or surface. u only is required for curve points, u and v for surface points and control points of non-rational trimming curves, and u, v and w (weight) for control points of rational trimming curves. Face elements Faces are defined using lists of vertex, texture and normal indices in the format vertex_index/texture_index/normal_index for which each index starts at 1 and increases corresponding to the order in which the referenced element was defined. Polygons such as quadrilaterals can be defined by using more than three indices. OBJ files also support free-form geometry which use curves and surfaces to define objects, such as NURBS surfaces. Vertex indices A valid vertex index matches the corresponding vertex elements of a previously defined vertex list. If an index is positive then it refers to the offset in that vertex list, starting at 1. If an index is negative then it relatively refers to the end of the vertex list, -1 referring to the last element. Each face can contain three or more vertices. f v1 v2 v3 .... Vertex texture coordinate indices Optionally, texture coordinate indices can be used to specify texture coordinates when defining a face. To add a texture coordinate index to a vertex index when defining a face, one must put a slash immediately after the vertex index and then put the texture coordinate index. No spaces are permitted before or after the slash. A valid texture coordinate index starts from 1 and matches the corresponding element in the previously defined list of texture coordinates. Each face can contain three or more elements. f v1/vt1 v2/vt2 v3/vt3 ... Vertex normal indices Optionally, normal indices can be used to specify normal vectors for vertices when defining a face. To add a normal index to a vertex index when defining a face, one must put a second slash after the texture coordinate index and then put the normal index. A valid normal index starts from 1 and matches the corresponding element in the previously defined list of normals. Each face can contain three or more elements. f v1/vt1/vn1 v2/vt2/vn2 v3/vt3/vn3 ... Vertex normal indices without texture coordinate indices As texture coordinates are optional, one can define geometry without them, but one must put two slashes after the vertex index before putting the normal index. f v1//vn1 v2//vn2 v3//vn3 ... Line elements Records starting with the letter "l" (lowercase L) specify the order of the