# Efficient C2 Continuous Surface Creation Technique Based on Ordinary Differential Equation

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The National Centre for Computer Animation, Bournemouth University, Poole BH12 5BB, UK

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Humain Ltd., Belfast BT1 2LA, UK

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Ulster University, York St, Belfast BT15 1ED, UK

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Author to whom correspondence should be addressed.

Received: 1 November 2019 / Revised: 4 December 2019 / Accepted: 10 December 2019 / Published: 23 December 2019

In order to reduce the data size and simplify the process of creating characters’ 3D models, a new and interactive ordinary differential equation (ODE)-based C2 continuous surface creation algorithm is introduced in this paper. With this approach, the creation of a three-dimensional surface is transformed into generating two boundary curves plus four control curves and solving a vector-valued sixth order ordinary differential equation subjected to boundary constraints consisting of boundary curves, and first and second partial derivatives at the boundary curves. Unlike the existing patch modeling approaches which require tedious and time-consuming manual operations to stitch two separate patches together to achieve continuity between two stitched patches, the proposed technique maintains the C2 continuity between adjacent surface patches naturally, which avoids manual stitching operations. Besides, compared with polygon surface modeling, our ODE C2 surface creation method can significantly reduce and compress the data size, deform the surface easily by simply changing the first and second partial derivatives, and shape control parameters instead of manipulating loads of polygon points.