18-Geom-A7 Geospatial Information Systems · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2017 — 04-Geom-A7 Geospatial Information Systems. Closed-book; any non-communicating calculator permitted. Format: fifteen questions of varied value totalling 100 marks; fifteen questions constitute a complete paper and all fifteen are solved in full below. Most answers are required in essay form. Datum and coordinate conventions follow the Canadian spatial reference framework — NAD83(CSRS) horizontally and CGVD2013 vertically.
Reference texts: P. A. Longley, M. F. Goodchild, D. J. Maguire & D. W. Rhind, Geographic Information Systems and Science (4th ed., Wiley, 2015); P. Bolstad, GIS Fundamentals: A First Text on Geographic Information Systems (6th ed., XanEdu, 2019); P. A. Burrough, R. A. McDonnell & C. D. Lloyd, Principles of Geographical Information Systems (3rd ed., Oxford, 2015); M. Worboys & M. Duckham, GIS: A Computing Perspective (2nd ed., CRC, 2004); H. Samet, The Design and Analysis of Spatial Data Structures (Addison-Wesley, 1990); ISO 19115 Geographic information — Metadata.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
(a) Definition. A map projection is a systematic mathematical transformation that maps positions on the curved surface of the Earth (a sphere or reference ellipsoid) onto a flat plane — i.e., a function that converts geographic coordinates (latitude φ, longitude λ) into planar Cartesian coordinates (x, y = f(φ, λ)). Because a curved surface cannot be flattened without stretching or tearing, every projection necessarily distorts some combination of area, shape, distance and direction; a given projection is designed to preserve one property (conformal, equal-area, equidistant or azimuthal) at the expense of the others.
(b) Why they are needed. Projections are required because GIS data, computer screens and paper maps are two-dimensional and planar, whereas the Earth is three-dimensional and curved. A flat, Cartesian (x, y) frame is needed so that positions can be plotted, stored, and — above all — so that distances, areas and bearings can be computed with ordinary plane geometry rather than complex spherical/ellipsoidal formulae. Overlay and analysis require all layers to share one planar coordinate system with controlled, known distortion. In short, projection converts geodetic positions on the globe into the metric planar coordinates (e.g., UTM/MTM northings and eastings) that mapping, measurement and spatial analysis depend on. In Canada, UTM and the 3° MTM zones are the standard projected grids.
