Plot Model Plotting Basics - Computational Methods - Lecture Slides, Slides of Calculus for Engineers

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Engr/Math/Physics 25

Chp5 MATLAB

Plots & Models 1

Learning Goals

• List the Elements of a COMPLETE Plot
  • e.g.; axis labels, legend, units, etc.
• Construct Complete Cartesian (XY) plots

using MATLAB

• Modify or Specify MATLAB Plot Elements: Line

Types, Data Markers, Tic Marks

• Distinguish between INTERPolation

and EXTRAPolation

Learning Goals cont

• Use Regression Analysis as quantified by

the “Least Squares” Method

• Calculate
  • Sum-of-Squared Errors (SSE or J)
    • The Squared Errors are Called “Residuals”
  • “Best Fit” Coefficients
  • Sum-of-Squares About the Mean (SSM or S)
  • Coefficient of Determination (r 2 )
• Scale Data if Needed
  • Creates more meaningful spacing

Learning Goals cont

• Build Math Models for Physical Data using

“nth^ ” Degree Polynomials

• Use MATLAB’s “Basic Fitting” Utility to find

Math models for Plotted Data

• Use MATLAB to Produce 3-Dimensional

Plots, including

• Surface Plots
• Contour Plots

Why Plot? cont

• Plots have TREMENDOUS Utility

in Two Major Areas

1. Communication

• To Help OTHERS understand the RESULTS of

Your Tests or Experiments or Theories

2. Analysis

• To Help You ANALYZE Data or

Theories to Determine the

Significance or Meaning of the Data

Plotting Trivia

• Rene Decartes (1596-1650)

Developed “Cartesian” (XY)

Plots in about 1637

• Florence Nightingale Developed the “Polar

Area Plot” (Pie Chart) in 1857

Gate Voltate to Balance ElectroStatic and Spring Forces vs. d

0

2

4

6

8

10

12

14

16

18

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2. Cantilever Height, d (μm)

Gate Potential (Vdc)

file = ElectroStatics_0104.xls

Threshold

Turn-On (Zip-Up)

Turn-Off (Peel-Off)

PARAMETERS

• E = 135 Gpa (PolySi)
• L = 100 μm
• W = 60 μm
• t = 3 μm• d
• Z = 300 μmo^ = 2 μm
• V (^) Th = 17.00396 Vdc
• V (^) r = 7.903 Vdc

V (^) r (^) Arrow CallOut

Theoretical Plot → NO Data Markers

Important Output Value

MATLAB Plot Example

• Consider a Rocket

Launch

 A Math Model for

the Height, y, vs.

the Distance, x:

y = 0. 43 1. 73 x

• Where both x & y are in units of miles

 Use MATLAB to Plot

y vs x for a 51 mi

DownRange Dist

Plot OutPut

• The plot appears in the Figure window
• Output from One of
  1. Use the menu system. Select Print on the File menu in the Figure window. Answer OK when you are prompted to continue the printing process.
  2. Type print at the command line. This command sends the current plot directly to the printer. 3. Save the plot to a file to be printed later or imported into another application such as PowerPoint. You need to know something about graphics file formats to use this file properly. See the subsection Exporting Figures.

Elements of a Useful Plot

• The essential features of a Maximally

Understandable Plot

1. Each axis must be labeled with the name of the quantity being plotted and its units.

• If two or more quantities having different units are plotted (such as when plotting both speed and distance versus time), then indicate the units in the axis label if there is room, or in the legend or labels for each curve

2. Each axis should have regularly spaced tick marks at convenient intervals - not too sparse, but not too dense - with a spacing that is easy to interpret and interpolate.

• e.g.; use 0.1, 0.2, and so on, rather than 0.13, 0.

Elements of a Useful Plot cont

6. Sometimes data symbols are connected by lines to help the viewer visualize the data, especially if there are few data points.  However, connecting the data points, especially with a solid line, might be interpreted to imply knowledge of what occurs between the data points. Take appropriate care to prevent such MisInterpretation.
7. If you are plotting points generated by evaluating a function (as opposed to measured data), do not use a symbol to plot the points. Instead, be sure to generate many points , and connect the points with solid lines.  The Curve should be SMOOTH

grid Command

• The grid command displays gridlines at the

tick marks corresponding to the tick labels.

• Type grid on to add gridlines;
• Type grid off to stop plotting gridlines.
• When used by itself, grid toggles this feature on

or off, but you might want to use grid on and

grid off to be sure.

LineWidth Command

• MATLAB’s Default width and color for a

plotted line are

• Thin
• Blue
• This “thin blue line” is often hard to SEE and

to PHOTOCOPY

• Use 'LineWidth',n, to increase WIDTH
• Use color-spec to make BLACK

Affect of grid, axis, LineWidth

(^00 5 10 15 20 25 30 35 40 45 )

1

2

3

4

Distance (mi)

Height (mi)

Rocket Height as a Function of Downrange Distance

plot(x,y, 'k', 'LineWidth', 3), xlabel('Distance (mi)'),... ylabel('Height (mi)'),grid on, axis([0 51 0 4.1]),... title('Rocket Height as a Function of Downrange Distance')

Command Session

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