## THE TOPEN FILE FORMAT.

(c) www.topen.org

The topen file format is designed to incorporate different spline-types inside one format. With a base knowledge on splines, it is possible to store information about B-Splines, NURBS, T-Splines and T-NURCCS. In this sense, it can be seen as a unification of existing spline formats.

The topen files can be viewed with the TLAB software (see Download section). A basic set of topen files comes with every package. However, for a better understanding, the following simple example can be useful.

#TOPEN v1 ################################################################################### # SECTION I - specifying the degree of the spline # degree 1 # ################################################################################### ################################################################################### # SECTION II - Start of the parametric mesh description # # vertices: # v <vertexId> v 0 v 1 v 2 v 3 v 4 # vector of knot lengths, used in the edge-definitions: kl 1 0.5 # edges: # e <edgeId> <vertexId1> <vertexId2> <edge-length-index> e 0 1 0 0 e 1 2 1 0 e 2 3 2 0 e 3 4 3 1 e 4 0 4 1 # faces: # f <faceId> <numberOfVertices> <vId>/<vertexMarked> <vId>/<vertexMarked> <....> f 0 5 0/1 1/1 2/1 3/1 4/0 # # End of the parametric mesh description ################################################################################### ################################################################################### # SECTION III - relating the control points to the parametric mesh # # control points: # cp <parentId> <wx> <wy> <wz> <w> # parentId is the id of a face for the even case and of a vertex for the odd case cp 0 0 0 5 1 0 cp 1 10 0 5 1 0 cp 2 10 10 5 1 0 cp 3 0 10 5 1 0 cp 4 0 5 8 1 0 # ###################################################################################

The topen file is divided into three sections.

The first section describes the degree of the spline. The example has the degree 1, which is an odd number like 3,5 or 7. It is important to know that the degree even or odd decides if the control points (defined in Section III) are related to faces or vertices of the parametric mesh (defined in Section II). Therefore, it is possible to change the degree of a topen spline by an increase or decrease of 2, without changing anything else. In comparison to B-Splines, where always the knot vector has to be adjusted, this is a big advantage.

In the second section the parametric space is formulated by a quadrilateral mesh. Each quadrilateral in the mesh is called face and can have an arbitrary amount of hanging vertices. Those are sometimes also called T-junctions or I-junctions, depending on their valence. A necessary condition of the parametric mesh (sometimes called T-mesh) is that every face spans a rectangle in the parametric space.

The last section places the control points to the faces or vertices of the parametric mesh.

If there are any question about the format please feel free to write an email to mike@topen.org.

Last change 3.12.2011