ON THE DEVELOPMENT OF A READY RECKONER TABLE FOR EVALUATING SURFACE-AREA OF GENERAL ELLIPSOIDS BASED ON NUMERICAL TECHNIQUES

Surface areas of food materials resembling general ellipsoids can be o btained from the principal dimensions by numerical techniques. Nodes w ere identified on the surface along the principal planes in the develo ped model for generating a series of flat triangular element grids and their assembly gave the surface area of the ellipsoidal material. The model was validated against simpler geometries, such as sphere, prola te spheroids and oblate spheroids, and was found to be accurate. With the combination of non-dimensional input in the model and scaling fact or a two-dimensional ready reckoner table of reduced surface areas was developed, which covered the entire range of sizes and shapes of gene ral ellipsoid. The method of obtaining the intermediate values in the table by univariate and bivariate linear interpolation was also outlin ed and the interpolation error was in the range of 0.0-0.57%. The nomo gram representation of the table can be utilised for rough estimates. The actual surface area of the object is obtained from the reduced sur face area by multiplying it by the scaling factor. (C) 1998 Elsevier S cience Limited. All rights reserved.