Shortest Path in a Polygon using Sublinear Space

\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\Polygon}{\mathsf{P}} \newcommand{\Space}{\overline{\mathsf{m}}} \newcommand{\pth}[2][\!]{#1\left({#2}\right)} We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon \Polygon with $n$ vertices in a read only memory, and additional working memory of size \Space, the new algorithm computes the shortest path (in \Polygon) in O( n^2 /\, \Space ) expected time. This requires several new tools, which we believe to be of independent interest

A New polygon based algorithm for filling regions

[[abstract]]Region filling is a fundamental operation in computer graphics and image processing. There are broadly two classes of region filling: polygon based and pixel based. The conventional polygon based region filling algorithm typically uses data structures of records and fields. Using these data structures, the region filling process slows down because of the time-consuming operations of records and fields. This paper proposes a new polygon based region filling algorithm by using the proposed data structures of triples. This results in use of more efficient triple operations involving arrays and elements to fill a region. Using data structures of triples, the y-coordinate modification problem that occurs in the conventional algorithm simply disappears. In addition, contrary to the conventional approach, which uses troublesome geometrical considerations in deciding the even number of elements in each linked list, the proposed triple model uses a simple criterion to meet the even number requirement. Most important of all is the fact that the proposed criterion is independent of the polygon geometry. The experimental results strongly support superiority of the proposed algorithm. It is verified that the proposed algorithm is both theoretically and experimentally better than the conventional algorithm.[[notice]]補正完

Doctor of Philosophy

dissertationMany algorithms have been developed for synthesizing shaded images of three dimensional objects modeled by computer. In spite of widely differing approaches the current state of the art algorithms are surprisingly similar with respect to the richness of the scenes they can process. One attribute these algorithms have in common is the use of a conventional passive data base to represent the objects being modeled. This paper postulates and explores the use of an alternative modeling technique which uses procedures to represent the objects being modeled. The properties and structure of such "procedure models" are investigated and an algorithm based on them is presented

A Method of Rendering CSG-Type Solids Using a Hybrid of Conventional Rendering Methods and Ray Tracing Techniques

This thesis describes a fast, efficient and innovative algorithm for producing shaded, still images of complex objects, built using constructive solid geometry ( CSG ) techniques. The algorithm uses a hybrid of conventional rendering methods and ray tracing techniques. A description of existing modelling and rendering methods is given in chapters 1, 2 and 3, with emphasis on the data structures and rendering techniques selected for incorporation in the hybrid method. Chapter 4 gives a general description of the hybrid method. This method processes data in the screen coordinate system and generates images in scan-line order. Scan lines are divided into spans (or segments) using the bounding rectangles of primitives calculated in screen coordinates. Conventional rendering methods and ray tracing techniques are used interchangeably along each scan-line. The method used is detennined by the number of primitives associated with a particular span. Conventional rendering methods are used when only one primitive is associated with a span, ray tracing techniques are used for hidden surface removal when two or more primitives are involved. In the latter case each pixel in the span is evaluated by accessing the polygon that is visible within each primitive associated with the span. The depth values (i. e. z-coordinates derived from the 3-dimensional definition) of the polygons involved are deduced for the pixel's position using linear interpolation. These values are used to determine the visible polygon. The CSG tree is accessed from the bottom upwards via an ordered index that enables the 'visible' primitives on any particular scan-line to be efficiently located. Within each primitive an ordered path through the data structure provides the polygons potentially visible on a particular scan-line. Lists of the active primitives and paths to potentially visible polygons are maintained throughout the rendering step and enable span coherence and scan-line coherence to be fully utilised. The results of tests with a range of typical objects and scenes are provided in chapter 5. These results show that the hybrid algorithm is significantly faster than full ray tracing algorithms

Detecting fish aggregations from reef habitats mapped with high resolution side scan sonar imagery

As part of a multibeam and side scan sonar (SSS) benthic survey of the Marine Conservation District (MCD) south of St. Thomas, USVI and the seasonal closed areas in St. Croix—Lang Bank (LB) for red hind (Epinephelus guttatus) and the Mutton Snapper (MS) (Lutjanus analis) area—we extracted signals from water column targets that represent individual and aggregated fish over various benthic habitats encountered in the SSS imagery. The survey covered a total of 18 km2 throughout the federal jurisdiction fishery management areas. The complementary set of 28 habitat classification digital maps covered a total of 5,462.3 ha; MCDW (West) accounted for 45% of that area, and MCDE (East) 26%, LB 17%, and MS the remaining 13%. With the exception of MS, corals and gorgonians on consolidated habitats were significantly more abundant than submerged aquatic vegetation (SAV) on unconsolidated sediments or unconsolidated sediments. Continuous coral habitat was the most abundant consolidated habitat for both MCDW and MCDE (41% and 43% respectively). Consolidated habitats in LB and MS predominantly consisted of gorgonian plain habitat with 95% and 83% respectively. Coral limestone habitat was more abundant than coral patch habitat; it was found near the shelf break in MS, MCDW, and MCDE. Coral limestone and coral patch habitats only covered LB minimally. The high spatial resolution (0.15 m) of the acquired imagery allowed the detection of differing fish aggregation (FA) types. The largest FA densities were located at MCDW and MCDE over coral communities that occupy up to 70% of the bottom cover. Counts of unidentified swimming objects (USOs), likely representing individual fish, were similar among locations and occurred primarily over sand and shelf edge areas. Fish aggregation school sizes were significantly smaller at MS than the other three locations (MCDW, MCDE, and LB). This study shows the advantages of utilizing SSS in determining fish distributions and density

MeshPipe: a Python-based tool for easy automation and demonstration of geometry processing pipelines

The popularization of inexpensive 3D scanning, 3D printing, 3D publishing and AR/VR display technologies have renewed the interest in open-source tools providing the geometry processing algorithms required to clean, repair, enrich, optimize and modify point-based and polygonal-based models. Nowadays, there is a large variety of such open-source tools whose user community includes 3D experts but also 3D enthusiasts and professionals from other disciplines. In this paper we present a Python-based tool that addresses two major caveats of current solutions: the lack of easy-to-use methods for the creation of custom geometry processing pipelines (automation), and the lack of a suitable visual interface for quickly testing, comparing and sharing different pipelines, supporting rapid iterations and providing dynamic feedback to the user (demonstration). From the user's point of view, the tool is a 3D viewer with an integrated Python console from which internal or external Python code can be executed. We provide an easy-to-use but powerful API for element selection and geometry processing. Key algorithms are provided by a high-level C library exposed to the viewer via Python-C bindings. Unlike competing open-source alternatives, our tool has a minimal learning curve and typical pipelines can be written in a few lines of Python code.Peer ReviewedPostprint (published version