BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples

Swept volume evaluation using the BSP-dexel representation for the 5-axis CNC machining simulation

A new approach to the construction of a volume swept by the cutting tool is proposed for modeling 5-axis computer numerical control milling. A tool is considered to take the form of an arbitrary body of revolution. The main difference of the proposed approach is to provide the possibility of direct construction of the bulk synchronous parallel-dexel model, which, in turn, provides an effective modeling of the cutting process. Thus, it was possible to expand the scope of the given model by including the possibility to simulate arbitrary 5-axis computer numerical control programs. To confirm the correctness of the proposed approach, a program implementation of the corresponding algorithms has been performed. Examples of modeling of 5-axis milling processing of real parts and data on time costs for the suggested modeling are given. The high efficiency of the proposed approach is proven by the results of the experiments

A high performance vector rendering pipeline

Vector images are images which encode visible surfaces of a 3D scene, in a resolution independent format. Prior to this work generation of such an image was not real time. As such the benefits of using them in the graphics pipeline were not fully expressed. In this thesis we propose methods for addressing the following questions. How can we introduce vector images into the graphics pipeline, namingly, how can we produce them in real time. How can we take advantage of resolution independence, and how can we render vector images to a pixel display as efficiently as possible and with the highest quality. There are three main contributions of this work. We have designed a real time vector rendering system. That is, we present a GPU accelerated pipeline which takes as an input a scene with 3D geometry, and outputs a vector image. We call this system SVGPU: Scalable Vector Graphics on the GPU. As mentioned vector images are resolution independent. We have designed a cloud pipeline for streaming vector images. That is, we present system design and optimizations for streaming vector images across interconnection networks, which reduces the bandwidth required for transporting real time 3D content from server to client. Lastly, in this thesis we introduce another added benefit of vector images. We have created a method for rendering them with the highest possible quality. That is, we have designed a new set of operations on vector images, which allows us to anti-alias them during rendering to a canonical 2D image. Our contributions provide the system design, optimizations, and algorithms required to bring vector image utilization and benefits much closer to the real time graphics pipeline. Together they form an end to end pipeline to this purpose, i.e. "A High Performance Vector Rendering Pipeline.

BoolSurf: Boolean Operations on Surfaces

We port Boolean set operations between 2D shapes to surfaces of any genus, with any number of open boundaries. We combine shapes bounded by sets of freely intersecting loops, consisting of geodesic lines and cubic Bézier splines lying on a surface. We compute the arrangement of shapes directly on the surface and assign integer labels to the cells of such arrangement. Differently from the Euclidean case, some arrangements on a manifold may be inconsistent. We detect inconsistent arrangements and help the user to resolve them. Also, we extend to the manifold setting recent work on Boundary-Sampled Halfspaces, thus supporting operations more general than standard Booleans, which are well defined on inconsistent arrangements, too. Our implementation discretizes the input shapes into polylines at an arbitrary resolution, independent of the level of resolution of the underlying mesh. We resolve the arrangement inside each triangle of the mesh independently and combine the results to reconstruct both the boundaries and the interior of each cell in the arrangement. We reconstruct the control points of curves bounding cells, in order to free the result from discretization and provide an output in vector format. We support interactive usage, editing shapes consisting up to 100k line segments on meshes of up to 1M triangles

Fast Exact Booleans for Iterated CSG using Octree-Embedded BSPs

We present octree-embedded BSPs, a volumetric mesh data structure suited for performing a sequence of Boolean operations (iterated CSG) efficiently. At its core, our data structure leverages a plane-based geometry representation and integer arithmetics to guarantee unconditionally robust operations. These typically present considerable performance challenges which we overcome by using custom-tailored fixed-precision operations and an efficient algorithm for cutting a convex mesh against a plane. Consequently, BSP Booleans and mesh extraction are formulated in terms of mesh cutting. The octree is used as a global acceleration structure to keep modifications local and bound the BSP complexity. With our optimizations, we can perform up to 2.5 million mesh-plane cuts per second on a single core, which creates roughly 40-50 million output BSP nodes for CSG. We demonstrate our system in two iterated CSG settings: sweep volumes and a milling simulation

WebGL-Based Simulation of Bone Removal in Surgical Orthopeadic Procedures

The effective role of virtual reality simulators in surgical operations has been demonstrated during the last decades. The proposed work has been done to give a perspective of the actual orthopeadic surgeries such as a total shoulder arthroplasty with low incidence and visibility of the operation to the surgeon. The research in this thesis is focused on the design and implementation of a web-based graphical feedback for a total shoulder arthroplasty (TSA) surgery. For portability of the simulation and powerful 3D programming features, WebGL is being applied. To simulate the reaming process of the shoulder bone, multiple steps has been passed to be able to remove the volumetric amount of bone which was touched by the reamer tool. A fast and accurate collision detection algorithm utilizing Möller –Trumbore ray-triangle method was implemented to detect the first collision of the bone and the tool in order to accelerate the computations for the bone removal process. Once the collision detected, a mesh Boolean operation using CSG method is being invoked to calculate the volumetric amount of bone which is intersected with the tool and should be removed. This work involves the user interaction to transform the tool in a Three.js scene for the simulated operation