MATLAB GRAPHICS PART II ADVANCED PLOTTING

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MATLAB GRAPHICS - PART IIADVANCED PLOTTING

• June 4, 99

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3-D PLOTTING

• There are numerous ways to display a function in
  3-D in black and white as well as color
• One way to interpret 3D data is a series of
  points in space given by (x,y,z) coordinates
• The direct extension of the 2-D plot function,
  plot(x,y), to 3-D is plot3(x,y,z)

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PLOTTING A CORKSCREW

• How would you model a corkscrew?
• Corkscrew, or spiral, is the 3-D equivalent of
  a spiral
• It goes around a circle but it also rises from
  the ground plane. So, what is its equation?

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3-D EQUATION

• A circle can be parametrically described by
• xcos(t)
• ysin(t)
• To make it rise from the ground plane, let zt
  and run t from 0 to 10pi.

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Try it!
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Try it!

• Another interesting plot is the same as corkscrew
  but you are going up around a cone rather than a
  cylinder. Can you write the code?

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DISPLAYING A FUNCTION AS A SET OF HEIGHTS

• A 3-D plot can be interpreted as heights above
  the ground plane. These heights are evaluated at
  some predefined grid points

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mesh and meshgrid

• To plot a function in 3D we need to understand
  mesh and meshgrid.
• meshgrid samples the ground plane into a grid of
  points
• x- 80.58
• yx
• x,ymeshgrid(x,y)
• x and y are now matrices
• mesh evaluates the function over the grid

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EXMAPLE SOMBRERO

• Sombrero, looking like a Mexican hat, is defined
  by sin(r)/r.
• r is the distance of a point (x,y) to the origin,
  i.e.
• r2x2y2

r
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Try it!
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SOMBRERO
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GENERATING TRUE AXIS UNITS

• Use of mesh (z) plots z vs. index positions not
  actual x or y values
• To plot z vs. actual units of x and y, just use x
  and y in the mesh command like
• mesh(x,y,z)
• Note that x and y can come from the output of
  meshgrid

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Try it!

• MATLAB has a built-in function called peaks
• How can you make the plot look smoother?

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What to do in the following slides

• Each slide shows a variation of the mesh command
  on a function z
• Since you already have z defined for both
  sombrero and peaks, for each slide duplicate the
  command shown and see the result for yourself

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CONTOUR PLOT

• Contours are slices of constant height that are
  then projected onto the ground plane
• In its simplest form meshc (z) does the job

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CURTAIN PLOT

• You can put your plot on a pedestal by using
  meshz (Z)

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CONTROLLING VIEWPOINT

• Viewpoint is controlled by two angles azimuth
  and elevation
• Azimuth is rotation around the Z-axis
• Elevation is rising above the ground plane

z
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DEFAULT VIEWPOINTS

• In MATLAB, default viewpoints are az- 37.5 and
  el30 degrees
• Zero degrees azimuth is like looking up the
  x-axis shown in the previous slide .
• 90 degrees of elevation is like looking directly
  down on the the surface

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Working with viewpoint

• The best way to understand viewpoint is to play
  around
• To understand the effect of elevation, fix your
  azimuth at 0 then change your elevation
• view(0,10),view(0,30),view(0,60)
• Or fix your elevation at 30 degrees and change
  your azimuth
• Compare view(30,60) with view(-20, 60)

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INTERPRETING SIGNS OF VIEWPOINT ANGLES

• Increasingly negative azimuth angle corresponds
  to holding the object in front of you and
  rotating it counterclockwise.
• Equivalently, it corresponds to keeping the
  object stationary and moving around it clockwise
• Positive elevation angle mean rising above the
  object. Elevation of 90 degrees means being
  directly overhead and looking down

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Homework1

• For the following function
• do a mesh plot then title and label all axis
• visually find out how deep the hole is?
• what is happening inside(looking underneath)?
• generate 3D contours(30 of them)
• Write a procedure that would cap the plot to
  70 of its peak value then plot it. Your plot
  should show a flat top

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GENERATING SHADED PLOTS

• mesh generates wiremesh plots(can see lines)
• To generate surfaces with solid shading, surf and
  its variations are used
• These variations are
• surf
• surfl (this is surf followed by lower case L)
• surfc

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Using surf

• Usage
• surf(x,y,z,C)
• (x,y) is generated via meshgrid and z is the
  height of the function.
• z-to-color mapping is done according to the
  entries into colormap via C. More on this later
• If surf(z) is used, color is proportional to
  height z.

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Plotting peaks using surf

• Generate the peaks function in the range (-4 to
  4) in increments of .5
• Then use
• surf(x,y,z)
• For comparison, use mesh and display it in a
  second window

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Try it!

• Look closely and see if you can tell the
  difference between surf and mesh

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mesh vs. surf

• Display mesh and surf side-by-side

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SOLID SHADING- shading

• To plot solid looking shapes, as opposed to
  wiremeshes, shading command comes in
• shading flat
• shading faceted
• shading interp

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Try it!

• Display one of your favorite 3D shapes you have
  done so far and in the command window type and
  observe
• shading flat
• shading faceted
• shading interp

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FLAT vs. FACETED vs. INTERPOLATED SHADING

• Flat shading assigns constant colors to surface
  patches
• Faceted shading assigns constant colors but also
  shows the wiremeshes
• Interpolated shading assigns colors proportional
  to height of the function

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3D CONTOURS

• contour projects 3D contours of a surface onto
  the ground plane
• contour3 shows the true 3D contours
• Usages are
• contour3(x,y,z,N)
• This command generates N contours of the function
  Z. Default is N10

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Try it!

• Display the peaks function over x and y ranging
  over - 5 to 5 in increments of 0.1
• Then do the following
• Display 50 2D contours using contour
• Display 50 3D contours using contour3d

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FEW EXAMPLES
20 contours
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Can you get this?

• Hint contour displays its plots on the z0 plane

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CONTROLLING LIGHTING DIRECTION-surfl

• You can shine light on a surface from a desired
  direction
• Shading is based on a combination of diffuse,
  specular and ambient lighting models
• Usage
• surfl(x,y,z,s)
• slighting directionaz,el where az and el are
  azimuth and elevation angles previously defined

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Lighting example

• Keep changing the s parameter and watch

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WATERFALL PLOTS

• An interesting effect can be generated by just
  plotting the rows of the Z matrix using
• waterfall(x,y,z)

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Putting several plots on a single page

• subplot(mnp) divides the page into
  m(rows)xn(columns) tiles then selects the pth
  tile for the current plot

This tile would be Referred to by subplot (235)
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Seeing subplot at work

• Lets say we want to partition the page into
  3x26 tiles. Simply type the following in the
  command window and see what happens
• subplot(232)
• subplot(235)
• subplot(233)
• subplot(234)
• subplot(236)

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Homework 2 placing 4 plots on a page

• Lets say we have 4 plots (choose your own) and
  want to arrange them on paper in the following
  styles
• Across the page in one row
• Vertical in one column
• In a matrix, 2x2 tiles on a page

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Special surfaces cylinder and sphere

• sphere(n) will generate a plot of unit sphere
  using (n1)2 points. Another usage is
• x,y,zsphere(25)
• surf(x,y,z)
• Similarly, we can generate a cylinder of radius 1
  using cylinder.

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Generalized cylinder

• Think of a cylinder with changing cross section

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How to do it?

• Usage
• Cylinder(radius) where radius is the growing
  cross sectional radius described by a vector

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Homework 3

• Plot zsin(sqrt(x2y2)). Plot it using
• mesh
• surf, surfl, surfc
• Experiment with shading flat, faceted,
  interpolated
• Experiment with lighting directions. For good
  effect type colormap(copper) after bringing up
  the plot.