The cuspidal curve from the intersection of bisector

Bezier curves, especially quartic Bezier curves, are used in the study to help create cuspidal curves. The goal is to design a cuspidal curve and calculate the control points of the quartic Bezier curve using the bisector of a triangle. To construct cuspidal curves, a novel technique is presented that blends quartic Bezier curves with the intersection of angle bisectors. Mathematical computations and geometric transformations are used to precisely calculate the sites of bisector crossings and create the related quartic Bezier curves. Control points on the triangle are defined using the intersection of angle bisectors, and the control points necessary to create the quartic Bezier curve are determined. By presenting a unique approach to creating cuspidal curves using quartic Bezier curves and angle bisector intersections, this paper contributes significantly to curve theory and singularity analysis. The discoveries provide to a better knowledge of the evolution and characteristics of cuspidal curves, as well as significant insights for applications in computer graphics, industrial design, and robotics.