The present disclosure provides a method of fabricating curvature-defined (C-D) or shape-defined (S-D) concave and convex polydimethylsiloxane (PDMS) surfaces and a method of fabricating C-D or S-D convex and concave gel surfaces for use in cell and tissue culturing and in other surface and interface applications, and provides a method of using C-D or S-D convex and concave surfaces with varying curvatures to direct cell attachment, spreading, and migration.