João Batista S. de Oliveira

Robust adaptive polygonal approximation of implicit curves

Abstract We present an algorithm for computing a robust adaptive polygonal approximation of an implicit curve in the plane. The approximation is adapted to the geometry of the curve because the length of the edges varies with the curvature of the curve. Robustness is achieved by combining interval arithmetic and automatic differentiation.

Two algorithms for automatic document page layout

This paper describes two approaches to the problem of automatically placing document items on pages of some output device. Both solutions partition the page into regions where each item is to be placed, but work on different input data according to the application: One approach assumes that previously defined rectangular items are to be placed freely on the page (as in a sales brochure), whereas the second approach places free-form items on pages divided into columns (as in a newspaper). Moreover, both approaches try to preserve the reading order provided by the input and use all available area on the page. The algorithms implementing those approaches and based on recursive page division are presented, as well as test results, possible changes and research directions.

Robust Approximation of Offsets, Bisectors, and Medial Axes of Plane Curves

Most methods for computing offsets, bisectors, and medial axes of parametric curves in the plane are based on a local formulation of the distance to a curve. As a consequence, the computed objects may contain spurious parts and components, and have to be trimmed. We approach these problems as global optimization problems, and solve them using interval arithmetic, thus generating robust approximations that need not be trimmed.

Measuring aesthetic distance between document templates and instances

Adaptive documents undergo many transformations during their generation, including insertion and deletion of content. One major problem in this scenario is the preservation of the aesthetic qualities of the document during those transformations.As adaptive documents are instances of a template, the aesthetic quality of an instance with respect to the template could be evaluated by aesthetic measures providing scores to any desired quality parameters. These parameters measure the deviation of the instance from the desired template. This evaluation could assure the quality of instances during their generation and final output.This paper introduces the use of document templates to support aesthetic measures of document instances. A score is assigned to a document instance according to the differences detected from the original template. Considering the original template as an ideal result, the quality of a document instance will decrease according to the number and severity of the changes applied to produce it. So, documents that are below a given threshold can be sent for further (possibly human) review, and any others are accepted.The amount of change with respect to the template will reflect the document quality, and in such a model the quality of instances can be considered as a distance from that original.

Support for arbitrary regions in XSL-FO

This paper proposes an extension of the XSL-FO standard which allows the specification of an unlimited number of arbitrarily shaped page regions. These extensions are built on top of XSL-FO 1.1 to enable flow content to be laid out into arbitrary shapes and allowing for page layouts currently available only to desktop publishing software. Such a proposal is expected to leverage XSL-FO towards usage as an enabling technology in the generation of content intended for personalized printing.

New slope methods for sharper interval functions and a note on Fischer's acceleration method

This paper presents algorithms evaluating sharper bounds for interval functionsF(X) :IRn →IR. We revisit two methods that use partial derivatives of the function, and develop four other inclusion methods using the set of slopesSf(x, z) off atx εX with respect to somez εIRn. All methods can be implemented using tools that automatically evaluate gradient and slope vectors by using a forward strategy, so the complex management of reverse accumulation methods is avoided. The sharpest methods compute each component of gradients and slopes separately, by substituting each interval variable at a time. Backward methods bring no great advantage in the sharpest algorithms, since object-oriented forward implementations are easy and immediate.Fischers acceleration scheme [2] was also tested with interval variables. This method allows the direct evaluation of the productf′(x) * (x−z) as a single real number (instead of working with two vectors) and we used it to computeF′(X) * (X−z) for an interval vectorX. We are led to decide against such acceleration when interval variables are involved.AbstractПредставлены алгоритмы для вычисления более точных границ интервальных ФункцийF(X) :IRn→ IR. Эаново рассмотрены два метода, иснольэюцие частные проиэводные Функции, и раэработано еще четыре лкалиэаионных метода, в которых рименяется множество наклоновSf(x, z) Φункцииf длчx εX о отнощению к некоторомуz εIRn. Все методы мозно реалиэовать с помощью средств, которые автоматически вычисляют векторы градиента и наклона с помошью опережаюшеи стратегии, таким обраэом исключив трудности, свяэанные с методами обратного накопления. Самые точные иэ этих методов вычисляют каждую комоненту градиентов и наклонов отдельно, одставляя о одной интервальной еременной эа раэ. Методы с эапаэдыванием не дают болыцого выигпыща в таких алгоритмах, носкольку обьектно-ориентированные методы с опережением реалиэуются с малыми эатратами труда и времени.Схема ускорения фишера [2] также была протестирована с интервальными еременными. Этот метод дедает воэможным прямое вычисление проиэведенияf′x) * (x−z) как одного вешественного числа (а не двух векторов). Мы испольэовали этот метод для вычисленияF′(X) * (X−z) с интервальным векторомX, но ришли к выводу, что этот метод ускорения не применим к интервальным еременным.

Robust adaptive approximation of implicit curves

We present an algorithm for computing a robust adaptive polygonal approximation of an implicit curve in the plane. The approximation is adapted to the geometry of the curve because the length of the edges varies with the curvature of the curve. Robustness is achieved by combining interval arithmetic and automatic differentiation.

A novel physics-based interaction model for free document layout

Marketing flyers, greeting cards, brochures and similar materials are expensive to produce, since these documents need to be personalized and typically require a graphic design professional to create. Either authoring tools are too complex to use or a predefined set of fixed templates is available, which can be restrictive and difficult to produce the desired results. Thus, simpler design tools are a compelling need for small businesses and consumers. This paper describes an interactive authoring method for creating free-form documents based on a force-directed approach, traditionally applied for graph layout problems. This is used for automatically distributing and manipulating images, text and decorative elements on a page, according to forces modeled after physical laws. Such approach can be used for enabling easy authoring of personalized brochures, photo albums, calendars, greeting cards and other free-form documents. A prototype has been developed for evaluation purposes, and is briefly described in this paper. Evaluation results are presented as well, showing that users enjoy the experience of designing a page by interacting with it, and that end results can be satisfactory.

Evaluating Lipschitz Constants for Functions Given by Algorithms

This paper describes an efficient method (O(n)) to evaluate the Lipschitz constant for functions described in some algorithmic language. Considering arithmetical operations as the basis of the algorithmic language and supported by control structures, the rules to evaluate such Lipschitz constants are presented and their correctness is proved. An extension of the method to evaluate Lipschitz constants over interval domains is also presented. Examples are presented, but the effectiveness of the method is doubtful when compared to other approaches, and effective enhancements based on slope evaluations are also explored.

Two new aesthetic measures for item alignment

This paper introduces two methods for measuring the alignment of items on a page with respect to its left/right margins. The methods are based on the path followed by the eyes as they follow the items from top to bottom of the page. Examples are presented and both methods are analyzed with respect to the axioms presented in [2], that describe how good alignment measure is supposed to behave.