Scaling

[michel123456]

It is the 2nd time on this forum that discussion goes about scaling and I'd like to make some point.

 

Before using CAD programs, I must admit that I had a different view about scaling.

My ancient view was simple: if you take a regular macroscopic object, say cup or a glass, and think that you must scale it 3 times, well things are simple: you get something like a vase.

 

So I remember my first steps in Autocad and I was really surprised that it was not so simple.

First of all, one has to consider that all CAD programs are ultimately mathematicals.

Secondly, these programs are terribly dumb: if you don't tell EVERYTHING to the program, the command does not execute.

 

Here comes the "scale" command and the sequence of steps in order to perform the scaling of a cup in Autocad.

 

1. select objects.

 

That's fine, the program must know what object you want to scale.

 

2. input the scale factor*.

 

That's fine, the program will follow my wish. I input number 3.

 

3. Specify base point

 

?????? Why the hell does the program need a base point in order to perform a scaling?

Well, the reason is that the base point will decide WHERE the result will appear. Because any scaling performs also a change in position of everything selected, except for the base point.

 

The remark may come from Autocad, but it is a real effect.

 

Some examples below

 

fig.1

 

In fig.1, you have a situation where Carolina and Dean are standing in a room. Next figures will follow with some examples with scaling from different base points A, B, C, D .

 

fig2.

 

fig 2. shows a scaling 3 that has been operated with basepoint A. One can already see that Carolina and Dean have changed position.

 

fig.3

 

fig 3. Scaling 3 has been done with center point B. Carolina and Dean are at another position. However the scale factor is the same as in fig.2

 

fig 4.

 

fig 4. Scaling 3 has been done for Carolina from her center C, and for Dean from his center D.

The result, with multiple base points, is a scramble. In fact these were 2 scalings represented in a single picture. However the scale factor is the same with fig.2 & 3.

 

In other words, if you make the attempt to make a scaling with base point from each point of this image, you must make an infinite number of scalings, and the result will be a mess. It will not be a scaling of the original picture, it will ressemble fig 4 in much worse.

 

That is one aspect of scaling.

 

* I have reversed intentionaly the sequence of orders. In Autocad the sequence is 1.3.2.

Edited May 15, 2014 by michel123456

[Strange]

Note that you can define scaling in different ways. For example, Adobe Illustrator has a both a Transform and a Transform Each command; these have different effects when applied to multiple (grouped) objects.

 

Given the wider context of the question, you can scale the relationship between the objects while treating the objects themselves as "atomic"; i.e. unaffected by the scaling operation. If you apply a scale factor in this way you will find that the rate at which the separation (or gap) between objects changes is proportional to how far apart they are. Without the objects themselves changing size. We observe something similar in the universe.

[michel123456]

Note that you can define scaling in different ways. For example, Adobe Illustrator has a both a Transform and a Transform Each command; these have different effects when applied to multiple (grouped) objects.

 

Given the wider context of the question, you can scale the relationship between the objects while treating the objects themselves as "atomic"; i.e. unaffected by the scaling operation. If you apply a scale factor in this way you will find that the rate at which the separation (or gap) between objects changes is proportional to how far apart they are. Without the objects themselves changing size. We observe something similar in the universe.

That is correct.

It is the second aspect os scaling:

_The base point does not change position.

_A point 1 metre away from the base point will be repositioned 3 metres away (in my example)==>the gap=2m

_A point 2 metres away will end 6 metres away==>gap=4m

_A point 3 metres will go 9 metres away==>gap=6m

_A point 4 metres will go 12 metres away ==>gap=8m

And so on.

 

 

Now, if scaling is happening in time t=1sec

you have a situation where

1. the base point has not moved (velocity=0)

2. some point has moved at radial velocity 2m/s

3. some other point has moved at v=4m/s

4. some other point has moved at v=6m/s

5. some other point has moved at v=8m/s

 

That looks pretty much like acceleration.

[swansont]

That looks pretty much like acceleration.

The difficulty lies in making the model reflect all of our observations, not just one subsection of them.

[michel123456]

The difficulty lies in making the model reflect all of our observations, not just one subsection of them.

The thread is about scaling, not about the model of the universe.

 

Anyway.

To me, it means that when scaling at a standard rate is applied to a macroscopical object, this object is submitted to acceleration.

It happens when using a pantograph.

 

For those who don't know or want to remind how work a pantograph , here is a small 5' video I found.

 

I hope it is clear that when you draw at scale, the overall time is t for making the drawing but the 2 paths are different.

It means if the original path is made at constant speed then the reproduced path (the pencil) is accelerated (or decelerated).

Edited May 18, 2014 by michel123456

[Enthalpy]

A vector can represent a distance or a position, then versus a reference. Usually we don't distinguish these vectors, but here we should.

 

If you scale a size, you don't need any reference nor scaling center. But if you scale a position, you need the position reference, or for the CAD, the scaling center.

 

This difference exists in maths.

http://en.wikipedia.org/wiki/Affine_space