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The G~1Splicing Of The Algebraic Interval Surface

Posted on:2013-02-15Degree:MasterType:Thesis
Country:ChinaCandidate:L LiFull Text:PDF
GTID:2248330395479628Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
In computer aided geometric design, the construction of blending surfaces is animportant research topic, the so-called blending surface is a curve or surface with a certaincontinuity of the transition surface. In other words, given two or more pieces of surface aswell as on the original surface of the boundary line, how to construct a surface in theboundary line of smooth connection between the surface and original surface. Because of itsstrong practicality in the field of automobiles, ships, aircraft and other industrialmanufacturing, has become an important academic branch of computer-aided geometricdesign (CAGD).The article first introduces the basic knowledge related to this article describes thedevelopment history of the blending surface, including the rolling sphere method, the PDEmethod, Wu’s method, feature set, such as the characteristic function method. Splicing methodof algebraic surfaces, such as: function spline method, potential method, Hermiteinterpolation, the method of Gro..bnerr bases, Syzygy, Wu’s method and piecewise algebraicsurface methods do. We also introduced interval arithmetic, interval curve, surface definition,development history and splicing.In the second chapter for the splicing of the algebraic interval surface, the use of..Grobnerbasis theory on the ideal of algebraic geometry, consecutive splicing of twoalgebraic interval surface smooth surface. This would resolve the past idealized zero thicknessto actual life and production of the same so as to achieve to avoid the error appears. Finally,the example demonstrates the effectiveness of this method.
Keywords/Search Tags:smooth stitching, algebraic surfaces, interval algebraic curves and surfaces, Grobner base
PDF Full Text Request
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