Shapemap unwrap symmetrical or mirrored objects

HI, everyone,
I am using a GH plugin called Shapemap to attach pattern to a symmetrical surface. In script, a planar outline of the surface is needed and a provided component(‘shapemap’) is used to unwrap the surface to produce that. The surface is symmetrical, but outline is not. which makes the pattern not symetrical. Looking for a solution of it.

Thanks.

proof of asymmetry
@Dixon @jessesn

Supplementary pic: the paterrn move to one side a little bit according to the axis