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S22 Mecatrônica |
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Title:
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ALGORITHIM TO DETERMINE THE INITIAL POINTS OF THE INTERSECTION CURVES BETWEEN BEZIER SURFACES THROUGH THE SOLUTION OF MULTIVARIABLE POLYNOMIAL SYSTEM
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Summary :
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THE DETERMINATION OF THE INTERSECTION CURVES BETWEEN BÉZIER SURFACES MAY BE SEEN AS THE COMPOSITION OF TWO SEPARATE PROBLEMS: DETERMINING INITIAL POINTS AND TRACING THE INTERSECTION CURVE FROM THESE POINTS. THE BÉZIER SURFACE IS REPRESENTED BY A PARAMETRIC FUNCTION (POLYNOMIAL WITH TWO VARIABLES) THAT MAPS A POINT IN THE TRIDIMENSIONAL SPACE FROM THE BIDIMENSIONAL PARAMETRIC SPACE. IN THIS ARTICLE, IT IS PROPOSED AN ALGORITHM TO DETERMINE THE INITIAL POINTS OF THE INTERSECTION CURVES OF BÉZIER SURFACES, BASED ON THE SOLUTION OF POLYNOMIAL SYSTEMS WITH THE PROJECTED POLYHEDRAL METHOD. IN ORDER TO ALLOW THE USE OF THIS METHOD, THE EQUATIONS OF THE SYSTEM MUST BE REPRESENTED IN TERMS OF THE BERNSTEIN BASIS, AND TOWARDS THIS GOAL IT IS PROPOSED A ROBUST AND RELIABLE ALGORITHM TO EXACTLY TRANSFORM A MULTIVARIABLE POLYNOMIAL IN TERMS OF POWER BASIS TO A POLYNOMIAL WRITTEN IN TERMS OF BERNSTEIN BASIS. |
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Author :
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Faustini, Mário Carneiro
Tsuzuki, Marcos S. G.
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Paper View :
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