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Shape aware normal interpolation for curved surface shading from polyhedral approximation

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Abstract

Independent interpolation of local surface patches and local normal patches is an efficient way for fast rendering of smooth curved surfaces from rough polyhedral meshes. However, the independently interpolating normals may deviate greatly from the analytical normals of local interpolating surfaces, and the normal deviation may cause severe rendering defects when the surface is shaded using the interpolating normals. In this paper we propose two novel normal interpolation schemes along with interpolation of cubic Bézier triangles for rendering curved surfaces from rough triangular meshes. Firstly, the interpolating normal is computed by a Gregory normal patch to each Bézier triangle by a new definition of quadratic normal functions along cubic space curves. Secondly, the interpolating normal is obtained by blending side-vertex normal functions along side-vertex parametric curves of the interpolating Bézier surface. The normal patches by these two methods can not only interpolate given normals at vertices or boundaries of a triangle but also match the shape of the local interpolating surface very well. As a result, more realistic shading results are obtained by either of the two new normal interpolation schemes than by the traditional quadratic normal interpolation method for rendering rough triangular meshes.

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Acknowledgements

We owe thanks to anonymous referees for their helpful comments on an earlier version of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, China

    Xunnian Yang

  2. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Jianmin Zheng

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  1. Xunnian Yang
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  2. Jianmin Zheng
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Correspondence to Xunnian Yang.

Additional information

This work is supported by NNSF of China grant (60970077) and the ARC 9/09 Grant (MOE2008-T2-1-075) of Singapore.

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Yang, X., Zheng, J. Shape aware normal interpolation for curved surface shading from polyhedral approximation. Vis Comput 29, 189–201 (2013). https://doi.org/10.1007/s00371-012-0715-y

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