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Scientific Visualization Using MATLAB

Dive into the world of scientific visualization using MATLAB with this comprehensive guide covering geometry, topology, data types, scalar and vector visualization, and essential resources for Fall 2011. Learn how to convert raw data into a viewable format and explore the structure, characteristics, and types of datasets. Understand the difference between structured and unstructured data, as well as different dataset types such as image data, rectilinear grids, polygonal data, and unstructured grids. Discover MATLAB data types and handle graphics while creating compelling visualizations for your scientific projects.

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Scientific Visualization Using MATLAB

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  1. Scientific Visualization Using MATLAB Robert Putnam putnam@bu.edu Scientific Visualization Using MATLAB - Fall 2011

  2. Outline • Introduction • Geometry / Topology / Data Types • Camera, lights, … • Scalar visualization • Vector visualization • Resources Scientific Visualization Using MATLAB - Fall 2011

  3. 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). *Adaptedfrom The ParaView Tutorial, Moreland Scientific Visualization Using MATLAB - Fall 2011

  4. Generic visualization pipeline Source(s) Filters(s) Output (Rendering) - - - - - - - - - - - - - - - - - - - - - data/geometry/topology graphics Scientific Visualization Using MATLAB - Fall 2011

  5. 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 2011

  6. Geometry v. Topology 0,1 1,1 2,1 3,1 0,0 1,0 2,0 3,0 Scientific Visualization Using MATLAB - Fall 2011

  7. 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 2011

  8. 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 2011

  9. 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 2011

  10. 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 2011

  11. 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 Examples of Dataset Types Scientific Visualization Using MATLAB - Fall 2011

  12. 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 2011

  13. 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 2011

  14. 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 2011

  15. 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 2011

  16. Handle graphics, GUIs • “Handle graphics” • Numerical id assigned to figure window and its components • GUI (for menus, sliders, etc.) Scientific Visualization Using MATLAB - Fall 2011

  17. 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 2011

  18. Handle Graphics Hierarchy • Root object • Figure object(s) Scientific Visualization Using MATLAB - Fall 2011

  19. Core graphics objects • Core graphics objects • axes (frame, defines coordinate • system) • line • text • rectangle • light • patch (filled polygons) • surface (3D grid of • quadrilaterals) • images (2D representation • of image) Scientific Visualization Using MATLAB - Fall 2011

  20. Code – figure function Command Window f = figure figure creates a new figure object using default property values. This automatically becomes the current figure and raises it above all other figures on the screen until a new figure is either created or called. Many graphics commands create figures (so, often there’s no need to invoke ‘figure’ command). gcf: current figure figure(f): make f current figure, and make visible close all: close all figure windows shg: show graphic window (ESC to return) gca: current axes Scientific Visualization Using MATLAB - Fall 2011

  21. 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 all possible values] Tip #1: Use ‘more on’ to keep list from scrolling. Tip #2: Try inspect(1) or propertyeditor(1). Tip #3: See ‘Handle Graphics Property Browser’ in User Guide / Graphics. Scientific Visualization Using MATLAB - Fall 2011

  22. MATLAB - Viewing Viewing control • One can alter the appearance of a graphical scene by adjusting the camera position, changing the perspective, changing the aspect ratio, etc. • Two primary functions: • Positioning the viewpoint to orient the scene – viewfunction • Setting the aspect ratio and relative axis scaling – axis function Scientific Visualization Using MATLAB - Fall 2011

  23. MATLAB – view function view • 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 or below the x-y plane. Scientific Visualization Using MATLAB - Fall 2011

  24. 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 2011

  25. Exercise – view Command Window: view1 samplefig; view([-20 25]); Scientific Visualization Using MATLAB - Fall 2011

  26. Exercise – view Command Window: view1 Figure menu: - Add X,Y labels - Rotate graph* - Examine values with data cursor - Save figure *Tip: use get(gca, ‘view’) or inspect(gca) to see new azimuth and elevation. Scientific Visualization Using MATLAB - Fall 2011

  27. MATLAB – axis function axis • Adjust the scaling of graph axes. • axis([xminxmaxyminymaxzminzmax]) 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 without rescaling. Scientific Visualization Using MATLAB - Fall 2011

  28. 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 2011

  29. 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 lighting 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 2011

  30. 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 2011

  31. MATLAB – Vis Algorithms • Scalar • Matrix to Surface • Slicing • Color Mapping • Contours / Isosurfaces • Vector • Oriented Glyphs • Streamlines Scientific Visualization Using MATLAB - Fall 2011

  32. 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 2011

  33. 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; camlight left; peaks is a function of two variables, obtained by translating and scaling Gaussian distributions 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). • Set breakpoint in editor, return to cmd. window. • F5 to start • F10 to step • Sh-F5 to exit debugger Scientific Visualization Using MATLAB - Fall 2011

  34. 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 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 2011

  35. Exercise – flow, slice Command Window:slice1 [x,y,z,v] = flow; 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, try sliceomatic(v). Scientific Visualization Using MATLAB - Fall 2011

  36. 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(map) sets the colormap to the matrix map. Scientific Visualization Using MATLAB - Fall 2011

  37. 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 2011

  38. MATLAB – colormap editor If you want even more control over color mapping, you can use the colormap editor. You open the colormap editor by selecting Colormap from the figure’s Edit menu. Tip: to view a list of colormaps, click ‘Tools’ Try: % [x y] = meshgrid(1:64); % image(x); Scientific Visualization Using MATLAB - Fall 2011

  39. 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 that have the specified value the same way isolines connect points of equal elevation. Scientific Visualization Using MATLAB - Fall 2011

  40. 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 2011

  41. 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 polygons defined by the coordinates of its vertices. Quiz: how would you change the light color? [Hint: try using ‘inspect’.] Scientific Visualization Using MATLAB - Fall 2011

  42. 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 2011

  43. 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 coloredaccording 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 2011

  44. 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 2011

  45. 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 2011

  46. MATLAB – vector algorithms Streamlines • 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 Scientific Visualization Using MATLAB - Fall 2011

  47. 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 2011

  48. Interactive data exploration Command Window:streamline2 Using – 1.0 and + 1.0 to adjust zval, try to find the two funnels. Scientific Visualization Using MATLAB - Fall 2011

  49. 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 2011

  50. Questions? • Tutorial survey: • - http://scv.bu.edu/survey/tutorial_evaluation.html Scientific Visualization Using MATLAB - Fall 2011

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