Data visualization using rational spline interpolation

AbstractA smooth curve interpolation scheme for positive, monotonic, and convex data has been developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The rational spline scheme has a unique representation. The degree of smoothness attained is C1

Convexity-preserving Bernstein–Be´ zier quartic scheme

A C1 convex surface data interpolation scheme is presented to preserve the shape of scattered data arranged over a triangular grid. Bernstein–Be´ zier quartic function is used for interpolation. Lower bound of the boundary and inner Be´zier ordinates is determined to guarantee convexity of surface. The developed scheme is flexible and involves more relaxed constraints

Circular Arc Approximation by Quartic H-Bézier Curve

The quartic H-Bézier curve is used for the approximation of circular arcs. It has five control points and one positive real free parameter. The four control points are carried out b

Positive Data Visualization Using Trigonometric Function

A piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of developed interpolant is

Monotone Data Visualization Using Rational Trigonometric Spline Interpolation

Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically

Shape Designing of Engineering Images Using Rational Spline Interpolation

In modern days, engineers encounter a remarkable range of different engineering problems like study of structure, structure properties, and designing of different engineering images, for example, automotive images, aerospace industrial images, architectural designs, shipbuilding, and so forth. This paper purposes an interactive curve scheme for designing engineering images. The purposed scheme furnishes object designing not just in the area of engineering, but it is equally useful for other areas including image processing (IP), Computer Graphics (CG), Computer-Aided Engineering (CAE), Computer-Aided Manufacturing (CAM), and Computer-Aided Design (CAD). As a method, a piecewise rational cubic spline interpolant, with four shape parameters, has been purposed. The method provides effective results together with the effects of derivatives and shape parameters on the shape of the curves in a local and global manner. The spline method, due to its most generalized description, recovers various existing rational spline methods and serves as an alternative to various other methods including v-splines, gamma splines, weighted splines, and beta splines

Circular Arc Approximation by Quartic H-Bézier Curve

The quartic H-Bézier curve is used for the approximation of circular arcs. It has five control points and one positive real free parameter. The four control points are carried out b

Reverse engineering of planar objects using gas

An automatic approach, for reverse engineering of digitized hand printed and electronic planar objects, is presented which is useful for vectorizing the generic shapes. The rational cubic functions were used to find the optimal solution of the curve fitting problem with the help of a soft computing technique genetic algorithm which finds appropriate values of shape parameters in the description of rational cubic functions

C1 positive scattered data interpolation

AbstractA local C1 surface construction scheme is presented to preserve the shape of positive scattered data arranged over a triangular grid. Each boundary curve of the triangle is constructed by a rational cubic function with two free parameters, and this rational function is also used for the side-vertex interpolation. The final surface patch is constructed by taking the convex combination of three side-vertex interpolants. For each triangular patch there are three boundary curves and three side-vertex interpolants. Simple sufficient data dependent constraints are derived on these free parameters to preserve the shape of the positive scattered data. The developed scheme is not only local and computationally economical but visually pleasing as well