Degenerate polynomial patches of degree 4 and 5 used for geometrically smooth interpolation in 3

نویسندگان

  • Marian Neamtu
  • Pia R. Pfluger
چکیده

The problem of interpolating scattered 3D data by a geometrically smooth surface is considered. A completely local method is proposed, based on employing degenerate triangular Bernstein{B ezier patches. An analysis of these patches is given and some numerical experiments with quartic and quintic patches are presented. Supported by the Netherlands Foundation of Mathematics (SMC) and the Netherlands Organization for the Advancement of Research (NWO).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Degenerate polynomial patches of degree 11 for almost <Emphasis Type="Italic">GC </Emphasis> <Superscript>2 </Superscript> interpolation over triangles

We consider the problem of interpolating scattered data in R 3 by an almost geometrically smooth GC 2 surface, where almost GC 2 means GC 2 except in a finite number of points (the vertices), where the surface is GC 1. A local method is proposed, based on employing so-called degenerate triangular Bernstein-B6zier patches. We give an analysis of quintic patches for GC I and patches of degree ele...

متن کامل

On G1 stitched bi-cubic Bézier patches with arbitrary topology

Lower bounds, mandating a minimal number and degree of polynomial pieces, represent a major achievement in the theory of geometrically smooth (G) constructions. On one hand, they establish a floor when searching for optimal constructions, on the other they can be used to flag complex constructions for potential flaws. In particular, quadrilateral meshes of arbitrary topology can not in general ...

متن کامل

gH-differentiable of the 2th-order functions interpolating

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

متن کامل

Smooth mesh interpolation with cubic patches

An algorithm for the local interpolation of a mesh of cubic curves with 3-and 4-sided facets by a piecewise cubic C ~ surface is stated and illustrated by an implementation. Precise necessary and sufficient conditions for oriented tangent-plane continuity between adjacent patches are derived, and the explicit constructions are characterized by the degree of the three scalar weight functions tha...

متن کامل

On G stitched bi-cubic Bézier patches with arbitrary topology

Lower bounds on the generation of smooth bi-cubic surfaces imply that geometrically smooth (G) constructions need to satisfy conditions on the connectivity and layout. In particular, quadrilateral meshes of arbitrary topology can not in general be covered with G-connected Bézier patches of bi-degree 3 using the layout proposed in [ASC17]. This paper analyzes whether the pre-refinement of the in...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Computer Aided Geometric Design

دوره 11  شماره 

صفحات  -

تاریخ انتشار 1994