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Interacting active surfaces: A model for three-dimensional cell aggregates

Fig 2

A smooth surface representing a cell is obtained based on a triangular control mesh with vertex positions X_a (A) and a set of basis functions per vertex a (B).

(A) To define the mapping between the control mesh and the cell surface, the barycentric coordinates of points in a triangular element e in the control mesh , which span a reference triangle, are used to define a point on the cell surface , (Eq (9)). Points are obtained by summing basis functions , weighted by X_a, over vertices a whose basis functions have a non-zero contribution to this element, an ensemble denoted 〈e〉. (B) Example of the basis function associated to a vertex in the mesh. For Loop subdivision surfaces basis functions, the basis function spans the first and second rows of elements surrounding the vertex (thicker white line). The vertices that interact with vertex a in the same cell, represented by the set 〈〈a〉〉 (green) are formed by the first, second, and third nearest neighbours in the mesh.

doi: https://doi.org/10.1371/journal.pcbi.1010762.g002