Jamaludin Ali

Universiti Sains Malaysia | USM · School of Mathematical Sciences

The construction of curves need to satisfy some conditions in order to achieve smooth pathways. In terms of designing highways, there are five design templates of transition curves. Usually, cubic and quintic Bézier curves are used to construct those five templates. However, quintic trigonometric Bézier curves can also be used to construct these fi...

This paper presents a path or curve generated based on Bezier curve. Derivation of smooth curve is one important subject for good visualization. Bezier curve is a smooth parametric curve but it is not a simple problem to properly assign its control points to determine the shape of the Bezier curve. Therefore, the Bezier curve of n-th order is deriv...

This paper describes a new function called quintic trigonometric Bezier curve that has the potential to estimate the maximum driving speed allowed for safe driving on roads. The shape parameters present in this trigonometric Bezier function gives more flexibility for users in designing highways. Since the curves do interpolate the points, small cha...

This paper describes the general method to develop S-shaped and C-shaped transition curves using Cubic Trigonometric Bezier Curve with two shape parameters which satisfy G² Hermite condition. Some numerical examples of S-shaped and C-shaped transition curve segment are presented.

This paper describes an alternative way in estimating design speed or the maximum speed allowed for a vehicle to drive safely on a road using curvature information from Bezier curve fitting on a map. We had tested on some route in Tun Sardon Road, Balik Pulau, Penang, Malaysia. We had proposed to use piecewise planar quintic Bezier curve while sati...

In scientific application and Computer Aided Design (CAD), users usually need to generate a spline passing through a given set of data, which preserves certain shape properties of the data such as positivity, monotonicity or convexity. The required curve has to be a smooth shape-preserving interpolant. In this paper a rational cubic spline in Timme...

The fifth degree of trigonometric Bézier curve called quintic with two shapes parameter is presented in this paper. Shape parameters provide more control on the shape of the curve compared to the ordinary Bézier curve. This technique is one of the crucial parts in constructing curves and surfaces because the presence of shape parameters will allow...

This study was concerned with shape preserving interpolation of 2D data. A piecewise C¹ univariate rational quadratic trigonometric spline including three positive parameters was devised to produce a shaped interpolant for given shaped data. Positive and monotone curve interpolation schemes were presented to sustain the respective shape features of...

The main purpose of this paper is shape-preserving interpolation for visualization of constrained data that will be smooth and pleasant. A rational cubic Ball function with three shape parameters will be introduced and used. A rational cubic Ball function is constructed according to the shape of the data that are constraint between two lines using...

This study was concerned with shape preserving interpolation of 2D data. A piecewise C 1 univariate rational quadratic trigonometric spline including three positive parameters was devised to produce a shaped interpolant for given shaped data. Positive and monotone curve interpolation schemes were presented to sustain the respective shape features o...

Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, curvature is the amount by which...

In this paper, the classification of two dimension objects under the projective transformation group, interested group in computer vision, is presented. Results between the proposed invariants with previous invariant features are compared to show the performance of the method.

A new way of designing font is developed for the font using Radial Basis Function. The approach using Radial Basis Function is used on the interpolation of point. The data point will be used to generate the curve which will then form the shape of the font. To generate the curve, we will use the general cubic spline which will use the data points to...

Parameterization techniques being a crucial part in constructing curves and surfaces. By integrating parameterization into Bezier curve, researchers manage to breed new types of curves that can be altered the way we dictate the shape of curves and surfaces by changing the values of parameters without changing the control points. Therefore, by using...

In scientific application and Computer Aided Design (CAD), users usually need to generate a spline passing through a given set of data which preserves certain shape properties of the data such as positivity, monotonicity or convexity [1]. The required curves have to be a smooth shape-preserving interpolation. In this paper a rational cubic spline i...

A new approach in verification of offline handwriting signature had been proposed. This approach use alpha-cut of triangular fuzzy number in verification of the signature where the value of alpha-cut will reduce the interval of confidence fuzzy interval. The best value of alpha-cut will make the confidence fuzzy interval in the smallest interval wh...

Blending method can be used to design many interesting curves, surfaces and objects. Some types of blending methods are linear, quadratic and cubic blending. These methods have similar concept to Bézier because the blending method only touch the first and last curve or surface without touching the intermediate curves or surfaces. These methods prod...

Segments of two given circular arcs can be blended to produce a segment of a new curve. The new curve that been produced which also known as blending curve is form in a C-shape. That’s mean the two circular arcs are blend at the same endpoints. Bezier Curve refer to [1] is the main application in this construction of blending curve. As the two circ...

This work presents invariants for planar curves with respect to the projective groups. Novel integral potentials for 2D curves are used to derive these invariants under the action of projective group with six degrees of freedom, based on Cartan’s theory of moving frame. Examples are given to support the work.

In this paper, we construct a cubic trigonometric Bézier curve with two shape parameters on the basis of cubic trigonometric Bernstein-like blending functions. The proposed curve has all geometric properties of the ordinary cubic Bézier curve. Later, based on these trigonometric blending functions a C 1 rational trigonometric spline with four shape...

Timmer function was introduced by Harry Timmer but the function did not get enough exposure since it did not satisfy the convex hull property. This function is an advance of Bezier function. The function is used in this paper as it produce a curve that near the control polygon and it easier to use as blending function. This function is being starte...

We discuss the problem of monotonicity preservation of surfaces through 3D monotone data. This can be done using a rational bi-cubic blended function that is an extension of a rational cubic function in the form of a cubic numerator and quadratic denominator. The function involves twelve shape parameters in each rectangular patch. Data dependent co...

A piecewise rational cubic function in the form of a cubic/quadratic has been extended to a rational bi-cubic blended function to visualize 3D convex data. It involves twelve shape parameters in each rectangular mesh for its representation. Simple data-dependent constraints are imposed on four shape parameters to conserve convexity of convex data....

This paper deals with the shape preserving interpolation problem for visualization of 3D positive data. A required display of 3D data looks smooth and pleasant. A rational bi-cubic function involving six shape parameters is presented for this objective which is an extension of piecewise rational function in the form of cubic/quadratic involving thr...

We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data using C 2 rational cubic sp...

This study is concerned with the visualization of monotone data using a piece-wise C1 rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational rigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free...

In CAD/CAM systems, rational polynomials, in particular the Bezier or NURBS forms, are useful to approximate the circular arcs. In this paper, a new representation method by means of rational cubic Timmer (RCT) curves is proposed to effectively represent a circular arc. The turning angle of a rational cubic Bezier and rational cubic Ball circular a...

Abstract. We discussed the transition curve of G 2 Hermite interpolation of boundary data that consist of two points, two unit tangent vectors, and two signed curvatures at those points, by using Bezier quartic spline of degree 4. It is shown that the solution of G 2 Hermite interpolation problem can be found by combining S-shape or C-shape transi...

In this paper a rational cubic function in the form of cubic/quadratic, with three shape parameters has been developed. Data dependent sufficient constraints are derived for one of these shape parameter to preserve the shape of constrained data that is lying above the straight line. Remaining two of these shape parameters are left free for designer...

In this paper, a class of quasi-quintic trigonometric Bezier curve with two shape parameters, based on newly constructed trigonometric basis functions, is presented. The new basis functions share the properties with Bernstein basis functions, so the generated curves inherit many properties of traditional Bezier curves. The presence of shape paramet...

This paper reports on a family of smooth transition curve rendered by a pair of Bezier quartic spiral. The family of Bezier quartic spiral form which was introduced has six degrees of freedom and will give advantage on diversity of the transition curve in the given constraints. Fair curves often referred on geometrical continuity G2 and monotonical...

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using a piecewi...

This work addresses the shape preserving interpolation problem for visualization of positive data. A piecewise rational function in cubic/quadratic form involving three shape parameters is presented. Simple data dependent conditions for a single shape parameter are derived to preserve the inherited shape feature (positivity) of data. The remaining...

The rational quadratic trigonometric Bézier curve with two shape parameters is presented in this paper, which is new in literature. The purposed curve inherits all the geometric properties of the traditional rational quadratic Bézier curve. The presence of shape parameters provides a control on the shape of the curve more than that of traditional B...

An improvised algorithm is proposed based on the work of Yoshimoto and Harada. The improvised algorithm results a graph which is called LDGC or Logarithmic Distribution Graph of Curvature. This graph has the capability to identify the beauty of monotonic planar curves with less effort as compared to LDDC by Yoshimoto and Harada.

The Generalized Cornu Spiral (GCS) was first proposed by Ali et al. in 1995 [9]. Due to the monotonocity of its curvature function, the surface generated with GCS segments has been considered as a high quality surface and it has potential applications in surface design [2]. In this paper, the analysis of GCS segment is carried out by determining it...

This paper dwells in developing a general algorithm for constructing a piecewise Ball Curve with curvature continuity (GC2). The proposed algorithm requires GC2 data in which the designer must define unit tangent vectors and signed curvatures at each interpolating points. As a numerical example, a vase is constructed using GC2 piecewise Ball Curve

Basis polynomials of quartic and quintic parametric interpolations are discussed to interpolate given data points. The aim is constructing a curve that exactly interpolates all data points. Besides, the shape of curve can be controlled by using parameters t and changing the magnitude of tangents, α and β. When large number of data points is given,...

In this paper, the method of finding the line constrained between two quadratic Bezier curves and also finding the line constrained between a quadratic Bezier curve and a circle is presented. The application of the line constrained can be used in the construction of railway tracks between any obstacle or rolling a ball to the other side of a wall i...

Branching is a process of connecting two adjacent contours called base and branch contours where the numbers of sub contours for each of both contours are different. All points between the contours have to be correctly paired to avoid a twisting surface. In contours connection, continuity is an issue to ensure the surface fit to the required smooth...

In this paper, we analyze the planar cubic Alternative curve to determine the conditions for convex, loops, cusps and inflection points. Thus cubic curve is represented by linear combination of three control points and basis function that consist of two shape parameters. By using algebraic manipulation, we can determine the constraint of shape para...

In CAGD/CAD research and education, users are involved with development of mathematical algorithms and followed by the analysis of the resultant algorithm. This process involves geometric display which can only be carried out with high end graphics display. There are many approaches practiced and one of the so-called easiest approaches is by using...

This paper focuses on multi-slice image reconstruction for CT images using Beta-spline. In reconstructing multi-slice images especially from living image, issues like continuity and accuracy contours arise. Commonly, high continuity is hard to be achieved because of the accuracy requirement and vice versa. Thus the image reconstruction process is p...

Many of the researchers or designers are mostly used the involute curves (known as one of the approximation curves) to design the profile of gears. This study intends to develop the transition (S transition and C spiral) curves using Bézier–like cubic curve function with G 2 (curvature) continuity as the degree of smoothness. Method of designing th...

In Computer Aided Geometric Design (CAGD), it is often needed to produce a positivity–preserving curve according to the given positive data. The main focus of this work is to address the problem of visualizing positive data in such a way that its display looks smooth and pleasant. A rational cubic spline function with three shape parameters has bee...

Beta-spline was developed in 1981 by Brian A. Barsky with the capability to preserve the G2 continuity, which is the main criterion insuccessfulcurve fitting. This curve is also well known with its two controlparameters that can be used in controlling the curve shape. The Beta-splinecurve was extended to several types to increase the locality contr...

This paper deals with problem of shape preserving interpolations for visualization of constrained data arranged on rectangular grid. The main focus of work is on the graphical display of constrained surface data in such a way that it is a smooth, pleasant as well as preserves the shape of data. A rational bi-cubic function has been developed for th...

This paper presents a result of approximation an arc circles by using a quartic Bezier curve. Based on the barycentric coordinates of two and three combination of control points, the interior control points are determined by forcing the curvature at median point as similar as the given curvature at end points. Hausdorff distance is used to investig...

The main focus of this paper is on the construction of S-shaped transition curve and extended to 2D and 3D spur gear tooth design. The curve and design is generated by using Cubic Trigonometric Bézier (T-Bézier, for short) function with two shape parameters and it has more flexibility for the interactive design due to low degree and presence of sha...

Designers in industries need to generate splines which can interpolate the data points in such a way that they preserve the inherited shape characteristics (positivity, monotonicity, convexity) of data. Among the properties that the spline for curves and surfaces need to satisfy, smoothness and shape preservation of given data are mostly needed by...

In this paper, the problem of shape preserving positive surface data visualization has been discussed. The visualization has been made in such a way where it presents a smooth, visually pleasant and interactive view of positive surface. An attempt has been made to extend the rational cubic function to a partially bi-cubic blended rational function...

An involute curve (or known as an approximated curve) is mostly used in designing the gear teeth (profile) especially in spur gear. Conversely, this study has the intention to redesign the spur gear teeth using the transition (S transition and C spiral) curves (also known as the exact curves) with curvature continuity (G2) as the degree of smoothne...

Transition curves with monotone curvature profile are widely applied in fair curve design. Advantage of using transition curve is that it can avoid the undesirable curvature extrema. Demonstration of transition curve in designing surface of revolution, particular of vase design can be often seen in literature. For these demonstrations, authors main...

A quartic trigonometric Bézier curve with two shape parameters based on newly constructed trigonometric basis functions is presented in this paper. The curve is drawn by using end point curvature conditions and carries all the geometric features of the ordinary quartic Bézier curve. The presence of shape parameters provides an opportunity to adjust...

In this paper, a newly constructed rational quadratic trigonometric Bézier curve with two shape parameters is presented. The purposed curve enjoys all the geometric properties of the traditional rational quadratic Bézier curve. The local control on the shape of the curve can be attained by altering the values of the shape arameters as well as the w...

In this paper, we extended the rational cubic function to rational bi-cubic function that presents a smooth, visually pleasant and interactive view of monotonicity preserving surface. Moreover, it involves six free parameters in its description. These free parameters are arranged in such a way where two of these are constrained to preserve the mono...

The main purpose of this paper is the visualization of convex data that results in a smooth, pleasant, and interactive convexity-preserving curve. The rational cubic function with three free parameters is constructed to preserve the shape of convex data. The free parameters are arranged in a way that two of them are left free for user choice to ref...

Human head is one of the most detail parts of human body. Reconstruction of human head must be precise to avoid misinformation of the product. Furthermore, head reconstruction especially face is used in several significant applications such as face recognition, head surgery, and face simulation. This study employs cubic Beta-spline as the fitted cu...

In this work, we have constructed a quadratic trigonometric Bézier curve with single shape parameter which is analogous to quadratic Bézier curve. We have adjusted the shape of the curve as desired, by simply altering the values of shape parameter, without changing the control polygon. The quadratic trigonometric Bézier curve can be made closer to...

In this paper, a visualization of positive data is made in such a fash-ion where it presents a smooth, pleasant and eye catching view of the positive surface to viewer. An attempt has been made in order to ex-tend a rational cubic function into a rational bi-cubic function for the preservation of positive data arranged over rectangular grid in the...

Beta-spline is built on G 2 continuity which guarantees smoothness of generated curves and surfaces using it. This curve is preferred to be used in object design rather than reconstruction. This study however, employs the Beta-spline in reconstructing a 3-dimensional G 2 image of the Stanford Rabbit. The original data consists of multi-slice binary...

In this paper, an attempt has been made to construct a shape preserving rational bi-cubic interpolant (cubic/quadratic) with twelve free parameters to depict a more pleasant and smooth display of positive surface through positive data. Simple data dependent constraints are derived for four free parameters to preserve the positivity of data while th...

The Generalized Cornu Spiral (GCS) was first proposed by Ali et al. in 1995 [1, 9]. Due to the monotonocity of its curvature function, the surface generated with GCS segments has been considered as a high quality surface and it has potential applications in surface design [12]. In this paper, the analysis of GCS segment is carried out by determinin...

This paper is concerned with finding approximate solution for the hypersingular integral equations. It is well known that hypersingular integrals are exist, if the density function f satisfied Hölder-continuous first derivative, i.e f∈C 1,α [-1,1]. Relating the hypersingular integrals to Cauchy principal-value integrals, we expand the kernel and th...

The main spotlight of this paper is the visual display of constrained data that looks smooth, pleasant and attractive. A C 1 piecewise rational cubic function has been constructed to preserve the shape of constrained data. The piecewise rational cubic function has three free parameters in its description. One free parameter is constrained to preser...

The process to reconstruct the curve or surfaces in CAGD should begin with the boundary extraction of the original image. The feature and the information of the image can be obtained from the boundary of the image. This process can help us to implement the other processes such as data extraction, corner detection, curves fitting or surface reconstr...

In this paper, we construct an S-shaped transition curve and spur gear tooth model. The attempt has been made to use the circle to circle technique an S-Shaped transition curve by using Cubic Trigonometric Bezier function (TBezier, for short) with two shape parameters . The shape parameters are used to control the S-shaped transition curves and pro...

This paper described the application of Generalised Cornu Spiral (GCS) in aesthetic design. The aim of using GCS in aesthetic design is because of it has the excellent curvature properties – the rational linear curvature profile. GCS is a transcendental function. Thus it is important to approximate the GCS by polynomial curve. The approximation is...

This paper presents the analysis of duct design using static and dynamic approaches. The static approach is used to find out applicability between the design and material applied. The material used in this paper is Thermoplastic Olefins (TPO). For the dynamic approach, the focusing is only on the CFD simulations. The fatigue life in this design and...

The main spotlight of this work is to visualize the monotone data to envision of very smooth and pleasant monotonicity preserving curves by using piecewise rational cubic function. The piecewise rational cubic function has three shape parameters in each interval. We derive a simpler constrains on shape parameters which assurance to preservation of...