Ear-clipping Based Algorithms of Generating High-quality Polygon Triangulation

A basic and an improved ear clipping based algorithm for triangulating simple polygons and polygons with holes are presented. In the basic version, the ear with smallest interior angle is always selected to be cut in order to create fewer sliver triangles. To reduce sliver triangles in further, a bound of angle is set to determine whether a newly formed triangle has sharp angles, and edge swapping is accepted when the triangle is sharp. To apply the two algorithms on polygons with holes, "Bridge" edges are created to transform a polygon with holes to a degenerate polygon which can be triangulated by the two algorithms. Applications show that the basic algorithm can avoid creating sliver triangles and obtain better triangulations than the traditional ear clipping algorithm, and the improved algorithm can in further reduce sliver triangles effectively. Both of the algorithms run in O(n2) time and O(n) space.Comment: Proceedings of the 2012 International Conference on Information Technology and Software Engineering Lecture Notes in Electrical Engineering Volume 212, 2013, pp 979-98

Improved algorithms for ear-clipping triangulation

We consider the problem of improving ear-slicing algorithm for triangulating a simple polygon. We propose two variations of ear-slicing technique for generating “good-quality” triangulation. The first approach is based on searching for the best triangle along the boundary. The second approach considers polygon partitioning on a pre-process before applying the ear-slicing. Experimental investigation reveals that both approaches yield better quality triangulation than the standard ear-slicing method

Memory-Constrained Algorithms for Simple Polygons

A constant-workspace algorithm has read-only access to an input array and may use only O(1) additional words of $O(\log n)$ bits, where $n$ is the size of the input. We assume that a simple $n$-gon is given by the ordered sequence of its vertices. We show that we can find a triangulation of a plane straight-line graph in $O(n^2)$ time. We also consider preprocessing a simple polygon for shortest path queries when the space constraint is relaxed to allow $s$ words of working space. After a preprocessing of $O(n^2)$ time, we are able to solve shortest path queries between any two points inside the polygon in $O(n^2/s)$ time.Comment: Preprint appeared in EuroCG 201

3-D shape modeling for hearing aid design

Advances in 3-D scanning and fabrication hardware as well as 3-D geometric design software have transformed a once labor intensive manual manufacturing into an efficient digital process for hearing aid design, resulting in higher quality, reduced cost, and better fitting devices. Future work in this field will continue to focus on increasing automation until the process is fully automatic

A Contribution to Triangulation Algorithms for Simple Polygons

Decomposing simple polygon into simpler components is one of the basic tasks in computational geometry and its applications. The most important simple polygon decomposition is triangulation. The known algorithms for polygon triangulation can be classified into three groups: algorithms based on diagonal inserting, algorithms based on Delaunay triangulation, and the algorithms using Steiner points. The paper briefly explains the most popular algorithms from each group and summarizes the common features of the groups. After that four algorithms based on diagonals insertion are tested: a recursive diagonal inserting algorithm, an ear cutting algorithm, Kong’s Graham scan algorithm, and Seidel’s randomized incremental algorithm. An analysis concerning speed, the quality of the output triangles and the ability to handle holes is done at the end

Three-dimensional histological specimen preparation for accurate imaging and spatial reconstruction of the middle and inner ear

PURPOSE:    This paper presents a highly accurate cross-sectional preparation technique. The research aim was to develop an adequate imaging modality for both soft and bony tissue structures featuring high contrast and high resolution. Therefore, the advancement of an already existing microgrinding procedure was pursued. The central objectives were to preserve spatial relations and to ensure the accurate three-dimensional reconstruction of histological sections. METHODS:    Twelve human temporal bone specimens including middle and inner ear structures were utilized. They were embedded in epoxy resin, then dissected by serial grinding and finally digitalized. The actual abrasion of each grinding slice was measured using a tactile length gauge with an accuracy of one micrometre. The cross-sectional images were aligned with the aid of artificial markers and by applying a feature-based, custom-made auto-registration algorithm. To determine the accuracy of the overall reconstruction procedure, a well-known reference object was used for comparison. To ensure the compatibility of the histological data with conventional clinical image data, the image stacks were finally converted into the DICOM standard. RESULTS:    The image fusion of data from temporal bone specimens’ and from non-destructive flat-panel-based volume computed tomography confirmed the spatial accuracy achieved by the procedure, as did the evaluation using the reference object. CONCLUSION:    This systematic and easy-to-follow preparation technique enables the three-dimensional (3D) histological reconstruction of complex soft and bony tissue structures. It facilitates the creation of detailed and spatially correct 3D anatomical models. Such models are of great benefit for image-based segmentation and planning in the field of computer-assisted surgery as well as in finite element analysis. In the context of human inner ear surgery, three-dimensional histology will improve the experimental evaluation and determination of intra-cochlear trauma after the insertion of an electrode array of a cochlear implant system