Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

Essential techniques for laparoscopic surgery simulation

Laparoscopic surgery is a complex minimum invasive operation that requires long learning curve for the new trainees to have adequate experience to become a qualified surgeon. With the development of virtual reality technology, virtual reality-based surgery simulation is playing an increasingly important role in the surgery training. The simulation of laparoscopic surgery is challenging because it involves large non-linear soft tissue deformation, frequent surgical tool interaction and complex anatomical environment. Current researches mostly focus on very specific topics (such as deformation and collision detection) rather than a consistent and efficient framework. The direct use of the existing methods cannot achieve high visual/haptic quality and a satisfactory refreshing rate at the same time, especially for complex surgery simulation. In this paper, we proposed a set of tailored key technologies for laparoscopic surgery simulation, ranging from the simulation of soft tissues with different properties, to the interactions between surgical tools and soft tissues to the rendering of complex anatomical environment. Compared with the current methods, our tailored algorithms aimed at improving the performance from accuracy, stability and efficiency perspectives. We also abstract and design a set of intuitive parameters that can provide developers with high flexibility to develop their own simulators

TriMe++: Multi-threaded triangular meshing in two dimensions

We present TriMe++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing procedure, making it suitable for fast generation of large-scale meshes. Three iterative meshing algorithms are implemented: the DistMesh algorithm, the centroidal Voronoi diagram meshing, and a hybrid of the two. We compare the performance of the three meshing methods in TriMe++, and show that the hybrid method retains the advantages of the other two. The software library achieves significant parallel speedup when generating a large mesh with $10^6$ points. TriMe++ can handle complicated geometries and generates adaptive meshes of high quality

Adaptive approximation of signed distance fields through piecewise continuous interpolation

In this paper, we present an adaptive structure to represent a signed distance field through trilinear or tricubic interpolation of values, and derivatives, that allows for fast querying of the field. We also provide a method to decide when to subdivide a node to achieve a provided threshold error. Both the numerical error control, and the values needed to build the interpolants, require the evaluation of the input field. Still, both are designed to minimize the total number of evaluations. C0 continuity is guaranteed for both the trilinear and tricubic version of the algorithm. Furthermore, we describe how to preserve C1 continuity between nodes of different levels when using a tricubic interpolant, and provide a proof that this property is maintained. Finally, we illustrate the usage of our approach in several applications, including direct rendering using sphere marching.This work has been partially funded by Ministeri de Ciència i Innovació (MICIN), Agencia Estatal de Investigación (AEI) and the Fons Europeu de Desenvolupament Regional (FEDER) (project PID2021-122136OB-C21 funded by MCIN/AEI/10.13039/501100011033/FEDER, UE). The first author gratefully acknowledges the Universitat Politècnica de Catalunya and Banco Santander for the financial support of his predoctoral grant FPI-UPC grant.Peer ReviewedPostprint (published version

Bounding Volume Hierarchies for Collision Detection

In virtual environment world, performing collision detection between various 3D objects requires sophisticated steps to be followed in order to properly visualize their effect. It is challenging due to the fact that multiple objects undergo various motion depending on the application’s genre. It is however an essential challenge to be resolved since it’s many use in the computer animation, simulation and robotic industry. Thus, object intersection between rigid bodies has become one of the most important areas in order to bring realism to simulation and animation