Ternary Interpolatory Subdivision Research Articles

Joint spectral radius and ternary hermite subdivision

In this paper we construct a family of ternary interpolatory Hermite subdivision schemes of order 1 with small support and {mathscr{H}}mathcal {C}^{2}-smoothness. Indeed, leaving the binary domain, it is possible to derive interpolatory Hermite subdivision schemes with higher regularity than the existing binary examples. The family of schemes we construct is a two-parameter family whose {mathscr{H}}mathcal {C}^{2}-smoothness is guaranteed whenever the parameters are chosen from a certain polygonal region. The construction of this new family is inspired by the geometric insight into the ternary interpolatory scalar three-point subdivision scheme by Hassan and Dodgson. The smoothness of our new family of Hermite schemes is proven by means of joint spectral radius techniques.

A Nonstationary Ternary 4-Point Shape-Preserving Subdivision Scheme

This paper uses the continued fraction technique to construct a nonstationary 4-point ternary interpolatory subdivision scheme, which provides the user with a tension parameter that effectively handles cusps compared with a stationary 4-point ternary interpolatory subdivision scheme. Then, the continuous nonstationary 4-point ternary scheme is analyzed, and the limit curve is at least C 2 -continuous. Furthermore, the monotonicity preservation and convexity preservation are proved.

Fractal behavior of ternary 4-point interpolatory subdivision scheme with tension parameter

In this paper, the fractal curves and surfaces of ternary 4-point interpolatory subdivision scheme are developed and analyzed. The fractal range of the tension parameter has also been determined. The behavior of fractal curves and surfaces corresponding to different values of parameter has been depicted through six examples which offers direct means for an effective generation of subdivision fractals. The real life applications of the proposed fractal subdivision scheme has also been demonstrated.

Generation of fractal curves and surfaces using ternary 4-point interpolatory subdivision scheme

In this paper, the generation of fractal curves and surfaces along with their properties, using ternary 4-point interpolatory subdivision scheme with one parameter, are analyzed. The relationship between the tension parameter and the fractal behavior of the limiting curve is demonstrated through different examples. The specific range of the tension parameter has also been depicted, which provides a clear way to generate fractal curves. Since the fractal scheme introduces, in the paper, have more number of control points therefore it gives more degree of freedom to control the shape of the fractal curve.

Fractal generation using ternary 5-point interpolatory subdivision scheme

This paper is devoted to explore the generation of fractal curves and surfaces using ternary 5-point interpolatory subdivision scheme. The fractal behavior of the limiting curves and surfaces is analyzed with the help of tension parameter. It may be noted that the proposed fractal scheme determines two intervals of range of shape control parameter. The behavior of the shape control parameter for the generation of fractals has been visualized through five examples which provides faster rate of generation of fractals.

A Nonlinear Ternary Circle-Preserving Interpolatory Subdivision Scheme

In this paper, we present a new nonlinear ternary interpolatory subdivision scheme which has the properties of convexity-preserving, circle-preserving and the limit curve iscontinuous. In each subdivision step, the newly generating points will be on the circle determined by the interpolatory point and its adjacent points. Numerical examples show that this algorithm is simple and curves generated by this subdivision scheme are fair curves.

IDSS: A Novel Representation for Woven Fabrics

The appearance of woven fabrics is intrinsically determined by the geometric details of their meso/micro scale structure. In this paper, we propose a multiscale representation and tessellation approach for woven fabrics. We extend the Displaced Subdivision Surface (DSS) to a representation named Interlaced/Intertwisted Displacement Subdivision Surface (IDSS). IDSS maps the geometric detail, scale by scale, onto a ternary interpolatory subdivision surface that is approximated by Bezier patches. This approach is designed for woven fabric rendering on DX11 GPUs. We introduce the Woven Patch, a structure based on DirectX’s new primitive, patch, to describe an area of a woven fabric so that it can be easily implemented in the graphics pipeline using a hull shader, a tessellator and a domain shader. We can render a woven piece of fabric at 25 frames per second on a low-performance NVIDIA 8400 MG mobile GPU. This allows for large-scale representations of woven fabrics that maintain the geometric variances of real yarn and fiber.

TERNARY INTERPOLATORY SUBDIVISION SCHEMES ORIGINATED FROM SPLINES

A generic technique for construction of ternary interpolatory subdivision schemes, which is based on polynomial and discrete splines, is presented. These schemes have rational symbols. The symbols are explicitly presented in the paper. This is accompanied by a detailed description of the design of the refinement masks and by algorithms that verify the convergence of these schemes. In addition, the smoothness of the limit functions is investigated. The ternary subdivision schemes, whose construction is based on continuous splines, become tools for fast computation ofıory s of arbitrary order at triadic rational points.

A new ternary interpolatory subdivision scheme for polyhedral meshes with arbitrary topology

Interpolation using ternary subdivision is an attractive characteristic in geometric modeling due to its advantage over commonly used binary subdivision. In this paper, a new ternary interpolatory subdivision scheme with one parameter based on arbitrarily triangular meshes is proposed. It can be used to any polyhedral meshes with arbitrary topology. The sufficient conditions of the convergence and the tangent plane continuity of the presented subdivision scheme are obtained using geometric methods and algebraic manipulations. It is simple, fast and has a better local property in comparison with the existing ternary interpolatory surface subdivision schemes.

An interpolating 4-point [formula omitted] ternary non-stationary subdivision scheme with tension control

In this paper we present a non-stationary 4-point ternary interpolatory subdivision scheme which provides the user with a tension parameter that, when increased within its range of definition, can generate C 2 -continuous limit curves showing considerable variations of shape. As a generalization we additionally propose a locally-controlled C 2 -continuous subdivision scheme, which allows a different tension value to be assigned to every edge of the original control polygon.

Fractal range of a 3-point ternary interpolatory subdivision scheme with two parameters

Abstract In this paper, we analyze the fractal property of Hassan’s 3-point ternary interpolatory subdivision scheme with two parameters. The fractal range of the scheme is obtained and illustrated. Many examples show that the obtained results suggest a clear direction to generate fractal curves and surfaces by using this scheme.

Effect of the two Hassan-Dodgson Parameters on the Shape of 3-point Ternary Interpolatory Subdivision Curve

Article Effect of the two Hassan-Dodgson Parameters on the Shape of 3-point Ternary Interpolatory Subdivision Curve was published on September 1, 2006 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 7, issue 3).

Fractal properties of interpolatory subdivision schemes and their application in fractal generation

In this paper, we present a novel method to analyze the fractal properties of the 4-point binary and the 3-point ternary interpolatory subdivision schemes. The relationship between the parameter and the fractal behavior of the limit curve of the two schemes is obtained, respectively. As an application of the obtained results, the generation of fractal curves and surfaces is discussed. Many examples show that the results presented in this paper offer a direct means for a fast generation of fractals.

An interpolating 4-point C2 ternary stationary subdivision scheme

A novel 4-point ternary interpolatory subdivision scheme with a tension parameter is analyzed. It is shown that for a certain range of the tension parameter the resulting curve is C 2. The role of the tension parameter is demonstrated by a few examples. There is a brief discussion of computational costs.