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Talks & Seminars
Title: Two Modeling Primitives for Computer Aided Geometric Design
Dr. Jinesh Machchhar, Technion-Israel Institute of Technology
Date & Time: August 7, 2018 11:00
Venue: Conference Room, 01st Floor, C Block, Dept. of CSE, Kanwal Rekhi Bldg.
Abstract:
Computer Aided Geometric Design concerns development of algorithms and accompanying software, towards design of parts and structures with a high degree of numerical precision. Target application domains include design of automobiles, aircrafts and buildings, among others. In this talk we discuss two kernel level modeling primitives. First, we propose a fast algorithm for computing the real roots of univariate polynomials given in the Bernstein basis. Traditionally, the polynomial is subdivided until a root can be isolated. In contrast, herein we aim to find a root only to subdivide the polynomial at the root. This subdivision based algorithm exploits the property that the Bezier curves interpolate the end-points of their control polygons. Upon subdivision at the root, both resulting curves contain the root at one of their end-points, and hence contain a vanishing coefficient that is factored out. The algorithm then recurses on the new sub-curves, now of lower degree, yielding a computational efficiency. Comparison of running times against the state-of-the-art on thousands of polynomials shows an improvement of about an order-of-magnitude. Second, we demonstrate a robust computational interface for precise modeling of microstructures towards 3D printing. This is achieved through functional composition of B-spline functions and allows separate design of the micro and the macro structures of an object. In particular, we demonstrate construction of recursive, fractal-like microstructures which are composed of trivariate tiles with C0-discontinuities. Applications include design of porous and composite materials. This is joint work with Gershon Elber.
Speaker Profile:
Jinesh Machchhar is a researcher in the field of applied geometry. He has been a post-doctoral fellow at the faculty of computer science at Technion-Israel Institute of Technology. He obtained his Ph.D. from IIT Bombay in 2015. He did his M.Tech from IIT Bombay and his bachelor of engineering from South Gujarat University. His research interests include geometric modeling, surface design and analysis, and software development for computer aided design and manufacturing.
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