From making 2D line plots to making 3D surface plots: How to preserve my current workflow?
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Hi there!
Below, I think the explanation, originally a comment by me, is more clear, so I am posting it here as the question.
Just to describe my workflow a bit more clearly: I loop through beta and, for each beta, I calculate values of F, a scalar-valued function, for all alpha = linspace(0, 2pi, 1001). I am only looping through beta, not alpha, which I really like. (I notice that nested loops can cause the code to take much longer to run.) I might choose 10 or 11 evenly spaced values of beta to loop through, using linspace( ).
Then, I made nice line plots, going from subplots to tiled layouts, which seems to be advantageous; e.g. global title, global colorbar, etc. are made easy using tiledLayout rather than with subplot. In my 2D line plots, each tile would have the 11 curves, with alpha being the independent variable, and I use colors from a colormap to show the variation in beta. This figure of 6 tiles, I think, is really pretty -- and communicative.
Now, instead of 2D line plots, I want to present this exact same information using 3D surface plots, just to compare and see which figure is more communicative. However, since my functions that I am plotting are scalar-valued functions, I am getting the error that my functions need to be matrices. By the way, I have plenty of vectors expressed as linear combinations of basis vectors, but the final functions to be plotted are all scalar-valued, gotten from using dot products.
So, as of now, I can basically write a poor man's version of a code that gives the surface plots (very pretty), but this is not good and systematic:
- I would like to continue looping through beta;
- To keep things organized and de-cluttered, I would like to continue calling my functions which are stored in separate files;
- For doing careful mathematics, I would like to continue expressing vectors as linear combinations of basis vectors; and
- I would like to keep all the functions to be plotted scalar-valued.
It seems if in the beginning of my surface-plotting code I define a meshgrid [Alpha,Beta] = meshgrid(alpha,beta), and use the variables Alpha and Beta as inputs, then I start running into issues with arrays having incompatible sizes. I have one current guess at a solution, as of now: Maybe define my functions locally in the same file as my surface-plotting code, rather than call them from another separate file? I would rather not do this, because my intuition is that my errors should be easy enough to fix.
I look forward to hearing from you.
Thanks for your time!
採用された回答
Theree is not enough information proviided to determine what the problem is. If ‘i’ and ‘j’ are scalars, or matrices conformable under matrix multiplication with ‘Alpha’ and ‘Beta’ (that have the same sizes), your code should work.
The problem is not in the quoted code.
alpha = linspace(0,pi,20)
alpha = 1×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
beta = linspace(0,10,100)
beta = 1×100
0 0.1010 0.2020 0.3030 0.4040 0.5051 0.6061 0.7071 0.8081 0.9091 1.0101 1.1111 1.2121 1.3131 1.4141 1.5152 1.6162 1.7172 1.8182 1.9192 2.0202 2.1212 2.2222 2.3232 2.4242 2.5253 2.6263 2.7273 2.8283 2.9293
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
[Alpha, Beta] = meshgrid(alpha, beta),
Alpha = 100×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
●
Beta = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010
0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020
0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030
0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040
0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051
0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061
0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071
0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081
0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
i = rand
i = 0.0240
j = rand
j = 0.1758
vx = cos(Alpha) * i
vx = 100×20
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
vy = sin(Beta) * j
vy = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177
0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353
0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524
0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691
0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850
0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001
0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142
0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271
0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
.
29 件のコメント
Hi Star Strider!
Let's say the basis vectors are rotating basis vectors:
ip = cos(theta)*i + sin(theta)*j
jp = -sin(theta)*i + cos(theta)*j, and
kp = k = [0,0,1].
I am using the basis vectors ip and jp.
So, at angle theta = 0, ip = (1,0,0) and jp = (0,1,0).
First, ‘i’ and ‘j’ do not appear to add anything, so just delete them. I cannot figure out how you define the third dimension of ‘ip’, ‘jp’ and ‘kp’.
If you want to define them such that:
So, at angle theta = 0, ip = (1,0,0) and jp = (0,1,0).
you will need to do something like this —
ip = @(theta) [ cos(theta) sin(theta) something_else]
jp = @(theta) [-sin(theta) cos(theta) something_else]
kp = @(theta) [something something someething_else]
If ‘theta’ is a column vector, that should work.
Beyond that, I am completely lost.
.
Hi Star Strider!
Yes the third coordinate of ip and jp is zero; my problem is quasi-2D.
The issue is, say I have this
velocity = vx * ip + vy * jp,
where vx = cos(beta)*sin(alpha),
and vy is something similar.
The surface plot will be against beta and alpha, so I write
beta = linspace(0,pi,20)
alpha = (0,pi/2,100).
But now, vx * ip gives the error that arrays are incompatible.
This is getting murkier rather than clearer —
alpha = linspace(0,pi,20)
alpha = 1×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
beta = linspace(0,10,100)
beta = 1×100
0 0.1010 0.2020 0.3030 0.4040 0.5051 0.6061 0.7071 0.8081 0.9091 1.0101 1.1111 1.2121 1.3131 1.4141 1.5152 1.6162 1.7172 1.8182 1.9192 2.0202 2.1212 2.2222 2.3232 2.4242 2.5253 2.6263 2.7273 2.8283 2.9293
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
[Alpha, Beta] = meshgrid(alpha, beta),
Alpha = 100×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Beta = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010
0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020
0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030
0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040
0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051
0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061
0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071
0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081
0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
i = rand
i = 0.2010
j = rand
j = 0.9653
vx = cos(Beta) .* sin(Alpha)
vx = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
vy = -sin(Beta) .* cos(Alpha)
vy = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954 0.0995 0.1008
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898 0.1979 0.2006
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822 0.2943 0.2984
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718 0.3878 0.3931
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576 0.4773 0.4839
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388 0.5619 0.5696
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144 0.6407 0.6496
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838 0.7131 0.7230
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462 0.7782 0.7889
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
ip = @(theta) [ cos(theta(:)) sin(theta(:)) 0]
ip = function_handle with value:
@(theta)[cos(theta(:)),sin(theta(:)),0]
jp = @(theta) [-sin(theta(:)) cos(theta(:)) 0]
jp = function_handle with value:
@(theta)[-sin(theta(:)),cos(theta(:)),0]
kp = @(theta) [0 0 1]
kp = function_handle with value:
@(theta)[0,0,1]
velocity = vx * ip(theta) + vy * jp(theta)
Unrecognized function or variable 'theta'.
% where vx = cos(beta)*sin(alpha),
%
% and vy is something similar.
%
% The surface plot will be against beta and alpha, so I write
beta = linspace(0,pi,20)
alpha = [0,pi/2,100]
vx_times_ip = vx .* ip(theta)
.
Sorry for the late response: I think I’ll loop through Beta?
Set theta = 0, since my model is invariant to changes in theta.
Perhaps —
alpha = linspace(0,pi,20)
alpha = 1×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
beta = linspace(0,10,100)
beta = 1×100
0 0.1010 0.2020 0.3030 0.4040 0.5051 0.6061 0.7071 0.8081 0.9091 1.0101 1.1111 1.2121 1.3131 1.4141 1.5152 1.6162 1.7172 1.8182 1.9192 2.0202 2.1212 2.2222 2.3232 2.4242 2.5253 2.6263 2.7273 2.8283 2.9293
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
theta = zeros(size(beta));
[Alpha, Beta] = meshgrid(alpha, beta),
Alpha = 100×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Beta = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010
0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020
0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030
0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040
0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051
0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061
0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071
0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081
0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
i = rand
i = 0.2369
j = rand
j = 0.3853
vx = cos(Beta) .* sin(Alpha)
vx = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
vy = -sin(Beta) .* cos(Alpha)
vy = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954 0.0995 0.1008
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898 0.1979 0.2006
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822 0.2943 0.2984
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718 0.3878 0.3931
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576 0.4773 0.4839
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388 0.5619 0.5696
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144 0.6407 0.6496
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838 0.7131 0.7230
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462 0.7782 0.7889
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
ip = @(theta) [ cos(theta(:)) sin(theta(:)) zeros(size(theta(:)))]
ip = function_handle with value:
@(theta)[cos(theta(:)),sin(theta(:)),zeros(size(theta(:)))]
jp = @(theta) [-sin(theta(:)) cos(theta(:)) zeros(size(theta(:)))]
jp = function_handle with value:
@(theta)[-sin(theta(:)),cos(theta(:)),zeros(size(theta(:)))]
kp = @(theta) [zeros(size(theta(:))) zeros(size(theta(:))) ones(size(theta(:)))]
kp = function_handle with value:
@(theta)[zeros(size(theta(:))),zeros(size(theta(:))),ones(size(theta(:)))]
ipm = ip(theta)
ipm = 100×3
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
jpm = jp(theta)
jpm = 100×3
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
for k = 1:3
velocity(:,:,k) = vx .* ipm(:,k) + vy .* jpm(:,k) % Cell Array Or 3D Matrix Necessary Here
end
velocity = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
velocity =
velocity(:,:,1) =
Columns 1 through 18
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995
0 0.0875 0.1727 0.2531 0.3266 0.3912 0.4452 0.4870 0.5155 0.5300 0.5300 0.5155 0.4870 0.4452 0.3912 0.3266 0.2531 0.1727
0 0.0730 0.1441 0.2112 0.2725 0.3264 0.3714 0.4063 0.4301 0.4422 0.4422 0.4301 0.4063 0.3714 0.3264 0.2725 0.2112 0.1441
0 0.0578 0.1140 0.1671 0.2156 0.2583 0.2939 0.3215 0.3403 0.3498 0.3498 0.3403 0.3215 0.2939 0.2583 0.2156 0.1671 0.1140
0 0.0419 0.0827 0.1213 0.1565 0.1875 0.2133 0.2334 0.2470 0.2540 0.2540 0.2470 0.2334 0.2133 0.1875 0.1565 0.1213 0.0827
0 0.0257 0.0507 0.0743 0.0958 0.1148 0.1306 0.1429 0.1512 0.1555 0.1555 0.1512 0.1429 0.1306 0.1148 0.0958 0.0743 0.0507
0 0.0092 0.0181 0.0265 0.0342 0.0409 0.0466 0.0509 0.0539 0.0554 0.0554 0.0539 0.0509 0.0466 0.0409 0.0342 0.0265 0.0181
0 -0.0075 -0.0147 -0.0216 -0.0279 -0.0334 -0.0380 -0.0415 -0.0440 -0.0452 -0.0452 -0.0440 -0.0415 -0.0380 -0.0334 -0.0279 -0.0216 -0.0147
0 -0.0240 -0.0474 -0.0694 -0.0896 -0.1073 -0.1221 -0.1336 -0.1414 -0.1454 -0.1454 -0.1414 -0.1336 -0.1221 -0.1073 -0.0896 -0.0694 -0.0474
0 -0.0403 -0.0795 -0.1165 -0.1504 -0.1802 -0.2050 -0.2242 -0.2374 -0.2440 -0.2440 -0.2374 -0.2242 -0.2050 -0.1802 -0.1504 -0.1165 -0.0795
0 -0.0562 -0.1108 -0.1625 -0.2097 -0.2512 -0.2858 -0.3126 -0.3309 -0.3402 -0.3402 -0.3309 -0.3126 -0.2858 -0.2512 -0.2097 -0.1625 -0.1108
0 -0.0715 -0.1411 -0.2068 -0.2668 -0.3196 -0.3637 -0.3978 -0.4211 -0.4329 -0.4329 -0.4211 -0.3978 -0.3637 -0.3196 -0.2668 -0.2068 -0.1411
0 -0.0861 -0.1698 -0.2489 -0.3213 -0.3848 -0.4379 -0.4790 -0.5070 -0.5213 -0.5213 -0.5070 -0.4790 -0.4379 -0.3848 -0.3213 -0.2489 -0.1698
0 -0.0998 -0.1969 -0.2886 -0.3724 -0.4461 -0.5076 -0.5553 -0.5878 -0.6043 -0.6043 -0.5878 -0.5553 -0.5076 -0.4461 -0.3724 -0.2886 -0.1969
0 -0.1125 -0.2219 -0.3253 -0.4198 -0.5028 -0.5721 -0.6259 -0.6625 -0.6811 -0.6811 -0.6625 -0.6259 -0.5721 -0.5028 -0.4198 -0.3253 -0.2219
0 -0.1240 -0.2447 -0.3587 -0.4628 -0.5544 -0.6308 -0.6901 -0.7305 -0.7510 -0.7510 -0.7305 -0.6901 -0.6308 -0.5544 -0.4628 -0.3587 -0.2447
0 -0.1343 -0.2650 -0.3884 -0.5012 -0.6004 -0.6831 -0.7473 -0.7910 -0.8132 -0.8132 -0.7910 -0.7473 -0.6831 -0.6004 -0.5012 -0.3884 -0.2650
0 -0.1432 -0.2825 -0.4141 -0.5344 -0.6402 -0.7284 -0.7968 -0.8435 -0.8672 -0.8672 -0.8435 -0.7968 -0.7284 -0.6402 -0.5344 -0.4141 -0.2825
0 -0.1507 -0.2972 -0.4357 -0.5622 -0.6735 -0.7663 -0.8383 -0.8874 -0.9123 -0.9123 -0.8874 -0.8383 -0.7663 -0.6735 -0.5622 -0.4357 -0.2972
0 -0.1566 -0.3089 -0.4528 -0.5843 -0.6999 -0.7964 -0.8712 -0.9222 -0.9481 -0.9481 -0.9222 -0.8712 -0.7964 -0.6999 -0.5843 -0.4528 -0.3089
0 -0.1609 -0.3174 -0.4653 -0.6004 -0.7192 -0.8184 -0.8952 -0.9476 -0.9742 -0.9742 -0.9476 -0.8952 -0.8184 -0.7192 -0.6004 -0.4653 -0.3174
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velocity =
velocity(:,:,1) =
Columns 1 through 18
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Columns 19 through 20
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-0.4213 -0.4156 -0.3985 -0.3705 -0.3325 -0.2853 -0.2304 -0.1692 -0.1034 -0.0348 0.0348 0.1034 0.1692 0.2304 0.2853 0.3325 0.3705 0.3985
-0.3277 -0.3232 -0.3099 -0.2882 -0.2586 -0.2219 -0.1792 -0.1316 -0.0804 -0.0271 0.0271 0.0804 0.1316 0.1792 0.2219 0.2586 0.2882 0.3099
-0.2308 -0.2276 -0.2183 -0.2029 -0.1821 -0.1563 -0.1262 -0.0927 -0.0566 -0.0191 0.0191 0.0566 0.0927 0.1262 0.1563 0.1821 0.2029 0.2183
-0.1315 -0.1297 -0.1243 -0.1156 -0.1037 -0.0890 -0.0719 -0.0528 -0.0323 -0.0109 0.0109 0.0323 0.0528 0.0719 0.0890 0.1037 0.1156 0.1243
-0.0308 -0.0304 -0.0292 -0.0271 -0.0243 -0.0209 -0.0169 -0.0124 -0.0076 -0.0025 0.0025 0.0076 0.0124 0.0169 0.0209 0.0243 0.0271 0.0292
0.0701 0.0692 0.0663 0.0617 0.0553 0.0475 0.0383 0.0282 0.0172 0.0058 -0.0058 -0.0172 -0.0282 -0.0383 -0.0475 -0.0553 -0.0617 -0.0663
0.1703 0.1680 0.1611 0.1498 0.1344 0.1154 0.0932 0.0684 0.0418 0.0141 -0.0141 -0.0418 -0.0684 -0.0932 -0.1154 -0.1344 -0.1498 -0.1611
0.2688 0.2652 0.2543 0.2364 0.2122 0.1821 0.1470 0.1080 0.0660 0.0222 -0.0222 -0.0660 -0.1080 -0.1470 -0.1821 -0.2122 -0.2364 -0.2543
0.3646 0.3596 0.3448 0.3207 0.2877 0.2469 0.1994 0.1465 0.0895 0.0301 -0.0301 -0.0895 -0.1465 -0.1994 -0.2469 -0.2877 -0.3207 -0.3448
0.4566 0.4504 0.4319 0.4016 0.3604 0.3093 0.2498 0.1834 0.1121 0.0377 -0.0377 -0.1121 -0.1834 -0.2498 -0.3093 -0.3604 -0.4016 -0.4319
0.5440 0.5366 0.5145 0.4785 0.4293 0.3685 0.2976 0.2185 0.1335 0.0449 -0.0449 -0.1335 -0.2185 -0.2976 -0.3685 -0.4293 -0.4785 -0.5145
Columns 19 through 20
0 0
0.0995 0.1008
0.1979 0.2006
0.2943 0.2984
0.3878 0.3931
0.4773 0.4839
0.5619 0.5696
0.6407 0.6496
0.7131 0.7230
0.7782 0.7889
0.8353 0.8469
0.8840 0.8962
0.9236 0.9364
0.9538 0.9670
0.9743 0.9878
0.9848 0.9985
0.9853 0.9990
0.9758 0.9893
0.9563 0.9696
0.9271 0.9399
0.8884 0.9007
0.8407 0.8523
0.7844 0.7952
0.7201 0.7300
0.6484 0.6574
0.5702 0.5781
0.4861 0.4928
0.3971 0.4026
0.3040 0.3082
0.2078 0.2107
0.1095 0.1111
0.0101 0.0103
-0.0894 -0.0906
-0.1880 -0.1906
-0.2847 -0.2886
-0.3784 -0.3837
-0.4684 -0.4748
-0.5535 -0.5612
-0.6330 -0.6418
-0.7061 -0.7158
-0.7719 -0.7826
-0.8299 -0.8414
-0.8794 -0.8916
-0.9200 -0.9327
-0.9512 -0.9643
-0.9726 -0.9861
-0.9842 -0.9978
-0.9858 -0.9994
-0.9772 -0.9908
-0.9588 -0.9720
-0.9305 -0.9434
-0.8928 -0.9051
-0.8459 -0.8576
-0.7905 -0.8014
-0.7270 -0.7370
-0.6560 -0.6651
-0.5784 -0.5864
-0.4949 -0.5017
-0.4063 -0.4120
-0.3136 -0.3180
-0.2177 -0.2207
-0.1196 -0.1213
-0.0203 -0.0206
0.0793 0.0804
0.1780 0.1805
0.2749 0.2787
0.3690 0.3742
0.4594 0.4658
0.5451 0.5526
0.6252 0.6338
0.6989 0.7086
0.7656 0.7761
0.8244 0.8358
0.8748 0.8869
0.9163 0.9289
0.9484 0.9615
0.9709 0.9843
0.9835 0.9971
0.9861 0.9997
0.9786 0.9921
0.9611 0.9744
0.9338 0.9467
0.8970 0.9094
0.8511 0.8629
0.7965 0.8075
0.7338 0.7439
0.6636 0.6727
0.5866 0.5947
0.5036 0.5106
0.4156 0.4213
0.3232 0.3277
0.2276 0.2308
0.1297 0.1315
0.0304 0.0308
-0.0692 -0.0701
-0.1680 -0.1703
-0.2652 -0.2688
-0.3596 -0.3646
-0.4504 -0.4566
-0.5366 -0.5440
velocity(:,:,3) =
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
% where vx = cos(beta)*sin(alpha),
%
% and vy is something similar.
%
% The surface plot will be against beta and alpha, so I write
% vx_times_ip = vx .* ip(theta)
.
Looping through beta and alpha causes issues with the functions not being matrices, and so the surface plot won't work. Let me try your suggestion above. Will report back sometime tonight. Thanks Star Strider!
My pleasure!
With respect to the surface plot, you could do something lke this —
alpha = linspace(0,pi,20)
alpha = 1×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
beta = linspace(0,10,100)
beta = 1×100
0 0.1010 0.2020 0.3030 0.4040 0.5051 0.6061 0.7071 0.8081 0.9091 1.0101 1.1111 1.2121 1.3131 1.4141 1.5152 1.6162 1.7172 1.8182 1.9192 2.0202 2.1212 2.2222 2.3232 2.4242 2.5253 2.6263 2.7273 2.8283 2.9293
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
theta = zeros(size(beta));
[Alpha, Beta] = meshgrid(alpha, beta),
Alpha = 100×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Beta = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010
0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020
0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030
0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040
0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051
0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061
0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071
0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081
0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
i = rand
i = 0.9926
j = rand
j = 0.5299
vx = cos(Beta) .* sin(Alpha)
vx = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
vy = -sin(Beta) .* cos(Alpha)
vy = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954 0.0995 0.1008
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898 0.1979 0.2006
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822 0.2943 0.2984
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718 0.3878 0.3931
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576 0.4773 0.4839
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388 0.5619 0.5696
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144 0.6407 0.6496
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838 0.7131 0.7230
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462 0.7782 0.7889
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
ip = @(theta) [ cos(theta(:)) sin(theta(:)) zeros(size(theta(:)))]
ip = function_handle with value:
@(theta)[cos(theta(:)),sin(theta(:)),zeros(size(theta(:)))]
jp = @(theta) [-sin(theta(:)) cos(theta(:)) zeros(size(theta(:)))]
jp = function_handle with value:
@(theta)[-sin(theta(:)),cos(theta(:)),zeros(size(theta(:)))]
kp = @(theta) [zeros(size(theta(:))) zeros(size(theta(:))) ones(size(theta(:)))]
kp = function_handle with value:
@(theta)[zeros(size(theta(:))),zeros(size(theta(:))),ones(size(theta(:)))]
ipm = ip(theta)
ipm = 100×3
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
jpm = jp(theta)
jpm = 100×3
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
for k = 1:3
velocity(:,:,k) = vx .* ipm(:,k) + vy .* jpm(:,k) % Cell Array Or 3D Matrix Necessary Here
end
velocity = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
velocity =
velocity(:,:,1) =
Columns 1 through 18
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995
0 0.0875 0.1727 0.2531 0.3266 0.3912 0.4452 0.4870 0.5155 0.5300 0.5300 0.5155 0.4870 0.4452 0.3912 0.3266 0.2531 0.1727
0 0.0730 0.1441 0.2112 0.2725 0.3264 0.3714 0.4063 0.4301 0.4422 0.4422 0.4301 0.4063 0.3714 0.3264 0.2725 0.2112 0.1441
0 0.0578 0.1140 0.1671 0.2156 0.2583 0.2939 0.3215 0.3403 0.3498 0.3498 0.3403 0.3215 0.2939 0.2583 0.2156 0.1671 0.1140
0 0.0419 0.0827 0.1213 0.1565 0.1875 0.2133 0.2334 0.2470 0.2540 0.2540 0.2470 0.2334 0.2133 0.1875 0.1565 0.1213 0.0827
0 0.0257 0.0507 0.0743 0.0958 0.1148 0.1306 0.1429 0.1512 0.1555 0.1555 0.1512 0.1429 0.1306 0.1148 0.0958 0.0743 0.0507
0 0.0092 0.0181 0.0265 0.0342 0.0409 0.0466 0.0509 0.0539 0.0554 0.0554 0.0539 0.0509 0.0466 0.0409 0.0342 0.0265 0.0181
0 -0.0075 -0.0147 -0.0216 -0.0279 -0.0334 -0.0380 -0.0415 -0.0440 -0.0452 -0.0452 -0.0440 -0.0415 -0.0380 -0.0334 -0.0279 -0.0216 -0.0147
0 -0.0240 -0.0474 -0.0694 -0.0896 -0.1073 -0.1221 -0.1336 -0.1414 -0.1454 -0.1454 -0.1414 -0.1336 -0.1221 -0.1073 -0.0896 -0.0694 -0.0474
0 -0.0403 -0.0795 -0.1165 -0.1504 -0.1802 -0.2050 -0.2242 -0.2374 -0.2440 -0.2440 -0.2374 -0.2242 -0.2050 -0.1802 -0.1504 -0.1165 -0.0795
0 -0.0562 -0.1108 -0.1625 -0.2097 -0.2512 -0.2858 -0.3126 -0.3309 -0.3402 -0.3402 -0.3309 -0.3126 -0.2858 -0.2512 -0.2097 -0.1625 -0.1108
0 -0.0715 -0.1411 -0.2068 -0.2668 -0.3196 -0.3637 -0.3978 -0.4211 -0.4329 -0.4329 -0.4211 -0.3978 -0.3637 -0.3196 -0.2668 -0.2068 -0.1411
0 -0.0861 -0.1698 -0.2489 -0.3213 -0.3848 -0.4379 -0.4790 -0.5070 -0.5213 -0.5213 -0.5070 -0.4790 -0.4379 -0.3848 -0.3213 -0.2489 -0.1698
0 -0.0998 -0.1969 -0.2886 -0.3724 -0.4461 -0.5076 -0.5553 -0.5878 -0.6043 -0.6043 -0.5878 -0.5553 -0.5076 -0.4461 -0.3724 -0.2886 -0.1969
0 -0.1125 -0.2219 -0.3253 -0.4198 -0.5028 -0.5721 -0.6259 -0.6625 -0.6811 -0.6811 -0.6625 -0.6259 -0.5721 -0.5028 -0.4198 -0.3253 -0.2219
0 -0.1240 -0.2447 -0.3587 -0.4628 -0.5544 -0.6308 -0.6901 -0.7305 -0.7510 -0.7510 -0.7305 -0.6901 -0.6308 -0.5544 -0.4628 -0.3587 -0.2447
0 -0.1343 -0.2650 -0.3884 -0.5012 -0.6004 -0.6831 -0.7473 -0.7910 -0.8132 -0.8132 -0.7910 -0.7473 -0.6831 -0.6004 -0.5012 -0.3884 -0.2650
0 -0.1432 -0.2825 -0.4141 -0.5344 -0.6402 -0.7284 -0.7968 -0.8435 -0.8672 -0.8672 -0.8435 -0.7968 -0.7284 -0.6402 -0.5344 -0.4141 -0.2825
0 -0.1507 -0.2972 -0.4357 -0.5622 -0.6735 -0.7663 -0.8383 -0.8874 -0.9123 -0.9123 -0.8874 -0.8383 -0.7663 -0.6735 -0.5622 -0.4357 -0.2972
0 -0.1566 -0.3089 -0.4528 -0.5843 -0.6999 -0.7964 -0.8712 -0.9222 -0.9481 -0.9481 -0.9222 -0.8712 -0.7964 -0.6999 -0.5843 -0.4528 -0.3089
0 -0.1609 -0.3174 -0.4653 -0.6004 -0.7192 -0.8184 -0.8952 -0.9476 -0.9742 -0.9742 -0.9476 -0.8952 -0.8184 -0.7192 -0.6004 -0.4653 -0.3174
0 -0.1636 -0.3227 -0.4730 -0.6104 -0.7312 -0.8320 -0.9101 -0.9634 -0.9904 -0.9904 -0.9634 -0.9101 -0.8320 -0.7312 -0.6104 -0.4730 -0.3227
0 -0.1646 -0.3247 -0.4759 -0.6142 -0.7357 -0.8371 -0.9157 -0.9693 -0.9965 -0.9965 -0.9693 -0.9157 -0.8371 -0.7357 -0.6142 -0.4759 -0.3247
0 -0.1639 -0.3234 -0.4740 -0.6117 -0.7327 -0.8337 -0.9120 -0.9654 -0.9925 -0.9925 -0.9654 -0.9120 -0.8337 -0.7327 -0.6117 -0.4740 -0.3234
0 -0.1616 -0.3187 -0.4672 -0.6030 -0.7222 -0.8218 -0.8990 -0.9516 -0.9783 -0.9783 -0.9516 -0.8990 -0.8218 -0.7222 -0.6030 -0.4672 -0.3187
0 -0.1576 -0.3109 -0.4557 -0.5881 -0.7044 -0.8015 -0.8768 -0.9282 -0.9542 -0.9542 -0.9282 -0.8768 -0.8015 -0.7044 -0.5881 -0.4557 -0.3109
0 -0.1520 -0.2999 -0.4395 -0.5672 -0.6794 -0.7731 -0.8457 -0.8952 -0.9203 -0.9203 -0.8952 -0.8457 -0.7731 -0.6794 -0.5672 -0.4395 -0.2999
0 -0.1449 -0.2858 -0.4189 -0.5406 -0.6475 -0.7368 -0.8060 -0.8531 -0.8771 -0.8771 -0.8531 -0.8060 -0.7368 -0.6475 -0.5406 -0.4189 -0.2858
0 -0.1362 -0.2688 -0.3939 -0.5084 -0.6090 -0.6929 -0.7580 -0.8024 -0.8249 -0.8249 -0.8024 -0.7580 -0.6929 -0.6090 -0.5084 -0.3939 -0.2688
0 -0.1262 -0.2490 -0.3650 -0.4710 -0.5642 -0.6420 -0.7023 -0.7434 -0.7643 -0.7643 -0.7434 -0.7023 -0.6420 -0.5642 -0.4710 -0.3650 -0.2490
0 -0.1149 -0.2267 -0.3323 -0.4289 -0.5137 -0.5846 -0.6395 -0.6769 -0.6959 -0.6959 -0.6769 -0.6395 -0.5846 -0.5137 -0.4289 -0.3323 -0.2267
0 -0.1025 -0.2021 -0.2963 -0.3824 -0.4580 -0.5212 -0.5701 -0.6035 -0.6204 -0.6204 -0.6035 -0.5701 -0.5212 -0.4580 -0.3824 -0.2963 -0.2021
0 -0.0890 -0.1755 -0.2572 -0.3320 -0.3976 -0.4524 -0.4949 -0.5239 -0.5386 -0.5386 -0.5239 -0.4949 -0.4524 -0.3976 -0.3320 -0.2572 -0.1755
0 -0.0745 -0.1470 -0.2155 -0.2781 -0.3332 -0.3791 -0.4147 -0.4390 -0.4513 -0.4513 -0.4390 -0.4147 -0.3791 -0.3332 -0.2781 -0.2155 -0.1470
0 -0.0594 -0.1171 -0.1716 -0.2215 -0.2653 -0.3019 -0.3303 -0.3496 -0.3594 -0.3594 -0.3496 -0.3303 -0.3019 -0.2653 -0.2215 -0.1716 -0.1171
0 -0.0436 -0.0860 -0.1260 -0.1626 -0.1948 -0.2216 -0.2425 -0.2566 -0.2638 -0.2638 -0.2566 -0.2425 -0.2216 -0.1948 -0.1626 -0.1260 -0.0860
0 -0.0273 -0.0540 -0.0791 -0.1021 -0.1222 -0.1391 -0.1522 -0.1611 -0.1656 -0.1656 -0.1611 -0.1522 -0.1391 -0.1222 -0.1021 -0.0791 -0.0540
0 -0.0108 -0.0214 -0.0314 -0.0405 -0.0485 -0.0551 -0.0603 -0.0639 -0.0657 -0.0657 -0.0639 -0.0603 -0.0551 -0.0485 -0.0405 -0.0314 -0.0214
0 0.0058 0.0114 0.0167 0.0215 0.0258 0.0294 0.0321 0.0340 0.0350 0.0350 0.0340 0.0321 0.0294 0.0258 0.0215 0.0167 0.0114
0 0.0223 0.0441 0.0646 0.0833 0.0998 0.1136 0.1242 0.1315 0.1352 0.1352 0.1315 0.1242 0.1136 0.0998 0.0833 0.0646 0.0441
0 0.0387 0.0763 0.1118 0.1443 0.1728 0.1966 0.2151 0.2277 0.2341 0.2341 0.2277 0.2151 0.1966 0.1728 0.1443 0.1118 0.0763
0 0.0546 0.1077 0.1579 0.2037 0.2440 0.2777 0.3038 0.3216 0.3306 0.3306 0.3216 0.3038 0.2777 0.2440 0.2037 0.1579 0.1077
0 0.0700 0.1380 0.2023 0.2611 0.3128 0.3559 0.3893 0.4121 0.4237 0.4237 0.4121 0.3893 0.3559 0.3128 0.2611 0.2023 0.1380
0 0.0846 0.1670 0.2448 0.3159 0.3783 0.4305 0.4709 0.4985 0.5125 0.5125 0.4985 0.4709 0.4305 0.3783 0.3159 0.2448 0.1670
0 0.0984 0.1942 0.2847 0.3674 0.4400 0.5007 0.5477 0.5798 0.5961 0.5961 0.5798 0.5477 0.5007 0.4400 0.3674 0.2847 0.1942
0 0.1112 0.2195 0.3217 0.4151 0.4973 0.5658 0.6190 0.6552 0.6736 0.6736 0.6552 0.6190 0.5658 0.4973 0.4151 0.3217 0.2195
0 0.1229 0.2425 0.3554 0.4587 0.5494 0.6252 0.6839 0.7239 0.7442 0.7442 0.7239 0.6839 0.6252 0.5494 0.4587 0.3554 0.2425
0 0.1333 0.2630 0.3855 0.4975 0.5959 0.6781 0.7418 0.7852 0.8072 0.8072 0.7852 0.7418 0.6781 0.5959 0.4975 0.3855 0.2630
0 0.1424 0.2809 0.4117 0.5313 0.6364 0.7242 0.7922 0.8385 0.8621 0.8621 0.8385 0.7922 0.7242 0.6364 0.5313 0.4117 0.2809
0 0.1500 0.2959 0.4337 0.5597 0.6704 0.7628 0.8345 0.8833 0.9081 0.9081 0.8833 0.8345 0.7628 0.6704 0.5597 0.4337 0.2959
0 0.1561 0.3078 0.4512 0.5823 0.6975 0.7937 0.8682 0.9191 0.9449 0.9449 0.9191 0.8682 0.7937 0.6975 0.5823 0.4512 0.3078
0 0.1605 0.3167 0.4642 0.5991 0.7176 0.8165 0.8932 0.9455 0.9720 0.9720 0.9455 0.8932 0.8165 0.7176 0.5991 0.4642 0.3167
0 0.1634 0.3223 0.4724 0.6097 0.7303 0.8310 0.9090 0.9622 0.9892 0.9892 0.9622 0.9090 0.8310 0.7303 0.6097 0.4724 0.3223
0 0.1646 0.3246 0.4758 0.6141 0.7356 0.8370 0.9156 0.9692 0.9964 0.9964 0.9692 0.9156 0.8370 0.7356 0.6141 0.4758 0.3246
0 0.1641 0.3236 0.4744 0.6122 0.7333 0.8345 0.9128 0.9663 0.9934 0.9934 0.9663 0.9128 0.8345 0.7333 0.6122 0.4744 0.3236
0 0.1619 0.3194 0.4681 0.6041 0.7236 0.8234 0.9007 0.9535 0.9802 0.9802 0.9535 0.9007 0.8234 0.7236 0.6041 0.4681 0.3194
0 0.1581 0.3118 0.4571 0.5899 0.7066 0.8040 0.8795 0.9310 0.9571 0.9571 0.9310 0.8795 0.8040 0.7066 0.5899 0.4571 0.3118
0 0.1526 0.3011 0.4414 0.5696 0.6823 0.7764 0.8493 0.8990 0.9242 0.9242 0.8990 0.8493 0.7764 0.6823 0.5696 0.4414 0.3011
0 0.1457 0.2873 0.4212 0.5435 0.6511 0.7408 0.8104 0.8578 0.8819 0.8819 0.8578 0.8104 0.7408 0.6511 0.5435 0.4212 0.2873
0 0.1372 0.2706 0.3967 0.5119 0.6132 0.6977 0.7632 0.8079 0.8306 0.8306 0.8079 0.7632 0.6977 0.6132 0.5119 0.3967 0.2706
0 0.1273 0.2511 0.3681 0.4751 0.5691 0.6475 0.7083 0.7498 0.7708 0.7708 0.7498 0.7083 0.6475 0.5691 0.4751 0.3681 0.2511
0 0.1161 0.2291 0.3358 0.4334 0.5191 0.5907 0.6462 0.6840 0.7032 0.7032 0.6840 0.6462 0.5907 0.5191 0.4334 0.3358 0.2291
0 0.1038 0.2047 0.3001 0.3873 0.4639 0.5279 0.5774 0.6113 0.6284 0.6284 0.6113 0.5774 0.5279 0.4639 0.3873 0.3001 0.2047
0 0.0904 0.1783 0.2613 0.3372 0.4040 0.4597 0.5028 0.5323 0.5472 0.5472 0.5323 0.5028 0.4597 0.4040 0.3372 0.2613 0.1783
0 0.0760 0.1500 0.2199 0.2838 0.3399 0.3868 0.4231 0.4479 0.4604 0.4604 0.4479 0.4231 0.3868 0.3399 0.2838 0.2199 0.1500
0 0.0609 0.1202 0.1762 0.2274 0.2724 0.3099 0.3390 0.3589 0.3689 0.3689 0.3589 0.3390 0.3099 0.2724 0.2274 0.1762 0.1202
0 0.0452 0.0892 0.1307 0.1687 0.2021 0.2299 0.2515 0.2662 0.2737 0.2737 0.2662 0.2515 0.2299 0.2021 0.1687 0.1307 0.0892
0 0.0290 0.0572 0.0839 0.1083 0.1297 0.1476 0.1614 0.1709 0.1757 0.1757 0.1709 0.1614 0.1476 0.1297 0.1083 0.0839 0.0572
0 0.0125 0.0247 0.0362 0.0468 0.0560 0.0637 0.0697 0.0738 0.0759 0.0759 0.0738 0.0697 0.0637 0.0560 0.0468 0.0362 0.0247
0 -0.0041 -0.0081 -0.0118 -0.0152 -0.0182 -0.0208 -0.0227 -0.0240 -0.0247 -0.0247 -0.0240 -0.0227 -0.0208 -0.0182 -0.0152 -0.0118 -0.0081
0 -0.0207 -0.0407 -0.0597 -0.0771 -0.0923 -0.1051 -0.1149 -0.1216 -0.1251 -0.1251 -0.1216 -0.1149 -0.1051 -0.0923 -0.0771 -0.0597 -0.0407
0 -0.0370 -0.0730 -0.1070 -0.1381 -0.1655 -0.1883 -0.2059 -0.2180 -0.2241 -0.2241 -0.2180 -0.2059 -0.1883 -0.1655 -0.1381 -0.1070 -0.0730
0 -0.0530 -0.1046 -0.1533 -0.1978 -0.2369 -0.2696 -0.2949 -0.3121 -0.3209 -0.3209 -0.3121 -0.2949 -0.2696 -0.2369 -0.1978 -0.1533 -0.1046
0 -0.0684 -0.1350 -0.1979 -0.2554 -0.3059 -0.3481 -0.3808 -0.4031 -0.4144 -0.4144 -0.4031 -0.3808 -0.3481 -0.3059 -0.2554 -0.1979 -0.1350
0 -0.0832 -0.1641 -0.2405 -0.3104 -0.3718 -0.4231 -0.4628 -0.4899 -0.5037 -0.5037 -0.4899 -0.4628 -0.4231 -0.3718 -0.3104 -0.2405 -0.1641
0 -0.0971 -0.1915 -0.2807 -0.3623 -0.4340 -0.4938 -0.5402 -0.5718 -0.5878 -0.5878 -0.5718 -0.5402 -0.4938 -0.4340 -0.3623 -0.2807 -0.1915
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velocity(:,:,1) =
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figure
hold on
for k = 1:size(velocity,3)
surfc(vx, vy, velocity(:,:,k))
end
Warning: Contour not rendered for constant ZData
view(-27,30)
colormap(turbo)
colorbar
grid on
axis('equal')
xlabel('v_x')
ylabel('V_y')
zlabel('velocity')
% where vx = cos(beta)*sin(alpha),
%
% and vy is something similar.
%
% The surface plot will be against beta and alpha, so I write
% vx_times_ip = vx .* ip(theta)
.
Hi Star Strider!
Can I loop through both beta and alpha? Also, my function is in a separate function file, which my surface plotting code calls. Does this cause issues? Should I instead keep my function locally defined within my surface plotting code? Thanks!
‘’Can I loop through both beta and alpha?
You have my permission! :-)
I‘m not certain whether you’re referring to the vectors or the matrices. The matrices will be duplicates of the original vectors, with ‘Alpha’ duplicating ‘alpha’ row-wise, and ‘Beta’ duplicating ‘beta’ column-wise.
I’m not certain about the rest, since I cannot even visualise what you want to do. One option is to plot each ‘page’ of your array (if it has separate pages — I’m not sure what you’re doing) as separate surf plots.
Plotting different results in different figures would not cause issues, and could be a solution.
(Note that I’m responding to hypothetical problems with hypothetical replies.)
.
Hi Star Strider,
For making surface plots, I have to use Beta and Alpha, the outputs from meshgrid(alpha, beta), as inputs to the functions. But before I get to the functions I want to code up terms, which are vectors, as linear combinations of rotating basis vectors. Matlab is telling me about arrays having incompatible sizes, when I try to do this, because Beta is a vector, Alpha is a vector, and a rotating basis vector is a vector. This is tricky to get right, in contrast to making simple line plots, where I didn’t have much issues. I’m a little frustrated with myself. I’m going to try again tomorrow. Goodnight, and thanks for your time!
My pleasure!
I’m obviously not able to understand what you are doing (since you haven’t revealed what that is), however if you have a function that takes the vectors α and β (or similarly-sized vectors for one or both) as arguments, the functions need to produce an appropriate-size matrix as an output that you can plot against α and β. To create an appropriate-size matrix from an argument vector, one option is to use the repmat function. That should make this easier.
.
Hi Star Strider!
So, just to describe my workflow a bit more clearly:
I loop through beta and then calculate values of F (a scalar-valued function) for all alpha = linspace(0, 2pi, 1001). I am only looping through beta, not alpha, which I really like.
I might choose 10 or 11 evenly spaced values of beta to loop through, using linspace( ).
Then, I made nice line plots, going from subplots to tiled layouts, which seems to be advantageous; e.g. global title, global colorbar, etc. are made easy using tiledLayout rather than with subplot.
In my 2D line plots, each tile would have the 11 curves, with alpha being the independent variable, and I use colors from a colormap to show the variation in beta. This figure of 6 tiles, I think, is really pretty -- and communicative.
Now, instead of 2D line plots, I want to present this exact same information using 3D surface plots, just to compare and see which figure is more communicative.
However, since my functions that I am plotting are scalar-valued functions, I am getting the error that my functions need to be matrices.
By the way, I have plenty of vectors expressed as linear combinations of basis vectors, but the final functions to be plotted are all scalar-valued, gotten from using dot products.
So, as of now, I can basically write a poor man's version of a code that gives the surface plots (very pretty), but this is not good and systematic:
- I would like to continue looping through beta;
- To keep things organized and de-cluttered, I would like to continue calling my functions which are stored in separate files; and
- For doing careful mathematics, I would like to continue expressing vectors as linear combinations of basis vectors, etc.
It seems if in the beginning of my surface-plotting code I define a meshgrid [Alpha,Beta] = meshgrid(alpha,beta), and use the variables Alpha and Beta as inputs, then I start running into issues with arrays having incompatible sizes.
I have one current guess at a solution, as of now:
Maybe define my functions locally in the same file as my surface-plotting code, rather than call them from another separate file? I would rather not do this, because my intuition is that my errors should be easy enough to fix.
I look forward to hearing from you.
Thanks for your time!
You can create matrices from the lines in the line plots by concatenating them into a matrix. They all have to have the same number of points (be the same size), and are functions of the inidepenedent variable at the same points.
There are ways to get around these restrictions (probably using the scatteredInterpolant function), however it impossiible to describe that process wiith only the information thus far provided.
x = linspace(0, pi/2, 333).';
f = [1 3 7 11 17];
y = sin(2*pi*x*f);
figure
plot(x, y)
grid
title('Line Plots of ‘y’')
legend(compose('Frequency %4.1f',f), Location='best')
figure
surfc(f, x, y)
grid
title('Surface Plot of ‘y’')
colormap(turbo)
colorbar
xlabel('Frequency')
ylabel('X')
zlabel('Function Value')
set(gca, 'XScale','log')
Same data, different representations.
.
I loop through beta and then calculate values of F (a scalar-valued function) for all alpha = linspace(0, 2pi, 1001). I am only looping through beta, not alpha, which I really like.
At this stage, save the scalar values for F in a 2d-matrix Fmat where Fmat(i,j) is the value you obtain for F if you evaluate it for (alpha(i),beta(j)). That's all you need for a later 3d-surface plot.
This works! And, now I've learned how to write scalar values to matrices.
Thanks so much!
Hi Star Strider!
I am OK now, I think! Let me go ahead and accept your answer. Thanks and have a great day!
I just have two lingering issues now:
While my entire 2D line-plot workflow is now preserved (really great) -- by pre-allocating and filling in matrices with function values, like Torsten indicated -- I still have array-size compatibility issues when I try to write vectors as linear combinations of basis vectors. Thus, I am able to make surface plots for some functions, but not for others. So, what size do you think the basis vectors should be?
Also, with regard to colors, they seem to be coloring a solid, sort of like filling a volume, and I think that's incorrect, because the 2D version of this 3D plot would then be wrong. The colors from a colormap should only be filling the curvy cross sections, not filling in the area underneath, for example, so that the 2D version vs. all alpha, should look exactly the same as the line plots vs. alpha. As is, the area underneath, say, a sine wave, is being filled in with color, which is not correct.
Before using the "surf"-command, check the sizes of the arrays/matrices involved to conform with the requirements explicitly given in the documentation of "surf":
Input Arguments
X — x-coordinates
matrix | vector
x-coordinates, specified as a matrix the same size as Z, or as a vector with length n, where [m,n] = size(Z). If you do not specify values for X and Y, surf uses the vectors (1:n) and (1:m).
The XData property of the Surface object stores the x-coordinates.
Example: X = 1:10
Example: X = [1 2 3; 1 2 3; 1 2 3]
Example: [X,Y] = meshgrid(-5:0.5:5)
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration
Y — y-coordinates
matrix | vector
y-coordinates, specified as a matrix the same size as Z or as a vector with length m, where [m,n] = size(Z). If you do not specify values for X and Y, surf uses the vectors (1:n) and (1:m).
The YData property of the surface object stores the y -coordinates.
Example: Y = 1:10
Example: Y = [1 1 1; 2 2 2; 3 3 3]
Example: [X,Y] = meshgrid(-5:0.5:5)
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration
Z — z-coordinates
matrix
z-coordinates, specified as a matrix. Z must have at least two rows and two columns.
Z specifies the height of the surface plot at each x-y coordinate. If you do not specify the colors, then Z also specifies the surface colors.
The ZData property of the surface object stores the z -coordinates.
Example: Z = [1 2 3; 4 5 6]
Example: Z = sin(x) + cos(y)
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration
The basis vectors should span the space they define. For example, in 3-space, there are three basis vectors. However to define a 3D plot, you can have as many (x,y,z) triplets to define what you want to plot as you have available memory in your computer.
I can’t envision what you want to do with the colours. One optiion would be to use logical indexing so that only the parts you want are coloured. The second is to do something similar to Create Multicolored Line however I have no iiidea what you are doing, so I can be no more specific.
Hi Star Strider!
So, the parameter Beta essentially expresses the amount of rotation that's in my system of interest, which is crucial. Thus, I want colors from a colormap to vary with Beta, not with function value or surface height. I had started with:
alpha = linspace( ... )
Beta = linspace( ... ),
and then looping through beta = Beta(z), and, for each beta, computing function values for all alpha.
I also wrote:
[X, Y] = meshgrid(alpha, Beta),
but later, if I write:
surf(X,Y,FL_hat,Beta),
I get an error the error:
Warning: Error creating or updating Surface
Error in value of property CData
Array is wrong shape or size.
If I instead write:
surf(X,Y,FL_hat,Y),
Then I seem to sort of get what I want; only now that the area underneath the curves are also being filled in with color, so that the 2D version of this surface plot, i.e. a line plot vs. all alpha, would be wrong; the 2D version should be a bunch of colored curves, not filled-in solids.
If I store scalar function values into a matrix, and, with this matrix, denoted by FL_hat, which has size 11 X 1001, I want to write linear combinations of FL_hat, say with FD_hat so that
Net force = FL_hat * ip + FD_hat * jp,
where ip and jp are basis vectors such as:
ip = cos(theta)*i + sin(theta)*j + 0*k
jp = -sin(theta)*i + cos(theta)*j + 0*k,
then how can I write such a linear combination without getting array-size compatibility issues?
In that patch example, ‘c’ is set equal to ‘y’. You can set it equal to whatever you want, providing (in this instance) that it has the same dimensions as the other arguments.
The colour array C has to be the same size as ‘Z’. In your quoted code, ‘Beta’ iis a vector, and that iis not going to work for ‘C’. In the context of your meshgrid call, you probably have to calculate the values of ‘Beta’ you use in the surf call from ‘X’, ‘Y’, or both. Since I’m not sure how you calculate the ‘Beta’ you want to use in your surf call, that’s as far as I can go with this for the time being.
Perhaps ‘Beta’ should be the value of ‘Y’ that you return from meshgrid? (Just a guess.)
.
You mean
ip = [cos(theta);sin(theta);0]
jp = [-sin(theta);cos(theta);0]
where theta is a scalar ?
Then FL_hat and FD_hat must have 3 columns, not 1001.
Hi Star Strider,
It is indeed Y, returned from meshgrid. Only that ... while the color variation is correct, the colors seem to be filling in solids, when (I think) they should only be filling in the surface area, so that the 2D version vs. all alpha should simply be colored curves / lines, not colored solids. The 2D version, rotated around, should recover the 2D line plot, I think. So, a sine wave seems to be colored underneath it, too, which is strange, and likely not correct, because the 2D version will be wrong. Hmm ...
Hi Star Strider!
I fixed this! Use NaN to create the pre-allocated matrices, not Zeros.
Not sure why, but this fixed the issue.
I think I have good working surface plots / tiles now, and I'll take a much-needed break for now, before jumping back in to work on this stuff.
Thanks again for your time and help!
With respect to filling in the patches, perhaps using mesh instead of surf will do what you want. (I’m stiill not sure what that is.)
Both zeros and NaN (or ones or rand or randn, etc.) will work for preallocation. The difference is that NaN values do not plot, and all the others, each having a finite value for every element, will plot.
その他の回答 (1 件)
Hi
To solve your problem of writing a scalar-valued function using meshgrid and linear combinations of rotating basis vectors, you need to ensure that all operations are element-wise and that the dimensions match properly.
function v_norm = velocity_norm(alpha, beta, theta)
% rotating basis vectors
ip = [cos(theta); sin(theta); 0];
jp = [-sin(theta); cos(theta); 0];
kp = [0; 0; 1]; % Not used in this example, but defined for completeness
% Calculate velocity components
vx = cos(alpha) * ip(1) + sin(beta) * jp(1);
vy = cos(alpha) * ip(2) + sin(beta) * jp(2);
vz = cos(alpha) * ip(3) + sin(beta) * jp(3);
% Calculate the norm of the velocity vector
v_norm = sqrt(vx.^2 + vy.^2 + vz.^2);
end
alpha = linspace(0, pi, 20);
beta = linspace(0, 10, 100);
[Alpha, Beta] = meshgrid(alpha, beta);
% Define the angle theta
theta = 0;
% Calculate the velocity norm for each alpha and beta
V_norm = velocity_norm(Alpha, Beta, theta);
figure;
surf(Alpha, Beta, V_norm);
xlabel('\alpha');
ylabel('\beta');
zlabel('Velocity Norm');
title('3D Surface Plot of Velocity Norm');
Hope this helps!
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