gradientm (Mapping Toolbox)

Numerical gradient, slope and aspect of matrix maps.

Syntax

[aspect,slope,gradN,gradE] = gradientm(map,maplegend)
[...] = gradientm(lat,lon,map)
[...] = gradientm(map,maplegend,ellipsoid)
[...] = gradientm(lat,lon,map,ellipsoid)
[...] = gradientm(lat,lon,map,ellipsoid,units)

Description

[aspect,slope,gradN,gradE] = gradientm(map,maplegend) computes the slope, aspect and north and east components of the gradient for a regular matrix map. If the map contains elevations in meters, the resulting aspect and slope are in units of degrees clockwise from north and up from the horizontal. The north and east gradient components are the change in the map variable per meter of distance in the north and east directions. The computation uses finite differences for the map variable on the default earth ellipsoid.

[aspect,slope,gradN,gradE] = gradientm(lat,lon,map) does the computation for a general matrix map.

[aspect,slope,gradN,gradE] = gradientm(map,maplegend,ellipsoid) and [aspect,slope,gradN,gradE] = gradientm(lat,lon,map,ellipsoid) use the provided ellipsoid definition. The ellipsoid vector is of the form [semimajor axes, eccentricity]. If the map contains elevations in the same units as ellipsoid(1), the slope and aspect are in units of degrees. This calling form is most useful for computations on bodies other than the earth.

[aspect,slope,gradN,gradE] = gradientm(lat,lon,map,ellipsoid,units) specifies the angle units of the latitude and longitude inputs. If omitted, 'degrees' are assumed. For elevation maps in the same units as ellipsoid(1), the resulting slope and aspect are in the specified units. The components of the gradient are the change in the map variable per unit of ellipsoid(1).

Example

Compute the gradient, slope, and aspect for a regular matrix map based on the MATLAB peaks matrix. Show the gradientm outputs as colors on a three-dimensional surfaces of elevation. The surfaces are shown with no vertical exaggeration.

map = 500*peaks(100);
maplegend = [ 1000 0 0];
[aspect,slope,gradN,gradE] = gradientm(map,maplegend);

figure
worldmap(gradN,maplegend,'none')
meshm(gradN,maplegend,size(map),map)
hcb = 
contourcmap(1,'jet','colorbar','on','ylabelstring','Gradient 
(North Component)');
view(3)
daspectm meters
camlight
shading interp; lighting phong
framem off

clmo surface
meshm(gradE,maplegend,size(map),map)
set(get(hcb,'ylabel'),'String','Gradient (East Component)');
shading interp; lighting phong

clmo surface
meshm(slope,maplegend,size(map),map)
contourcmap(10,'hot','colorbar','on','ylabelstring','Sloep 
(degrees)')
colormap(flipud(colormap))
shading interp; lighting phong


clmo surface
meshm(aspect,maplegend,size(map),map)
contourcmap(30,'hsv','colorbar','on','ylabelstring','Aspect 
(degrees)')
shading interp; lighting phong

load korea
[aspect,slope,gradN,gradE] = gradientm(map,maplegend);
worldmap(slope,maplegend);
contourcmap(1,'cool','colorbar','on','ylabelstring','Slope 
(degrees)')
hidem(gca)

Remarks

Coarse digital elevation models may considerably underestimate the local slope. For the above map, the elevation points are separated by about 10 kilometers. The terrain between two adjacent points is modelled as a linear variation, while actual terrain may vary much more abruptly over such a distance.

See Also

gradient
Approximate gradient

viewshed
Visible areas from a point on a digital elevation map

`gradient`	Approximate gradient
`viewshed`	Visible areas from a point on a digital elevation map

getseeds grepfields