Matrix-Driven Quartic Overhauser (QOVR) Surface Structural Framework: Continuity Limitations, Computer Graphics Algorithms, and Software Implementation

This study introduces the spatial and analytical construction of the Quartic Overhauser (QOVR) surface generation framework designed to address boundary alignment and localized shape modification constraints. This framework implements a variable-parameter fourth-degree novel matrix formulation to achieve parameter tracking across orthogonal coordinate axes. The analytical pipeline integrates directional spline blending functions with symmetric spatial control matrices, ensuring that internal knot vector variations allow localized surface adjustments while maintaining the position convergence of global edge boundaries. Computational verification confirms that while the current formulation satisfies explicit C0 positional closure and C1 tangent continuity conditions across the internal and boundary interfaces without triggering global curvature propagation, with edge joint separation, or wave-like artefacts, C2 curvature continuity is not maintained. As demonstrated by three-dimensional mesh models and colormap visualizations, the spatial intensity fields condense strictly within the immediate neighborhood of the modified element, verifying that the displacement effect decreases progressively as the distance from the perturbed control points increases. This explicit decoupling aligns with structural symmetry and boundary alignment across adjacent geometric patches, satisfying manufacturing and reverse engineering sealing requirements.