Abstract

Mathematical formulation of unsmooth surfaces such as the physical earth poses several difficulties. To achieve an accurate formulation, each and every point of the surface must be defined, which is practically impossible. Therefore, in modelling such surfaces there is a need for an adequate number and distribution of reference points as well as an appropriate interpolation method. Working on computerised three-dimensional (3D) models, users can dynamically make various analyses on the surface, one of which is the volume calculation. The accuracy of the volume calculation depends on the appropriateness of the interpolation method used in creating 3D models. The present study, which aims to investigate the accuracy of the calculated volumes of objects with irregular structures, uses an artificial object with irregular form whose volume can be indirectly calculated. Using different interpolation methods on this artificial object through photogrammetrically measured reference points, 3D surface models were formed and volumes were calculated. A comparison between the measured and calculated volume figures revealed that the Inverse Distance Weighting (INDW), Nearest Neighbour (NENE) and Triangulation with Linear (TLIN) interpolation methods yielded more accurate results than the other methods. In order to investigate the volumetric accuracy, the same procedure was applied to a regular geometrically-shaped conical frustum and a pyramidal frustum with different numbers of faces, whose reference points on the surface were reproduced in accordance with mathematical rules. The volume of the pyramidal frustum which was obtained using different interpolation methods was then compared to that of the pyramidal frustum which was mathematically calculated and that of the conical frustum which was taken as the reference surface. The comparison demonstrated that the Data Metrics (DMET), INDW and Minimum Curvature (MCRV) interpolation methods yielded better results in terms of volumetric accuracy.

Keywords: Interpolation methods, DTM, landform volume, volumetric accuracy.