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Monge method in creating regular polyhedrons models

Koźniewski E

Journal Biuletyn of Polish Society for Geometry and Engineering Graphics

2014

Vol. 26

41--46

Physical face (paper) models of polyhedrons, particularly Platonic solid models, are formed by drawing the nets before them. Other construction requirements makes us the task to run a solid (physical or virtual) model. Beside the solid faces their mutual angles or angles to the selected plane is needed to know. Sometimes other parameters such as a distance parallel faces is good to know. If we choose the geometric way, it does not perform calculations that can be performed using a AutoCAD program. Then turns out to be a very helpful Monge method. The paper contains a proposal to carry out such a task.

Fizyczne ściankowe (np. papierowe) modele wielościanów, w szczególności wielościanów foremnych tworzy się rysując wcześniej na płaszczyźnie ich siatki. Inne wymagania konstrukcyjne stawia nam zadanie wykonania monolitycznego (bryłowego) modelu materialnego za pośrednictwem np. modelu wirtualnego. Obok ścian bryły musimy znać wtedy ich wzajemne kąty nachylenia lub kąty nachylenia do wybranej płaszczyzny lub inne parametry takie jak odległość ścian równoległych. Jeśli wybierzemy drogę geometryczną, to bez wykonywania obliczeń można zrealizować to za pomocą programu AutoCAD. Wówczas bardzo pomocną okazuje się metoda Monge’a. Praca zawiera propozycję zrealizowania takiego zadania.

Czestochowa-faces

Kompanets L., Rydzek S.

Computing, Multimedia and Intelligent Techniques

2005

Vol. 1 nr 1

51-60

Traditionally, in face authentication/identification methods the presumption concerning face/head symmetry is used. For novel applications that concern creating techniques by means of which it is possible to reproduce the extraordinary complexity of skin, muscle, eye and hair movements that convey emotion, gesture, psychological state or psycho-sociological traits, we begin to create new research direction called Biometrics of Asymmetrical Face. Apart from the direct study of new biometric technique type -the ophthalmogeometrical one - the new essential problem in this direction is the ability of interpretation of untapped "subtle" primary face information in psychological construct terms. The new direction study is based on modern knowledge of face authentic-ation/identification methods, the ophthalmogeometry, and functional brain asymmetry phenomena, knowledge of psychological testing of personal types. In the paper, it is presented a novel type of precise normalized model of a face called Czestochowa-face model, in the sense suiting the specification of the problem of mod-rn and prospect person's authentication/identification techniques creation in live biometrics. In addition the ophthalmogeometrical technique will be created and partially researched and attention has been also drawn to interdisciplinary research context. Beside the first-hand usage, the new technique may be employed in the areas of human-computer interaction, identification of cognition-psyche type of personality for personnel management, advanced education, and so on.