Title: Rational Ruled surfaces construction by interpolating dual unit vectors representing lines
Authors: Aspragathos, Nikos A.
Papageorgiou, Stavros G.
Citation: WSCG '2006: Short Papers Proceedings: The 14-th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2006: University of West Bohemia, Plzen, Czech Republic, January 31 - February 2, 2006, p. 141-148.
Issue Date: 2006
Publisher: Václav Skala - UNION Agency
Document type: konferenční příspěvek
URI: http://wscg.zcu.cz/WSCG2006/Papers_2006/Short/!WSCG2006_Short_Proceedings_Final.pdf
ISBN: 80-86943-05-4
Keywords: 3D povrchy;duálové vektory;lineární geometrie;parametrizace povrchu
Keywords in different language: ruled surfaces;dual vectors;line geometry;surface parametrization
Abstract: In this paper, a new representational model is introduced for the rational family of ruled surfaces in Computer Graphics. The surface parameterization is constructed using the NURBS basis functions and line geometry. The ruled surface is defined by interpolating directly dual unit vectors representing lines, which is a single parametric surface and its shape depends on the control lines. All the advantages of the NURBS basis such as shape control and the local modification property are also applicable and bequeathed to the dual NURBS ruled surface. The problem of drawing the lines defined by dual unit vectors is also resolved. Towards this direction, we propose a simple technique to calculate the surface’s striction curve in order to draw the rulings of the surface within the striction curve neighborhood. The on-screen 3D plot of the surface is realized in a pre-defined specific region close to the striction curve. With the proposed technique a natural representation of the ruled surface is derived. The shape of the surface can be intrinsically manipulated via the control lines that possess one more degree of freedom than the control points. Our method can find application not only in CAD but in the areas of NC milling and EDM.
Rights: © Václav Skala - UNION Agency
Appears in Collections:WSCG '2006: Short Papers Proceedings

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