Synthesis of Epsilon Kappa Curves with a GUI in OpenGL for Curve Manipulation

Abstract

In this study, we strive to synthesize different variants of the Epsilon kappa curves which is an extension of an interpolating spline called the κ-curve. κ-curves had been applied as the curvature tool of Adobe Illustrator and Photoshop and are exceedingly valued by all designers. In this research we synthesize Epsilon Kappa curves and show its features through the generation of the curve with OpenGL. Main purpose of the GUI is to visually represent the free and easy manipulation of the curve. After the creation of the GUI in OpenGL we will try to create various shapes to further understand the properties of the curve. By doing so we are able to prove the usage of the curve in CAD and 3D design software. We have used Glut functions to represent and create the curve in the GUI. Finally, we were able to verify that the generated curves are almost G 2-continuous everywhere and the curve overcomes the disadvantages of the κ-curve.