L. L. Schumaker. Triangulation methods. Topics in Multivariate Approximation, C. K. Chui, L. L. Schumaker and F. I. Utreras, eds., Academic Press, 1987, 219--232. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Edge Insertion for Optimal Triangulations - Bern, Edelsbrunner, Eppstein.. (1993) (15 citations) (Correct)
....Though usually simple to verify, conditions (I) and (II) are somewhat restrictive. It would be interesting to find conditions weaker than (I) even though the price to pay may be implementations of the paradigm that take more than cubic time. Listings of optimality criteria can be found in [Barn77, BeEp92, Lind83, Schu87]. Furthermore, implementations for criteria satisfying (I) and (II) that run in time o(n 3 ) and o(n 2 log n) are sought. Acknowledgment The authors thank two anonymous referees for suggestions on improving the style of this paper. ....
L. L. Schumaker. Triangulation methods. Topics in Multivariate Approximation, C. K. Chui, L. L. Schumaker and F. I. Utreras, eds., Academic Press, 1987, 219--232.
Edge Insertion for Optimal Triangulations - Bern, Edelsbrunner, Eppstein.. (1992) (15 citations) (Correct)
....as maxmin (short for maximizes the minimum) or minmax of some triangle or edge measure. The first quantifier is over all triangulations of the same point set and the second is over all triangles or edges of a triangulation. Two example criteria are maxmin area and maxmin inscribed circle (see [Schu87]) The problem of automatically generating optimal triangulations for a given point set has been a subject for research since the 1960 s (see e.g. the discussion in [Geor71] Exhaustive search can be ruled out since a set of n points has, in general, exponentially many triangulations. In spite ....
....Though simple to be verified, conditions (I) and (II) are somewhat restrictive. It would be interesting to find conditions weaker than (I) even though the price to pay may be implementations of the paradigm that take more than cubic time. Listings of optimality criteria can be found in [Barn77, Lind83, Schu87]. Furthermore, implementations for criteria satisfying (I) and (II) that run in time o(n 3 ) and o(n 2 log n) are sought. ....
L. L. Schumaker. Triangulation methods. Topics in Multivariate Approximation, C. K. Chui, L. L. Schumaker and F. I. Utreras, eds., Academic Press, 1987, 219--232.
Optimal Two-Dimensional Triangulations - Tan (1993) (4 citations) (Correct)
....applications 10 suggest the criterion of min max length. Of course, this is ignoring the tradeoff and interplay between angle and length criteria; they may not be optimized simultaneously. We can still formulate the problem on min max length criterion (which also appears in [PeKe87, page 175] [Schu87, page 221], and [WaPh84, page 218] and provide a solution in Chapter 5. Problem 3 How fast can we compute a min max length triangulation of a point set The following problems on length criteria are still open. Problem 4 is the reverse of the previous problem, and Problem 5 is notoriously difficult ....
.... interesting measure as it signifies the importance of the vertex in computations [FrFi91] It is, however, an NPcomplete problem to decide whether a point set with constraining edges has a triangulation with vertex degree at most 7 [Jans92] No solution is known for the next problem compiled from [Schu87, page 222], Barn77, page 84] GeSh90, page 202] and [GCR77, Lind83] Problem 6 Can a min max or a max min optimal triangulation based on any one of the following quality measures be computed efficiently: area; aspect ratio; degree; radius of inscribed circle; ratio of the area of the inscribed circle to ....
L. L. Schumaker. Triangulation methods. Topics in Multivariate Approximation, C. K. Chui, L. L. Schumaker and F. I. Utreras, eds., Academic Press, 1987, 219--232.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC