MATLAB中DEM山体阴影的生成技巧

在地理绘图中，我们使用的DEM数据添加山体阴影使得绘制的图件显得更加的美观。

GIS中使用ArcGIS软件就可以达到这一目的，或者使用GMT，同样可以得到山体阴影的效果。

本文提供了一个MATLAB的函数，可以得到山体阴影。

clear all;clc;close all
load demo.mat
%% draw hillshade
x=x(:,1);
y=y(1,:);
hs=hillshade_esri(z,x,y);
subplot(1,2,1)
imagesc(x,y,z')
axis image
set(gca,'ydir','normal')
title('DEM')
colormap(gray)
caxis([min(z(:)) max(z(:))])
subplot(1,2,2)
imagesc(x,y,hs')
axis image
set(gca,'ydir','normal')
title('Hillshade')
colormap(gray)
hold on
caxis([min(hs(:)) max(hs(:))])
drawnow

其中调用的函数 hillshade_esri.m如下：

function h = hillshade_esri(dem,X,Y,varargin)
% PUPROSE: Calculate hillshade for a digital elevation model (DEM) based on
%          the algorithm posted on http://edndoc.esri.com/arcobjects/9.2/net/shared/geoprocessing/spatial_analyst_tools/how_hillshade_works.htm
% -------------------------------------------------------------------
% USAGE: h = hillshade_esri(dem,X,Y,varagin)
% where: dem is the DEM to calculate hillshade for
%        X and Y are the DEM coordinate vectors
%        varargin are parameters options
%
% OPTIONS:
%        'azimuth'  is the direction of lighting in deg (default 315)
%        'altitude' is the altitude of the lighting source in
%                   in degrees above horizontal (default 45)
%        'zfactor'  is the DEM altitude scaling z-factor (default 1)
%        'plotit'   creates a simple plot of the hillshade
%
% EXAMPLE:
%       h=hillshade_esri(peaks(50),1:50,1:50,'azimuth',45,'altitude',100,'plotit')
%       - calculates the hillshade for an example 50x50 peak surface.
%       - changes the default settings for azimuth and altitude.
%       - creates an output hillshade plot

% See also: GRADIENT, CART2POL
%
% Note: Uses ESRIs hillshade algorithm, the output will be the same as the
% output with ArcGIS Hillshade Function.
%
% Felix Hebeler, Dept. of Geography, University Zurich, February 2007.
% modified by Andrew Stevens (astevens@usgs.gov), 5/04/2007
% modified by Wenbin Jiang (jwbalbert@gmail.com), 7/06/2011

%% configure inputs
%default parameters
azimuth=315;
altitude=45;
zf=1;
plotit=0;

%parse inputs
if isempty(varargin)~=1     % check if any arguments are given
    [m1,n1]=size(varargin);
    opts={'azimuth';'altitude';'zfactor';'plotit'};
    for i=1:n1;             % check which parameters are given
        indi=strcmpi(varargin{i},opts);
        ind=find(indi==1);
        if isempty(ind)~=1
            switch ind
                case 1
                    azimuth=varargin{i+1};
                case 2
                    altitude=varargin{i+1};
                case 3
                    zf=varargin{i+1};
                case 4
                    plotit=1;
            end
        end
    end
end

%% Initialize paramaters
dx=abs(X(2)-X(1));  % get cell spacing in x and y direction
dy=abs(Y(2)-Y(1));  % from coordinate vectors

% lighting azimuth
azimuth = 360.0-azimuth+90; %convert to mathematic unit
azimuth(azimuth>=360)=azimuth-360;
azimuth = azimuth * (pi/180); %  convert to radians

%lighting altitude
altitude = (90-altitude) * (pi/180); % convert to zenith angle in radians

%% calc slope and aspect (radians)
im=length(X);
jm=length(Y);
fx=zeros(im,jm);
fy=zeros(im,jm);
asp=zeros(im,jm);
for i=2:im-1
    for j=2:jm-1
        fx(i,j)=((dem(i+1,j+1)+2*dem(i+1,j)+dem(i+1,j-1))-(dem(i-1,j+1)+2*dem(i-1,j)+dem(i-1,j-1)))/8/dx;
        fy(i,j)=((dem(i-1,j-1)+2*dem(i,j-1)+dem(i+1,j-1))-(dem(i-1,j+1)+2*dem(i,j+1)+dem(i+1,j+1)))/8/dy;
        if fx(i,j)~=0
            asp(i,j) = atan2(fy(i,j),-fx(i,j));
            if asp(i,j)<0
                asp(i,j)=asp(i,j)+2*pi;
            end
        else
            if fy(i,j)>0
                asp(i,j)=pi/2;
            elseif fy(i,j)<0
                asp(i,j)=3*pi/2;
            end
        end
    end
end
grad = hypot(fx,fy);
grad=atan(zf*grad); %steepest slope

%% hillshade calculation
h = 255.0*( (cos(altitude).*cos(grad) ) + ( sin(altitude).*sin(grad).*cos(azimuth-asp)) ); % ESRIs algorithm
h(h<0)=0; % set hillshade values to min of 0.
h=setborder(h,1,NaN); % set border cells to NaN

%% plot results if requested
if plotit==1
    figure
    imagesc(X,Y,h')
    axis image
    set(gca,'ydir','normal')
    colormap(gray)
end

%% -- Subfunction--------------------------------------------------------------------------
function grid = setborder(grid,bs,bvalue)
grid(1:bs,:)=bvalue; %toprows
grid(size(grid,1)-bs+1:size(grid,1),:)=bvalue; %bottom rows
grid(:,1:bs)=bvalue; %left cols
grid(:,size(grid,2)-bs+1:size(grid,2))=bvalue;

其中有三个参数可以修改：azimuth=315;altitude=45;zf=1;

1. 修改 azimuth，the direction of lighting in deg，下图的变化范围为0：360：
6. GIF

2.修改 altitude，the altitude of the lighting source in degrees above horizontal，下图变化范围为0：180：

GIF

3.修改 zf，the DEM altitude scaling z-factor ，下图变化范围为1：50：

GIF

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