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18-Geom-A7 Geospatial Information Systems · December 2015

Question 7 of 12: Cartesian versus Geodetic Coordinates

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — December 2015 — 04-Geom-A7 Geospatial Information Systems. Closed-book; an approved Casio or Sharp calculator is permitted. Format: twelve short-answer questions of varying value totalling 100 marks; all questions constitute a complete exam and are solved in full below. 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); J. P. Snyder, Map Projections — A Working Manual (USGS PP 1395); ISO 19115 Geographic information — Metadata.

Question 7: Cartesian versus Geodetic Coordinates (8 marks)

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.

ellipsoid surfacePh (ellipsoidal ht)φnormal to ellipsoidEhNlocal Cartesian (grid E,N + height h)
Figure — Geodetic coordinates (φ, λ, h) locate a point by the ellipsoid normal, longitude and ellipsoidal height; projected/local Cartesian (E, N, h) express the same point on a plane grid with a linear height.

(a) 3-D Cartesian (E, N, h). Use projected/plane Cartesian coordinates when working at local to regional scale where distances, areas and directions must be computed by ordinary plane trigonometry — the everyday world of engineering surveying, cadastral mapping, GIS analysis, construction layout and municipal data. Grid coordinates (a projection such as UTM or 3° MTM, plus an orthometric or ellipsoidal height) are convenient because they are rectangular, additive and directly usable in CAD/GIS overlay, buffering and area calculation. They are ideal when the area of interest is small enough that projection scale distortion is negligible or can be handled by a scale factor, and when the data will be combined with other planar layers. (A geocentric Earth-Centred-Earth-Fixed X, Y, Z Cartesian system, by contrast, is used internally for datum transformations and satellite geodesy.) (b) 3-D Geodetic (φ, λ, h). Use geodetic (curvilinear) coordinates — latitude, longitude and ellipsoidal height on a defined ellipsoid/datum — when working over large regions, nationally or globally, where the Earth's curvature cannot be ignored, and when data must be datum-defined and projection-independent so it can later be projected into any grid. Geodetic coordinates are the natural output of GNSS positioning, the basis of national and continental reference frames (NAD83(CSRS), ITRF, WGS84), and the required form for global datasets, datum transformations, long-line geodetic computations and any exchange of position that must remain unambiguous regardless of projection. In short: Cartesian grid coordinates for local planar analysis and mapping; geodetic coordinates for wide-area, GNSS-based and datum-referenced work.