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Mathematical moddeling of 3-D Surfaces of arbitrary shapes for computer graphics
Faculty
Engineering
Year:
1996
Type of Publication:
Theses
Pages:
223
Authors:
Mohamed Mohamed Ali Mohamed Said
BibID
10424984
Keywords :
Mathematics
Abstract:
In this work, the problem of construct ing mathemat icalmodels of a 3-D surfaces of arbitrary shapes is considered. Asurvey is presented for previous work and a comparison betweenexisting models imply that the field is dominated by modelsbased on parametric funct ion. However, the parametr icfunctions used is a subclass of the implicit algebraicfunctions, the parametric functions are not closed under manygeometric operations under which the implicit algebraicfunctions are closed, the algebraic degree of a degreen-parametric surface is n2 and a bidegree n-parametric surfacecan be of algebraic degree up to 2n2, whereas for a surfacedefined by an implicit algebraic equation its algebraic degreeis the same as the degree of the defining equation, more~verthe point classification problem is greatly simplified whenusing implicit algebraic representation. For these reasons andothers, attention is focused on modeling with implicitfunction, especially that of low degree.A mathemat ical model is developed to controlsingularities of quadrics and cubics, also a mathematicalmodel for detrmining the equations of the projections of theintersection of two algebraic surfaces is established.The above entities are utilized in constructing threemodels for 3-D surfaces of arbi trary shapes based on lowdegree implicit functions. In the first model the buildingunit is a quadratic patch with natural intersection boundariesand a near et overall continuity. In the second model thebuilding unit is a cubic implicit patch with quadraticparametric boundary curves. A CO overall continuity isgauranteed wi th at least two degrees of freedom used tocontrol singularities and to enhance the overall continuity tobe eO+. In the third model a side vertex interpolation schemeis used to construct three cubic patches for every inputtriangular face, these patches are then combined to produce asurface with an overall et continuity.The necessary transformations, hidden-surfaces elimination,shades, and shadows are examined for completeness of the work.
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Author Related Publications
Mohamed Mohamed Ali Mohamed Said, "Mathematical moddeling of 3-D Surfaces of arbitrary shapes for computer graphics", 1996
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