Spatial Databases: Digital Terrain Model Spring, 2018 Ki-Joune Li

2.5-D Objects vs. 3-D Objects Representation Methods of Terrain 2.5-D representation 3-D representation 3-Dimensional Objects More rich information More complicated and larger than 2-D objects 2.5- Data F:(x,y)  h : one height value at each point Efficient to represent surfaces or field data p8 p7 p6 p2 p1 p4 p5 l1 l3 l2 l4 p3 l7 l8 l12 l9 l11 l10 l5 l6 A1 A2 A3 A4 A5 A6

Representation of 2.5-D data Well-Known Methods Contour Lines DEM (Digital Elevation Model) TIN (Triangulated Irregular Network)

Contour Lines (Contour Lines, Iso-lines) Most popular method for paper maps Set of pairs (polygon, h) Nested polylines Contour line # Polygon # height I1 PG4 150 I2 PG3 200 I3 PG8 250 I4 PG9 300 I2 I1 I4 I3

Contour Lines (Contour Lines, Iso-lines) Not good for digital maps due to Size of data Difficulty to process and extract useful information Low accuracy due to multiple approximations to compute contour lines from measured points

DEM (Digital Elevation Model) Grid division and one height data to each grid 2-D array of height data 156

DEM (Digital Elevation Model) Most popular method due to its simplicity Problems Large volume of data Expensive computation as well as large amount data Low accuracy due to stair-effect

TIN (Triangulated Irregular Network) Set of triangulated mashes Relatively Small Volume (x1,y1,z1) Find height by triangular interpolation p (x3,y3,z3) (x2,y2,z2)

Triangular Interpolation by TIN Nodes are measured points Normal vector of the plane n p(x, y, z) (x1,y1,z1) (x2,y2,z2) (x3,y3,z3) For a given point p(x, y) the height z is computed by the equation a (x- x1) + b (y- y1) + c (z- z1) = 0

TIN (Triangulated Irregular Network) Triangulation Delaunay Triangulation Triangulation that circumcircle of a triangle is an empty circle Duality of Voronoi diagram Providing accurate interpolation method Constraint Triangulation Respect break lines: No intersection with break lines Example: Falls

Data Structure for TIN Two tables Triangle Table Node Table ⓩ ③ ① D A ⑩ B C ⑥ ④ ⑤ J H F I G ⑨ ⑦ ⑧ Triangle Table Node Table T# Nodes Adjacent Triangles N1 N2 N3 T1 T2 T3 A 1 2 4 B EX 5 F C . . . J 6 9 10 E I N# x y z 1 10 2 20 25 15 . . .

Weak Points of TIN Large Volume of Data Tradeoff Relationship between Size and Accuracy Loss of Geo-morphological Properties Originally designed for Height Estimation No consideration on the representation of Geo-morphological Properties

Geo-morphological Properties vs. Height Height of this point ? 745.6 m What is the optimal path from p to q ? p q Very difficult to find it with only height data → Need some geomorphological Information. (e.g. saddle points and ridges) By TIN, they are implicitly and partially described We should derive them But not the full information TIN

SPIN TIN : Height Representation With a set of triangles and Linear interpolation SPIN: Geo-morphological Representation With a set of geo-morphological (or Structural) polygons Constrained (Delaunay) Triangulation and

Example of SPIN Structural Sections : Ridges, Valleys and Boundaries Structural Polygon : bounded by structural sections

Ridge and Valley Geomorphological Properties to be Considered by SPIN Ridges, Valley and Transfluent Most Frequently Used Geomorphological Information Drainage Network, Path Analysis, etc. Not Derivable from TIN

Example of SPIN

Observations of SPIN Some structural sections Dangling Sections Constraints of Triangulation Face of a Structural Polygon : no more plane surface More than three vertices But relatively Homogeneous Number of vertices Significantly Reduced Improvement of Accuracy

Adjacency of Polygons Polygonal Irregular Network Adjacency Graph Improve Search Performance A C D E F B F E A B D C

Basic Algorithms with SPIN Estimation of Height

SPIN : Plane Region

SPIN : Mountain Region

Comparison