How to reduce the complexity of convex hull of moving points?

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I have implemented the convex hull algorithm for N randomly generated points. As per my requirement, I am advancing this. In those N points, K points will change their positions. I have to calculate convex hull again. I am just recomputing the convex hull again. But this is taking so much time (high complexity). Since I have already one hull, and some of those only moving points. Can I use this property anyway and is there any possibility to reduce the complexity of this problem?

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