Cubic Curve Fitting Method in Reconstruction of Chinese Calligraphy Outline

Curve plays a significant role in CAGD and brings the good impact of computers to manufacturing industries in designing 2 and 3-dimensional shapes and objects. Reconstruction of Chinese calligraphy outline based on the actual character is presented in this paper. Chinese calligraphy is the stylized artistic writings of Chinese characters. It is believed that this writing may help to express the feelings and ideas of the writers, which are difficult to be described. The shapes, smooth lines, and perfect curves are among the important qualities which are particularly emphasized in selecting good Chinese calligraphy. The Cubic B-Spline, Cubic Trigonometric Spline, and Cubic Trigonometric Bezier were used to generate the curves. The factors that have influenced the effects of the curves modifications were examined based on the changes of control polygon and the values of shape parameter. The fastest approach was then chosen by measuring the processing time required to construct the complete design. Results show the Cubic Trigonometric Bezier curve produced the closest curves to the control polygon, accurate to the actual character with λ = 1 and CPU time taken is 2.032 seconds. This is followed by Cubic Trigonometric Spline and Cubic B-Spline.

Two Extensions of the Quadratic Nonuniform B-Spline Curve with Local Shape Parameter Series

Two extensions of the quadratic nonuniform B-spline curve with local shape parameter series, called the W3D3C1P2 spline curve and the W3D4C2P1 spline curve, are introduced in the paper. The new extensions not only inherit most excellent properties of the quadratic nonuniform B-spline curve but also can move locally toward or against the fixed control polygon by varying the shape parameter series. They are C1 and C2 continuous separately. Furthermore, the W3D3C1P2 spline curve includes the quadratic nonuniform B-spline curve as a special case. Two applications, the interpolation of the position and the corresponding tangent direction and the interpolation of a line segment, are discussed without solving a system of linear functions. Several numerical examples indicated that the new extensions are valid and can easily be applied.

Offset Approximation of Rational Trigonometric Bezier ´ Curves

Offset curves are one of the crucial curves, but the presence of square root function in the representation is main hindrance towards their applications in CAD/CAM. The presented technique is based on offset approximation using rational trigonometric Bezier curves. The idea is ´ to construct a new control polygon parallel to original one. The two end points of the offset control polygon have been taken as exact offset end points, while the middle control points and weights have been computed using definition of parallel curves. As a result, offsets of rational and nonrational trigonometric Bezier curves have been approximated by rational ´ cubic trigonometric Bezier curve. An error between exact and approxi- ´ mated offset curves have also been computed to show the efficacy of the method.

NEW CUBIC TIMMER TRIANGULAR PATCHES WITH C¹ AND G¹ CONTINUITY

In this study, a new cubic Timmer triangular patch is constructed by extending the univariate cubic Timmer basis functions. The best scheme that lies towards the control polygon is cubic Timmer curve and surface compared to the other methods. From the best of our knowledge, nobody has extended the univariate cubic Timmer basis to the bivariate triangular patch. The construction of the proposed cubic Timmer triangular patch is based on the main idea of the cubic Ball and cubic Bezier triangular patches construction. Some properties of the new cubic Timmer triangular patch are investigated. Furthermore, the composite cubic Timmer triangular patches with parametric continuity (C1) and geometric continuity (G1) are discussed. Simple error analysis between the triangular patches and one test function is provided for each continuity type. Numerical and graphical results are presented by using Mathematica and MATLAB.

Exact computation for existence of a knot counterexample

Previously, numerical evidence was presented of a self-intersecting Bezier curve having the unknot for its control polygon. This numerical demonstration resolved open questions in scientic visualization, but did not provide a formal proof of self-intersection. An example with a formal existence proof is given, even while the exact self-intersection point remains undetermined.

A CAD-BASED CONCEPTUAL METHOD FOR SKULL PROSTHESIS MODELLING

The geometric modeling of a personalized part of the tissue built according to individual morphology is an essential requirement in anatomic prosthesis. A 3D model to fill the missing areas in the skull bone requires a set of information sometimes unavailable. The unknown information can be estimated through a set of rules referenced to a similar yet known set of parameters of the similar CT image. The proposed method is based on the Cubic Bezier Curves descriptors generated by the de Casteljou algorithm in order to generate a control polygon. This control polygon can be compared to a similar CT slice in an image database. The level of similarity is evaluated by a meta-heuristic fitness function. The research shows that it is possible to reduce the amount of points in the analysis from the original edge to an equivalent Bezier curve defined by a minimum set of descriptors. A study case shows the feasibility of method through the interoperability between the prosthesis descriptors and the CAD environment.