Methods for defining G~2 curves with conic segments are introduced in this paper, the conic is represented by implicit equation. Firstly, a method for interpolating two given endpoints, two given tangent directions at the endponints as well as a curveature at either endpoint is presented. Secondly, a method for interpolating a point sequence in a plane with conic segments is offered. Lastly, a method for fitting a point sequence in a plane is given. The methods are very robust for any 2D data sequences. The global G~2 continuity can be hold whether the data set is open or closed.
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