Part (1) This SBIR Phase I project is to expand an existing multi-dimension interpolation software (up to 4D) developed by FANG, INC. The intellectual merits (IM) of the proposed activity are, (a) To provide a breakthrough in interpolation application; (b) To promote software development by use of Internet web technology. It is known in the interpolation field that approximation of high-dimension space is difficult to handle and quite often computationally unwieldy and intractable. Most of the available software, if not all, are restricted to or less than 5-dimension. The interpolation method proposed in this project can be extended in a straightforward manner to more than 10 or 100 dimension and far beyond. The project proposed is focused on the software development to scale up the capability of the existing software to 10-dimension and the capacity of accommodating up to 3,000 input data locations. Standard software design and coding work will be performed with the use of HTML and JavaScript languages. Software testing will be done to assure the correctness of software operation. It is anticipated that the produced software can be directly applied to, engineering design, information data mining, environmental modeling, social studies, econometrics, geostatistics, etc. Part (2) The innovation of interpolation method proposed in SBIR Phase I provides an easy way to construct an interpolant formula which can be applied with the use of irregular, random data points as well as regularly spaced data points. The interpolant can be extended to any higher dimension with huge amount of input data points. The broader impacts of the proposed work are described in the following areas, (a) It gives an unified treatment which covers the interpolation application in arbitrary dimension. It deals with the so- called "curse of dimension" directly and efficiently. The interpolant does not require any further intensive computing to search for coefficients; or root, contrary to other methods; (b) The interpolant is derived through mathematical analysis and can be applied to different application areas, weather analysis, social and demographic study, geological survey, etc. Furthermore, the interpolant can be used in obtaining volume estimate in 3D surface reconstruction, and support optimization study of engineering design as discussed in the proposal; (c) Teaming with visualization graphics (to be developed in Phase II) plus the technical niche, the interpolation software shall be an attractive and competitive software product in the commercial market.