Low level direct interpolation for parametric curves

We present an algorithm for the direct interpolation of parametric curves with a CNC machine -- The algorithm expresses parametric planar curves as sequences of discrete axes movements of BLU size of the machining tool -- Therefore, the curve C(u) is directly approximated by the pulse trains, hence eliminating one source of the machining error

Low level direct interpolation for parametric curves

This article presents an algorithm for the direct interpolation of parametric planar curves C(u) with a CNC machine. It expresses parametric planar curves as sequences of machine tool axes discrete movements of BLU size. Therefore, the curve C(u) is directly approximated by the pulse trains, hence eliminating one source of the machining errors

On the number of sides necessary for polygonal approximation of black-and-white figures in a plane

A bound on the number of extreme points or sides necessary to approximate a convex planar figure by an enclosing polygon is described. This number is found to be proportional to the fourth root of the figure's area divided by the square of a maximum Euclidean distance approximation parameter.An extension of this bound, preserving its fourth root quality, is made to general planar figures. This is done by decomposing the general figure into nearly convex sets defined by inflection points, cusps, and multiple windings.A procedure for performing actual encoding of this type is described. Comparisons of parsimony are made with contemporary figure encoding schemes

Improved clustering approach for junction detection of multiple edges with modified freeman chain code

Image processing framework of two-dimensional line drawing involves three phases that are detecting junction and corner that exist in the drawing, representing the lines, and extracting features to be used in recognizing the line drawing based on the representation scheme used. As an alternative to the existing frameworks, this thesis proposed a framework that consists of improvement in the clustering approach for junction detection of multiple edges, modified Freeman chain code scheme and provide new features and its extraction, and recognition algorithm. This thesis concerns with problem in clustering line drawing for junction detection of multiple edges in the first phase. Major problems in cluster analysis such as time taken and particularly number of accurate clusters contained in the line drawing when performing junction detection are crucial to be addressed. Two clustering approaches are used to compare with the result obtained from the proposed algorithm: self-organising map (SOM) and affinity propagation (AP). These approaches are chosen based on their similarity as unsupervised learning class and do not require initial cluster count to execute. In the second phase, a new chain code scheme is proposed to be used in representing the direction of lines and it consists of series of directional codes and corner labels found in the drawing. In the third phase, namely feature extraction algorithm, three features proposed are length of lines, angle of corners, and number of branches at each corner. These features are then used in the proposed recognition algorithm to match the line drawing, involving only mean and variance in the calculation. Comparison with SOM and AP clustering approaches resulting in up to 31% reduction for cluster count and 57 times faster. The results on corner detection algorithm shows that it is capable to detect junction and corner of the given thinned binary image by producing a new thinned binary image containing markers at their locations

Parallelization for image processing algorithms based chain and mid-crack codes

Freeman chain code is a widely-used description for a contour image. Another mid-crack code algorithm was proposed as a more precise method for image representation. We have developed a coding algorithm which is suitable to generate either chain code description or mid-crack code description by switching between two different tables. Since there is a strong urge to use parallel processing in image related problems, a parallel coding algorithm is implemented. This algorithm is developed on a pyramid architecture and a N cube architecture. Using link-list data structure and neighbor identification, the algorithm gains efficiency because no sorting or neighborhood pairing is needed. In this dissertation, the local symmetry deficiency (LSD) computation to calculate the local k-symmetry is embedded in the coding algorithm. Therefore, we can finish the code extraction and the LSD computation in one pass. The embedding process is not limited to the k-symmetry algorithm and has the capability of parallelism. An adaptive quadtree to chain code conversion algorithm is also presented. This algorithm is designed for constructing the chain codes of the resulting quadtree from the boolean operation of two quadtrees by using the chain codes of the original one. The algorithm has the parallelism and is ready to be implemented on a pyramid architecture. Our parallel processing approach can be viewed as a parallelization paradigm - a template to embed image processing algorithms in the chain coding process and to implement them in a parallel approach

Aplicaciones de la aritmética en coma fija a la representación de primitivas gráficas de bajo nivel

La aritmética en coma fija tiene la propiedad de realizar operaciones con números decimales con un coste computacional entero. A pesar de no estar soportada de forma nativa por los lenguajes de programación y por las CPUs generalistas, es la aritmética ideal para aplicaciones de control industrial, simulación, informática gráfica, multimedia y señal digital, etc. Su falta de normalización y soporte impide su uso extendido en muchos campos de la informática. Esta tesis justifica la utilización de esta aritmética en el campo de los gráficos por computador. A partir de un estudio de implementación y normalización de la aritmética, se estudian incrementos de potencia relativos y precisiones obtenidas y su aplicación a la simulación discreta y de vuelo. Se analizan los algoritmos de dibujo de primitivas básicas como las líneas, con y sin aliasing, su recortado y el dibujo de circunferencias y elipses. Se presentan algunas implementaciones de algoritmos basados en la coma fija y se analiza la mejora del coste computacional y de la precisión obtenida respecto de los algoritmos de fuerza bruta y de los tradicionales. Mientras los algoritmos tradicionales suelen entregar un error comprendido entre los 0.32 y 0.45 píxeles, dependiendo de la primitiva analizada, los algoritmos basados en la coma fija no superan los 0.25 de media, igualando el error teórico generado por los algoritmos de fuerza bruta. Por otro lado, los algoritmos basados en la aritmética en coma fija suelen mejorar la velocidad media de los algoritmos tradicionales, pudiéndose a veces conseguir aceleraciones elevadas si se utilizan técnicas de paralelización. Éste sería el caso de la versión paralela del algoritmo DDA con y sin antialiasing que podría dibujar una recta con coste temporal logarítmico respecto de su longitud en píxeles. Los algoritmos obtenidos son tan sencillos que pueden ser implementados algunos de ellos en hardware dentro de un procesador gráfico de forma muy eficiente.Mollá Vayá, RP. (2001). Aplicaciones de la aritmética en coma fija a la representación de primitivas gráficas de bajo nivel [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/15406Palanci