An Interactive Parametric Framework for Quartic Overhauser (QOVR) Splines in Geometric Modeling with Local Shape Control and C1 Continuity

This study presents a continuous geometric framework utilizing a novel quartic Overhauser (QOVR) spline with adjustable local parameters. The proposed spline is constructed as an alternative representation from an algebraic blending mechanism of three parabolic segments defined over a five-point control configuration. This structure enables flexible spline definitions through internal parametric knots without modifying the spatial locations of the control points. The resulting formulation maintains C1 continuity, ensuring smooth transitions between adjacent spline segments. The QOVR spline offers structural advantages in interactive design and computational geometry environments. To evaluate the computational steps, a dedicated object-oriented prototyping framework was introduced to organize, visualize, and analyze the proposed spline. This arrangement facilitates continuous visualization, interactive adjustment of local parameters, and multi-segment implementations. Exported coordinates further allow independent numerical verification in external computational environments when required. The QOVR spline achieves a balance between geometric flexibility and boundary condition invariance. By allowing independent parametric knot adjustments without disrupting the global continuity constraints, the proposed design offers direct local morphological flexibility during geometric synthesis. This study introduces the QOVR spline integrated into an object-oriented prototyping framework, offering a distinct algebraic design for interactive geometric environments and computer-aided design (CAD) setups.