanics we derive the discrete equations of motion and present a simulation scheme with support for user-in-the-loop interaction, geometric constraints and contact treatment. The interplay between accuracy and computational cost is discussed in depth, and practical approximations are analyzed with an emphasis on robustness and efficiency, as required by interactive simulation. The first part of the thesis focuses on deformable material discretization using the Finite Element Method with simplex elements and a corotational linear constitutive model, and presents our contributions to the solution of widely reported robustness problems in case of large stretch deformations and finite element degeneration. First,we introduce a stress differential approximation for quasi-implicit corotational linear FEM that improves its results for large deformations and closely matches the fullyimplicit solution with minor computational overhead. Next, we address the problem ofrobustness and realism in simulations involving element degeneration, and show that existing methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new continuous-time approach, degeneration-aware polar decomposition, that avoids such flaws and yields robust degeneration recovery. In the second part we focus on geometry representation and contact determination for deformable solids with highly detailed surfaces. Given a high resolution closed surface mesh we automatically build a coarse embedding tetrahedralization and a partitioned representation of the collision geometry in a preprocess. During simulation, our proposed contact determination algorithm finds all intersecting pairs of deformed triangles using a memory-efficient barycentric bounding volume hierarchy, connects them into potentially disjoint intersection curves and performs a topological flood process on the exact intersection surfaces to discover a minimal set of contact points. A novel contact normal definition is used to find contact point correspondences suitable for contact treatment.Aquesta tesi tracta sobre la simulació interactiva de sòlids deformables amb superfícies detallades, modelats amb el Mètode dels Elements Finits (FEM) Corotacionals. A partir de la mecànica del continuu derivem les equacions del moviment discretes i presentem un esquema de simulació amb suport per a interacció d'usuari, restriccions geomètriques i tractament de contactes. Aprofundim en la interrelació entre precisió i cost de computació, i analitzem aproximacions pràctiques fent èmfasi en la robustesa i l'eficiència necessàries per a la simulació interactiva. La primera part de la tesi es centra en la discretització del material deformable mitjançant el Mètode dels Elements Finits amb elements de tipus s'implex i un model constituent basat en elasticitat linial corotacional, i presenta les nostres contribucions a la solució de problemes de robustesa àmpliament coneguts que apareixen en cas de sobreelongament i degeneració dels elements finits. Primer introduïm una aproximació dels diferencials d'estress per a FEM linial corotacional amb integració quasi-implícita que en millora els resultats per a deformacions grans i s'apropa a la solució implícita amb un baix cost computacional. A continuació tractem el problema de la robustesa i el realisme en simulacions que inclouen degeneració d'elements finits, i mostrem que els mètodes existents presenten inconvenients que posen en perill la robustesa plausibilitat de la simulació en aplicacions interactives. Proposem un enfocament nou basat en temps continuu, la descomposició polar amb coneixement de degeneració, que evita els inconvenients esmentats i permet corregir la degeneració de forma robusta. A la segona part de la tesi ens centrem en la representació de geometria i la determinació de contactes per a sòlids deformables amb superfícies detallades. A partir d'una malla de superfície tancada construím una tetraedralització englobant de forma automàtica en un preprocés, i particionem la geometria de colisió. Proposem un algorisme de detecció de contactes que troba tots els parells de triangles deformats que intersecten mitjançant una jerarquia de volums englobants en coordenades baricèntriques, els connecta en corbes d'intersecció potencialment disjuntes i realitza un procés d'inundació topològica sobre les superfícies d'intersecció exactes per tal de descobrir un conjunt mínim de punts de contacte. Usem una definició nova de la normal de contacte per tal de calcular correspondències entre punts de contacte útils per al seu tractament.Postprint (published version

RAY-TRACED COLLISION DETECTION FOR DEFORMABLE BODIES

This paper presents a new approach to collision detection and modeling between deformable volumetric bodies. It allows deep intersections while alleviating the difficulties of distance field update. A ray is shot from each surface vertex in the direction of the inward normal. A collision is detected when the first intersection belongs to an inward surface triangle of another body. A contact force between the vertex and the matching point is then created. Experiments show that this approach is fast and more robust than traditional proximity-based collisions.

ADVANCED MOTION MODELS FOR RIGID AND DEFORMABLE REGISTRATION IN IMAGE-GUIDED INTERVENTIONS

Image-guided surgery (IGS) has been a major area of interest in recent decades that continues to transform surgical interventions and enable safer, less invasive procedures. In the preoperative contexts, diagnostic imaging, including computed tomography (CT) and magnetic resonance (MR) imaging, offers a basis for surgical planning (e.g., definition of target, adjacent anatomy, and the surgical path or trajectory to the target). At the intraoperative stage, such preoperative images and the associated planning information are registered to intraoperative coordinates via a navigation system to enable visualization of (tracked) instrumentation relative to preoperative images. A major limitation to such an approach is that motions during surgery, either rigid motions of bones manipulated during orthopaedic surgery or brain soft-tissue deformation in neurosurgery, are not captured, diminishing the accuracy of navigation systems. This dissertation seeks to use intraoperative images (e.g., x-ray fluoroscopy and cone-beam CT) to provide more up-to-date anatomical context that properly reflects the state of the patient during interventions to improve the performance of IGS. Advanced motion models for inter-modality image registration are developed to improve the accuracy of both preoperative planning and intraoperative guidance for applications in orthopaedic pelvic trauma surgery and minimally invasive intracranial neurosurgery. Image registration algorithms are developed with increasing complexity of motion that can be accommodated (single-body rigid, multi-body rigid, and deformable) and increasing complexity of registration models (statistical models, physics-based models, and deep learning-based models). For orthopaedic pelvic trauma surgery, the dissertation includes work encompassing: (i) a series of statistical models to model shape and pose variations of one or more pelvic bones and an atlas of trajectory annotations; (ii) frameworks for automatic segmentation via registration of the statistical models to preoperative CT and planning of fixation trajectories and dislocation / fracture reduction; and (iii) 3D-2D guidance using intraoperative fluoroscopy. For intracranial neurosurgery, the dissertation includes three inter-modality deformable registrations using physic-based Demons and deep learning models for CT-guided and CBCT-guided procedures