Preprints (KIV)
Permanent URI for this collection
Browse
Recent Submissions
Item Point in Polygon Algorithm with O(1) Complexity(1994) Skala, VáclavAlgorithms for point-in-polygon problem solution are very often used in computer graphics applications. The naive implementation has O(N) processing time complexity or O(lg N)complexity if a convex polygon is considered. A new algorithm of O(l) processing complexity was developed. The important feature of the algorithm is that preprocessing complexity is O(N) and memory requirements depend on geometrical properties of the given polygon. Usage of the algorithm is expected in applications where many points are tested whether resides in the given polygon or not. The presented approach can be considered as alternative to the parallel processing usage. Experimental results are includes, too.
Item An Algorithm for Line Clipping by Convex Polyhedron in E3 with O(N1/2) Complexity(1994) Skala, VáclavA new algorithm for line clipping against convex polyhedron is given. The suggested algorithm is faster for higher number of facets of the given polyhedron than the traditional Cyrus-Beck's and others algorithms with complexity O(N). The suggested algorithm has O(N) complexity. The suggested algorithm has O(N) complexity in worst case and expected O(N1/2) complexity. The speed up is achieved because of "known order" of triangles. Some principal results of comparisons of selected algorithms are presented and give some idea how the proposed algorithm could be used effectively.Item An Efficient Algorithm for Line Clipping by Convex and Non-covex Polyhedrons in E3(Wiley, 1996) Skala, VáclavA new algorithm for clipping lines againts convex polyhedron with O(N) complexity is given with modification for non-convex polyhedron. The suggested algorithm is faster for higher number of facets of the given polyhedron than the traditional Cyrus-Beck's algorithm. Some principal results of comparison of all algorithms are shown and give some imagination how the proposed algorithm could be used effectively.
Item O(lg N) Line Clipping Algorithm in E2(Pergamon Press, 1994) Skala, VáclavA new O(lg N) line clipping algorithm in E2 against a convex window is presented. The main advantage of the presented algorithm is the principal acceleration of the line clipping problem solution. A comparison of the proposed algorithm with others shows a significant improvement in run-time. Experimental results for selected known algorithms are also shown.Item Urychlování algoritmu sledování paprsku metodou dělení prostoru a paralelizací výpočtu(1995) Bláha, Petr; Skala, VáclavThe ray tracing technique is very often used for image synthesis. Many methods for its acceleration have been developed. This paper presents two possible solutions - modifications of space subdivision method and application of parallel processing, with obtained experimental results.Item Algoritmy se strukturální složitostí menší než optimální aneb K čemu je programování(1995) Skala, VáclavNew algorithms Point-in-Polygon and line clipping algorithms are very often used especially in computer graphics applications. Algorithms usually have O(N) or O(lg N) complexities. New algorithms with O(l) expected complexity has been developed using pre-processing. The interesting feature of presented algorithms is that memory requirements depend on geometrical properties of polygons. The presented approach can be considered as an alternative method to parallel processing.Item Trading Time for Space: an O(1) Average time Algorithm for Point-in-Polygon Location Problem. Theoretical Fiction or Practical Usage?(1996) Skala, VáclavAlgorithms for Point in polygon problem solution are very often used especially in computer graphics applications The naive implementation has O(N) processing time complexity or O(lg N) complexity if a convex polygon is considered . A new algorithm of O(l) processing complexity was developed . The important feature of the algorithm is that preprocessing complexity is O (N) and memory requirements depend on geometrical properties of the given polygon Usage of the algorithm is expected in applications where many points are tested whether resides in the given polygon or not. The presented approach can be considered as alternative to the parallel processing usage. Experimental results are included, too.Item Line Clipping in E3 with Expected Complexity O(1)(Polska Akademia Nauk, 1996) Skala, VáclavA new line clipping algorithm against convex polyhedron in E3 with an expected complexity O(1) is presented. The suggested approach is based on two orthogonal projections to E2 co-ordinate system and on pre-processing of the given polyhedron. The pre-processing enables to speed up solution significantly. The proposed method is convenient for those applications when many lines are clipped against constant convex polyhedron. Theoretical considerations and experimental results are also presented.Item A Comparison of O(1) and Cyrus-Beck Line Clipping Algorithms in E2 and E3(Univerzita Komenského, 1996) Skala, Václav; Lederbuch, Pavel; Sup, BohumírA comparison of a new algorithm for line clipping in E2 and E3 by convex polygon and/or polyhedron with O(1) processing complexity and Cyrus- Beck algorithm is presented. The new algorithm in E2 is based on dual space representation and space subdivision technique. The principle of algorithm in E3 is based on the projection of polyhedron to three orthogonal E2 coordinate systems. Algorithms have optimal complexities O(1) and demonstrates that preprocessing can be used to speed up the line clipping significantly. Obvious applications are for one polygon and/or polyhedron and many clipped lines. Detailed theoretical estimations and experimental results are also presented.Item Line Clipping in E2 with O(1) Processing Complexity(Elsevier, 1996) Skala, VáclavA new algorithm for line clipping by convex polygon with O(1) processing complexity is presented. It is based on dual space representation and space subdivision technique. The suggested algorithm also demonstrates that pre-processing can be used in order to speed up solution of some problems in computer graphics applications significantly. Theoretical considerations and experimental results are also presented.Item A Fast Algorithm for Line Clipping by Convex Polyhedron in E3(Elsevier, 1997) Skala, VáclavA new algorithm for line clipping against convex polyhedron is given. The suggested algorithm is faster for higher number of facets of the given polyhedron than the traditional Cyrus-Beck's and others algorithms with complexity O(N) . The suggested algorithm has O(N) complexity in the worst case and expected O(N) complexity. The speed up is achieved because of "known order" of triangles. Some principal results of comparisons of selected algorithms are presented and give some imagination how the proposed algorithm could be used effectively.Item A Comparison of Fundamental Methods for Iso-surface Extraction(Polska Akademia Nauk, 2004) Patera, Jan; Skala, VáclavIn this paper four fundamental methods for an iso-surface extraction are compared, based on cell decomposition to tetrahedra. The methods are compared both on mathematically generated data sets as well as on real data sets. The comparison using mathematical data is made from different points of view such as area approximation, volume approximation. On the other hand, the Hausdorff distance and root mean square are used to compare methods on real data sets. The presented comparison can be helpful when deciding among tested methods which one to choose, as well as when we need to compare a newly developed method with other existing approaches.Item Efficient Hash Function for Duplicate Elimination in Dictionaries(Slovenská technická univerzita v Bratislavě, 2009) Skala, Václav; Hrádek, JanFast elimination of duplicate data is needed in many areas, especially in the textual data context. A solution to this problem was recently found for geometrical data using a hash function to speed up the process. The usage of the hash function is extremely efficient when incremental elimination is required especially for processing large data sets. In this paper a new construction of the hash function is presented, giving short clusters with few collisions only. The proposed hash function is not a perfect hash function, nevertheless it gives similar properties to it. The hash function used takes advantage of the relatively large amount of available memory on modern computers, and works well with large data sets. Experiments have proved that different approaches should be used for different types of languages, because the structures of Slavonic and Anglo-Saxon languages are different. Therefore, tests were made with a Czech dictionary having 2.5 million words and an English dictionary having 130 thousands words. Algorithm was also tested for a few other languages. Experimental results are presented in this paper as well.Item Fast Oexpected(N) Algorithm for Finding Exact Maximum Distance in E2 Instead of O(N2) or O(N lgN)(AIP Publishing, 2013) Skala, VáclavThis paper describes novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run-time needed to find an exact maximum distance of two points in E2. The proposed algorithm has been evaluated experimentally on larger different datasets. The proposed algorithm gives a significant speed-up to applications, when medium and large data sets are processed. It is over 10 000 times faster than the standard algorithm for 106 points randomly distributed points in E2. Experiments proved the advantages of the proposed algorithm over the standard algorithm and convex hull diameters approaches.Item New Geometric Continuity Solution of Parametric Surfaces(American Institute of Physics, 2013) Skala, VáclavThis paper presents a new approach to computation of geometric continuity for parametric bi-cubic patches, based on a simple mathematical reformulation which leads to simple additional conditions to be applied in the patching computation. The paper presents an Hermite formulation of a bicubic parametric patch, but reformulations can be made also for Bézier and B-Spline patches as well. The presented approach is convenient for the cases when valencies of corners are different from the value 4, in general.Item Modified Gaussian Elimination without Division Operations(American Institute of Physics, 2013) Skala, VáclavA new modified method based on the Gaussian elimination method for solution of linear system of equations in the projective space is formulated. It is based on application of projective extension of the Euclidean space and use of homogeneous coordinates. It leads to an elimination of division operation and higher precision due to division operation elimination. The approach is based on understanding that a solution of the linear system is equivalent to the extended cross-product, i.e. . As it can be seen there no division is needed. Use of the projective representation enables to avoid division operation and use advantages of the matrix-vector architectures. Division operations have to be used only if the final result of computation has to be in the Euclidean representation. The proposed method was implemented in C# and C++ and experimentally verified. It is especially convenient for computations on GPUs based architectures.Item A Global Optimization Algorithm for Rotation Alignment of Spherical Surfaces(Springer, 2013) Pan, Rongjiang; Skala, Václav; Müller, RolfWe propose a new approach to global optimization algorithm based on controlled random search techniques for rotational alignment of spherical surfaces with associated scalar values. To reduce the distortion in correspondence and increase efficiency, the spherical surface is first re-sampled using a geodesic sphere. The rotation in space is represented using the modified Rodrigues parameters. Correspondence between two spherical surfaces is implemented in the parametric domain. We applied the methods to the alignment of beam patterns computed from the outer ear shapes of bats. The proposed method is compared with other approaches such as alignment based on principal component analysis (PCA), exhaustive search in the discrete space of rotations defined by Euler angles and direct search using uniform samples over the rotation group SO(3). Experimental results demonstrate that the proposed rotation alignment obtained using the proposed algorithm has a high degree of precision and give the best result among the other four approaches.Item Algorithms Complexity and Non-linear Co-ordinates Theoretical Fiction or Practical Use?(Tula State University, 2000) Skala, VáclavThere are some applications, where the polar, cylindrical or spherical co-ordinate systems can be used for finding a solution of given problem. Especially some technical problems [Lio97a], like sonar and radar applications, where the distance from an object is measured under known angles, flow computation, radiation, medical imaging and ultrasound imaging etc. could benefit from their use. It is a usual practice that all the data from those applications are transformed to the cartesian orthogonal co-ordinate system, where all data are processed. The data are than displayed directly or transform back to the original co-ordinate system. Nevertheless it is well known that representation of a point in E2 is different drom a line representation and therefore the processing pipeline have to respect this fact. The polar, cylindrical and spherical co-ordinate systems offer some possibilities how to handle graphical information in an unambiguous way and also make an effective processing. On the other hand, it is necessary to say that in usual practical graphical applications the direct use of non-linear co-ordinates can be quite complicated can hopefully lead to new understanding of some fundamental algorithms and developing of new more effective methods.Item Triangular Mesh Decimation in Parallel Environment(Universitat de Girona, 2000) Franc, Martin; Skala, VáclavThe aim of the computer graphics is to visualise models of real-world objects. The visualization of large and complex models is required more and more often frequently. This is followed by number of operations which must be done before own visualization, whether it be an analysis of input data (e.g. searching for an isosurface) or a model simplification. In spite of huge progress made in graphics hardware field in last years, we still need to increase a performance using optional algorithms and programming techniques. One of the techniques that enhance the power in parallel computation. It can be seen that multiprocessor computers are more often available even for ordinary users. Together with Microsoft Windows expansion we have easy and comfortable tools for multiprocessor (multithread) programming as well. We present an original efficient and stable algorithm for triangle mesh simplification in parallel environment. We use a method based on our original super independent set of vehicles to avoid critical sections. Programs have been verified on MS Windows platform using standard Borland Delphi classes for multithread programming.Item Projective Geometry and Duality for Graphics, Games and Visualization(ACM, 2012) Skala, Václav
