Abstract: A method of creating texture maps for three-dimensional surfaces may include receiving a polygonal mesh defining a shape of a three-dimensional object. The method may further include determining positions of points identifying a plurality of curves on a surface of the polygonal mesh. The method may further include producing a mesh cutout having a border defined by a closed loop line comprising the plurality of curves. The method may further include determining that a projection of the mesh cutout onto a flat surface produces a value of a visual distortion metric that does not exceed a defined distortion threshold. The method may further include creating a texture map by projecting a two-dimensional image onto a surface of the mesh cutout. The method may further include using the texture map to produce a visual representation of the three-dimensional object.