Optimal simplification of polygonal chain for rendering

Abstract

For a given polygonal chain, we study the min-# problem, which consists in finding an approximate and ordered subchain with a minimum number of vertices. Previous approaches simplify the input chain relative to an approximation criterion which minimizes the gap between the original chain and the simplified subchain. Nevertheless, no criterion allows us to directly control the visual quality of the final rendered result. Moreover, efficient methods produce peculiar simplifications or entail a useless increase in the number of vertices. A quadratic complexity is then required to bypass these misbehaviors and to obtain a good perceptual quality. We define a new criterion which retains the shape of the original chain and which guarantees that the distance between the rendered simplification is at most half a pixel away from the original chain. Thus, our criterion does not produce an incorrect simplification. Based on a flexible tolerance region, it does not involve any side effect that would increase the number of vertices of the simplification. Moreover, our method reaches a near-linear time complexity and its implementation is based on classical functions. To our knowledge, this is the first algorithm providing all these advantages.

Efficient Observer-Dependent Simplification in Polygonal Domains

“…The only similar work to the results of this paper is the rendering based simplification of Buzer [7], which depends on the resolution of the display screen without considering the observer position. There are several interesting open directions in applying and extending this notion.…”

Computing polygonal path simplification under area measures

“…Using the area of union of these regions is a natural parameter to be used as the error of simplification of p i p j . This error measure is called sum-area and has been considered before [5,23,24]. In some applications, like simplification of borders between two neighboring countries, the difference between the areas of the regions defined by p i p j and P(i, j) on both sides of p i p j are important.…”

“…In some applications, like simplification of borders between two neighboring countries, the difference between the areas of the regions defined by p i p j and P(i, j) on both sides of p i p j are important. This error measure is called diff-area and has been considered in [5]. Diff-area for link p i p j in Fig.…”

“…Recently, Bose et al [5] revisited the line simplification problem under area error measures and proposed simplification algorithms for x-monotone paths. For sum-area error measure, they bounded the input path by two vertical lines at p 1 and p n and a horizontal segment lying above P according to Fig.…”

A Heuristic Homotopic Path Simplification Algorithm

“…, p n−1 } be the points of a given polygonal path, where n is the size of P . We assume that the input path is not self-intersecting, which is a common assumption [1,2,3]. A polygonal path Q = {q 1 = p 0 , q 2 , .…”