Scientific Visualization Using MATLAB
Robert Putnam
[email protected]
Scientific Visualization Using MATLAB - Fall 2012
Outline

Introduction

Geometry / Topology / Data Types

Camera, lights, …

Scalar visualization

Vector visualization

Resources
Scientific Visualization Using MATLAB - Fall 2012
Scientific Visualization
• Visualization: converting raw data to a form that is
viewable and understandable to humans.
• Scientific visualization: specifically concerned
with data that has a well-defined representation in
2D or 3D space (e.g., from simulation mesh or
scanner).
*Adapted from The ParaView
Tutorial, Moreland
Scientific Visualization Using MATLAB - Fall 2012
Generic visualization pipeline
Filters(s)
data/geometry/topology
Scientific Visualization Using MATLAB - Fall 2012
---------------------
Source(s)
Output
(Rendering)
graphics
Geometry v. Topology

Geometry of a dataset ~= points
0,1
1,1
2,1
3,1
0,0
1,0
2,0
3,0

Topology ~= connections among points, which
define cells

So, what’s the topology here?
Scientific Visualization Using MATLAB - Fall 2012
Geometry v. Topology
0,1
1,1
2,1
3,1
0,0
1,0
2,0
3,0
Scientific Visualization Using MATLAB - Fall 2012
Geometry v. Topology
0,1
1,1
2,1
3,1
0,0
1,0
2,0
3,0
or
0,1
1,1
2,1
3,1
0,0
1,0
2,0
3,0
Scientific Visualization Using MATLAB - Fall 2012
Geometry v. Topology
or
0,1
1,1
2,1
3,1
0,1
1,1
2,1
3,1
0,0
1,0
2,0
3,0
0,0
1,0
2,0
3,0
or
0,1
1,1
2,1
3,1
0,0
1,0
2,0
3,0
Scientific Visualization Using MATLAB - Fall 2012
Geometry v. Topology
or
0,1
1,1
2,1
3,1
0,1
1,1
2,1
3,1
0,0
1,0
2,0
3,0
0,0
1,0
2,0
3,0
or
or
0,1
1,1
2,1
3,1
0,1
1,1
2,1
3,1
0,0
1,0
2,0
3,0
0,0
1,0
2,0
3,0
Scientific Visualization Using MATLAB - Fall 2012
Geometry/Topology Structure

Structure may be regular or irregular
– Regular (structured)
• need to store only beginning position, spacing, number of points
• smaller memory footprint per cell (topology can be generated on the fly)
• examples: image data, rectilinear grid, structured grid
– Irregular (unstructured)
• information can be represented more densely where it changes quickly
• higher memory footprint (topology must be explicitly written) but more freedom
• examples: polygonal data, unstructured grid
Scientific Visualization Using MATLAB - Fall 2012
Examples of Dataset Types

Structured Points (Image Data)
– regular in both topology and geometry
– examples: lines, pixels, voxels
– applications: imaging CT, MRI

Rectilinear Grid
– regular topology but geometry only partially
regular
– examples: pixels, voxels

Structured Grid (Curvilinear)
– regular topology and irregular geometry
– examples: quadrilaterals, hexahedron
– applications: fluid flow, heat transfer
Scientific Visualization Using MATLAB - Fall 2012
Examples of Dataset Types (cont)

Polygonal Data
– irregular in both topology and geometry
– examples: vertices, polyvertices, lines,
polylines, polygons, triangle strips

Unstructured Grid
– irregular in both topology and geometry
– examples: any combination of cells
– applications: finite element analysis,
structural design, vibration
Scientific Visualization Using MATLAB - Fall 2012
Characteristics of Data

Data is organized into datasets for visualization
– Datasets consist of two pieces
• organizing structure
– points (geometry)
– cells (topology)
• data attributes associated with the structure

Data is discrete
– Interpolation functions generate data values in between known points
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – Data Types
Basic data type
– The basic data type is the array.
–
“Arrays in MATLAB are N-dimensional, with an infinite number of trailing
singleton dimensions. Trailing singleton dimensions past the second are not
displayed or reported on (e.g., with size). No array has fewer than two
dimensions.”
– A vector is an Nx1 (or 1XN) array (and a scalar is a 1x1 array):
– Array dimensions are generally reported (e.g., by ‘whos’) in “row by column”
order (i.e., y by x).
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – Data Types
Volume Data
– Data defined on three-dimensional grids
– Two 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
Scientific Visualization Using MATLAB - Fall 2012
Handle graphics, GUIs
•
“Handle graphics”
• Numerical id assigned to figure window and its components
•
GUI (for menus, sliders, etc.)
Scientific Visualization Using MATLAB - Fall 2012
Figure
Figure
– 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.
Scientific Visualization Using MATLAB - Fall 2012
Handle Graphics Hierarchy
•
•
Root object
• (computer screen)
Figure object(s)
Scientific Visualization Using MATLAB - Fall 2012
Core graphics objects
•
Core graphics objects
• axis (frame, defines coordinate
system)
• line
• text
• rectangle
• light
• patch (filled polygons)
• surface (3D grid of
quadrilaterals)
• image (2D representation)
Scientific Visualization Using MATLAB - Fall 2012
Code – figure function
Command Window
f = figure
figure creates a new figure object using
default property values. It becomes the
current figure and is raised above all other
figures on the screen until a new figure is
either created or called. Many graphics
commands create figures, so often there is
no need to invoke the ‘figure’ command
explicitly.
gcf: current figure
figure(f): set current figure to f and make
visible
close all: close all figure windows
shg: show graphic window (ESC to return)
Scientific Visualization Using MATLAB - Fall 2012
gca: current axis object
Exercise – figure property list
Command Window:figure1.m
f = figure('Name','Test Window','Position',[100 500 350 350],'MenuBar','none')
or
f = figure
set (f, 'Name', 'Test Window')
set (f, 'Position', [100 500 350 350])
set (f, 'MenuBar', 'none')
Type
get(f,’Name’)
to see f’s ‘Name’ property, or
get(f)
to see all properties [or set(f) to see possible values]
Tip #1: Use ‘more on’ to keep list from scrolling.
Tip #2: Try inspect(f) or plottools(f).
Scientific Visualization Using MATLAB - Fall 2012
Tip #3: See ‘Handle Graphics Property
Browser’ in User Guide.
MATLAB - Viewing
Viewing control
– One can alter the appearance of a figure by adjusting the camera position,
changing the perspective, changing the aspect ratio, etc.
– Two primary functions:
• Positioning the viewpoint to orient the scene – view function
• Setting the aspect ratio and relative axis scaling – axis function
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – view function
view
– The viewpoint is specified by
defining azimuth and elevation with
respect to the origin:
– Azimuth is a polar angle in the
x-y plane, with positive angles
indicating counterclockwise
rotation of the viewpoint from
the -y axis.
– Elevation is the angle above
or below the x-y plane.
Scientific Visualization Using MATLAB - Fall 2012
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.
Scientific Visualization Using MATLAB - Fall 2012
Exercise – view
Command Window: view1
samplefig;
view([-20 25]);
Scientific Visualization Using MATLAB - Fall 2012
Exercise – view
Command Window: view1
Figure menu:
- Add X,Y labels
- Rotate graph*
- Examine values with data cursor
- Save figure
*Tip: after rotating graph, use
get(gca, ‘view’) or inspect(gca) to see
new azimuth and elevation.
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – axis function
axis
– Adjust the scaling of graph axes.
– axis([xmin xmax ymin ymax zmin zmax]) sets the limits for the x-axis, y-axis and
z-axis of the current axis object.
– axis vis3d freezes aspect ratio properties to enable rotation of 3-D objects
without rescaling.
Scientific Visualization Using MATLAB - Fall 2012
Code – axis function
Command Window: axis1
samplefig;
view([-20 25]);
axis([0 30 0 30 -15 15]);
% axis auto;
axis vis3d;
% axis normal;
Tip: Note the effect of using axis
‘normal’ instead of ‘vis3d’
Scientific Visualization Using MATLAB - Fall 2012
MATLAB - Lighting
Lighting
– 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 light shading (e.g., interpolation) method (e.g., ‘flat’,
‘gouraud’, ‘phong’)
• material - sets the specular (mirror-like) reflectance properties of lit objects
(e.g., ‘shiny’, ‘dull’, ‘metal’)
• camlight - creates or moves a light with respect to the camera position
• shading - controls the color shading of surface and patch graphic objects
(e.g., ‘flat’, ‘faceted’, ‘interp’)
Scientific Visualization Using MATLAB - Fall 2012
Exercise – lighting, material, etc.
Command Window:lighting1
samplefig;
light;
lighting phong;
material (‘shiny’);
camlight left;
shading interp;
Try changing lighting,
material, shading, etc.,
using command or function
syntax. E.g.
material dull;
or
material(‘dull’);
Scientific Visualization Using MATLAB - Fall 2012
Phong lighting + flat shading?
MATLAB – Vis Algorithms
• Scalar
– Matrix to Surface
– Slicing
– Color Mapping
– Contours / Isosurfaces
• Vector
– Oriented Glyphs
– Streamlines
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – scalar algorithms
Matrix 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 the
surface.
Scientific Visualization Using MATLAB - Fall 2012
Exercise – surf, meshgrid,
breakpoints, etc.
Command Window:surf1 [step through]
[X,Y] = meshgrid(-3:0.25:3);
Z = peaks(X,Y);
s = surf(X,Y,Z);
axis([-3 3 -3 3 -10 10]);
l = light;
lighting phong;
h = camlight (‘left’);
peaks is a function of two variables, obtained by
translating and scaling Gaussian distributions
[X,Y] = meshgrid(x,y) duplicates the vectors x and y
across the rows and columns respectively of arrays X and
Y. (meshgrid(x) is equivalent to meshgrid(x,x)).
Scientific Visualization Using MATLAB - Fall 2012
1.
2.
3.
4.
Set breakpoint in editor
F5 to start, then C-0 to return to cmd. window
F10 to step
Sh-F5 to exit debugger
MATLAB – scalar algorithms
Slicing
– 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 scalars or 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 interpolation into the volume V using the
current colormap.
Scientific Visualization Using MATLAB - Fall 2012
Exercise – flow, slice
Command Window:slice1
[x,y,z,v] = flow;
f = figure;
xslice = 5;
yslice = 0;
zslice = 0;
s = slice(x,y,z,v,xslice,yslice,zslice);
light;
lighting phong;
camlight('left');
shading interp;
The flow dataset represents the speed profile of a submerged jet within an infinite tank.
Tip: try slice_angle to see a diagonal slice, viewedge_middle(v) for custom datatip, or for the
adventurous, sliceomatic(v).
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – scalar algorithms
Color 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:
• Three-column 2-D matrix
• Each row of the matrix defines a single color by specifying three RGB
component values in the range of zero to one.
• Created with array operations or with one of the several color table generating
functions (e.g., jet, hsv, hot, cool, summer, and gray). (Do
‘doc colormap to see current list.)
• colormap() returns the current colormap
• colormap(map) sets the colormap to the matrix map.
Scientific Visualization Using MATLAB - Fall 2012
Code – colormap function
Command Window:colormap1
[x,y,z,v] = flow;
xslice = 5;
yslice = 0;
zslice = 0;
s = 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;
Pop quiz: how would you reverse the order
of the entries in the colormap after running
colormap1?
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – colormap editor
If you want even more control over color
mapping, you can use the colormap editor.
You can open the colormap editor by selecting
Colormap from the figure’s Edit menu.
Tip: to view a list of
colormaps, click ‘Tools’
For a quick look at the
current colormap, try:
% imagesc(1:64);
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – scalar algorithms
Contours / Isosurfaces
– Construct 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 to create surfaces that have the specified value.
Scientific Visualization Using MATLAB - Fall 2012
Code – contour function
Command Window:contour1
[X,Y] = meshgrid(-3:0.25:3);
Z = peaks(X,Y);
isovalues = (-3.0:0.5:3.0);
[C h] = contour(X,Y,Z,isovalues);
grid on;
Pop quiz: Compare with
imagesc(Z) in another figure
window. Why are the colors
different?
Scientific Visualization Using MATLAB - Fall 2012
Ex. – isosurface step-through
Command Window:isosurface1
[x,y,z,v] = flow;
isovalue = -1;
purple = [1.0 0.5 1.0];
i = isosurface(x,y,z,v,isovalue);
p = patch(i);
isonormals(x,y,z,v,p);
set(p,'FaceColor',purple,'EdgeColor','none');
view([-10 40]);
grid on;
l = light('Position', [-10, -2, 20]);
lighting gouraud;
patch is the low-level graphics function that creates patch
graphics objects. A patch object is one or more filled
polygons defined by the coordinates of its vertices.
Scientific Visualization Using MATLAB - Fall 2012
Quiz: how would you change the light color?
[Hint: try using ‘inspect’.]
Interactive data exploration
Editor Window:isosurface1
To explore different isosurface values,
highlight the ‘-1’ in this line:
isovalue = -1;
then use the %1.1 button repeatedly to
see isosurfaces of successively
smaller value.
When you’ve gotten to -0.03 or so, rotate
the model, then turn on a camlight.
*Again, for the adventurous, try sliceomatic(v) and hold down
the left mouse button on the colorbar to see a variable isosurface.
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – vector algorithms
Oriented Glyphs
– Draw an oriented, scaled glyph for each vector.
– Glyphs are polygonal objects such as cones or arrows.
– Orientation and scale of glyph indicate the direction and magnitude of the vector.
– Glyphs 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.
Scientific Visualization Using MATLAB - Fall 2012
Code – coneplot function
Command Window:coneplot1
load wind;
xmin = min(x(:));
xmax = max(x(:));
ymin = min(y(:));
ymax = max(y(:));
zmin = min(z(:));
zmax = max(z(:));
scale = 4;
[cx cy cz] = meshgrid(xmin:10:xmax,ymin:5:ymax,zmin:2:zmax);
coneplot(x,y,z,u,v,w,cx,cy,cz,scale,'quiver');
view([-35 60]);
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.
Scientific Visualization Using MATLAB - Fall 2012
Ex. – improved coneplot
Command Window:coneplot#
1. Use ‘cone’ instead of ‘quiver’: coneplot2
2. Use color to indicate windspeed: coneplot3
3. In coneplot4, use +1 button to move up one xy plane
at a time by incrementing z value:
[cx cy cz] = meshgrid(xmin:2:xmax,ymin:2:ymax,1);
Scientific Visualization Using MATLAB - Fall 2012
MATLAB – vector algorithms
Streamlines
– The path a massless particle would take flowing through a vector field.
– Can be used to convey the structure of a field by providing a snapshot of the flow
at a given time.
– Multiple streamlines can be created to explore interesting features in the field.
– Computed via numerical integration (integrating product of velocity and delta T).
– streamline(X,Y,Z,U,V,W,startx,starty,startz) draws stream lines from the vector
volume data.
• X, Y, and Z define the coordinates for the vector field.
• U, V, and W define the vector field.
• startx, starty, startz define the starting positions of the streamlines.
Scientific Visualization Using MATLAB - Fall 2012
Code – streamline function
Command Window:streamline1
load 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];
[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]);
grid off;
Scientific Visualization Using MATLAB - Fall 2012
Interactive data exploration
Command Window:streamline2
Using – 1.0 and + 1.0 to adjust zval, try to
find the two funnels.
The rotate tool can be helpful when viewing
the streamlines. To save the current camera
position, use save_camera_struct.
Scientific Visualization Using MATLAB - Fall 2012
MATLAB - Resources

IS&T tutorials
– Introduction to MATLAB
www.bu.edu/tech/research/training/tutorials/MATLAB/
– Using MATLAB to Visualize Scientific Data
www.bu.edu/tech/research/training/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/
Scientific Visualization Using MATLAB - Fall 2012
Questions?

Tutorial survey:
- http://scv.bu.edu/survey/tutorial_evaluation.html
Scientific Visualization Using MATLAB - Fall 2012