The Great Pyramid Challenge

[davegee]

DEFINITION OF PAN Z

I will attempt to define Pan Z.

But first I must explain my terminology.

An object in O&A has a "NATURAL HEIGHT" and an "APPARENT HEIGHT".

If an object is created in PS being 800 pixels wide and 600 pixels high and added to PTE O&A its "NATURAL HEIGHT" is 600 pixels.

If the same object is turned through 90 degrees its "APPARENT HEIGHT" is 800 pixels but its "NATURAL HEIGHT" is still 600 pixels.

The definition:

PAN Z applied to an object is a function of the "NATURAL HEIGHT" of its parent frame.

e.g. if +/- 100% PAN Z is applied to an object which has a parent frame which is 800 wide by 600 high the object will move by +/- 300 pixels.

Open to comments.

DG

[fh1805]

Dave,

Can I go back to the accuracy debate, please? In your earlier postings in this topic you stressed the need for accuracy in respect of the "slope angle" and quoted a value at four decimal places. Did you notice that PTE apparently rounded down the X and Y rotation values to just two decimal places in the 3D Parameters fields? You can prove this as follows: key in a three decimal place value into either X Rotate or Y Rotate. For as long as you keep that object the selected object it shows three decimal places. Select a different object, do nothing and re-select the previous object and the values now show as two decimal places. (That test was done using v7 beta 9). The software may have retained full precision "under the covers"; but its external appearance is of rounding to two decimal places. Perhaps your desire for mathematical accuracy cannot be matched by the software? Another point to get clarified via Igor, I think. I'm not saying you're wrong to seek mathematical accuracy, just that there must now be some doubt as to the product's ability to deliver. It may just be a cosmetic issue in the way the data is presented back to the user: then again, it may not!

regards,

Peter

[fh1805]

Further to that last post of mine about accuracy...

If I've got my trigonometry correct, the difference in height of a right angle triangle having a base angle of 52.9573 and one having a base angle of 52.96 is less than one quarter of a pixel on a base side of 1920 pixels. (See screenshot for spreadsheet values)

regards,

Peter

[Jean-Cyprien]

Hi Peter,

I was trying to make rapidly an example of "What is Pan Z value and how to use it",

I think if you write a number with 3 decimals, PTE takes them, but if you want to copy the number, only 2 decimals are put. I'll see and return.

If my little work could be useful (without too much mistakes, I hope !)

PanZ.zip

[fh1805]

Jean-Cyprien,

Merci, mon ami. A little longer to view each slide would have been nice. But you have enabled keyboard control so it is possible to pause on each slide and really study what you are describing. Thank you for taking the time to provide these explanations.

regards,

Peter

[Jean-Cyprien]

Y're welcome Peter,

always a problem to put the right duration for different people !

Number of decimal places

I don't know how much decimal places PTE takes to run the calculation.

But if I put 6 decimal places for a number, this number is correctly taken into the file, with 6 decimal places, even after copying the keypoint, or the file (picture or frame)... and even if PTE changes rapidly the number to let see only 2 decimal places.

You can see that by copying the file on Excel (for example)

Avec toutes mes amitiés, Peter

[davegee]

Peter,

I can't argue about PTE rounding off the figure.

However, I must admit to doing a bit of reverse engineering in designing the challenge. I tried to get a figure for the angle which produced the nearest "whole pixel" dimensions for the sides. The figure which then came up was 92.9573.

Whilst the actual slope of the Great Pyramid is 92.xx it slightly less than my 92.9573.

If you look at Sheila's Template you'll see that her rounding up or down has produced a much more inaccurate result than yours and mine did. Somehow, her figure came to 666 as opposed to our 664.

Notwithstanding the number of decimal places issue, I still maintain that being as accurate as possible is to be desired when trying to impart a principle on others who might be trying to learn from our efforts.

If I were using Excel I would be looking for a large number of decimal places in the calculations phases but rounding off the final result. Does that not make sense?

DG

[davegee]

Jean-Cyprien,

You and I are saying the exact same thing in slightly different ways.

However, I would advocate the use of "custom built" Frames (independent of screen resolution) to simplify the process.

For instance, if a frame of 400x400 is used in the construction of a 400x400 cube then the PAN Z values are always 100%.

You could also use an 800x800 Frame to construct the 400x400 Cube in which case the PAN Z values would be 50%.

One further point:

PAN Z is not necessary in the construction of a cube. It is only necessary for moving the cube backwards or forwards relative to the viewer.

Pan Z was not used and was not needed in the construction of the Photo Frame elsewhere in this thread.

Going back to the FRAME itself, I am reminded that JPD sometimes used a CALE which was of a fixed height but ONLY ONE PIXEL WIDE.

He was way ahead of his time!!

DG

[Jean-Cyprien]

Hi Dave

« However, I would advocate the use of "custom built" Frames (independent of screen resolution) to simplify the process.

For instance, if a frame of 400x400 is used in the construction of a 400x400 cube then the PAN Z values are always 100%.

You could also use an 800x800 Frame to construct the 400x400 Cube in which case the PAN Z values would be 50%. »

I agree, but not with different sizes of frame. When I want to built some complex object (for example Choupinette, or Christmas present), I use a frame of 200x200 as JPD has recommended.

With this size of frame, the values of Pan X and Pan Y AND Pan Z are directly done in pixel. This is a lot easier than to multiply or divide by the height, and the width of the screen to get a percentage.

« PAN Z is not necessary in the construction of a cube. »

Sure. There are a lot of different possibilities to built a cube without the Pan Z value.

« It is only necessary for moving the cube backwards or forwards relative to the viewer. »

Yes and No. If you are just using Pan Z to do this, it's the same thing using the Zoom value with the « Common/Perspective correction for Zoom ». If you try also to use different moving speeds (accelerate, slow down, smoth), of course you need Pan Z. Or to do something else in 3D.

« Pan Z was not used and was not needed in the construction of the Photo Frame elsewhere in this thread.  »

Yes, Pan Z is useful but not always necessary.

« Going back to the FRAME itself, I am reminded that JPD sometimes used a CALE which was of a fixed height but ONLY ONE PIXEL WIDE. »

I know this, but it's no more useful.

« He was way ahead of his time!! »

Certainly, he had a lot of great ideas, the possibilities to give life to them, and his kindness was a remarkable one.

Jean-Cyprien

[fh1805]

Further to the debate about accuracy and precision...

I've just opened my PTE project file in Notepad and had a look at what PTE has saved. Because I was folding three of my sides in from the "opened out" horizontal position, I entered the rotate value as 127.043 for these three sides (127.043 = 180-52.9573 rounded to three decimal places) and entered 52.957 for the fourth side. Within the PTE project file these values are stored as 127.042994 for side#4 and side#3, 127.040002 for side#2 and 52.957001 for side#1. Within the PTE O&A window, all four values are shown to just two decimal places.

So, I think this confirms that PTE internally works to six decimal places. But why the different conversions of 127.043?

Dave, this suggests to me that your push for absolute mathematical accuracy is, at times, likely to be thwarted by PTE's variation in its own precision. Or am I missing something highly significant in what PTE is doing?

regards,

Peter

[davegee]

Hi Peter,

If you explore the link I gave you and enter, for instance, my figure (52.9573) for the angle and then Sheila's 53 together with a base dimension of 400 you'll see that the result is a difference of 1 pixel.

My suggested figure gives 663.999xxxxxx (664)

Sheila's angle gives 664.65xxxxx (665??)

My suggestion is that the ONE pixel difference is noticeable and COULD be magnified by other factors, especially when the different monitor resolutions are taken into account.

Try those figures in Excel and see if they are the same (?) - they should be.

If a Maths Exam paper gave a figure of 52.9573 to work with then that's the figure I would use - it's there for a purpose.

It's not that big a deal but my background tells me that I should be as accurate as possible in these things. I have to trust Igor's and PTE's maths capabilities until someone proves otherwise.

DG

P.S. Regarding your 127.04xxxx figure, what would happen if you started from a completely folded (flattened or collapsed) object and asked it to open all sides out to 52.9573? Would that be more accurate?That's the way I approached this excercise.