Aesthetic shapes are usually actualized as 3D objects represented by free-form surfaces. The main components used to achieve aesthetic surfaces are 2D and 3D curves, which are the elements most basic for determining the shapes and silhouettes of industrial products. Bézier, B-Spline and NURBS are types of flexible curves developed for various design intents. These curves, however produce complex curvature functions that may undermine the formulation of shape aesthetics. A viable solution to this problem is to formulate aesthetic curves and surfaces from well-defined curvatures to improve aesthetic design quality. This paper advocates formalizing aesthetic curve and surface theories to fill the gapmentioned above, which has existed since the 1970s. This paper begins by reviewing on fair curves and surfaces. It then extensively discusses on the technicalities of Log-Aesthetic (LA) curves and surfaces and touches on industrial design applications. These emerging LA curves have a high potential for being used as standards to generate, evaluate and reshape aesthetic curves and surfaces, thus revolutionizing efficiency in developing curve and shape aesthetics.

Topological indices are invariant numerical quantities of a graph that give facts about the structure of graphs and are found to be very helpful in predicting the physical properties of aluminophosphates. The characteristics of aluminophosphates are similar to the characteristics of zeolites. Two examples of current applications are natural gas dehydration and humidity sensors. Researchers in chemistry and materials science are synthesizing new frameworks. There are many layers and holes in these substances. The technique used to predict natural behaviors among the physicochemical characteristics of chemical molecules in their basic network is known as topological indices. This study explains the vertex version of distance-based topological indices, the entropy of topological indices and their numerical analysis.

A topological index is a numerical measure that characterises the whole structure of a graph. Based on vertex degrees, the idea of an atom-bond connectivity index was introduced in chemical graph theory. Later, different versions of the ABC index were created, and some of these indices were recently designed. In this paper, we present the edge version of the atom-bond connectivity index, edge version of the multiplicative atom-bond connectivity index, and atom-bond connectivity temperature () index for the line graph of subdivision graph of tadpole graph , ladder graph , and wheel graph . Numerical simulation has also been shown for some novel families of atom-bond connectivity index comparing the three types of indices which can be useful for QSAR and QSPR studies.

This paper proposes the reconstruction of craniofacial fracture using rational cubic Ball curve. The idea of choosing Ball curve is based on its robustness of computing efficiency over Bezier curve. The main steps are conversion of Digital Imaging and Communications in Medicine (Dicom) images to binary images, boundary extraction and corner point detection, Ball curve fitting with genetic algorithm and final solution conversion to Dicom format. The last section illustrates a real case of craniofacial reconstruction using the proposed method which clearly indicates the applicability of this method. A Graphical User Interface (GUI) has also been developed for practical application.

RADIUS BASED BLOCK LOCAL BINARY PATTERN ON T-ZONE FACE AREA FOR FACE RECOGNITION