ENGG1811 Computing for Engineers Week 11 Part C Matlab: 2D and 3D plots

Transcription

1 ENGG1811 Computing for Engineers Week 11 Part C Matlab: 2D and 3D plots ENGG1811 UNSW, CRICOS Provider No: 00098G1 W11 slide 1

2 More on plotting Matlab has a lot of plotting features Won t go through them in details Good to know what s possible and when you want to use it, look up the documentation Some of these slides (if marked with ) are for references and we won t be going through them in details in the lecture ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 2

3 Plot appearance Line and marker styles values encoded in a short optional string following each x, y pair in a plot-type command Line colour, r=red, b=blue, g=green, w=white, c=cyan, m=magenta, y=yellow, k=black >> plot(x, y, 'b*- '); % more x, y, stylestrings can follow Marker style,.=point, o=circle, x=x, *=star, s=square, v=down triangle, ^=up triangle, etc Line style, - =solid, - - =dashed, :=dotted, -.=dash dot See Matlab documentation ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 3

4 Additional control Additional characteristics of the lines and markers are specified by extra pairs of arguments to plot of the form 'propertyname', value, Properties include LineWidth in pixels (integer) MarkerSize in pixels MarkerEdgeColor string, same codes as for lines MarkerFaceColor string, same codes as for lines ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 4

5 LaTeX formatting Labels, titles and legend text can be formatted using a scheme used for typesetting mathematical documents LaTeX (pronounced lay-teck ) embeds codes or escape sequences using backslash and other special characters \it{text} \bf{text} italic, boldface* _{text} ^{text} subscript, superscript \lambda \SIGMA Greek lowercase (λ), upper (Σ) \circ \pm \neq \infty symbols ± \rightarrow \uparrow arrow symbols (also left, down) \_ \^ \{ \} \\ literal _ ^ { } or \ Can omit { } if a single character, for example \itx See Chapman Table 3-2 * Font style changes do not properly terminate in Matlab versions to 2012b ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 5

6 LaTeX equation examples %% % Einstein's famous equation is $E = m c^2$. % % $$\sum_{i=1}^{\infty} \frac{1}{2^i} = 1$$ % % $$\int_{0}^{\infty} x^2 e^{- x^2} dx = \frac{\sqrt{\pi}}{4}$$ gives this result (though equations are images, not scalable text): If you are really interested, try help latex (part of the syms package, converts a symbolic expression to a LaTeX equation) ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 6

7 Polar plots Polar plots have angles 0 to 2π in place of x, and magnitude (distance from the origin) in place of y Chapman Example 3.3 cardiod microphone response gain (relative sensitivity) varies with angle θ (0 = directly in front) according to the formula gain = 2g(1 + cosθ ) >> g = 0.5; % gain coefficient, characteristic of mic >> theta = linspace(0, 2*pi, 121); % 360/(121-1) = 3 degrees >> gain = 2*g * (1 + cos(theta)); >> polar(theta, gain, 'r- '); % red, solid, 1px line >> title('\bfcardiod microphone gain versus angle \it{\theta}'); ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 7

8 Annotations Figure window has a toolbar to add elements and save Plot browser Add/edit legend Select tool View Plot Edit Toolbar to access annotation tools such as arrows, shapes and text boxes File Save As (*.fig) See Chapman section 3.3 Not a full graphics editor, so results are only approximate ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 8

9 Other plot types Chart types similar to OpenOffice Calc/Excel bar(x,y) vertical bar chart barh(x,y) horizontal bar chart stem(x,y) marker and vertical line stairs(x,y) like bar, but only top of skyline shown pie(x, explode) use with caution compass(x,y) polar with arrow to each Cartesian point If y is a matrix instead of a vector, each column is a separate plot applies to all plot types that accept y values as second argument See Matlab documentation ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 9

10 3D line plots 3 dimensional line plots can be generated by passing three equal sized vectors to plot3 Example: decaying oscillations in a mechanical system in two dimensions (Chapman 8.3.1) x( t) = e cos2t y( t) = t = linspace(0, 10, 200); x = exp(- 0.2*t).* cos(2*t); y = exp(- 0.2*t).* sin(2*t); plot(x, y, 'Linewidth', 2); title ( 2D Line Plot'); xlabel( x'); ylabel( y'); grid on; plot3(x, y, t, 'Linewidth', 2); sin 2t % 2D plot % 3D plot, time is z (up) title ( 3D Line Plot'); xlabel( x'); ylabel( y'); zlabel( t'); grid on; e 0.2t 0.2t Code in plot3d_demo.m ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 10

11 3D time-based plot 3D plot shows the effect of time arguably better than as distance along the 2D plot Even better, the 3D view has interactive rotation ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 11

12 3D mesh and surface plots Data that has two independent variables (for example, temperature measured at many coordinates in 2D space) can be visualised as a 3D plot x and y are normally the independent variables z is normally the dependent variable can be displayed in three ways 1. as a mesh or wireframe of individual line plots 2. as a continuous surface, with colouring to highlight the slope at each point 3. as a series of contours, slices parallel to the x-y plane mesh(x, y, z); surf(x, y, z); contour(x, y, z); The x, y and z matrices have exactly the same shape ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 12

13 Preparing to plot For 2D plot, for each value of x, you need the corresponding value in y x = linspace(0, 10, 200); y = exp(- 0.2*t).* cos(2*t); For 3D plot, for each pair of (x,y), you need the corresponding value of z ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 13

14 3D plot arrays Example: z(x, y) = x exp( x 2 y 2 ) evaluated at x = 0,1,2 and y = -3,-2,-1,0 (1,-2) (1,-3) y = -3 (0,-3) (2,-3) -2-1 (0,-2) (0,-1) (2,-2) (2,-1) Correction: This arrow should be pointing at the number or the (3,3) element 0 (0, 0) (2,0) z(2,-1) x=0 1 2! # x = # # # " $ & & & & %! # y = # # # " $ & & & & %! # z = # # # " $ & & & & % ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 14

15 3D plot arrays, continued Having the arrays structured this way allows you to calculate the z value using array operators Fortunately you can easily construct the x and y arrays from their respective vectors using meshgrid: >> [x,y] = meshgrid([0,1,2], [- 3,- 2,- 1,0]); >> z = x.* exp(- x.^2 - y.^2); >> surf(x,y,z); >> xlabel( x'); >> ylabel( y'); >> zlabel( z'); Code in vis_demo.m Also, includes heatmap. Mesh doesn t have surface shading: ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 15

16 Automatic screen rotation How can a smartphone tell how the user is holding the phone? We will use 3D plot to understand how this is done

17 Smart phone and accelerometer (1) Smartphones have accelerometers for measuring acceleration in 3 directions ê Axes of accelerometer è Accelerometer readings. The phone was moved in the +ve y direction. That caused an acceleration in +ve y direction (green line)

18 Smart phone and accelerometer (2) An important part of problem solving is to understand how things work. Visualisation (charts, graphs etc) is extremely helpful. Demo: We will use the Android Physics Toolbox to see how accelerometers react to motion. This toolbox can be obtained from: id=com.chrystianvieyra.physicstoolboxsuite&hl=en Similar apps are also available for iphones If you are interested to find out how the accelerometers inside smartphones are manufactured, see here:

19 4 orientations We label the orientation according to which edge is pointing down MX (for minus x), MY (for minus y) PX (for plus x), PY (for plus Y) PX MY PY MX

20 Let us start simple We considered two orientations: MY and MX We assumed the phone is vertical We wanted to find a condition based on the accelerations to classify the orientation Basically a if-else statement, but what is the condition? MY This condition depends on the acceleration True cond? False MX MY MX

21 Let us plot acceleration versus time Can you find some characteristics on the acceleration to differentiate between the orientations MX and MY? ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 21

22 Plot y-acc versus x-acc Orientation MX x-acceleration big y-acceleration small Pseudo-code: If y-acc > x-acc orientation MY Orientation MY x-acceleration small y-acceleration big else orientation MX ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 22

23 A different perspective y > x line x = y x > y Finding the Boolean expression is the same as finding a line that can separate the acceleration of different orientations into separate regions ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 23

24 Classify 4 orientations We want to classify 4 orientations We no longer assume that the phone is vertical Experiment Put the phone in each orientation Tilt the phone but keeping one of +x, -x, +y, -y down Measure the acceleration in 3-directions Time plot on the next page Let us use 3D plot instead ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 24

25 Time plot PX PY MY MY Matlab feature: subplot ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 25

26 Only need x- and y-acceleration The surprise is that acceleration in the z-direction is not needed at all! ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 26

27 An exercise for you: boat hull* A simple model for the hull of a boat is given by y = 2 B 2x z L D where y is the width of the hull from the centre line, x is the distance along the centre line, and z is the depth of the hull. B is the beam (max width), L is the length and D is the draft (max depth). This hull is 8m long, with 3m beam and 1.5m draft. 2 * Based on Holloway, p.144 Project 15. ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 27

28 Implementing the model x and z are the independent variables, and range from L/2 to L/2, and D to 0 respectively use linspace and meshgrid to generate these arrays The first half of the y values (the starboard side) are produced by the formula, the second set of y values has the opposite sign to display both halves (thus avoiding a massive maritime disaster!), use the command hold on between plot commands axis equal maintains aspect ratio (uniform scales) You can try use the 3D rotation tool to examine the shape does mesh or surf give the better view? experiment with shading (faceted, flat or interp) ENGG1811 UNSW, CRICOS Provider No: 00098G W9 slide 28