کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6876365 1442460 2018 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bézier curves that are close to elastica
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر گرافیک کامپیوتری و طراحی به کمک کامپیوتر
پیش نمایش صفحه اول مقاله
Bézier curves that are close to elastica
چکیده انگلیسی
We study the problem of identifying those cubic Bézier curves that are close in the L2 norm to planar elastic curves. The problem arises in design situations where the manufacturing process produces elastic curves; these are difficult to work with in a digital environment. We seek a sub-class of special Bézier curves as a proxy. We identify an easily computable quantity, which we call the λ-residual eλ, that accurately predicts a small L2 distance. We then identify geometric criteria on the control polygon that guarantee that a Bézier curve has λ-residual below 0.4, which effectively implies that the curve is within 1% of its arc-length to an elastic curve in the L2 norm. Finally we give two projection algorithms that take an input Bézier curve and adjust its length and shape, whilst keeping the end-points and end-tangent angles fixed, until it is close to an elastic curve.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer-Aided Design - Volume 104, November 2018, Pages 36-44
نویسندگان
, , , ,