Natasha Dejdumrong

Efficient Algorithms for Non-Rational and Rational Bézier Curves

In this paper, a new basis with linear computational complexity has been introduced and used to form non-rational and rational curves. Two algorithms for computing points on non-rational and rational proposed curves are expressed with their linear complexity. Moreover, the relationships between these proposed curves and the Bezier curves, for both non-rational and rational forms, are given by using polar form and homogeneous coordinate approaches. Consequently, two efficient algorithms with linear complexity have been introduced to be used in drawing non-rational and rational Bezier curves.

Monomial Forms for Curves in CAGD with their Applications

There are several methods used for plotting curves in CAGD, e.g., by directly computing their basis functions (polynomials) or using their recursive algorithms. For the former method, evaluating a curve using their basis functions is a tedious task because their equations need to be solved by using complicated formulae computations. Whereas for the latter method, implementing a program by using recursive algorithm is simpler than the former method but it takes more computational time. Thus, an alternative method for constructing curves by using the monomial form is introduced. Employing monomial form approach, a curve can be computed by using monomial matrix operations. Because the matrix multiplications can be done in parallel programming, the performance of generating a curve for high degree can be increased. In the mean time, there exists the monomial functions for any degree Bézier curves. However, there has been no monomial functions for any other kinds of CAGD curves. This work proposes several monomial functions for Said-Ball, Wang-Ball, DP, Dejdumrong and NB1 curves. Consequently, these monomial functions will be useful and convenient for readily computing the derivatives, degree elevations, degree reductions and conversions among these curves.

A Shape Preserving Verification Technique for Parametric Curves

Typically, the shape preserving property for a parametric curve can be verified by checking for the total positivity of the collocation matrix or finding the existence of corner cutting algorithm as presented in [8]. However, there are several cases that although the curve is satisfied the shape preserving property, the shape of the curve does not preserve the shape of the control points, e.g., Delgado-Pena curves (DP curves). Hence, an alternative algorithm for the shape preserving verification was proposed based on five factors for verifying shape preserving property: the position of the control points, the order of the control points, the type of the curve, the weights of the rational curves, and the number of duplicate control points. Ultimately, four varieties of parametric curves, e.g., Bezier, Said-Ball, Wang- Ball and DP Curves, were verified and compared for their shape preserving property.

Approximating Online Handwritten Image by Bézier Curve

In this paper, a Bezier curve is construct to represent a hand-drawn image, expressed in the forms of a set of consecutive dots. Using inputs sampling points, an online handwritten curve is converted into a vectored curve by Newton-Lagrange interpolation. Although Newton-Lagrange curve can be used well in the approximation of the handwritten curve, their polynomials are not appropriate in the applications of computer aided geometric design (CAGD). Therefore, Newton-Lagrange curve will then be converted into a corresponding Bezier curve. Ultimately, the final result from the conversion can be expressed in the forms of the Bezier control points. As a result, these Bezier curve represents the given handwritten curve image.

Multiple degree elevation and constrained multiple degree reduction for DP curves and surfaces

In this paper, the problem of single and multiple degree elevation and reduction for DP curves and surfaces is considered and expressed in matrix representations. Using monomial matrix representations of the univariate DP polynomials, single and multiple degree elevation matrices can be derived by minor extension of this monomial matrix. Given this result, matrices of constrained single and multiple degree reduction can be readily obtained. Finally, important and sufficient conditions for degree reduction can also be found from these resulting matrices.

Online Handwriting Thai Character Recognition

This research is a study of structure and method in handwriting Thai characters for conversion and computer use. This paper covers the creation of an online handwriting recognition system through the use of linear interpolation approach. The character sampling is done with 10 significant points for the vector creations of angles and rotation directions. The linear-interpolated characters will then be compared with an XML database in which contains predefined character information. The best matched character is then further analyzed for character uniqueness such as tail and size before concluding the found character(s). This system supports the writing of different character styles including slanted, scaled and rotated characters. The average recognition rates are of 90.88% correctness for matched character and 98.75% correctness for a candidate group of found characters in which is satisfactory and effective for Thai handwriting character recognition.

An Approach to the Feature-Based Comparisons for the Rational Curves

In image processing, the curve comparisons can be achieved by extracting the curve information from the bitmapped images. The revealed curves are represented in the forms of the sets of pixel information. Thus, the determination of curve matching is to compare pixel by pixel, which is time consuming. On the contrary, for vector graphics images, there have been no methods written in the literatures referred about directly comparing the parametric curves either in the rational or non-rational (polynomial) forms. In this paper, the relationships between two curves can be classified into 4 main categories: curve congruence, curve proportion, curve similarity and curve difference. The comparison algorithms for two given parametric curves either non-rational or rational curves are then established. These algorithms can be simply determined by verifying some important geometric features, e.g., the blending functions, the locations of their control points and their weights. In this connection, since a rational curve can be transformed into a non-rational one, the curve comparison algorithms for polynomial curves can also be applied for the cases of the rational curves.

Rational DP-Ball Curves

In this paper, a normalized totally positive (NTP) basis given by Delgado and Pena is used to form non-rational and rational DP-Ball curves. The relationships between rational Bezier and rational DP-Ball curves are given using homogeneous coordinates. Consequently, an efficient algorithm with linear computational complexity is introduced in order to be used in evaluating the points on rational Bezier curve. Although the elegant de Casteljau algorithm is proven to be simple and stable. Unfortunately, compared with the linear time complexity of the proposed algorithm, it is not efficient. This algorithm can be used as an alterative algorithm to the popular Wang algorithm

Rice Phenology Monitoring Using PIA Time Series MODIS Imagery

This paper presents the method to determine rice cropping pattern in Thailand for future prediction of water supply demand, pricing, and other related issues including governmental policies. Datasets was obtained from an orbital instrument called a Moderate-Resolution Imaging Spectroradiometer (MODIS) operated by NASA. A Normalized Difference Vegetation Index (NDVI) was derived from MODIS datasets once every 16 days. This image data has been analyzed using image processing techniques in order to determine rice cropping area in Thailand. Rice cropping data is represented as a time series displaying type of rice crop in which peak data points indicate rice cropping cycle in each year. A Progressive Iterative Approximation (PIA) is used for signal smoothing and reducing noise by providing a Bezier curve representation of time-series data. The experimental results show that using PIA technique for noise reduction yields better results comparing with a common filtering method like Savitzky Golay filter.

Thai Font Type Recognition Using Linear Interpolation Analysis

A new approach to Thai font type recognition that is presented in this paper is based on linear interpolation analysis of the character contour. The algorithm can perform effectively and classify font type obviously. The same font type show high similarity coefficient which is 83.95 but the different font types is below 35.54.