دانلود رایگان مقاله ساخت انحنای پیوسته bi-4 برای سطوح اسکافلد و sphere مانند

Abstract

Scaffold surfaces bound geometric structures that have a dual characterization as a curve network and a solid. A subset of scaffold surfaces can be modeled with minimal single-valence (MSV) meshes, i.e. meshes consisting of vertices of a single irregular valence n two of which are separated by exactly one regular, 4-valent vertex. We present an algorithm for constructing piecewise bi-quartic surfaces that join with curvature continuity to form scaffold surfaces for MSV meshes, for n=5,…,10. Additionally, for sphere-like meshes, we exhibit bi-quartic curvature continuous surfaces with polar parameterization.

6. Conclusion

We introduced a special class of curvature continuous surfaces of low and likely least polynomial degree and few(est) number of pieces for the special class of MSV meshes. MSV meshes occur in nature and engineering practice alike. We focused on the main cases, MSV meshes with valence 5, 6 or 8 but also covered more esoteric valences. Valence 3 requires special consideration. Since the result would be sphere-like surfaces, we opted to instead use a more flexible polar construction. Our curvature continuous polar surfaces of degree bi-4 have a simple derivation. Their key structure is the quadratic expansion at the pole. Together, the two families offer a structurally simple solution to the modeling of a common but special class of shapes. Curvature and highlight shading show the bi-4 scaffold surfaces to have shape at least as good as the state-of-the-art methods of Table 1 and typically indistinguishable from [10].