A Piecewise Bezier Surface Interpolation Model for Facial Surface Visualization

Abstract

Facial surface visualization is a fundamental task in geometric modeling, particularly for applications that require smooth and accurate representation of facial geometry. This paper proposes a piecewise Bézier surface interpolation model for the visualization of facial surfaces constructed from facial landmark data. The proposed approach partitions the facial parametric domain into multiple overlapping patches, where each patch is interpolated independently using a tensor-product Bézier surface formulation. Bernstein polynomial basis functions are employed to compute the surface control points through a least-squares interpolation strategy. A Gaussian blending mechanism is subsequently applied to ensure smooth transitions and geometric continuity between adjacent patches. The resulting composite Bézier surface produces a continuous and visually coherent facial surface while preserving essential geometric characteristics such as curvature variation and boundary structure. Experimental results demonstrate that the proposed model achieves stable and smooth surface visualization even when constructed from sparse facial landmark data. These findings indicate that the proposed piecewise Bézier surface interpolation framework provides an effective and mathematically well-defined solution for facial geometry visualization and computer-aided geometric design applications.