How to calculate a grid based on 4 curved edges?

You can use a parametric representation to map points from a unit square with corners 1, 1, -1, 1, -1, -1, 1, -1 onto the Bezier quad by transforming from one coordinate system to the other by calculating the Jacobean from one to the other This article shows you how. It's a common thing to do in finite element analysis, because most modern elements are expressed in terms of shape functions in a parametric space. You have to transform from the parametric to element coordinates using the techniques shown in that article.

You can use a parametric representation to map points from a unit square with corners 1, 1, -1, 1, -1, -1, 1, -1 onto the Bezier quad by transforming from one coordinate system to the other by calculating the Jacobean from one to the other. This article shows you how. It's a common thing to do in finite element analysis, because most modern elements are expressed in terms of shape functions in a parametric space.

You have to transform from the parametric to element coordinates using the techniques shown in that article.

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