Designing three dimensional graphic objects using the polynomial of trigonometric curves with a shape parameter and the sweep surface / Noor Khairiah Razali and Nursyazni Mohamad Sukri

The desired shape of Bezier and B-spline curves can be meeting by adjusting the control points, knot vectors and degrees. This adjustment was complicated and costly. In this project, the trigonometric polynomial with a shape parameter curves and rotational sweeping method was introduced as an alternative method in generating the variety of symmetrical three dimensional objects and designs easily, flexibly and less costly in time of working the calculation. The trigonometric polynomial curves were analogous to B-spline curves, but the curves can be manipulated based on the value of shape parameter, on a fixed control polygon and same control point. This property was an advantage in generating three dimensional objects using rotation sweep surface method, where the curve was rotated at y-axis with 360o degree. This polynomial was studied based on open and close uniform curves and applied in rotational sweep method to create three dimensional objects. The shape of the vase was generated as examples of three dimensional objects and the variety designs were produced by manipulated the value of shape parameter

Designing three dimensional graphic objects using the polynomial of trigonometric curves with a shape parameter and the sweep surface head of project / Noor Khairiah Razali and Nursyazni Mohamad Sukri

The desired shape of Bezier and B-spline curves can be meeting by adjusting the control points, knot vectors and degrees. This adjustment was complicated and costly. In this project, the trigonometric polynomial with a shape parameter curves and rotational sweeping method was introduced as an alternative method in generating the variety of symmetrical three dimensional objects and designs easily, flexibly and less costly in time of working the calculation. The trigonometric polynomial curves were analogous to B-spline curves, but the curves can be manipulated based on the value of shape parameter, on a fixed control polygon and same control point. This property was an advantage in generating three dimensional objects using rotation sweep surface method, where the curve was rotated at y-axis with 360o degree. This polynomial was studied based on open and close uniform curves and applied in rotational sweep method to create three dimensional objects. The shape of the vase was generated as examples of three dimensional objects and the variety designs were produced by manipulated the value of shape parameter

Finding antipodal point grasps on irregularly shaped objects

Two-finger antipodal point grasping of arbitrarily shaped smooth 2-D and 3-D objects is considered. An object function is introduced that maps a finger contact space to the object surface. Conditions are developed to identify the feasible grasping region, F, in the finger contact space. A “grasping energy function”, E , is introduced which is proportional to the distance between two grasping points. The antipodal points correspond to critical points of E in F. Optimization and/or continuation techniques are used to find these critical points. In particular, global optimization techniques are applied to find the “maximal” or “minimal” grasp. Further, modeling techniques are introduced for representing 2-D and 3-D objects using B-spline curves and spherical product surfaces

Constrained modification of the cubic trigonometric Bézier curve with two shape parameters

A new type of cubic trigonometric Bézier curve has been introduced in [1]. This trigonometric curve has two global shape parameters λ and µ. We give a lower boundary to the shape parameters where the curve has lost the variation diminishing property. In this paper the relationship of the two shape parameters and their geometric effect on the curve is discussed. These shape parameters are independent and we prove that their geometric effect on the curve is linear. Because of the independence constrained modification is not unequivocal and it raises a number of problems which are also studied. These issues are generalized for surfaces with four shape parameters. We show that the geometric effect of the shape parameters on the surface is parabolic. Keywords: trigonometric curve, spline curve, constrained modificatio

Control vectors for splines

Traditionally, modelling using spline curves and surfaces is facilitated by control points. We propose to enhance the modelling process by the use of control vectors. This improves upon existing spline representations by providing such facilities as modelling with local (semi-sharp) creases, vanishing and diagonal features, and hierarchical editing. While our prime interest is in surfaces, most of the ideas are more simply described in the curve context. We demonstrate the advantages provided by control vectors on several curve and surface examples and explore avenues for future research on control vectors in the contexts of geometric modelling and finite element analysis based on splines, and B-splines and subdivision in particular.This is the final published manuscript. It is available from Elsevier in Computer-Aided Design here: http://www.sciencedirect.com/science/article/pii/S0010448514001973