matlab for visualization ray gasser [email protected] is&t scientific visualization tutorial –...

Matlab for VisualizationMatlab for Visualization

Ray Gasser

[email protected]

IS&T Scientific Visualization Tutorial – Spring 2010

MATLABMATLABMATrix LABoratory

– high performance language for technical computing

– interpreted language (compiler available)

– interactive GUI

– command line interface (Command Window)

– application specific toolboxes available (Parallel Computing, Statistics, etc.)

– coupled with Maple for Symbolic computation

– good documentation available (user guides, demos, videos, etc.)

– professional support services available from MathWorks


MATLAB – Data TypesMATLAB – Data TypesMatrix

– the basic data type is the matrix/array

– a vector is just a 1D array

– 2 facilities available for displaying vectors and matrices as graphs

• MATLAB interactive GUI plotting tool

• MATLAB graphics commands from the Command Window


MATLAB – Data TypesMATLAB – Data Types


Volume Data– data defined on three-dimensional grids

– multidimensional arrays of scalar or vector data

– defined on lattice structures representing values sampled in 3-D space

– 2 basic types

• Scalar volume data

• single data values for each point

• examples: temperature, pressure, density, elevation

• Vector volume data

• two or three values for each point (components of a vector)

• magnitude and direction

• examples: velocity, momentum

MATLAB - Graphics ModelMATLAB - Graphics ModelGraphics Model

– used to create visual representations of data

– two basic types of graphics objects:• Core graphics objects

• lines

• text

• rectangles

• patches (filled polygons)

• surfaces (3D grid of vertices)

• images (2D matrix representation of image)

• light sources

• axes (define coordinate system)

• Composite graphics objects

• core graphics objects grouped together


MATLAB – figure functionMATLAB – figure functionFigure

– all graphical output directed to a graphics window called a figure

– separate from the Command Window

– can contain menus, toolbars, user-interface objects, context menus, axes, or any

other type of graphics object.

– to create a new figure, use the figure function

• (type figure in a Command Window)


Code – figure functionCode – figure functionCommand Window

figure


MATLAB - PropertiesMATLAB - PropertiesProperties

– every graphics object has a set of properties associated with it

– defines different attributes of an object, such as its color, size, position, etc.

– usually specified by name/property pairs

– figure( 'PropertyName', propertyvalue, ...)

– can be set at creation time or later by using the set function

• Command Windowf = figure

set (f, 'Name','Test Window')


Code – property listCode – property listCommand Window

figure('Name','Test Window','Position',[100 500 350 350],'MenuBar','none')


MATLAB - ViewingMATLAB - ViewingViewing

– the process of displaying a graphical scene from various directions by adjusting

the camera position, changing the perspective, changing the aspect ratio, etc.

– the particular orientation you set to display the visualization

– composed from two basic functions:

• positioning the viewpoint to orient the scene – view function

• setting the aspect ratio and relative axis scaling – axis function


MATLAB – view functionMATLAB – view functionview

– the viewpoint is specified by

defining azimuth and elevation with

respect to the axis origin

– azimuth is a polar angle in the x-y

plane, with positive angles

indicating counterclockwise

rotation of the viewpoint. Elevation

is the angle above (positive angle)

or below (negative angle) the x-y

plane.


MATLAB – view function (cont)MATLAB – view function (cont)view

– MATLAB automatically selects a viewpoint that is determined by whether the plot

is 2-D or 3-D

• For 2-D plots, the default is azimuth = 0° and elevation = 90°

• For 3-D plots, the default is azimuth = -37.5° and elevation = 30°

– view(2) sets the default 2D view, with az = 0, el = 90.

– view(3) sets the default 3D view, with az = –37.5, el = 30.

– view(az,el) or view([az,el]) set the viewing angle for a 3D view.


Code – view functionCode – view functionCommand Window

Z = peaks(20);

figure;

h = surf(Z);

view([-20,25]);


The peaks function is an example function of two variables, obtained by translating and scaling Gaussian distributions. peaks(n) returns an n-by-n matrix

The surf function create 3-D surface plots of matrix data.

MATLAB – axis functionMATLAB – axis functionaxis

– enables you to adjust the aspect ratio of graphs.

– enables you to adjust the scaling of graphs.

– axis([xmin xmax ymin ymax zmin zmax]) sets the limits for the x-axis, y-axis and

z-axis of the current axes.

– axis vis3d freezes aspect ratio properties to enable rotation of 3-D objects (If you

will be interactively rotating the visualization in the figure window you should use

the vis3d option.)


Code – axis functionCode – axis functionCommand Window

Z = peaks(20);

figure;

h = surf(Z);

view([-20,25]);

axis([0 30 0 30 -15 -15]);


MATLAB - LightingMATLAB - LightingLighting

– enhances the visibility of surface shape and provides a 3D perspective to your

visualization.

– several commands enable you to position light sources and adjust the

characteristics of lit objects:

• light - creates a light object

• lighting - selects a lighting method

• material - sets the reflectance properties of lit objects

• camlight - creates or moves a light with respect to the camera position

• shading - controls the color shading of surface and patch graphic objects


Code - lightingCode - lightingCommand Window

Z = peaks(20);

figure;

h = surf(Z);

view(3);

axis on;

light;

lighting phong;

camlight('left');

shading interp;


MATLAB – Vis AlgorithmsMATLAB – Vis Algorithms• Modeling

– Matrix to Surface

– Slicing

• Scalar– Color Mapping

– Contours / Isosurfaces

• Vector– Oriented Glyphs

– Streamlines

•


MATLAB – modeling algorithmsMATLAB – modeling algorithmsMatrix to Surface

– a surface is defined by the z-coordinates of points above a rectangular grid in the

x-y plane.

– formed by joining adjacent points with straight lines.

– useful for visualizing large matrices.

– surf(X,Y,Z) creates a shaded surface using Z for the color data as well as

surface height. X and Y are vectors or matrices defining the x and y components

of a surface.


Code – surf functionCode – surf functionCommand Window

[X,Y] = meshgrid(-3:0.25:3);

Z = peaks(X,Y);

figure;

surf(X,Y,Z);

view(3);

axis([-3 3 -3 3 -10 10]);

grid on;

light;

lighting phong;

camlight('left');


meshgrid(x,y) transforms the domain specified by vectors x and y into arrays X and Y, which can be used to evaluate functions of two variables and three-dimensional mesh/surface plots. meshgrid(x) is the same as [X,Y] = meshgrid(x,x).

MATLAB – modeling algorithmsMATLAB – modeling algorithmsSlicing

– a slice is a "cross-section" of the dataset.

– any kind of surface can be used to slice the volume.

– the simplest technique is to use a plane to define the cutting surface.

– slice (X,Y,Z,V,sx,sy,sz) draws slices of the volume V along the x, y, z directions

in the volume V at the points in the vectors sx, sy, and sz. X, Y, and Z are 3D

arrays specifying the coordinates for V.

– the color at each point is determined by 3-D interpolation into the volume V.


Code – slice functionCode – slice functionCommand Window

[x,y,z,v] = flow;

figure;

xslice = 5;

yslice = 0;

zslice = 0;

slice(x,y,z,v,xslice,yslice,zslice);

view(3);

axis on;

grid on;

light;

lighting phong;

camlight('left');

shading interp;


The flow dataset represents the speed profile of a submerged jet within an infinite tank (an example of scalar volume data).

MATLAB – scalar algorithmsMATLAB – scalar algorithmsColor Mapping

– each scalar value in data set is mapped through a lookup table to a specific color.

– the color lookup table is called the colormap

• a three-column 2-D matrix

• each row of the matrix defines a single color by specifying three values in the

range of zero to one (RGB components).

• created with either array operations or with one of the several color table

generating functions (jet, hsv, hot, cool, summer, and gray).

• colormap(map) sets the colormap to the matrix map.


Code – colormap functionCode – colormap functionCommand Window

[x,y,z,v] = flow;

figure;

xslice = 5;

yslice = 0;

zslice = 0;

slice(x,y,z,v,xslice,yslice,zslice);

view(3);

axis([0 10 -4 4 -3 3]);

grid on;

colormap (flipud(jet(64)));

colorbar('vertical');

shading interp;


MATLAB – colormap editorMATLAB – colormap editor

If you want even more control over the color

mapping, you can use the colormap editor.

You open the colormap editor by selecting

Colormap from the Edit menu of the figure.


MATLAB – scalar algorithmsMATLAB – scalar algorithmsContours / Isosurfaces

– constructs a boundary between distinct regions in the data.

– contours are lines or surfaces of constant scalar value.

– isolines for two-dimensional data and isosurfaces for three-dimensional data.

– contour(X,Y,Z,v) draws a contour plot of matrix Z with isolines at the data values

specified in the vector v.

– isosurface(X,Y,Z,V,isovalue) computes isosurface data from the volume data V

at the isosurface value specified in isovalue. The isosurface function connects

points that have the specified value the same way isolines connect points of

equal elevation.


Code – contour functionCode – contour functionCommand Window

[X,Y] = meshgrid(-3:0.25:3);

Z = peaks(X,Y);

figure;

isovalues = (-3.0:0.5:3.0);

contour(X,Y,Z,isovalues);

view(2);

axis on;

grid on;


Code – isosurface functionCode – isosurface functionCommand Window

[x,y,z,v] = flow;

isovalue = -1;

purple = [1.0 0.5 1.0];

figure;

p = patch(isosurface(x,y,z,v,isovalue));

isonormals(x,y,z,v,p);

set(p,'FaceColor',purple,'EdgeColor','none');

view([-10 40]);

axis on;

grid on;

light;

lighting phong;

camlight('left');


patch is the low-level graphics function that creates patch graphics objects. A patch object is one or more polygons defined by the coordinates of its vertices.

MATLAB – vector algorithmsMATLAB – vector algorithmsOriented Glyphs

– draw an oriented, scaled glyph for each vector.

– glyphs are polygonal objects such as a cone or an arrow.

– orientation and scale of glyph indicate the direction and magnitude of the vector.

– glyph may be colored according to vector magnitude or some other scalar value.

– coneplot(X,Y,Z,U,V,W,Cx,Cy,Cz) plots vectors as cones or arrows.

• X, Y, Z define the coordinates for the vector field

• U, V, W define the vector field

• Cx, Cy, Cz define the location of the cones in the vector field

• coneplot(...,'quiver') draws arrows instead of cones.


Code – coneplot functionCode – coneplot functionCommand Windowload wind;

xmin = min(x(:));

xmax = max(x(:));

ymin = min(y(:));

ymax = max(y(:));

zmin = min(z(:));

zmax = max(z(:));

scale = 4;

figure;

[cx cy cz] = meshgrid(xmin:5:xmax,ymin:5:ymax,zmin:2:zmax);

coneplot(x,y,z,u,v,w,cx,cy,cz,scale,'quiver');

view([-35 60]);

axis on;

grid off;


The wind dataset represents air currents over North America. The dataset contains six 3-D arrays: x, y, and z are coordinate arrays which specify the coordinates of each point in the volume and u, v, and w are the vector components for each point in the volume.

MATLAB – vector algorithmsMATLAB – vector algorithmsStreamlines

– the path a massless particle takes flowing through a velocity field (i.e. vector field)

– can be used to convey the structure of a vector field by providing a snapshot of

the flow at a given instant in time.

– multiple streamlines can be created to explore interesting features in the field.

– computed via numerical integration (integrating product of velocity times delta T).

– streamline(X,Y,Z,U,V,W,startx,starty,startz) draws stream lines from the vector

volume data.

• X, Y, Z define the coordinates for the vector field

• U, V, W define the vector field

• startx, starty, startz define the starting positions of the streams


Code – streamline functionCode – streamline functionCommand Windowload wind;

xmin = min(x(:));

xmax = max(x(:));

ymin = min(y(:));

ymax = max(y(:));

zmin = min(z(:));

zmax = max(z(:));

purple = [1.0 0.5 1.0];

figure;

[sx sy sz] = meshgrid(xmin,ymin:10:ymax,zmin:2:zmax);

h = streamline(x,y,z,u,v,w,sx,sy,sz);

set(h,'LineWidth',1,'Color',purple);

view([-40 50]);

axis on;

grid off;


MATLAB - ResourcesMATLAB - Resources IS&T tutorials

– Introduction to MATLAB http://scv.bu.edu/documentation/tutorials/MATLAB/

– Using MATLAB to Visualize Scientific Data http://scv.bu.edu/documentation/tutorials/visualization-with-matlab/

Websites– www.mathworks.com/products/matlab/

– www.mathworks.com/access/helpdesk/help/techdoc/index.html

– www.mathworks.com/academia/student_center/tutorials

Wiki– http://matlabwiki.mathworks.com/

MATLAB Workshop end March beginning April 2010


SourcesSources

Getting Started with MATLAB, version 7, The MathWorks, Inc.

Using MATLAB, version 7, The MathWorks, Inc.

Using MATLAB Graphics, version 7, The MathWorks, Inc.

http://www.mathworks.com/access/helpdesk/help/techdoc/index.html


matlab for visualization ray gasser [email protected] is&t scientific visualization tutorial –...

Documents

graphics window

matlab figure function

volume data data

vector data

matlab data types matrix

figure function type

matlab viewing

set function command