DEM Data Models and Their Comparison: 18-Geom-B1 Digital Terrain Modelling, December 2017, Q1

Question 1: DEM Data Models and Their Comparison (10 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.

Given. Digital elevation data may be organized in several ways; the question asks for the three dominant structures and a structured comparison.

Find. (1.1) the three most common DEM data models, and (1.2) a tabular comparison across six characteristics.

1.1 — The three most common DEM data models. (a) the regular grid (raster) model — elevations stored at the nodes of a square lattice of fixed spacing; (b) the triangulated irregular network (TIN) — irregularly located mass points joined into non-overlapping (usually Delaunay) triangles; and (c) the contour (digital line) model — the surface represented by strings of digitized iso-elevation lines (with spot heights). Grid and TIN dominate modern practice; the contour model persists from map-derived data.

1.2 — Comparison.

Characteristic	Regular grid (raster)	TIN	Contour lines
Structure	Matrix of square cells; one Z per node at fixed spacing	Network of non-overlapping triangles over irregular points	Strings of vector iso-lines at a fixed contour interval
Georeferencing	Implicit — only origin and cell size stored; (X,Y) inferred from row/column	Explicit — (X,Y,Z) stored for every vertex plus triangle topology	Explicit — (X,Y) digitized along each line, one Z per line
Storage	Compact per node but redundant — flats over-sampled to resolve the roughest zone	Efficient — density adapts to terrain, but topology adds overhead	Moderate; volume grows with line detail; poor compression on complex relief
Data analysis	Simple, fast matrix algebra (slope, aspect, hydrology, map algebra)	Efficient once built, but algorithms need triangle adjacency	Weak — usually converted to grid/TIN before analysis
Applications	Hydrology, viewshed, orthorectification, regional/national base DEMs	Engineering design, earthworks, sites needing breaklines	Cartographic display, legacy topographic mapping
Terrain representation	Uniform resolution; rounds off sharp features between posts	Adaptive; vertices placed on breaklines/peaks/pits — highest fidelity	Good along lines but sparse and ambiguous between contours

Concept & Theory

Topic. The three canonical DEM data structures and their trade-offs.

Key relations. Grid storage $\approx n_Z$ (topology implicit); TIN storage $\approx n(X,Y,Z) + \sim\!2n$ triangles (topology explicit, by Euler $\#\triangle \approx 2n-2-h$); contour data $\propto$ line length $\times$ point density.

Why this works. Each model trades simplicity against adaptivity: the grid buys fast, implicit-topology analysis at the cost of uniform (often wasteful) sampling; the TIN buys feature fidelity and adaptive density at the cost of stored topology; contours preserve the cartographic form but are poor for computation. The right choice follows the intended use.

Common pitfall. Treating the contour model as analysis-ready — it must be interpolated to a grid or TIN first, and naive interpolation between widely spaced contours flattens ridges and valleys.

Source. Li, Zhu & Gold, Digital Terrain Modeling, ch. 2; Maune, DEM Users Manual, ch. 1–2.

Question 1 of 12: DEM Data Models and Their Comparison

Question 1: DEM Data Models and Their Comparison (10 marks)