## 675 Reputation

15 years, 181 days

## Here is my configuration...

@Christopher2222 Thanks for your answer. I have a Dell Inspiron 1545 with an Intel Pentium Dual Core T4500 at 2.3 GHz, 800 MHz, 1 MB Cache.

Memory is 4 GB DDR2 800 MHz 2 Dimm

Graphics is an Intel Graphics Media Accelerator X4500D

For the past few months the operating system has been Windows 10.

## Polygon to triangles...

@Carl Love Thanks Carl. Your advice would be useful in specific cases.

## Great tutorial...

@Rouben Rostamian  Your tutorial gave me a good understanding of barycentric coordinates. As evidence of this I modified, in your answer to my question, a copy of your code which maps the planar triangle to the unit circle to map this same triangle to an ellipsoid. I don't see how this could have been done without barycentric coordinates.

A final question; can barycentric coordinates apply to any planar polygon of more than three sides?

@Rouben Rostamian  Rouben, your worksheet shows me the solution to my questions 1 and 2 and I overlooked a simple answer to question 3.

I regularly scan Maple Primes to find new Maple programming techniques and, occasionally, new math techniques and your worksheet has amazed me in both regards.

I had no knowledge of barycentric coordinates but now I see they have great power in solving otherwise tough math problems and they define a vector (V) which provides all the coordinates within the triangle as lambda1 and lambda2 cycle through their ranges.

Try as I might, there are several statements in your worksheet that baffle me.

I can't find a clear explanation or example in Maple 15 help pages of the syntax %T.

Please explain why the correct ranges for plotting the planar triangle are the ones you specified in your plot3d command.

Why does the statement V / sqrt(V^%T . V); not evaluate i.e. acts as an inert command?

Please also explain why plotting the unnormalized V gives a planar triangle while plotting the normalized V plots the same triangle fitted to the surface of the unit sphere.

Please explain why the ranges of function U within the spacecurves of the normalized V provide the edges of the spherical triangle.

Your worksheet is an education in itself and I greatly appreciate your attention.

## @vv I moved my archive to my person...

@vv I moved my archive to my personal documents library and now can successfully save and delete expressions in it. Thank you for your wonderful advice.

BTW the procedure I most recently saved contained the short version of VectorCalculus[CrossProduct] namely &x. When I executed this procedure today &x did not work but replacing it with the full command did work. Yet &x worked in the same procedure yesterday.. a mystery!!

## @dharr Yes, these also do the job. ...

@dharr Yes, these also do the job. Thanks.

## @tomleslie Thanks for your help. Th...

@tomleslie Thanks for your help. The warning does look like a bug.

## Making a procedure available in multiple...

@acer The second link in your answer above works beautifully. I have now archived, and invoked in several worksheets, a procedure which rotates a complex 3D display around any position vector and executes several times faster than plottools[rotate] around a line defined by two points.

Thanks hugely!

## LibraryTools,libname, etc....

@acer Thanks for this advice. However I have zero experience with library archives and the initialization file and I  find the help pages confusing. Please give me or refer me to an example of a specific procedure being saved to a specific .mla library archive and then invoked in a subsequent worksheet so I can duplicate your commands to accomplish this.

## Desktop choices for fast Maple execution...

@roman_pearce Thanks for the extensive survey of processors!

## Desktop choices for fast Maple execution...

@acer Thanks for your quick response. This is useful information

## Reuleaux tetrahedron...

Hi Kitonum,

Thanks for the rotate command.

I have modified your worksheet to display a Meissner tetrahedron, a shape with truly constant width.

The modifications are lengthy, so if you want to see the modified worksheet I can paste it into my next Maple Primes comment or send it to you as an email attachment.

Regards...Earl

## Rouleaux tetrahedron...

Hi Kitonum,

Thank you greatly for this code which accurately displays a true Rouleaux tetrahedron. I knew how to plot a sphere with centre at a given vertex but not how to limit its extent within its intersections with the spheres with centres at the other three vertices.

The eliminate command is new to me, but the help text for it does not describe how the elimination process is conducted. Can you refer me to such a description, perhaps in another web site?

Best regards...Earl

## Rouleaux tetrahedron...

Hi, Thanks for your reply. I'm in no hurry since I am a 72 year old retired computer programmer who codes Maple applications in math and physics for my own edification and amusement. Any further information you can give me will be much appreciated.

## Rouleaux tetrahedron...

Hi acer,

Thanks for the code to display a Rouleaux tetrahedron (Rt).

I executed the code you posted in Maple 15, but the MathApp you provided a link to gave an error when I tried to execute it in Maple 15. Does this MathApp depend on commands from a later version of Maple?

However I don't think the image the code produced for me is a correct shape. As you can see in Wikipedia's website for Rouleaux_tetrahedron, the correct shape is not a surface of revolution since the faces of a Rt meet at an angle.

The Meissner tetrahedron, a modification of a Rt which changes the latter into a true constant width object, also is not a surface of revolution. The modification process can be seen at web site Meissner_en.pdf.

Earl

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