MathCAD - Advanced Graphics and Animation
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Transcript MathCAD - Advanced Graphics and Animation
PH36010
Numerical Methods
Advanced Plotting and Animation
Advanced Plotting in
MathCAD
• Polar Plots
• 3D Plots
–
–
–
–
Surface
Contour
Scatter
Bar
• Vector Field Plots
Polar Plots #1
• X-Y Plot wrapped around a
circle
r=cos2()
90
1 20
1
60
0 .8
0 .6
1 50
30
0 .4
0 .2
F( )
1 80
0
0
2 10
3 30
2 40
3 00
2 70
0 33
3 .7 491
Polar Plots #2
k
•r=e
k 0.2
r e
k
0 0.1 6
90
1 20
40
60
30
1 50
30
20
10
r
1 80
0
0
2 10
3 30
2 40
3 00
2 70
Uses for Polar Plots
• Rotating Machines
– Stirling engine
– Vibration
• Arctic & Antarctic systems
3D surface plots
Simple #1
• Plot of data stored in array
• Indices of array represent x-y
plane
• Value of matrix is z value
–
–
–
–
Define size of matrix & indices
Determine values for x & y
Fill matrix
Plot
3D surface plots
Simple #2
N
100
xi
0 N
5 0.1i
f( x y)
Mi j
i
e
2
x
f xi yj
yj
y
2
j
0 N
5 0.1j
• Define size &
indices
• Define Range
for x & y
• 2D-Gaussian
• Fill matrix
3D surface plots
Simple #3
M
3D surface plots
Simple #4 – Lighting
M
Contour Plot
- from 3d plot data
• Format plot type -> Contour plot
M
Simple 3D plots
Limitations
• X & Y axes scaled in indices
• Suited to continuous single
valued functions
• More advanced 3D plots
available
3D Scatter plot
• Plot of individual points
• Supply with 3 vectors of equal
length (X,Y,Z)
• Points plotted:
– X0,Y0,Z0
– X1,Y1,Z1
–…
3D scatter plot
Photon Scatter in 3D
( XX YY ZZ)
3D surface plots
Parametric Plot
• Plot complex surfaces
• From Resource Centre Guide to 3D
plotting
( X Y Z)
3D parametric plot
Example - 1002 for H
X- & YAxes
scaled
in m
( X Y Z100 )
Parametric Plots
How to… #1
•
•
•
•
•
•
Rubber sheet N x M
Wrap sheet around surface
XXa,b is x-coord of point a,b
YYa,b is y-coord of point a,b
ZZa,b is z-coord of point a,b
(XX,YY,ZZ) will plot surface
Parametric Plots
Example 1 - Gaussian
N
100
xmin
5
xmax
5
x
xmax xmin
ymin
5
ymax 5
y
ymax ymin
i
0 N
j
xmin x i
YYi j
ymin y j
f( x y)
ZZi j
e
N
0 N
XXi j
2
x
N
• Ranges
defined as
before
y
2
f XXi j YYi j
• Fill XX & YY
matrices
• Fill ZZ matrix
Parametric Plots
Example 1 - Gaussian
• Note:
– Axes
scaled
( XX YY ZZ)
The SeriesVector()
program
SeriesVector( Start Finish nSteps )
Finish Start
nSteps
for i 0 nSteps
Resulti Start i
Result
(increment) and i (loop count) are
‘local’ to function.
Function builds Result vector
Returned on last line of program
Parametric Plots
Polar 3D #1
nr
r
n
Xi j
100
i
0 nr
SeriesVector 0 m 10 a 0 nr
30
j
0 n
SeriesVector
( n)
ricos j
Yi j
risin j
• Create r vector
0-10 radii, 100
teps
• Create vector
-180..180 deg,
30 steps
• Fill X & Y
vectors
Paramteric Plots
Polar 3D #2
r
100 ( r )
a0
Define 100 function
a
e 0
1
3
2
Z100i j
3
a 0 100 ri
Fill Z matrix with
100 function
NB Only depends on r
3D parametric plot
Example - 1002 for H
X- & YAxes
scaled
in m
( X Y Z100 )
Plot of 2102 for H
• X & Y matrices as before
• Z now depends on r,q
r
210 ( r )
1
r e
2 a 0
cos ( )
32 a 0
5
2
Z210i j
3
a 0 210 ri j
3D parametric plot
Example - 2102 for H
( X Y Z210 )
Pretty Pictures
From Resource Centre
Plot multiple Surfaces
Pretty Pictures #3
Planetary Orbit
• 3 objects
– Planet : (xe,ye,ze)
– Star : (xs,ys,zs)
– Orbit: (xp,yp,zp)
( xe ye ze) ( xs ys zs) ( xp yp zp)
Animation
Principles
• Make output depend on FRAME
• Tools|Animation|Record…
to display dialog
–
–
–
–
–
Fill in first & last frames
Drag cursor around area to animate
Select ‘Animate’ to go
View with AVI player
Save to disk
• Help|Quicksheets|Graphing and
Visualization
Animation
Hints and Tips
• Fix scale of graphs
• Watch out for:
– Size of AVI files
– Long calculation times
• Can test by using
FRAME:=
– Delete afterwards
• Put indicator in movie
Animation Example #1
Cannon Ball with drag
Animation Example #2
LCR at resonance
Animation Example #3
Heat Flow in Plate
Animation Example #4
Planetary Orbits
3D with lighting &
shadows