An Interpolant Based on Line Segment Voronoi Diagrams

نویسندگان

  • Hisamoto Hiyoshi
  • Kokichi Sugihara
چکیده

This paper considers the interpolation for multi-dimensional data using Voronoi diagrams. Sibson's interpolant is well-known as an interpolation method using Voronoi diagrams for discretely distributed data, and it is extended to continuously distributed data by Gross. On the other hand, the authors studied another interpolation method using Voronoi diagrams recently. This paper outlines the authors' interpolant brie y, and extends the author's interpolant to linearly distributed data based upon the discussion using integrations.

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

Hierarchical Data Representations Based on Planar Voronoi Diagrams

Multiresolution representation of high-dimensional scattered data is a fundamental problem in scientific visualization. This paper introduces a data hierarchy of Voronoi diagrams as a versatile solution. Given an arbitrary set of points in the plane, our goal is the construction of an approximation hierarchy using the Voronoi diagram as the essential building block. We have implemented two Voro...

متن کامل

Polyline-sourced Geodesic Voronoi Diagrams on Triangle Meshes

This paper studies the Voronoi diagrams on 2-manifold meshes based on geodesic metric (a.k.a. geodesic Voronoi diagrams or GVDs), which have polyline generators. We show that our general setting leads to situations more complicated than conventional 2D Euclidean Voronoi diagrams as well as point-source based GVDs, since a typical bisector contains line segments, hyperbolic segments and paraboli...

متن کامل

Terrain Modeling using Voronoi Hierarchies

We present a new algorithm for terrain modeling based on Voronoi diagrams and Sibson’s interpolant. Starting with a set of scattered data sites in the plane with associated function values defining a height field, our algorithm constructs a top-down hierarchy of smooth approximations. We use the convex hull of given sites as domain for our hierarchical representation. Sibson’s interpolant is us...

متن کامل

Farthest line segment Voronoi diagrams

The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction algorithm that is easy to implement. No restr...

متن کامل

An Expected Linear-Time Algorithm for the Farthest-Segment Voronoi Diagram

We present linear-time algorithms to construct tree-structured Voronoi diagrams, after the sequence of their regions at infinity or along a given boundary is known. We focus on Voronoi diagrams of line segments, including the farthest-segment Voronoi diagram, the order-(k+1) subdivision within a given order-k Voronoi region, and deleting a segment from a nearest-neighbor diagram. Although tree-...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998