AbstractThis paper presents a method to construct the Delaunay triangulation for creating a polygon patch model, which is used as a graphic model for applications such as computer graphics and virtual reality. This method is based on the conventional incremental method to construct the Voronoi diagram, but has two characteristics that are especially suitable for a three‐dimensional geometric modeling. One of these characteristics is that a point can be removed from the mesh. This feature is useful for the interactive modeling application in which points are often removed and moved. The other is that a line, which lies between two points, can be constrained to be an edge of the mesh. This is necessary for creating an accurate three‐dimensional model. Without this feature, the mesh usually obtained has totally different three‐dimensional structure from the real object. A process to apply this method to a radial range image is described as well as the details of this method. Experimental results and evaluation of this method are also