We construct low degree patches that contain any given 3D polynomial curve as a pregeodesic (i.e. geodesic up to reparametrization). A curve is a pregeodesic if and only if its rectifying plane coincides with the tangent plane to the surface, we use this fact to construct patches through pregeodesics. We also discuss the G¹ connection of (1,k) patches with abutting pregeodesics
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