Research On Spatial Interpolation Method Of Volume Function Based On Generalized Three Prism

Spatial interpolation of 3D data field is an important research field in 3D geological modeling.Based on the material with certain bedding structures,which is relative uniform and change slowly in the direction of the bedding,but changes quickly in the direction of the wear layer(perpendicular to the direction of the plane).This paper firstly proposes a new concept of spatial interpolation,basing on the difference of the rate of change of wear layer and bedding layer.This paper studies interpolation methods of three prism for the three prism element having a clear direction.Using the tetrahedron and hexahedron volume coordinates theory,this paper draws up the three prism volume linear interpolation basing on the three prism volume coordinates.This paper studies three prism spline elements with 15 nodes(three prism two interpolation)basing on the tetrahedron volume coordinates and B net method,considering the continuous transition of properties of the adjacent three prism,adjusting properties of geological model in the direction of the bedding and wear layer.In order to realize the interpolation methods above,basing on the borehole sampling points of geological data,the study area geological body is divided into generalized three prism partition,which are divided into a number of sub domains without intersecting,and then we simulate the property field(attribute values to the sample points).Finally,this paper shows 3D visualization of the interpolation results with openGL,showing the continuous change of the non-uniform properties of the bedding and wears layer orientation in different locations with horizontal,vertical sections and trellis diagrams,comparing with traditional methods such as IDW and Kriging.The results show that the linear interpolation and the two interpolation with 15 node are better than the traditional interpolation methods in the conditions of 3D geological model considering layered strata,they can well express the change of the field of the property,the effects of the two interpolation with 15 nodes is the best.In this paper,the research on the three prism interpolation algorithm is great significance in the field of 3D data field.