Three-dimensional CAD becomes high-performance. And in late year's three-dimensional printer and scanners spread. Rendering can perform by using point group data which were taken in with three-dimensional scanners, but are not often suitable for various three dimensions processing such as a correction or the addition of the three-dimensional shape. Therefore convert point group data into masks such as irregular triangular mesh or non-same rational B spline surface form and often generally are handled it. When provided point group data include a loss area, there are many cases that an error occurs and cannot make a conversion to a polygon shape and a free-form surface shape. So we present way for the reduction of the conversion error to occur when I convert point group data having a loss department into the free curved surface. To solve the problem, knowledge data of the Delaunay triangulation to XML-based shape expression X3D.