• The KIPS Transactions:PartA
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• v.9A no.1
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• pp.99-104
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• 2002

The goal of this paper is to generalize the concept of Bezier curves and surfaces defined on the vector space $R_n$ to Lie groups, which is a new generation method of curves (called Bezier curves) on Lie groups. The defined Bezier curves and surfaces are alsways smooth because of the properties of Lie groups. We apply this method to smooth motion interpolation or smooth trajectory generation for moving rigid body in space.

• The Journal of Korean Association of Computer Education
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• v.9 no.1
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• pp.89-95
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• 2006

The local geometric properties such as curvatures and normal vectors play important roles for analyzing the local shape of objects in the fields of computer graphics and computer vision. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the curvatures of meshes because there is no exact mathematical definition of curvature at vertices on 3D meshes. Therefore, In this paper, we indicate the fatal error in computing the sectional curvatures of the most previous discrete curvature estimations. Moreover, we present a discrete curvature estimation to overcome the error, which is based on the parabola interpolation and the geometric properties of Bezier curves. Therefore, We can well distinguish between the sharp vertices and the flat ones, so our method may be applied to a variety of geometric operations.