Intersection of a line and a convex hull of points cloud

An algorithm for intersection a line and a convex hull of points cloud is presented. The algorithm doesn't require the convex hull construction. The points cloud can be arbitrary and not sorted, no topology, face list or edge list is known. The algorithm uses only vertices coordinates. Standard transformation of coordinates is performed and the points cloud is bisected by two perpendicular planes. Yielded 1D points set lies at the line. Bounds of the set are intersection points of the points cloud and the line. The algorithm was compared against the obvious algorithm which uses intersection of the line and all possible faces (sets of three points). Presented algorithm is much faster than the obvious one. © 2013 R. P. Koptelov and A. M. Konashkova

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

Modified skala's plane tested algorithm for line-polyhedron intersection

Three modifications of known Skala's line clipping algorithm are presented. Basic Skala's algorithm represents the line as two intersected planes. Line intersects a triangular face of polyhedron only if both planes intersect the triangle. Following along the first plane triangles tested against the second plane and then line-triangle or line-half space intersection is tested. First modification consists in saving some temporary variables. Second modification consists in choosing of direction from the first triangle. Third modification consists in utilization of some precomputed values and a novel line-triangle intersection test. Three modifications give up to 26 % performance gain. © 2015 A. M. Konashkova

Ray tracing algorithms for zonal radiative heat transfer

Целью работы является повышение точности и быстродействия методов трассировки лучей и учета наличия препятствий на пути излучения в системах со сложной геометрией. Выполнено сравнительное исследование методов трассировки лучей для расчета зонального теплообмена, а также разработаны программы, реализующие трассировку лучей известными методами. Показано, что стандартный метод трассировки сквозь неравномерную сетку, как наиболее удобную структуру данных для лучистого теплообмена, приводит к проблеме пропадания лучей. Разработан робастный метод трассировки лучей, решающий данную проблему и обладающий немного лучшим быстродействием. Разработан новый алгоритм пересечения прямой с выпуклым многогранником. Алгоритм дает решение проблемы пересечения при неизвестном списке граней многогранника, которая часто возникает в задачах САПР и геометрических вычислениях в реальном времени. Все описываемые алгоритмы реализованы в виде программ и готовы к использованию. Полученные результаты могут применяться в моделировании теплообмена, компьютерной графике, САПР и визуализации результатов расчета.The aim of this work is increasing accuracy and performance of ray tracing and obstructions handling in systems of complex geometry. Known ray tracing methods are compared in context of radiative heat transfer. Methods of ray tracing and radiative view factors evaluation are implemented in computer programs. It is shown that the standard ray tracing with non uniform mesh (the most suitable geometrical structure for radiative heat transfer) fails with loss of some rays in geometry. Robust ray tracing algorithm is developed that solves the problem. The algorithm is also slightly faster than the standard one. New ray – convex polyhedron intersection algorithm is developed. It solves the intersection problem if polyhedron faces are unknown – usual case in CAD and real-time calculations. All described algorithms are implemented as computer programs and are ready to use. Obtained investigation results can be applied in modeling of radiative heat transfer, computer graphics, CAD and scientific visualization.Программа развития УрФУ на 2013 год (п.1.2.2.3

Real-Time Ultrasound Simulation for Medical Training and Standardized Patient Assessment

With the increasing role played by ultrasound in clinical diagnostics, ultrasound training in medical education has become more and more important. The clinical routine for ultrasound training is on real patients; therefore monitored and guided examinations involving medical students are quite time-constrained. Furthermore, standardized patients (SPs), who are increasingly used in medical school for teaching and assessing medical students, need to be augmented. These SPs are typically healthy individuals who can not accurately portray the variety of abnormalities that are needed for training especially when medical examinations involve instrument interactions. To augment SPs in a realistically effective way and also address the resourced time constraints for sonography training, a computerized ultrasound simulation is essential for medical education. In this dissertation, I investigate a real-time ultrasound simulation methodology based on a virtual 3-dimentional (3-D) mesh organ. This research has developed the simulation technology to augment SPs with synthetic ultrasound images. I present this methodology and its use in simulating echocardiography. This simulated echocardiogram displays the various oriented sonographs in real time according to the placement of a mock transducer without the need of an actual patient

PuzzleFlex: kinematic motion of chains with loose joints

This paper presents a method of computing free motions of a planar assembly of rigid bodies connected by loose joints. Joints are modeled using local distance constraints, which are then linearized with respect to configuration space velocities, yielding a linear programming formulation that allows analysis of systems with thousands of rigid bodies. Potential applications include analysis of collections of modular robots, structural stability perturbation analysis, tolerance analysis for mechanical systems, and formation control of mobile robots.Comment: Accepted at the 2020 IEEE International Conference on Robotics and Automation (ICRA

A numerical algorithm for L2L_2 semi-discrete optimal transport in 3D

This paper introduces a numerical algorithm to compute the $L_2$ optimal transport map between two measures $\mu$ and $\nu$, where $\mu$ derives from a density $\rho$ defined as a piecewise linear function (supported by a tetrahedral mesh), and where $\nu$ is a sum of Dirac masses. I first give an elementary presentation of some known results on optimal transport and then observe a relation with another problem (optimal sampling). This relation gives simple arguments to study the objective functions that characterize both problems. I then propose a practical algorithm to compute the optimal transport map between a piecewise linear density and a sum of Dirac masses in 3D. In this semi-discrete setting, Aurenhammer et.al [\emph{8th Symposium on Computational Geometry conf. proc.}, ACM (1992)] showed that the optimal transport map is determined by the weights of a power diagram. The optimal weights are computed by minimizing a convex objective function with a quasi-Newton method. To evaluate the value and gradient of this objective function, I propose an efficient and robust algorithm, that computes at each iteration the intersection between a power diagram and the tetrahedral mesh that defines the measure $\mu$. The numerical algorithm is experimented and evaluated on several datasets, with up to hundred thousands tetrahedra and one million Dirac masses.Comment: 23 pages, 14 figure

Fast and Accurate Visibility Preprocessing

Visibility culling is a means of accelerating the graphical rendering of geometric models. Invisible objects are efficiently culled to prevent their submission to the standard graphics pipeline. It is advantageous to preprocess scenes in order to determine invisible objects from all possible camera views. This information is typically saved to disk and may then be reused until the model geometry changes. Such preprocessing algorithms are therefore used for scenes that are primarily static. Currently, the standard approach to visibility preprocessing algorithms is to use a form of approximate solution, known as conservative culling. Such algorithms over-estimate the set of visible polygons. This compromise has been considered necessary in order to perform visibility preprocessing quickly. These algorithms attempt to satisfy the goals of both rapid preprocessing and rapid run-time rendering. We observe, however, that there is a need for algorithms with superior performance in preprocessing, as well as for algorithms that are more accurate. For most applications these features are not required simultaneously. In this thesis we present two novel visibility preprocessing algorithms, each of which is strongly biased toward one of these requirements. The first algorithm has the advantage of performance. It executes quickly by exploiting graphics hardware. The algorithm also has the features of output sensitivity (to what is visible), and a logarithmic dependency in the size of the camera space partition. These advantages come at the cost of image error. We present a heuristic guided adaptive sampling methodology that minimises this error. We further show how this algorithm may be parallelised and also present a natural extension of the algorithm to five dimensions for accelerating generalised ray shooting. The second algorithm has the advantage of accuracy. No over-estimation is performed, nor are any sacrifices made in terms of image quality. The cost is primarily that of time. Despite the relatively long computation, the algorithm is still tractable and on average scales slightly superlinearly with the input size. This algorithm also has the advantage of output sensitivity. This is the first known tractable exact solution to the general 3D from-region visibility problem. In order to solve the exact from-region visibility problem, we had to first solve a more general form of the standard stabbing problem. An efficient solution to this problem is presented independently