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International audience; Composite pressure vessels made by filament winding processes are commonly used in aerospace design due to weight saving compared to metal parts. This technique involves complexities in analyzing the geometry especially in the dome section. Tools already exist to predict the geometrical characteristics like winding angle, ply thickness or some singularities. However they are limited to specific sequence dome lay-up. A numerical tool has been developed to simulate windings layer after layer. The goal is to deal with any kind of sequence dome lay-up calculation. To ensure this there are three main challenges that are seldom cited in scientific literature. The first is when the geometry of the current ply overlaps the inferior ply. The second is the management of convex parts of a ply. Finally, our mathematical tool is able to deal with the accumulation of composite fibers near the polar boss outer radius.