Three-dimensional graphics

Three-dimensional graphics is the area of computer graphics that deals with producing two-dimensional representations, or images, of three-dimensional synthetic scenes, as seen from a given viewing configuration. The level of sophistication of these images may vary from simple wire-frame representations, where objects are depicted as a set of segment lines, with no data on surfaces and volumes, to photorealistic rendering, where illumination effects are computed using the physical laws of light propagation. All the different approaches are based on the metaphor of a virtual camera positioned in 3D space and looking at the scene. Hence, independently from the rendering algorithm used, producing an image of the scene always requires the resolution of the following problems: 1. Modeling geometric relationships among scene objects, and in particular efficiently representing the situation in 3D space of objects and virtual cameras; 2. Culling and clipping, i.e. efficiently determining which objects are visible from the virtual camera; 3. Projecting visible objects on the film plane of the virtual camera in order to render them. This chapter provides an introduction to the field by presenting the standard approaches for solving the aforementioned problems.168-17

Format and basic geometry of a perspective display of air traffic for the cockpit

The design and implementation of a perspective display of air traffic for the cockpit is discussed. Parameters of the perspective are variable and interactive so that the appearance of the projected image can be widely varied. This approach makes allowances for exploration of perspective parameters and their interactions. The display was initially used to study the cases of horizontal maneuver biases found in experiments involving a plan view air traffic display format. Experiments to determine the effect of perspective geometry on spatial judgements have evolved from the display program. Several scaling techniques and other adjustments to the perspective are used to tailor the geometry for effective presentation of 3-D traffic situations

Duality, Barycentric Coordinates and Intersection Computation in Projective Space with GPU support

This paper presents solution of selected problems using principle of duality and projective space representation. It will be shown that alternative formulation in the projective space offers quite surprisingly simple solutions that lead to more robust and faster algorithms which are convenient for use within parallel architectures as GPU (Graphical Processor Units-NVIDIA-TESLA/Fermi) or SCC (Intel-Single-chip Cloud Computing), which can speed up solutions of numerical problems in magnitude of 10-100. There are many geometric algorithms based on computation of intersection of lines, planes etc. Sometimes, very complex mathematical notations are used to express simple mathematical solutions, even if their formulation in the projective space offers much more simple solution. It is shown that a solution of a system of linear equations is equivalent to generalized cross product, which leads with the duality principle to new algorithms. This is presented on a new formulation of a line in 3D given as intersection of two planes which is robust and fast, based on duality of Plücker coordinates. The presented approach can be used also for reformulation of barycentric coordinates computations on parallel architectures. The presented approach for intersection computation is well suited especially for applications where robustness is required, e.g. large GIS/CAD/CAM systems etc

Intersection of triangles in space based on cutting off segment

The article proposes a new method for finding the triangle-triangle intersection in 3D space, based on the use of computer graphics algorithms -- cutting off segments on the plane when moving and rotating the beginning of the coordinate axes of space. This method is obtained by synthesis of two methods of cutting off segments on the plane -- Cohen-Sutherland algorithm and FC-algorithm. In the proposed method, the problem of triangle-triangle intersection in 3D space is reduced to a simpler and less resource-intensive cut-off problem on the plane. The main feature of the method is the developed scheme of coding the points of the cut-off in relation to the triangle segment plane. This scheme allows you to get rid of a large number of costly calculations. In the article the cases of intersection of triangles at parallelism, intersection and coincidence of planes of triangles are considered. The proposed method can be used in solving the problem of tetrahedron intersection, using the finite element method, as well as in image processing.Comment: Convergent Cognitive Information Technologies. Convergent 2019. Communications in Computer and Information Science, in press, Springer, Cham. http://it-edu.oit.cmc.msu.ru/index.php/convergent/convergent2019 (14 pages, 11 figures

Planar PØP: feature-less pose estimation with applications in UAV localization

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We present a featureless pose estimation method that, in contrast to current Perspective-n-Point (PnP) approaches, it does not require n point correspondences to obtain the camera pose, allowing for pose estimation from natural shapes that do not necessarily have distinguished features like corners or intersecting edges. Instead of using n correspondences (e.g. extracted with a feature detector) we will use the raw polygonal representation of the observed shape and directly estimate the pose in the pose-space of the camera. This method compared with a general PnP method, does not require n point correspondences neither a priori knowledge of the object model (except the scale), which is registered with a picture taken from a known robot pose. Moreover, we achieve higher precision because all the information of the shape contour is used to minimize the area between the projected and the observed shape contours. To emphasize the non-use of n point correspondences between the projected template and observed contour shape, we call the method Planar PØP. The method is shown both in simulation and in a real application consisting on a UAV localization where comparisons with a precise ground-truth are provided.Peer ReviewedPostprint (author's final draft

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