The present invention discloses a conformal periodic flattening method for a surface with
genus, and relates to the field of surface flattening. The steps are as follows: for an input triangular mesh surface, first check the
genus number of the surface. If the
genus number is greater than 1,
cut the surface into multiple sub-surfaces with genus 1, otherwise
record the original surface as a sub-surface; secondly, search for the ring
handle ring and tunnel ring of each sub-surface and
cut them; then establish a periodic condition for the ring slit boundary inside each sub-surface, establish a flipping condition for the slit boundary between two sub-surfaces, construct a coupled conformal
energy minimization model and solve it, obtain the vertex mapping coordinates, periodic translation and flip center; finally, construct a conformal periodic flattened mesh for each sub-surface according to the results. The method of the present invention constructs a periodic condition and flipping condition based on the slit, calculates the conformal periodic flattening mapping by conformal
energy minimization, ensures the high conformality of the mapping at the slit, and is applicable to any surface with genus.