orthogonal Vectors

[Areeda]

OK the mathematical portion of my brain is atrophying at least the linear algebra part. I think this is a symptom of CRS syndrome.

Given a vector like (1,0,0) how do I find 2 of the 4 orthogal vectors? Please don't assume it's on a usual axis how about (.577,.577,.577)

Thanks,

Joe

 

[Areeda]

Just a little explanation:

I'm playing with a 3D plot, very aviation related, and I want to draw the axes as a solid like a cylinder or a rectangle rather than a line.

The plot is a histogram of air flow (RPM * MP compensated for temperature) vs fuel flow.

In 2D it looks like this

The line represents the stochiometric burn (peak EGT) the color represent how much time we spent at that air/fuel combination when greater than 30 kts ground speed.

The 3D plot looks sort of like this (my program is just starting to work)

I want to get the axis labeled in gph and % air flow. Actually I'd like % power but that's wierd in a way we can talk about later.

The current problem though is to get the axes to look like a solid object instead of a infinitesimally thin line.

Joe

 

[SCCutler]

...looks like the logo for Touchstone Pictures to me...

 

[tonycondon]

joe,

for an orthogonal vector i believe you use the cross product.

 

[ScottM]

joe,

for an orthogonal vector i believe you use the cross product.

Use the dot product and set it equal to 0

[x1, y1, z1] * [x2, y2, z2] = 0

x1x2+ y1y2 + z1z2 = 0

 

[gismo]

Use the dot product and set it equal to 0

[x1, y1, z1] * [x2, y2, z2] = 0

x1x2+ y1y2 + z1z2 = 0

Isn't that the very definition of "orthogonal"?

 

[Clark1961]

Just a little explanation:

I'm playing with a 3D plot, very aviation related, and I want to draw the axes as a solid like a cylinder or a rectangle rather than a line.

The plot is a histogram of air flow (RPM * MP compensated for temperature) vs fuel flow.

In 2D it looks like this

The line represents the stochiometric burn (peak EGT) the color represent how much time we spent at that air/fuel combination when greater than 30 kts ground speed.

The 3D plot looks sort of like this (my program is just starting to work)


I want to get the axis labeled in gph and % air flow. Actually I'd like % power but that's wierd in a way we can talk about later.

The current problem though is to get the axes to look like a solid object instead of a infinitesimally thin line.

Joe

I'm not exactly sure what you want but it sounds like you'd like the axes to show up better by using a larger symbol/object.

If that's true, the simple approach is to define a new data series and that series is a dummy created to lay on the desired axis. The dummy series is easy to build since it's just two or three columns (depends on plot type) with mostly zero values. Set the symbol to be something you like and there you have it. I've done this in Excel to get the visual effect I wanted. In fact, I can recreate the plots you've shown in Excel.

Of course, if my interpretation of what you're trying to accomplish is wrong then by all means ignore this post.

 

[Areeda]

I think I've got a handle on my problem, but I'm still working to hard to do something simple. It is kind of fun knocking rust of of linear algebra I haven't used in so long. What I've done is use the dot product against the x,y,and z axis to find one that is not parallel. The cross product of those gives me one orthogonal to the original vector and the cross product of that gives me 2. Gotta be an easier way.

The latest version of excel is 2002 and I tried to generate generate something like this without luck. What I have is 280 columns and 100 rows, each cell represents height. What kind of chart displays data like that?

Joe

 

[Clark1961]

The histogram can be displayed using the 3D column chart type. The data must be organized with appropriate row labels and column headers in order for Excel to digest the input. After that it is just a matter of selecting the data, the chart type, and then formatting the resultant chart. Of course, with Excel the formatting takes the most time since the defaults are rather bland.

In 2D form the chart may take a bit more work to get the points colored as nicely as you have in your example. A contour plot might work if the data are well behaved.

There are some good resources on the net. I started learning from www.j-walk.com and branched out to the many other resources.

Data presentation is really an art - hang in there with your project.

 

[Areeda]

I'm making progress. I now draw these cylinders (well actually octagons) for the axis and the peak egt (stoichiometric) line. Not too obvious at this resolution but still looks better than the one pixel lines.

It is more impressive when you can rotate it but I don't quite have it as a craplet yet.

Joe