18-Geom-B1 Digital Terrain Modelling · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2017 — 3 hours, closed book (one approved Casio or Sharp calculator permitted). The schedule prints TWELVE questions and states that "10 questions constitute a complete paper": Part A (Q1–Q8) is compulsory, Part B requires ONE of Q9–Q10, and Part C requires ONE of Q11–Q12, for a 100-mark paper. All twelve questions are solved below for completeness (a candidate would answer only Q1–Q8 plus one from each of Parts B and C).
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, 2014); Isaaks & Srivastava, An Introduction to Applied Geostatistics (Oxford, 1989). Canadian datums throughout (NAD83(CSRS), CGVD2013).
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. A continuous terrain surface that must be represented by a finite set of measured heights.
Find. (3.1) the sampling process and the parameters that control it; (3.2) one named sampling method with its advantages and disadvantages.
3.1 Terrain sampling process and parameters. Sampling is the selection of a finite set of surface points whose heights are measured so that the continuous terrain can later be reconstructed by interpolation. It proceeds by choosing where (the spatial pattern of points) and how densely to measure, subject to the fidelity required and the cost budget. The governing parameters are: the sampling interval / density (spacing between points, which sets the resolution and, by a Nyquist argument, the smallest feature that can be recovered — $\Delta \le \tfrac{1}{2}\lambda_{\min}$); the spatial pattern or distribution (regular grid, random, or feature-driven irregular); the orientation/alignment of the sampling scheme relative to the terrain grain; and the deliberate inclusion of feature-specific points — breaklines, spot heights at peaks, pits and saddles — that a blind pattern would miss. These parameters are balanced so the model meets its accuracy specification at minimum data volume, ideally by making density adaptive to terrain roughness and slope.
3.2 A sampling method — progressive (adaptive) sampling. In progressive sampling the terrain is first measured on a coarse regular grid; the local surface curvature (second differences) is analysed, and wherever the curvature or estimated interpolation error exceeds a threshold the grid is refined (halved) in that patch, the test repeated, and the process iterated. The result is a locally dense, globally sparse sample — fine on rough or steep ground, coarse on smooth flats. Advantages: density automatically matches terrain complexity, so accuracy is met with far fewer points than a uniform fine grid, avoiding both over-sampling of flats and under-sampling of rough zones; it is objective and automatable. Disadvantages: it requires repeated passes/interaction (costlier to run than a single-pass grid), the refinement is driven by curvature and can still miss linear discontinuities unless breaklines are added separately (hence the hybrid “composite sampling”), and the irregular output needs a TIN or interpolation to become a usable surface.
