Image segmentation and preserve the boundary of the image using b-spline basis

This paper focuses the knot insertion in the B-spline collocation matrix, with nonnegative determinants in all n x n sub-matrices. Further by relating the number of zeros in B-spline basis as well as changes (sign changes) in the sequence of its B-spline coefficients. From this relation, we obtained an accurate characterization when interpolation by B-splines correlates with the changes leads uniqueness and this ensures the optimal solution. Simultaneously we computed the knot insertion matrix and B-spline collocation matrix and its sub-matrices having nonnegative determinants. The totality of the knot insertion matrix and B-spline collocation matrix is demonstrated in the concluding section by using the input image and shows that these concepts are fit to apply and reduce the errors through mean square error and PSNR values

Approximation of Generalized Ovals and Lemniscates towards Geometric Modeling

This paper considers an approach towards the building of new classes of symmetric closed curves with two or more focal points, which can be obtained by generalizing classical definitions of the ellipse, Cassini, and Cayley ovals. A universal numerical method for creating such curves in mathematical packages is introduced. Specific aspects of the provided numerical data in computer-aided design systems with B-splines for three-dimensional modeling are considered. The applicability of the method is demonstrated, as well as the possibility to provide high smoothness of the curvature profile at the specified accuracy of modeling.

Utilización de bases wavelet para la resolución numérica de ecuaciones diferenciales

En este trabajo de tesis se estudiaron estrategias matemáticas orientadas en particular, a la resolución numérica de operadores diferenciales del tipo Lu = f mediante el método Wavelet-Galerkin (W-G). El marco proporcionado por el Análisis Multirresolución (AMR) permitió analizar y formalizar el diseño de una técnica numérica con cuya implementación se lograron óptimos resultados. La estructura AMR de las B-splines cúbicas sugiere la definición de una base sobre intervalo con un requerimiento extra de ortogonalidad sobre sus derivadas entre distintas escalas de aproximación. Se desarrolló en esta tesis un método para la confección de esta base, teniendo en cuenta su estructura sobre intervalo y estudiando en particular las wavelets de borde y sus específicas condiciones de suavidad y soporte. Al aplicar W-G esta particular estrategia conduce a matrices de rigidez ralas o esparcidas, o bien diagonales por bloques, donde además cada bloque suele ser una matriz banda. Así estas propiedades garantizan matrices bien condicionadas, con número de condición pequeño, acotado e independiente del nivel de aproximación. Esto permite definir algoritmos de alta eficiencia computacional logrando resultados con elevada convergencia a la solución y bajo costo computacional.

Solitary waves of the RLW equation via least squares method

Integration using least squares method in space and Crank–Nicolson approach in time is managed to set up an algorithm to solve the RLW equation numerically. Trial functions in the least square method consist of a combination of the quartic B-spline functions. Integration of the RLW equation gives a system of algebraic equations. The solutions consisting of a combination of the quartic B-splines are given for some initial and boundary value problems of RLW equation.

A Multi(two)-Nozzle Cable-Driven Parallel Robot For 3D Printing Building Construction: Path Optimization and Vibration Analysis

This paper proposes a multi-nozzle cable-driven parallel robot for 3D printing building construction. This system has two independently moving nozzles mounted on the existing printing head. The printing time can be reduced dramatically with this system as the travel path of the printing head can be reduced to almost half thanks to those two nozzles that print almost half of the printing contour. To fully take advantage of two nozzle structures effectively, the path of the printing head is optimized to secure the minimum travel length of both the printing head and two nozzles. The smoothness of the optimal path is secured by applying the non-uniform rational B-splines (NURBS). In addition, free vibration of the proposed CDPR printer’s structure is analyzed to improve the printing quality and help the control of the proposed CDPR plain by using a finite element formulation of cables of the proposed robot.