451-208 Computational Methods in Geomatics

620-142 Mathematics B or equivalent subject and 620-160 Experimental Design and Data Analysis

The objective of this subject is to apply theories gained in earlier mathematical studies to fundamental problems associated with practice in Geomatics.

Topics covered include spherical trigonometry including properties of spherical triangles, development of fundamental formulae relating elements, area and spherical excess, application in navigation, map projections and positional astronomy; vector geometry for geomatics including vector representation of spatial relationships between points, line and planes, applications in positioning, mining surveying, solid modelling, reference frames and spatial analysis representations of curves on the ellipsoid as vector chains; geometry of the ellipsoid, the ellipsoid as a geodetic reference surface, coordinate systems, geocentric cartesian, curvilinear and universal transverse mercator (UTM), plane curves, loxodromes and geodesics computations on the UTM map grid; transformations between reference frames, rotation matrices for moving vectors between reference frames, properties of orthogonal matrices, conformal transformations in two and three dimensions; and algorithms for solving simultaneous linear equations, algorithms for general and symmetric matrix inversion, conditioning matrices for inversion, solutions for redundant linear equations, solutions for non-linear simultaneous equations, applications to curve fitting by least squares methods.

Not more than 3 hours of written examinations and tests and not more than the equivalent of 60 pages of written assignments and reports on practical work. The relative weighting of the assessment components will be published at the commencement of the subject.