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It is an unsolved problem to design a model-based control in nonplanar sloshing cases. This is because the whole shape of the liquid surface is a complex curve (a set of an infinite number of points) in coordinate spaces. This paper solves this problem. First, the whole shape of the liquid surface corresponding to the output measured by a camera is a single point in a polynomial space as well as the input and the state. Second, without any physical parameter identification, input-output modeling on polynomial space, unlike existing types of modeling, captures the whole dynamics even in nonplanar sloshing cases and is linked to design of implementable controllers. 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