Implicit models inherently support automatic blending and trivial collision detection which makes them an effective tool for designing complex organic shapes with many applications in various areas of research including surgical simulation systems. However, slow rendering speeds can adversely affect the performance of simulation and modelling systems. In addition, when the models are incorporated in a surgical simulation system, interactive and smooth cutting becomes a required feature for many procedures. In this research, we propose a comprehensive framework for high-performance rendering and physically-based animation of tissues modelled using implicit surfaces. Our goal is to address performance and scalability issues that arise in rendering complex implicit models as well as in dynamic interactions between surgical tool and models. Complex models can be created with implicit primitives, blending operators, affine transformations, deformations and constructive solid geometry in a design environment that organizes all these in a scene graph data structure called the BlobTree. We show that the BlobTree modelling approach provides a very compact data structure which supports the requirements above, as well as incremental changes and trivial collision detection. A GPU-assisted surface extraction algorithm is proposed to support interactive modelling of complex BlobTree models. Using a finite element approach we discretize those models for accurate physically-based animation. Our system provides an interactive cutting ability using smooth intersection surfaces. We show an application of our system in a human skull craniotomy simulation. / Graduate / 0984 / pourya.shirazian@gmail.com

BlobTree modelling has been used in several solid modelling packages to rapidly prototype models by making use of boolean and sketch-based modelling. Using these two techniques, a user can quickly create complex models as combinations of simple primitives and sketched objects. Because the BlobTree is based on continuous field-values, it offers a lot of possibilities to create and control smooth transitions between surfaces, something more complicated in other modelling approaches. In addition, the data required to describe a BlobTree is very compact. Despite these advantages, the BlobTree has not yet been integrated into state of the art industrial workflows to create models. This thesis identifies some shortcomings of the BlobTree, presents potential solutions to those problems and demonstrates an application that makes use of the BlobTree's compact representation. A main criticism is that the evaluation of a large BlobTree can be quite expensive, and, therefore, many applications are limited in the complexity of models that can be created interactively. This work presents an alternative way of traversing a BlobTree that lowers the time to calculate field-values by at least an order of magnitude. As a result, the limit of model complexity is raised for interactive modelling applications. In some domains, certain models need more than one designer or engineer to be created. Often, several iterations of a model are shared between multiple participants until it is finalized. Because the description of a BlobTree is very compact, it can be synchronized efficiently in a collaborative modelling environment. This work presents CollabBlob, an approach to collaborative modelling based on the BlobTree. CollabBlob is lock-free, and provides interactive feedback for all the participants, which helps with a fast iteration in the modelling process. In order to extend the range of models that can be created within CollabBlob, two areas of BlobTree modelling are improved in the context of this thesis. CAD modelling often makes use of a feature called filleting to add additional surface features, which could be caused by a manufacturing process. Filleting in general creates smooth transitions between surfaces, something that the BlobTree can do with less mathematical complexity than approaches needed in Constructive Solid Geometry (CSG), in the case of fillets between primitives. However, little research has been done on the construction of fillets between surfaces of a single BlobTree primitive. This work outlines Angle-Based Filleting and the Surface Fillet Curve, two solutions to improve the specification of fillets in the BlobTree. Sketch-based implicit modelling generates 3D shapes from 2D sketches by sampling the drawn shape and using the samples to create the implicit field via variational interpolation. Additional samples inside and outside the sketched shape are needed to generate a field compatible with BlobTree modelling and state of the art approaches use offset curves of the sketch to generate these samples. The approach presented in this work reduces the number of sample points, thus accelerating the interpolation time and improving the resulting implicit field. / Graduate / 0984 / herbert.grasberger@gmail.com

We present an implicit approach for constructing smooth isolated or interconnected 3-D inscribed volumes which can be employed for volumetric modeling of various kinds of spongy or porous structures, such as volcanic rocks, pumice stones, Cancellus bones *, liquid or dry foam, radiolarians, cheese, and other similar materials. The inscribed volumes can be represented in their normal or positive forms to model natural pebbles or pearls, or in their inverted or negative forms to be used in porous structures, but regardless of their types, their smoothness and sizes are controlled by the user without losing the consistency of the shapes. We introduce two techniques for blending and creating interconnections between these inscribed volumes to achieve a great flexibility to adapt our approach to different types of porous structures, whether they are regular or irregular. We begin with a set of convex polytopes such as 3-D Voronoi diagram cells and compute inscribed volumes bounded by the cells. The cells can be irregular in shape, scale, and topology, and this irregularity transfers to the inscribed volumes, producing natural-looking spongy structures. Describing the inscribed volumes with implicit functions gives us a freedom to exploit volumetric surface combinations and deformations operations effortlessly / Graduate