Minimal roughness property of the Delaunay triangulation: a shorter approach
نویسنده
چکیده
Powar, P.L., Minimal roughness property of the Delaunay triangulation: a shorter approach, Computer Aided Geometric Design 9 (1992) 491-494. Recently Rippa (1990) has investigated an interesting result which states that “The Delaunay triangulation of the data points minimizes the roughness measure of a Piecewise Linear Interpolating Surface (PLISJ for any fixed set of function values”. This result is based on a Key Lemma which is technical and quite lengthy. We get the result of that Lemma in a much simpler and shorter way.
منابع مشابه
Minimal roughness property of the Delaunay triangulation
A set of scattered data in the plane consists of function values measured on a set of data points in R2. A surface model of this set may be obtained by triangulating the set of data points and constructing the Piecewise Linear Interpolating Surface (PLIS) to the given function values. The PLIS is combined of planar triangular facets with vertices at the data points. The roughness measure of a P...
متن کاملA Monotonicity Property for Weighted Delaunay Triangulations
where i is the linear interpolation of f over the triangle Ti in T and the sum is over all triangles in the triangulation. One may consider changing the triangulation by exchanging two triangles joined by an edge, forming a quadrilateral, by the triangles obtained by switching the diagonal of the quadrilateral; this is called an edge ip or a 2 ! 2 bistellar ip. He showed that the roughness of...
متن کاملMinimal Set of Constraints for 2D Constrained Delaunay Reconstruction
Given a triangulation T of n points in the plane, we are interested in the minimal set of edges in T such that T can be reconstructed from this set (and the vertices of T ) using constrained Delaunay triangulation. We show that this minimal set consists of the non locally Delaunay edges of T , and that its cardinality is less than or equal to n+ i=2 (if i is the number of interior points in T )...
متن کاملOn Generalized Diamond Spanners
Given a set P of points in the plane and a set L of non-crossing line segments whose endpoints are in P , a constrained plane geometric graph is a plane graph whose vertex set is P and whose edge set contains L. An edge e has the α-visible diamond property if one of the two isosceles triangles with base e and base angle α does not contain any points of P visible to both endpoints of e. A constr...
متن کاملFormal Study of Plane Delaunay Triangulation
This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe triangulations, we rely on a combinatorial hypermap specification framework we have been developing for years. We embed hypermaps in the plane by attaching coor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Computer Aided Geometric Design
دوره 9 شماره
صفحات -
تاریخ انتشار 1992