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- W2786122936 abstract "Non-Uniform Rational B-Splines (NURBS) has been an important research topic in the CAD/CAM community in the last two decades. The basic fundamentals of NURBS can be best explained from the projective geometric point of view. The projective geometric point of view is in turn, best explained by using the geometric algebra invented by Hermann Grassmann.This dissertation consists of three parts: (1) NURBS curve interpolation, (2) developable surface interpolation and (3) an introduction to Grassmann algebra. In the first two parts we solve some important practical problems in geometric modeling.In the first part, we study the NURBS curve interpolation problem. Given a set of discrete data points, we determine parameters and knots and find the related control points and their positive weights for the interpolation. Our output curves are free from poles. This is an improvement over the usual methods of NURBS interpolation which have no control over the weights. To secure this control over the positivity of the weights we use quadratic programming.In the second part we propose some algorithms for constructing by interpolation a developable surface from a given boundary curve and certain normal vectors to control the direction of the generators. A method is presented to keep the edge of regression of the developable surface away from the given boundary curve if it crosses the boundary curve. We also use quadratic programming to achieve the interpolation.In the last part, after describing the basic geometric operations of point addition and multiplication in Grassmann algebra we show how they can be used to describe duality, ruled surfaces, and the de Casteljau algorithm. All this is done in a coordinate free manner, characteristic of Grassmann algebra." @default.
- W2786122936 created "2018-02-23" @default.
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- W2786122936 date "1996-01-01" @default.
- W2786122936 modified "2023-09-24" @default.
- W2786122936 title "Design of rational curves and developable surfaces" @default.
- W2786122936 hasPublicationYear "1996" @default.
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