This document presents a new method for analyzing steep slope models (SSM) in GIS using vector algebra. SSMs in the form of triangle meshes are built from point clouds obtained via terrestrial photogrammetry. Normal vectors of each triangle are used to compute slope and aspect. The values are saved as attributes. Python scripts implement the procedures as a GIS plug-in tool. As a case study, the method analyzes slopes of the Kościelec Mountain in Poland. Results show the ability to preserve extreme slope values and introduce SSMs into GIS for monitoring, interpretation, and environmental modeling of steep mountain areas.

1. VECTOR ALGEBRA FOR STEEP SLOPE MODELS ANALYSIS
Natalia Kolecka 1
1 Department of GIS, Cartography and Remote Sensing, Jagiellonian University, Krakow, Poland – nkolecka@gis.geo.uj.edu.pl
The most powerful and effective method of relief representation are Digital Elevation Models In mountainous regions many steep and even overhang parts of rock walls and slopes can be
(DEMs) – mathematical models of surface of the Earth. They are significant component of observed. In 2.5D GIS they stay unexplored and even unnoticed, as GRID and TIN are not able to
Geographic Information Systems (GIS) and play important role in environmental modeling. The describe such a relief, having birds eye perspective. From the terrestrial point of view, the steep
basic parameters that allow terrain characterization are slope gradient and aspect. They can be slopes are sometimes very huge and various. Such a perspective can be introduced via computer
calculated from DEMs. Geographic Information Systems offer many algorithms that allow grid graphics software that allows 3D surface modeling by means of mesh, e.g. 3D triangular network.
and TIN (Triangular Irregular Network) surface models analysis. Nevertheless, in most
applications grid data are used, and 3x3 kernel (window) is moving along the grid in x and y This work presents a new concept that implements 3D mesh in GIS and utilize vector algebra to
directon to compute value for each cell. The method, however, tends to underestimate slope analyze such a surface. The idea is based on using normal vectors to compute slope and aspect of
when using low-resolution grids or on rough surfaces. each triangle in a mesh. The computed values are saved as their attributes. Complete procedures
The traditional DEMs encompass only simplified depiction, as they are limited to 2.5D models, are written in Python programming language and implemented into popular GIS software to work
where one planar (X,Y) position refers to only one vertical (Z) value. as a plug-in tool.
METHODOLOGY
In this work, steep slope models (SSM) in the shape of triangle Z
mesh were used. They were built from point clouds, obtained STL ASCII – the file exchange format:
using terrestrial photogrammetry, by means of 3D surface
triangulation. solid name normal vector
Y facet normal nux nuy nuz of each triangle
outer loop
vertex x1 y1 z1
vertex x2 y2 z2
vertex x3 y3 z3 coordinates
endloop of vertexes
endfacet of each triangle
endsolid name
Python
triangle – basic programming
reference unit X
language
The normal vector n is a vector perpendicular to the planar
surface – triangle in this case. The unit vector in direction of
vector n is called vector nu and comprises of 3 components in
major axes directions:
nux, nuy, nuz
They are used to compute slope (ς) and aspect (ψ) of the surface,
CAD / computer graphic environment according to equations:
GENERATE file:
id SSMs introduction
x1 y1 z1 NORMAL file:
x2 y2 z2 id ni nj nk into GIS
x3 y3 z3
END
STUDY AREA
In this study one of the most popular places in the Polish Tatra
Mountains was chosen – surroundings of the Gąsienicowa Valley
and Orla Perć (legendary alpine tourist route). Differences in
altitude reach 800 m, landscape changes from sub-alpine dwarf
pine shrubs, through alpine meadows right up to bare rocks.
Broad valleys are surrounded by steep rock cliffs.
Western walls of the Kościelec Mountain (2155 m) – the exact
object of the investigation – are one of the most interesting and
popular rock climbing areas in the Polish High Tatra Mts. The
wall is about 300 meters high, has varied relief and some parts
are overhung.
RESULTS and CONCLUSION
slope [°] slope [°]
1 2 3
aspect
slope [°]
Following conclusions can be drawn on 3D analysis based on vector algebra:
• it can be very efficient and useful when it comes to monitoring,
interpretation and environmental modeling of steep mountain slopes,
• it enables basic reference unit minimization Results of the test model analysis: slope (upper)
• It enables preservation of extreme values that can be introduced and aspect (lower):
and analyzed in GIS environment. in orthogonal projection onto XY plane (Fig. 1)
and in perspective view (Fig. 2)
Results of slope analysis (Fig. 3):
in orthogonal projection onto XY plane (upper) and in perspective view (lower)
References:
1. Corripio J.G., 2003. Vectorial algebra algorithms for calculating terrain parameters from DEMs and solar radiation modelling in mountainous
terrain. International Journal of Geographical Information Science, Vol. 17, No. 1, s. 1-23.
2. Hodgson, M. E., 1998. Comparison of angles from surface slope/aspect algorithms. Cartography and Geographic Information Systems, 25, 173–185. Natalia Kolecka is grant holder of Doctus - Małopolski fundusz stypendialny dla doktorantów (fund for
3. Hodgson M.L., Gaile G.L. , 1999. Cartographic modeling approach for surface orientation-related applications. Photogrammetric Engineering and PhD students from Małopolska, whose thesis is innovative and very significant for the region), co-
financed by the European Union within the framework of the Human Capital Programme.
Remote Sensing 65:85–95.