The 2D Orientation Interpolation Problem: A Symmetric Space Approach
In this paper, we propose a novel construction of Bezier curves of two dimensional (2\)D) orientations using the geometry of real projective plane \mathrm{\mathbb {R}P^{2} Unlike the commonly adopted unit 2 sphere model (S^{2} \mathrm{\mathbb {R}P^{2} is naturally embedded in the (3\)D special orthogonal group \mathrm{SO(3) It is also a symmetric space that is equipped with a particular class of isometries called geodesic symmetry, which allows us to generate any geodesics using the exponential map of \mathrm{SO(3) We implement the generated geodesics to construct Bezier curves for direction interpolation.
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