Abstract
Most surface-blending methods are able to blend surfaces with tangent continuity. However, curvature continuity has become increasingly important in geometric modelling and its applications, such as computer animation, computer-aided design and virtual reality. In this paper, we present a method which is able to achieve C 2 continuity based on the use of partial differential equations (PDE). A sixth order partial differential equation with one vector-valued parameter is introduced to produce such blending surfaces. Since computational efficiency is crucial for interactive computer graphics applications, we have developed a unified closed form (analytical) method for the resolution of this sixth order PDE. Therefore blending surfaces of up to C 2 smoothness can be generated in real time.
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Zhang, J.J., You, L. (2002). Rapid Generation of C 2 Continuous Blending Surfaces. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46080-2_10
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DOI: https://doi.org/10.1007/3-540-46080-2_10
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