Edit Mode: how to make edges with mark stream straight for texture paint?

The edges on shoe look straightly and fine in the edit mode. I painted the sew-looking on UV image. on 3D viewport, the sew-looking on shoe looks like curve. So, I turned into texture paint mode and noticed the edges turns into curve. I dont want to paint sew- looking that look like curve.I figure to get them straight in edit mode but not success. Any suggestion to make them straight work before i could work in texture paint mode?
thanks…