Data processing method for transforming a first 3D surface suitable for coating a first object into a second 3D surface suitable for coating a second object, and associated computer program and processing device

Data processing device (1) for transforming a first 3D surface (SS) which is adapted to cover a first object (OS) and is formed of a mesh of first 2D elementary surfaces into a second 3D surface (SC) which is adapted to cover a second object (OC) and is formed of a mesh of second 2D elementary surfaces, said processing device being adapted to determine transformations of the first elementary surfaces into respective second elementary surfaces and comprising:

• a supervisor adapted to run iteratively a set of modules comprising a first updating module and a second updating module;
• the first updating module adapted to, in a (k+1)th iteration operation, k being an integer greater than or equal to 0, for each of a plurality of couples comprising a first elementary surface and a second elementary surface derived from a transformation of the first elementary surface and having been delivered by the second updating module following the kth iterative operation of the supervisor, determine the projection of said second elementary surface on the plane of said respective elementary surface and define a current 2D transformation matrix Tk+1t for said couple,
• where Tk+1t=Pkt′(Pt)−1 and Pt=[pn+1−pi]i=1 to n, Pk t′=[p′n+1,k−p′i,k]i=1 to n;
• wherein pi, for i=1 to n, are the vertices of the first elementary surface t of a couple and pn+1 is obtained by offsetting the vertex p1 by a vector normal to said first surface, of given norm;
• wherein (pt)−1 is the inverse of the matrix pt when the first elementary surfaces are triangles and is a pseudo-inverse matrix of the matrix pt otherwise;
• wherein p′i,k, i=1 to n, are the vertices of said projection of the second elementary surface and p′n+1,k is obtained by offsetting the vertex p′1,k of said normal vector;
• the second updating module adapted to, in a (k+1)th iteration operation by the supervisor, k being an integer greater than or equal to 0, determine the second elementary surfaces obtained for the (k+1)th iteration as those minimizing a function including at least the term
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• wherein Tk+1t are the transformation matrices defined by the first module in the (k+1)th iteration operation by the supervisor;
• where {tilde over (P)}k+1t=[{tilde over (p)}n+1,k+1−{tilde over (p)}i,k+1]i=1, . . . ,n′
• wherein {tilde over (p)}i,k+1, for i=1 to n, are the vertices of the second elementary surface of the couple as determined in the (k+1)th iteration and {tilde over (p)}n+1,k+1 is obtained by offsetting the vertex {tilde over (p)}1,k+1 by a vector normal to said second surface, of given norm.