Scientific Visualization Using MATLAB Robert Putnam putnambu edu

Scientific Visualization Using MATLAB Robert Putnam putnam@bu. edu Scientific Visualization Using MATLAB - Fall 2016

Outline Introduction Geometry / Topology / Data Types Camera, lights, … Scalar visualization Vector visualization Resources Scientific Visualization Using MATLAB - Fall 2016

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 2 D or 3 D space (e. g. , from simulation mesh or scanner). *Adapted from The Para. View Tutorial, Moreland Scientific Visualization Using MATLAB - Fall 2016

Generic visualization pipeline Filters(s) data/geometry/topology Scientific Visualization Using MATLAB - Fall 2016 ----------- Source(s) Output (Rendering) graphics

Geometry v. Topology Geometry of a dataset ~= points 0, 0 0, 1 0, 2 0, 3 1, 0 1, 1 1, 2 1, 3 Topology ~= connections among points, which define cells So, what’s the topology here? Scientific Visualization Using MATLAB - Fall 2016

Geometry v. Topology 0, 0 0, 1 0, 2 0, 3 1, 0 1, 1 1, 2 1, 3 Scientific Visualization Using MATLAB - Fall 2016

Geometry v. Topology 0, 0 0, 1 0, 2 0, 3 1, 0 1, 1 1, 2 1, 3 or 0, 0 0, 1 0, 2 0, 3 1, 0 1, 1 1, 2 1, 3 Scientific Visualization Using MATLAB - Fall 2016

Geometry v. Topology or 0, 0 0, 1 0, 2 0, 3 1, 0 1, 1 1, 2 1, 3 Scientific Visualization Using MATLAB - Fall 2016

Geometry v. Topology or 0, 0 0, 1 0, 2 0, 3 1, 0 1, 1 1, 2 1, 3 or or 0, 0 0, 1 0, 2 0, 3 1, 0 1, 1 1, 2 1, 3 Scientific Visualization Using MATLAB - Fall 2016

Geometry/Topology 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 2016

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 2016

Examples of Dataset Types (cont) Polygonal Data – irregular in both topology and geometry – examples: vertices, polyvertices, lines, 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 2016

Characteristics of 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 2016

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 Nx 1 (or 1 XN) array (and a scalar is a 1 x 1 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 2016

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 2016

Handle graphics, GUIs • “Handle graphics” • Numerical id assigned to figure window and its components • GUI (for menus, sliders, etc. ) Scientific Visualization Using MATLAB - Fall 2016

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 2016

Handle Graphics Hierarchy • • Root object • (computer screen) Figure object(s) Scientific Visualization Using MATLAB - Fall 2016

Core graphics objects • axis (frame, defines coordinate system) • line • text • rectangle • light • patch (filled polygons) • surface (3 D grid of quadrilaterals) • image (2 D representation) Scientific Visualization Using MATLAB - Fall 2016

Code – figure function Command Window f = 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(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 2016 gca: current axis object

Exercise – figure property list Command Window: figure 1. m f = figure('Name', 'Test Window', 'Position', [100 500 350], 'Menu. Bar', 'none') or f = figure set (f, 'Name', 'Test Window') set (f, 'Position', [100 500 350]) set (f, 'Menu. Bar', '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 2016

MATLAB - 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 2016

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 2016

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 2 D view, with az = 0, el = 90. – view(3) sets the default 3 D view, with az = – 37. 5, el = 30. – view(az, el) or view([az, el]) set the viewing angle for a 3 D view. Scientific Visualization Using MATLAB - Fall 2016

Exercise – view Command Window: view 1 samplefig; view([-20 25]); Scientific Visualization Using MATLAB - Fall 2016

Exercise – view Command Window: view 1 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. **Tip: Control resolution with print command, e. g. : print –dpng –r 300 foo. png Scientific Visualization Using MATLAB - Fall 2016

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 vis 3 d freezes aspect ratio properties to enable rotation of 3 -D objects without rescaling. Scientific Visualization Using MATLAB - Fall 2016

Code – axis function Command Window: axis 1 samplefig; view([-20 25]); axis([0 30 -15 15]); % axis auto; axis vis 3 d; Tip: Note the effect of commenting out ‘axis vis 3 d’ Scientific Visualization Using MATLAB - Fall 2016

MATLAB - Lighting – Enhances the visibility of surface shape and provides a 3 D perspective to your visualization. – Several commands enable you to position light sources and adjust the characteristics of lit objects: • light - creates a light object • camlight – “ “ with respect to the current camera position • 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’) • shading - controls the color shading of surface and patch graphic objects (e. g. , ‘flat’, ‘faceted’, ‘interp’) Scientific Visualization Using MATLAB - Fall 2016

Exercise – lighting, material, etc. Command Window: lighting 1 samplefig; 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 2016 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 2016

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 2 D arrays. – 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. – (See MATLAB PLOTS menu for other 2 D vis options, e. g. , imagesc, hist. Can also right-click on 2 D array to see plot options. ) Scientific Visualization Using MATLAB - Fall 2016

Exercise – surf, breakpoints, etc. Command Window: surf 1 [step through] [X, Y, Z] = peaks(25); s = surf(X, Y, Z); axis tight; l = light; lighting phong; h = camlight (‘left’); peaks is a function of two variables, obtained by translating and scaling Gaussian distributions Scientific Visualization Using MATLAB - Fall 2016 1. 2. 3. 4. Set breakpoint in editor F 5 to start, then C-0 to return to cmd. window F 10 to step Sh-F 5 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 at the points in the scalars or vectors sx, sy, and sz. X, Y, and Z are 3 D arrays specifying the geometry of V. – The color at each point is determined by interpolation into the volume V using the current colormap. Scientific Visualization Using MATLAB - Fall 2016

Exercise – flow, slice Command Window: slice 1 [x, y, z, v] = flow; f = figure; xslice = 5; yslice = 0; * zslice = 0; * s = slice(x, y, z, v, xslice, yslice, zslice); 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). *Tip: use [] to get no slice for a given Scientific Visualization Using MATLAB - Fall 2016 axis

MATLAB – scalar algorithms Color Mapping – Each scalar value in a 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. , parula, jet, hsv, hot, cool, Fall, and gray). (Do ‘doc colormap’ to see current list. ) • colormap() returns the current colormap • colormap(map) sets the colormap to the matrix map. • caxis(‘auto’) maps colors linearly between the min and max data values. To scale manually, supply min and max values (e. g. , caxis([-2. 3, 15]) Scientific Visualization Using MATLAB - Fall 2016

Code – colormap function Command Window: colormap 1 [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 colormap 1? Scientific Visualization Using MATLAB - Fall 2016

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 an interactive list of colormaps, click icon for ‘Show Plot Tools and Dock Figure’, then click Property Editor For a quick look at the current colormap, try: % image(1: size(colormap)); Scientific Visualization Using MATLAB - Fall 2016

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 2 D 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 2016

Code – contour function Command Window: contour 1 [X, Y, Z] = peaks(25); isovalues = linspace(min(Z(: )), max(Z(: )), 20); [C h] = contour(X, Y, Z, isovalues); grid on; Pop quiz: Compare with imagesc(Z) in another figure window. Why are the colors different? Compare with pcolor(Z) Try clabel(C, h) to get contour line labels. Scientific Visualization Using MATLAB - Fall 2016 Try also contour 3 a.

Ex. – isosurface step-through Command Window: isosurface 1 [x, y, z, v] = flow; isovalue = -1; purple = [1. 0 0. 5 1. 0]; i = isosurface(x, y, z, v, isovalue); p = patch(i); set(p, 'Face. Color', purple, 'Edge. Color', 'none'); view([-10 40]); grid on; l = light('Position', [-10, -2, 20]); lighting gouraud; isonormals(x, y, z, v, p); 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 2016 Quiz: how would you change the light color? [Hint: try using ‘inspect’. ]

Interactive data exploration Editor Window: isosurface 1 To explore different isosurface values, highlight the ‘-1’ in this line: isovalue = -1; Right-click, choose ‘Increment Value and Run Section’, 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 2016 **Also try isosurface 2 for colormap indexing

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 2016

Code – coneplot function Command Window: coneplot 1 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 2016

Ex. – improved coneplot Command Window: coneplot# 1. Use ‘cone’ instead of ‘quiver’: coneplot 2 2. Use color to indicate windspeed: coneplot 3 3. In coneplot 4, use +1 button to move up one xy plane at a time by incrementing zval: zval = 1; Scientific Visualization Using MATLAB - Fall 2016

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. – 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 2016

Code – streamline function Command Window: streamline 1 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, 'Line. Width', 1, 'Color', purple); view([-40 50]); grid off; See also streamparticles 1 Scientific Visualization Using MATLAB - Fall 2016

Interactive data exploration Command Window: streamline 2 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. For a quick and easy animation, try: streamline 2 loop 2 play Scientific Visualization Using MATLAB - Fall 2016

Output to file Command Window: streamline 2 Save figure with [File][Save] or Save low-to-medium-res image with [File][Save As] or Save high-res image with >>> print -dtiff -r 300 streamline 2. tif Scientific Visualization Using MATLAB - Fall 2016

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 2016

Questions? Tutorial survey: - http: //scv. bu. edu/survey/tutorial_evaluation. html Scientific Visualization Using MATLAB - Fall 2016