Three-dimensional (3D) mesh segmentation techniques are described. In one example, a geometry segmentation system determines a vertex direction for each vertex in a 3D mesh. A segment generation module is then employed to generate segments (e.g., as developable geometries) from the 3D mesh. To do so, a vertex selection module selects an initial vertex having an associated vertex direction. A face identification module then identifies a face in the 3D mesh using that initial vertex and at least one other vertex. A segment determination module compares the vertex direction associated with the initial vertex with a normal determined for the face. If the vertex direction is orthogonal to the normal (e.g., within a threshold amount), the face is added to the segment, and sets another one of the vertices of the face as the initial vertex and the process repeats.