Hi, I’m Andria Joseph, a Computer Science student from Howard University. This summer, I worked with Dr. Carl Moore, Dr. Rodney Roberts, and my mentor Egwuchukwu Kalu on a project exploring how to improve surface interaction in virtual environments by refining how normal vectors are calculated at intersections in 2D geometry a critical step for realistic touch-based VR applications. The problem: normal vectors become undefined at sharp planar intersections, which causes discomfort and inaccurate feedback during user interactions in virtual reality. Our solution involved using offset curves and circular arcs to smooth these intersections and generate well-defined normals. Using Python, we: • Generated connected 2D line segments. • Calculated the normals for each. • Constructed offset curves by shifting each segment perpendicular to its normal. • Smoothed intersections with circular arcs, particularly for sharp or 90° turns. Our results showed that larger offsets increase curvature, which improves smoothness but may alter the original path. Obtuse angles produced gentler transitions, while acute and right angles required arc-based smoothing. These findings have implications for: • Enhanced user comfort and control in VR by minimizing sharp transitions. • Improved design and prototyping tools for modeling complex virtual shapes. Next steps include extending these techniques to 3D surfaces, studying how curvature affects user interactions, and validating their performance in immersive VR environments.