18-Geom-B1 Digital Terrain Modelling · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2015 — 3 hours, closed book (an approved Casio or Sharp calculator permitted). TWELVE numbered questions constitute a complete paper; each is of varying value and the margin schedule totals 100 marks. Most answers are required in essay format, so clarity and organization are graded. All twelve questions are solved below for completeness.
Reference texts: Li, Zhu & Gold, Digital Terrain Modeling — Principles and Methodology (CRC Press, 2005); Maune (ed.), Digital Elevation Model Technologies and Applications: The DEM Users Manual (2nd ed., ASPRS, 2007); Wilson & Gallant, Terrain Analysis — Principles and Applications (Wiley, 2000); Wolf, Dewitt & Wilkinson, Elements of Photogrammetry with Applications in GIS (4th ed., McGraw-Hill); Natural Resources Canada High-Resolution DEM (HRDEM) and CDEM product specifications. Canadian datums throughout (NAD83(CSRS), CGVD2013).
Note: this December 2015 paper is the same twelve-question essay set as the December 2014 04-Geom-B1 exam, re-ordered and with one definition changed (Q3(e) asks for the contour interval where the 2014 paper asked for the interpolation method). The margin marks are internally consistent this year — every sub-part annotation matches its header weight and the schedule sums to 100.
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.
Given. Two competing structures for storing a terrain surface—a regular raster grid, and an irregular point set organized as a Triangulated Irregular Network (TIN).
Find. The advantages and disadvantages of each structure for data volume, surface-representation accuracy and contour generation.
(a) Data volume. The grid is compact per point—only the $Z$ array plus an origin and spacing need be stored, with the $(X,Y)$ position implicit—so per stored node it is minimal and simple to compress. Its disadvantage is that density is uniform: to resolve the roughest zone the whole area is oversampled, wasting storage on flats. The TIN stores $(X,Y,Z)$ and explicit triangle topology (roughly $2n$ triangles for $n$ points), so each point is heavier, but the total point count is far lower because density adapts—dense on rough ground, sparse on smooth. Net: grids can balloon on large uniform-resolution jobs; TINs are efficient for variable terrain but carry topology overhead.
(b) Accuracy of surface representation. The TIN generally represents the surface more faithfully because vertices can be placed exactly on breaklines, ridges, peaks and pits, so slope discontinuities are honoured and no important point is averaged away; triangle facets follow the real morphology. The grid forces samples onto arbitrary node locations that rarely coincide with terrain features, so sharp edges are rounded and small features between posts are lost unless the grid is very fine. The grid's advantage is a smooth, artefact-free look on gentle terrain; its weakness is fidelity at discontinuities.
(c) Contour generation. From a grid, contouring is algorithmically simple and fast (threading contours cell-by-cell through a raster with bilinear interpolation), giving smooth, evenly-formed lines—but the contours can wander or produce artefacts where breaklines are ignored, and flat areas create ambiguity. From a TIN, contours are generated by linear interpolation along triangle edges; because breaklines are built in, the contours respect ridges and channels and are geomorphologically correct, but they can look faceted/angular (straight segments across each facet) and need smoothing for cartographic quality. In short: grids give smoother-looking but less structurally-correct contours; TINs give structurally-correct but more angular contours.
