Kursus Matlab di Jakarta Selatan KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060: 2D graphics and D graphics in Matlab

2D graphics and D graphics in Matlab

• 2D graphics

- plot

- axes & labels

- multiple plots

- special plots

• 3D graphics

- line

- surface

• Polynomials

• Interpolation & splines

• Optimisation

• Integration, differentiation & ODEs

• Data-structures

• Object Oriented

• GUIs

• Toolboxes

27 3D MAPS IN MATLAB, A CASE STUDY

• To date we have concentrated on the Matlab programming language & its constructs

• Today’s lecture looks at employing the various language features we have seen

- solve a semi-artificial problem

- larger in scale than those seen in class or assignments

- a suite of related functions for the creation and manipulation of pseudo-realistic 3D maps

References: Matlab Competency Exercises

Matlab Lectures

27.1 Problem Specification

• DSTO’s Synthetic Environment Research Facility (SERF) is looking for some 3D terrain generation suitable for their various wargame simulations.

• The program(s):

- should generate 3D digital terrain suitable for incorporation into their CAEN (Close Action ENvironment) system

- should produce the data as a grid of heights at equi-spaced intervals

- should generate terrain that allows the exploration of hidden movement, line-of-sight, and other important issues for small unit actions.

- should generate terrain that is plausible

- should be capable of generating different (random) terrain each time

- should be capable of generating terrain of any arbitrary size

- should not employ algorithms that are too computationally complex: i.e., there is no need to model true geological forces

27.2 Basic Approach & Data Structure

• Basic Approach:

- employ a suite of related functions which create and manipulate maps

- a function to initiate the process with a random grid of heights

- functions to “mimic” certain gross physical processes: weathering, river addition, meteor impact, etc.

- each function is independent of the others: the map data-type is simply passed to and from functions

• Data Structure:

- a 2D array (matrix) matches the problem well

- element values for the matrix represent the height at that point

- indices (row & column) represent the evenly spaced horizontal grid atop which the heights “sit”

Approach (Cont)

27.3 Map Creation – Algorithm

• Generate a map of initial, random heights

• Notes:

- Matlab has in-built uniform and normally distributed random number generators

Top-Level Algorithm

handle variable arguments

if grid required

calculate meshgrid

generate a matrix (map) of random values of the appropriate size

Handle Variable Arguments

if no size specified for the map then

set size to default (50x50)

else if only one size specified

set 2nd size dimension to match the first

27.4 Map Creation – Example

original=mapGen(50,60);

surf(original);

shading interp;

colormap copper;

axis off;

<print>

contour(original);

colormap default;

axis off;

<print>

27.5 Created Map

27.6 Map Creation – Code

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% MAPGEN Generate a random map (grid of

% elevation data)

% [X,Y,Z] = mapGen - Generate a 50x50 grid of

% elevation data

% Z = mapGen - as above but without the meshgrid

% (X & Y)

% [X,Y,Z] = mapGen(N) - Generate an NxN grid

% of elevation data

% Z = mapGen(N) - as above but without the

% meshgrid (X&Y)

% [X,Y,Z] = mapGen(N,M) - Generate an NxM grid

% of elevation data

% Z = mapGen(N,M) - as above without the

% meshgrid (X & Y)

% Author: Spike

% Date: 11/10/98 (modified 1/4/1999)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [X, Y, Z] = mapGen(xSize,ySize)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Provide a default size if none given

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if nargin==0

xSize=50;

ySize=50;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Else if a square map then set both dimensions

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

elseif nargin==1

ySize=xSize;

end;

Map Creation Code (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Create x and y arrays (vectors) ranging from 0

% to 1. These are then used by meshgrid to

% generate the X & Y matrices required by surf()

% and other 3D plot functions

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if nargout==3

x=linspace(0,1,xSize);

y=linspace(0,1,ySize);

[X Y]=meshgrid(x,y);

% Make a grid of all x & y combinations

end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% The "real" work. Create a set of heights for

% the map as a matrix of size xSize by ySize.

% Heights are derived from a uniform

% distribution with mean 0 and std. dev. of 1.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if nargout==3

Z=randn(xSize,ySize);

else

X=randn(xSize,ySize);

end;

27.7 Map Smoothing/Weathering – Algorithm

• Smooth/weather a map an by averaging the height of a point with those about it

• Notes:

- the user may specify how many times to apply the smoothing and what weighting to apply to the old-point and those about it.

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Top-Level Algorithm

handle variable arguments

for the number of smoothings requested

smooth the entire map

Smooth the Entire Map

for each point on the map’s surface

calculate the mean height of the points

surrounding it

set new height as weighted sum of old height

and mean height of those surrounding

For each point on the Map’s Surface

for every row in the matrix

for every column (within the row)

Note: Due to points along edges of the map having less surrounding points, the four edges and the four corner points are dealt with separately as special cases. Hence there are actually 6 loops plus 4 special one-off cases: the double loop above for the general cases (points not on an edge), one loop for each of the four edges, and the four corners.

27.8 Map Smoothing – Example

after50=mapSmooth(original,50);

surf(after50);

shading interp;

colormap copper;

axis off

<print>

contour(after50);

axis off;

colormap default;

<print>

27.9 Smoothed Map

27.10 Map Smoothing – Code

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% MAPSMOOTH Smooth an existing map (2D elevation data)

% map=mapSmooth(oMap) smooths an existing map

% once with a weight of 0.5 for surrounding

% points.

% map=mapSmooth(oMap,iterations) repetitively

% smooths the map `iteration' times.

% map=mapSmooth(oMap,iterations,surroundWeight)

% repetively smooths the map with the given

% weighting. SurroundWeight should be within

% 0 to 1. 0 implies no smoothing. 1 implies

% maximum smoothing.

% See Also mapGen, mapMeteor, mapPlateau,

% mapRiver, mapFloor

% Author: Spike

% Date: 11/10/98

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function smoothed = mapSmooth(oMap,iterations,surroundWeight)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Default to only one application of smoothing.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if nargin==1

iterations=1;

end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% No weight provided: defaults to 0.5 value.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if nargin==1 | nargin==2

surroundWeight=0.5;

end;

Map Smoothing Code (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Determine the edges of the map.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xUpper=size(oMap,1);

yUpper=size(oMap,2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Main body of program:

% for the number of times smoothing must be applied

% for each row

% for each column on that row

% smooth the current point with those

% around it.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for ntimes=1:iterations % For the number of

% smoothings requested

for i=2:xUpper-1 % For each row

% (besides top& bottom)

for j=2:yUpper-1 % For each column

% (besides left and

% right most)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Calculate smoothed value at (i,j) as

% weighted sum of old value and mean of

% those surrounding it.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

surround=mean([oMap(i-1,j-1),oMap(i-1,j), oMap(i-1,j+1),...

oMap(i,j-1),oMap(i,j+1),...

oMap(i+1,j-1), oMap(i+1,j), oMap(i+1,j+1)]);

smoothed(i,j)=surroundWeight*surround + ...

(1.0-surroundWeight)*oMap(i,j);

end;

Map Smoothing Code (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% The special cases --> All along the edges.

% These don't have a full 8 points surrounding

% them and hence the smoothing is different

% Left-most and right-most column

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for i=2:xUpper-1

smoothed(i,1)=(1.0-surroundWeight)* oMap(i,1)+...

surroundWeight*mean([oMap(i-1,1), oMap(i+1,1), oMap(i,2),...

oMap(i-1,2), oMap(i+1,2)]);

smoothed(i,yUpper)=(1.0-surroundWeight)* oMap(i,yUpper)+...

surroundWeight*mean([oMap(i-1,yUpper), oMap(i+1,yUpper),...

oMap(i,yUpper-1), oMap(i-1,yUpper-1), oMap(i+1,yUpper-1)]);

end;

%%%%%%%%%%%%%%%%%%%

% Top & bottom row

%%%%%%%%%%%%%%%%%%%

for i=2:yUpper-1

smoothed(1,i)=(1.0-surroundWeight)* oMap(1,i)+...

surroundWeight*mean([oMap(1,i-1), oMap(1,i+1), oMap(2,i),...

oMap(2,i-1), oMap(2,i+1)]);

smoothed(xUpper,i)=(1.0-surroundWeight)*o Map(xUpper,i)+...

surroundWeight*mean([oMap(xUpper,i-1), oMap(xUpper,i+1),...

oMap(xUpper-1,i), oMap(xUpper-1,i-1), oMap(xUpper-1,i+1)]);

end;

Map Smoothing Code (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% The extra special case of the four corners.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

smoothed(1,1)=(1.0-surroundWeight)* oMap(1,1)+surroundWeight*mean([...

oMap(1,2), oMap(2,1), oMap(2,2)]);

smoothed(1,yUpper)=(1.0-surroundWeight)* oMap(1,yUpper)+...

surroundWeight*mean([oMap(1,yUpper-1), oMap(2,yUpper),...

oMap(2,yUpper-1)]);

smoothed(xUpper,1)=(1.0-surroundWeight)* oMap(xUpper,1)+...

surroundWeight*mean([oMap(xUpper-1,1), oMap(xUpper,2),...

oMap(xUpper-1,2)]);

smoothed(xUpper,yUpper)=(1.0-surroundWeight)* oMap(xUpper,yUpper)+...

surroundWeight*mean([oMap(xUpper-1,yUpper), oMap(xUpper,yUpper-1),...

oMap(xUpper-1,yUpper-1)]);

oMap=smoothed;

end;

27.11 Crater Addition – Algorithm

• Add a meteor impact crater to an existing map

• Note:

- user can specify location, depth and radius for the impact

Top-Level Algorithm

handle variable arguments

for every point on the map

if it lies within the crater then

set a new height of the crater depth

else if it lies on the crater’s rim

set a new crater rim height

else

leave the height unchanged

Handle variable arguments

if no radius or incorrectly specified radius

randomly determine one as roughly 10% of the

smaller dimension

if no depth specified then

randomly determine a depth as roughly the lowest

point on the map

if no centre for crater provided or out-of-bounds

randomly determine a centre

27.12 Crater Addition – Example

afterMeteor=mapMeteor(after50,10,min(min(after50)),30,30);

surf(afterMeteor);

axis off;

shading interp;

colormap copper;

<print>

contour(afterMeteor);

colormap default;

axis off;

<print>

27.13 Cratered Map

27.14 Crater Addition – Code

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% MAPMETEOR Add a meteor impact to an existing map.

% mapMeteor(oMap) - adds a single impact to

% the map such that its depth is

% approximately that of the lowest valley on

% oMap, and its radius is approximately 10%

% of the smallest dimension of the map.

% mapMeteor(oMap,radius) - adds a single

% meteor as above but with radius of

% "radius" units.

% mapMeteor(oMap,radius,depth) - as above but

% uses the specified depth.

% mapMeteor(oMap,radius,depth,xCentre,yCentre) –

% as above but rather than randomly located

% it is centred at xCentre, yCentre.

% Author: Spike

% Date: 1/2/99

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function newMap = mapMeteor(oMap,radius,depth,xCentre,yCentre)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Build the map to hold the new depths

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

newMap=zeros(size(oMap,1),size(oMap,2));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% We don't have an acceptable radius. Make one

% as approximately 10% of the length of the

% shortest side of the map.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if (nargin==1 | radius>min(size(oMap,1),size(oMap,2)));

radius=min(size(oMap,1),size(oMap,2))* …

(10.0+randn)/100.0;

end;

Crater Addition Code (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% We don't have a supplied depth. Generate one

% that is roughly the same as the current lowest

% valley.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if (nargin<3)

depth=min(min(oMap));

depth=depth*(100.0+randn)/100.0;

end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Find the difference between the highest peak

% and lowest valley. This will be used

% subsequently to try and place an appropriately

% sized rim around the edge of the impact

% crater.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

difference=max(max(oMap))-depth;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% No centres provided, or not valid centre.

% Generate a random centre for the impact.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if (nargin<5 | xCentre<1 | xCentre>size(oMap,2) | yCentre<1 | yCentre>size(oMap,1))

xCentre=round(rand*size(oMap,2));

yCentre=round(rand*size(oMap,1));

end;

Crater Addition Code (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% For each point on the surface determine

% whether it is now part of the impact or not.

% If it is then set its depth to be depth. If it

% isn't then preserve the old height.

% NOTE: There should be a "cleaner" way of doing

% this without loops (such as the find()

% function) but the calculate of inside or

% outside the circle [needs to be done for i & j

% values simultaneously] seems to preclude such

% an approach.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for iIndex=1:size(oMap,2)

for jIndex=1:size(oMap,1)

distFromCentre=(iIndex-xCentre)*(iIndex-xCentre)+...

Kursus Matlab di Jakarta Selatan KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060

Selasa, 13 Januari 2015

2D graphics and D graphics in Matlab

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