الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
Wide angle viewing may be considered as one of the important tools in transforming from the three-dimensional space to the images plane. This has been previously arranged using various techniques such as imaging through composing multiple overlapped images, i.e. mosaics, panoramic projection using cylindrical surface, and stereographic projection using spherical surface. One of the important projections used in wide angle viewing is the ”Parabolic Perspective Double Projection” in which the paraboloid is used as a reflection surface. Such technique is modeled as the para catadioptric camera system. The imaging technique is executed through central projection of space objects on the paraboloid using the surface focus as a center of projection, then, orthogonal projection of centrally projected elements onto the surface directory plane. Positional problems of such projection have been handled graphically and analytically, from the researcher’s opinion, metric problems had not been previously studied. The only problems touched metric problems for such projection are the so called ”Camera Calibration” in which analytical comparison between the image and the original planar figure is carried out. Considering metric problems as important and essential tool for any projection, this thesis handles such problems, which include determining true lengths of lines and their inclination angles to projection plane, studying perpendicularity between lines and planes, and angle between two lines, between line and plane or between two planes. The analysis was executed both graphically, adopting descriptive geometry, and analytically exploiting two images. Various applications related to metric problems were introduced graphically. Representation of true lengths of lines in various positions, shortest distance between a given point and a given line, minimum distance between two skew lines, distance between two parallel lines, and distance between two parallel planes are done. Also, perpendicularity problems such as representation of line perpendicular to a given plane in particular positions from a given point and representation of incident and reflected light rays onto mirror plane are presented. Problems of determining the angle between two skew lines, angle between line and plane, and angle between two intersecting planes were also executed. Finally, metric problems related to single para catadioptric image and given information are considered. According to the non-conformality of the parabolic perspective double projection, no distinguished geometric feature exerted from studying metric problems. The merit granted in this analysis is the genuine and pioneer study of metric problems for such projection which is widely used in wide range viewing and modeling the catadioptric camera systems. The most important contributions of this thesis are the determination of points space positions, true lengths of lines, determination of line perpendicular to a given plane and a plane perpendicular to a given line and angle between two intersecting lines. These issues are determined using two different images of the geometrical element from two para catadioptric cameras systems. These topics have great advantageous in studying photogrammetry, surveillance and robot manipulation by replacing convenient camera systems with para catadioptric camera system.