AI 中文总结
本研究提出矩阵驱动的四次Overhauser（QOVR）曲面框架，采用可变参数四次架构与对称控制矩阵，实现局部形状调整与边界不变性，验证其满足C^0、C^1连续性，可用于制造与逆向工程。
AI 中文摘要
本研究介绍了用于解决边界对齐和局部形状修改约束的四次Overhauser（QOVR）曲面生成框架的空间与解析构建方法。该框架采用可变参数的四次新型架构，以实现正交坐标轴间的精确参数隔离。其解析流程将方向样条混合函数与对称空间控制矩阵相结合，确保内部节点向量的变化可实现局部曲面调整，同时保持全局边界的绝对位置不变性。计算验证表明，当前公式虽满足内部与边界界面的显式C^0位置闭合及C^1切线连续性条件，且不会引发全局曲率传播、边节点分离或波状伪影，但无法维持C^2曲率连续性。三维网格模型与色图可视化结果显示，空间强度场严格集中在被修改单元的紧邻区域内，验证了位移效应随距受扰动控制点的距离增加呈指数衰减。这种显式解耦保留了相邻几何面片间的结构对称性与边界不变性，满足制造与逆向工程的密封标准。
英文摘要
This study introduces the spatial and analytical construction of the Quartic Overhauser (QOVR) surface generation framework designed to resolve boundary alignment and localized shape modification constraints. This framework implements a variable parameter fourth degree novel architecture to achieve exact parameter isolation 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 preserving the absolute positional invariance of global edge boundaries. Computational verification confirms that while the current formulation satisfies explicit C^0 positional closure and C^1 tangent continuity conditions across the internal and boundary interfaces without triggering global curvature propagation, edge joint separation, or wave-like artifacts, C^2 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 exponentially as the distance from the perturbed control points increases. This explicit decoupling preserves structural symmetry and boundary invariance across adjacent geometric patches, satisfying manufacturing and reverse engineering sealing criteria. Keywords: Quartic Overhauser surface; computer aided geometric design (CAGD); local shape control; geometric continuity; symmetric tensor products; computer graphics algorithms; software implementation framework.
CommentsThis is a preprint version of a manuscript submitted to a journal for peer review. Repository available at: https://github.com/HakanUst/QOVR-Surface
