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12.010 Computational Methods of Scientific Programming Lecturers Thomas A Herring, Room 54-820A, Chris Hill, Room 54-1511,

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Presentation on theme: "12.010 Computational Methods of Scientific Programming Lecturers Thomas A Herring, Room 54-820A, Chris Hill, Room 54-1511,"— Presentation transcript:

1 12.010 Computational Methods of Scientific Programming Lecturers Thomas A Herring, Room 54-820A, tah@mit.edu Chris Hill, Room 54-1511, cnh@gulf.mit.edu Web page http://www-gpsg.mit.edu/~tah/12.010http://www-gpsg.mit.edu/~tah/12.010 11/18/2010112.010 Lec 18

2 11/18/201012.010 Lec 182 Overview Today Examine image and 3-D graphics in Matlab

3 11/18/201012.010 Lec 183 Simple 3-D graphics Simple line and scatter plots use plot3 which takes 3 vectors as arguments and plots them much like 2-D plot. t = linspace(0,10*pi); figure(1); clf; plot3(sin(t),cos(t),t)

4 11/18/201012.010 Lec 184 Mesh plots [X,Y,Z] = peaks(30); % 30x30 version of Gaussians mesh(X,Y,Z) xlabel('X-axis'), ylabel('Y-axis'), zlabel('Z-axis') colorbar;daspect([1 1 2.5]); title('Lec 19.2: Mesh Plot of Peaks')

5 11/18/201012.010 Lec 185 Transparency control [X,Y,Z]=sphere(12); subplot(1,2,1) mesh(X,Y,Z), title('Lec 3a: Opaque') hidden on axis square off subplot(1,2,2) mesh(X,Y,Z), title('Lec 3b: Transparent') hidden off axis square off

6 11/18/201012.010 Lec 186 Mesh with contour meshc(X,Y,Z) % mesh plot with underlying contour plot

7 11/18/201012.010 Lec 187 Surface plots Surface plots are like mesh except that the surface is filled The appearance of these plots depends on the method of shading and how they are light. The commands here are: –surf -- surface plot shading flat has flat facetted look shading interp interpolates the surface and looks smoother –surfc -- surface plot with contours (like meshc) –surfl -- surface with lighting –surfnorm -- surface with normal plotted Following figures give example of these commands using the peaks(30) data set. We can look at these plots in Matlab and change colormap and view angles

8 11/18/201012.010 Lec 188 Standard surf Generated using surf[X,Y,Z]

9 11/18/201012.010 Lec 189 Surf with shading flat The command shading flat added

10 11/18/201012.010 Lec 1810 Surf with shading interp Command shading interp used

11 11/18/201012.010 Lec 1811 Surfl used Command surfl is surface with lighting; here the colormap is changed to pink to enhance effect

12 11/18/201012.010 Lec 1812 Surfnorm to add normals Generated on a 15 grid to keep down clutter.

13 11/18/201012.010 Lec 1813 Working with irregular data Previous figures were generated using a regular grid of X and Y values from which Z values can be computed. Routine griddata takes irregularly spaced x y data with associated z values and fits a surface to a regularly specified grid of values. Mesh surf etc can be used to plot results Routines trimesh and trisurf form Delanunay triangles to irregular data and plot based on these facetted surfaces.

14 Griddata example 11/18/201012.010 Lec 1814

15 Trisurf example 11/18/201012.010 Lec 1815

16 Vertical view of each figure 11/18/201012.010 Lec 1816

17 11/18/201012.010 Lec 1817 Inside 3-D objects Matlab has methods for visualization of 3-D volumes These are figure generated to display some quantity which is a function of X Y and Z coordinates. Examples would be temperature is a 3-D body Functions slice and contourslice are used to see inside the body. Slice can be along coordinate planes or a surface shape can be specified. Isosurface renders the shape of the volume at a particular value. (Equivalent to a 3-D contour map with just one contour shown).

18 11/18/201012.010 Lec 1818 Slice along coordinate axes slice(X,Y,Z,V,[0 3],[5 15],[-3 5]) x cut 0 & 3; y cut 5 & 15, z cut -3 & 5

19 11/18/201012.010 Lec 1819 Slice with contours added contourslice(X,Y,Z,V,3,[5 15],[])

20 11/18/201012.010 Lec 1820 Oscillating sinusoidal surface

21 11/18/201012.010 Lec 1821 Isosurface viewing Previous cut at level 2 using isosurface

22 11/18/201012.010 Lec 1822 Example with outer volume filled Added called to isocaps

23 11/18/201012.010 Lec 1823 Examples using Matlab flow function

24 11/18/201012.010 Lec 1824 Matlab flow example This example needs to be viewed in 3-D in Matlab. Here color map shows fine structure.

25 11/18/201012.010 Lec 1825 Making AVI Movies hf = figure('Position',[50 50 797 634]); set(fig,'DoubleBuffer','on'); set(gca,'Visible','off','Position',[0 0 1 1],'NextPlot','replace'); mov = avifile('YibalTotalANC.avi','FPS',1); for n = 2:35 f = sprintf('TotalANC%3.3d.jpg',n); Im = imread(f,'JPG'); hi = image(Im); Fr = getframe; mov = addframe(mov,Fr); end

26 11/18/201012.010 Lec 1826 Viewing real data Example of reading a geo-tiff file and displaying it on a Northing/Easting grid Main feature here is using imfinfo to retrieve information about the contents of an image file and then imread to read the image data Imagesc used to display image with coordinates: imagesc([UTMR(1:2)],[UTMR(3:4)], Def)

27 11/18/201012.010 Lec 1827 Figure generated imagesc

28 11/18/201012.010 Lec 1828 Summary Matlab has many 3-D view methods and functions available There are many options to many of these and sometime experimentation is needed to find out what works best. Demo example in Matlab can yield good ideas on how to solve specific problems.

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