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B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications. [ABSTRACT FROM AUTHOR]

Multiple sequence alignment is a crucial task in a number of biological analyses like secondary structure prediction, domain searching, phylogeny, etc. MSAProbs is currently the most accurate alignment algorithm, but its effectiveness is obtained at the expense of computational time. In the paper we present QuickProbs, the variant of MSAProbs customised for graphics processors. We selected the two most time consuming stages of MSAProbs to be redesigned for GPU execution: the posterior matrices calculation and the consistency transformation. Experiments on three popular benchmarks (BAliBASE, PREFAB, OXBench-X) on quad-core PC equipped with high-end graphics card show QuickProbs to be 5.7 to 9.7 times faster than original CPU-parallel MSAProbs. Additional tests performed on several protein families from Pfam database give overall speed-up of 6.7. Compared to other algorithms like MAFFT, MUSCLE, or ClustalW, QuickProbs proved to be much more accurate at similar speed. Additionally we introduce a tuned variant of QuickProbs which is significantly more accurate on sets of distantly related sequences than MSAProbs without exceeding its computation time. The GPU part of QuickProbs was implemented in OpenCL, thus the package is suitable for graphics processors produced by all major vendors. [ABSTRACT FROM AUTHOR]

We have developed a general-purpose Monte Carlo simulation code, called penMesh, that combines the accuracy of the radiation transport physics subroutines from PENELOPE and the flexibility of a geometry based on triangle meshes. While the geometric models implemented in most general-purpose codes-such as PENELOPE's quadric geometry-impose some limitations in the shape of the objects that can be simulated, triangle meshes can be used to describe any free-form (arbitrary) object. Triangle meshes are extensively used in computer-aided design and computer graphics. We took advantage of the sophisticated tools already developed in these fields, such as an octree structure and an efficient ray-triangle intersection algorithm, to significantly accelerate the triangle mesh ray-tracing. A detailed description of the new simulation code and its ray-tracing algorithm is provided in this paper. Furthermore, we show how it can be readily used in medical imaging applications thanks to the detailed anatomical phantoms already available. In particular, we present a whole body radiography simulation using a triangulated version of the anthropomorphic NCAT phantom. An example simulation of scatter fraction measurements using a standardized abdomen and lumbar spine phantom, and a benchmark of the triangle mesh and quadric geometries in the ray-tracing of a mathematical breast model, are also presented to show some of the capabilities of penMesh. [ABSTRACT FROM AUTHOR]

This paper presents an innovative computer graphic method for viewshed generation from big point clouds. The proposed approach consists in simplification of typical methods for viewshed formation that are based on sorting and binary trees. The proposed method is based on the k-d tree concept optimized with radial segmentation and a dedicated mathematical algorithm for subtree rejection. The final visualization of the viewshed is designed with a graphic method using triangulated irregular network (TIN) surfaces from the accepted subtrees. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an irregular stock cutting system (NEST) developed on AutoCAD software platform. A detail description to its mechanism is included. This development is based on two known techniques: the bitmap representation to transform all shapes drawn by AutoCAD into pixel matrices before nesting, and the bottom-left-fill algorithm for nesting. The system NEST is developed for further research works on practical stock cutting problems. It provides two important parameters: one is the precision level which decides how the bitmap representation can precisely describe a shape and therefore affects the time taken by nesting procedure; the other is the unit rotation angle which make a shape self-rotates in steps with small angle and to be finally placed on sheet material with its best self-rotation angle. NEST can tightly position every shape on a sheet material and performs satisfyingly from practical view point. The nesting result is demonstrated by the original drawings of all shapes and the sheet material instead of their graphics transformed from pixel matrices. Several tests are carried out to show its performance. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a novel method that represents the highly complex point sets by clustering and reconstructing the points to normal-mapped B-spline surfaces (NBSs). The main idea is to construct elaborate normal maps on simple surfaces for the realistic rendering of complex point-set models. Based on this observation, we developed the coarse, NBSs to approximate the original point datasets with fine surface details. In our algorithm, a genetic clustering algorithm is proposed to automatically segment the point samples into several clusters according to their statistical properties, and a network of B-spline patches with normal maps are constructed according to the clustering results. In respect to signal processing, our algorithm decouples the original data into two collections: coarse geometry information and fine surface details. The multi-level B-spline surfaces are employed to describe the coarse geometry information, and the normal maps are constructed to capture the fine surface details. Our experimental results show that this representation facilitates the modeling and rendering of complex point sets without losing the visual qualities. [Copyright &y& Elsevier]

In geometric modeling and processing, computer graphics and computer vision, smooth surfaces are approximated by discrete triangular meshes reconstructed from sample points on the surfaces. A fundamental problem is to design rigorous algorithms to guarantee the geometric approximation accuracy by controlling the sampling density. This paper gives explicit formulae to the bounds of Hausdorff distance, normal distance and Riemannian metric distortion between the smooth surface and the discrete mesh in terms of principle curvature and the radii of geodesic circum-circle of the triangles. These formulae can be directly applied to design sampling density for data acquisitions and surface reconstructions. Furthermore, we prove that the meshes induced from the Delaunay triangulations of the dense samples on a smooth surface are convergent to the smooth surface under both Hausdorff distance and normal fields. The Riemannian metrics and the Laplace–Beltrami operators on the meshes are also convergent to those on the smooth surfaces. These theoretical results lay down the foundation for a broad class of reconstruction and approximation algorithms in geometric modeling and processing. Practical algorithms for approximating surface Delaunay triangulations are introduced based on global conformal surface parameterizations and planar Delaunay triangulations. Thorough experiments are conducted to support the theoretical results. [Copyright &y& Elsevier]

Abstract: This paper presents an intuitive, freehand sketching application for Computer Aided Design (CAD) that can reconstruct a 3D object from a single, flat, freehand sketch. A pen is used to draw 2D sketches consisting of straight and curved strokes connected at vertices. The sketches are processed by a reconstruction algorithm that uses the angular distribution of the strokes and their connectivity to determine an orthogonal 3D axis system whose projection correlates with the observed stroke orientations. The axis system is used to determine a plausible depth for each vertex. This approach works well for drawings of objects whose edges predominantly conform to some overall orthogonal axis system. A second, independent optimization procedure is then used to reconstruct each curved stroke in the original sketch, assuming that the curve is planar. New strokes can be attached to the 3D object, or drawn directly onto the object''s faces. An implementation of the reconstruction algorithm based on Levenberg–Marquardt optimization allows objects with over 50 strokes to be reconstructed in interactive time. [Copyright &y& Elsevier]

Tooth segmentation on dental model is an essential step of computer-aided-design systems for orthodontic virtual treatment planning. However, fast and accurate identifying cutting boundary to separate teeth from dental model still remains a challenge, due to various geometrical shapes of teeth, complex tooth arrangements, different dental model qualities, and varying degrees of crowding problems. Most segmentation approaches presented before are not able to achieve a balance between fine segmentation results and simple operating procedures with less time consumption. In this article, we present a novel, effective and efficient framework that achieves tooth segmentation based on a segmentation field, which is solved by a linear system defined by a discrete Laplace-Beltrami operator with Dirichlet boundary conditions. A set of contour lines are sampled from the smooth scalar field, and candidate cutting boundaries can be detected from concave regions with large variations of field data. The sensitivity to concave seams of the segmentation field facilitates effective tooth partition, as well as avoids obtaining appropriate curvature threshold value, which is unreliable in some case. Our tooth segmentation algorithm is robust to dental models with low quality, as well as is effective to dental models with different levels of crowding problems. The experiments, including segmentation tests of varying dental models with different complexity, experiments on dental meshes with different modeling resolutions and surface noises and comparison between our method and the morphologic skeleton segmentation method are conducted, thus demonstrating the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In the context of computer-aided design, computer graphics and geometry processing, the idea of generative modeling is to allow the generation of highly complex objects based on a set of formal construction rules. Using these construction rules, a shape is described by a sequence of processing steps, rather than just by the result of all applied operations: shape design becomes rule design. Due to its very general nature, this approach can be applied to any domain and to any shape representation that provides a set of generating functions. The aim of this survey is to give an overview of the concepts and techniques of procedural and generative modeling, as well as their applications with a special focus on archeology and architecture. [ABSTRACT FROM AUTHOR]