Attempting to spin and elongate/shorten a rectangle with transformation matrices

[AndrewBot88]

Me again! I've got a slightly more complex problem this time. I'm trying to have a rectangle spin around its bottom point and change size as it does so such that its length is always equal to L + L*cos(θ) (where L is the original length). The rotation is simple enough and I've got that working; the scale is a bit more complicated and I'm not entirely sure if it's working (I can't really test it without having both work together). To figure out the X and Y scaling I created this triangle:



I used the values for the legs as the X and Y scale values in my matrix. If you see an error here just let me know and go ahead and ignore the rest of this post.

Otherwise, that gives me this matrix (A) for the rotation:

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cos(θ)  -sin(θ)  Rtx
sin(θ)   cos(θ)  Rty
0        0       1

Where Rtx and Rty are the X and Y translation for the rotation. As mentioned before, this works fine. The scaling matrix (B) is:

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Sx  0  Stx
0   Sy Sty
0   0   1

(I think you can figure out what the variables stand for)

As best I can tell this works; using it without the rotation matrix makes the rectangle stay in place and change its dimensions in a way that seems plausible. Getting the product of A*B gives us:

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Sx*cos(θ)  -Sy*sin(θ)  Stx*cos(θ)-Sty*sin(θ)+Rtx
Sx*sin(θ)   Sy*cos(θ)  Stx*cos(θ)+Sty*cos(θ)+Rty
0           0          1

But using this matrix causes the rectangle to fly all over the place and just generally not do what I would like it to. Can anybody help?

In case it helps, here is the complete code for the skin:

[Rainmeter]
Update=50

[MeasureAngle]
Measure=Calc
Formula=(MeasureAngle % (2*Pi)) + 0.2

[MeasureRotateTX]
Measure=Calc
Formula=150-Cos(MeasureAngle)*150-Sin(MeasureAngle)*150
[MeasureRotateTY]
Measure=Calc
Formula=150+Sin(MeasureAngle)*150-Cos(MeasureAngle)*150

[MeasureScaleX]
Measure=Calc
Formula=Clamp(Cos(MeasureAngle)+Cos(MeasureAngle)**2, 1, 2)
[MeasureScaleY]
Measure=Calc
Formula=Clamp(Sin(MeasureAngle)+Sin(MeasureAngle)*Cos(MeasureAngle), 1, 2)
[MeasureScaleTX]
Measure=Calc
Formula=150-150*MeasureScaleX
[MeasureScaleTY]
Measure=Calc
Formula=150-150*MeasureScaleY

[MeasureFinalTX]
Measure=Calc
Formula=MeasureScaleTX*Cos(MeasureAngle)-MeasureScaleTY*Sin(MeasureAngle)+MeasureRotateTX
[MeasureFinalTY]
Measure=Calc
Formula=MeasureScaleTX*Sin(MeasureAngle)+MeasureScaleTY*Cos(MeasureAngle)+MeasureRotateTY

[MeterBG]
Meter=IMAGE
w=300
h=300
SolidColor=200,200,255,255
[MeterRectangle]
Meter=IMAGE
w=50
h=10
x=150
y=145
SolidColor=0,0,0
;TransformationMatrix=(Cos([MeasureAngle]));(-1*Sin([MeasureAngle]));(Sin([MeasureAngle]));(Cos([MeasureAngle]));[MeasureRotateTX];[MeasureRotateTY]
;TransformationMatrix=[MeasureScaleX];0;0;1;[MeasureScaleTX];0
;TransformationMatrix=([MeasureScaleX]*Cos([MeasureAngle]));(-1*[MeasureScaleY]*Sin([MeasureAngle]));([MeasureScaleX]*Sin([MeasureAngle]));([MeasureScaleY]*Cos([MeasureAngle]));[MeasureFinalTX];[MeasureFinalTY]
AntiAlias=1
DynamicVariables=1

[balala]

First of all, again you've messed up the rotation matrix. You have to be careful, because according to the manual (the third frame in the Transformations section):

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TransformationMatrix
This defines a 3x2 matrix which can be used to transform the meter. There must be exactly 6 values separated by ';'-character (e.g. "1;0;0;1;0;0") which define the matrix in order of "m11;m12;m21;m22;m31;m32".

            |m11 m21 m31|
            |m12 m22 m32|

which means that your rotation matrix (the first matrix you've posted) is a bit wrong: the negative term should be the other sinus, from the second row, first column, not from the first row, second column.
According to this, the matrix would be:

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cos(θ)    sin(θ)    Rtx
-sin(θ)   cos(θ)    Rty
0         0         1

This will affect the calculations made to get the final matrix. This matrix would be:

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Sx*cos(θ)    Sx*sin(θ)    Sx*Rtx+Stx
-Sy*sin(θ)   Sy*cos(θ)    Sy*Rty+Sty
0            0            1

According to this result, you have to replace the Formula options of the [MeasureRotateTX], [MeasureRotateTY], [MeasureFinalTX] and [MeasureFinalTY] measures, as it follows (leave untouched the other measures):

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[MeasureRotateTX]
Measure=Calc
Formula=( 150 - ( 150 * Cos ( MeasureAngle )) - ( 150 * Sin ( MeasureAngle )))

[MeasureRotateTY]
Measure=Calc
Formula=( 150 + ( 150 * Sin ( MeasureAngle )) - ( 150 * Cos ( MeasureAngle )))

[MeasureFinalTX]
Measure=Calc
Formula=( MeasureScaleX * MeasureRotateTX + MeasureScaleTX )

[MeasureFinalTY]
Measure=Calc
Formula=( MeasureScaleY * MeasureRotateTY + MeasureScaleTY )

I know that's not yet perfect, but in the followings, I'll try to figure out better formulas.

[AndrewBot88]

According to the documentation and the guide (Transformations section, where it specifies the letters) the syntax of the following matrix:

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a  b  c
d  e  f
0  0  1

should be

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TransformationMatrix=a;b;d;e;c;f

unless I'm horribly misreading something.

[balala]

unless I'm horribly misreading something.

Yeah, I think you're "horribly misreading something"!
I can't find the following form of the matrix in the Transformation Matrix Guide:

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a  b  c
d  e  f
0  0  1

which you've posted.
Everywhere I see the following form:

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a  c  tx
b  d  ty
0  0  1

and the corresponding TransformationMatrix option: TransformationMatrix=a;b;c;d;tx;ty.
Also read the third frame of the Transformations section of the TransformationMatrix Guide (you've also talked about this section), which says:

Code: Select all

TransformationMatrix
This defines a 3x2 matrix which can be used to transform the meter. There must be exactly 6 values separated by ';'-character (e.g. "1;0;0;1;0;0") which define the matrix in order of "m11;m12;m21;m22;m31;m32".

            |m11 m21 m31|
            |m12 m22 m32|

Follow the order of terms in the matrix and in the text. You can see that the order you're using is totally wrong. You've interchanged the place of more terms. If you'll place them properly, I think your problems, at least partially, will be fixed.
In the meantime, I think I fixed the code, here is it:

Code: Select all

[Rainmeter]
Update=50

[MeasureAngle]
Measure=Calc
Formula=(MeasureAngle % (2*Pi)) + 0.2

[MeasureRotateTX]
Measure=Calc
Formula=( 150 - ( 150 * Cos ( MeasureAngle )) - ( 150 * Sin ( MeasureAngle )))

[MeasureRotateTY]
Measure=Calc
Formula=( 150 + ( 150 * Sin ( MeasureAngle )) - ( 150 * Cos ( MeasureAngle )))

[MeasureScaleX]
Measure=Calc
Formula=Clamp(Cos(MeasureAngle)+Cos(MeasureAngle)**2, 1, 2)

[MeasureScaleY]
Measure=Calc
Formula=Clamp(Sin(MeasureAngle)+Sin(MeasureAngle)*Cos(MeasureAngle), 1, 2)

[MeasureScaleTX]
Measure=Calc
Formula=150-150*MeasureScaleX

[MeasureScaleTY]
Measure=Calc
Formula=150-150*MeasureScaleY

[MeasureFinalTX]
Measure=Calc
Formula=( MeasureScaleTX * Cos(MeasureAngle) + MeasureRotateTX )

[MeasureFinalTY]
Measure=Calc
Formula=( MeasureRotateTY - MeasureScaleTX * Sin(MeasureAngle))

[MeterBG]
Meter=IMAGE
w=300
h=300
SolidColor=200,200,255,255
LeftMouseUpAction=[!TogglePauseMeasure "MeasureAngle"]

[MeterRectangle]
Meter=IMAGE
w=50
h=10
x=150
y=145
SolidColor=0,0,0
TransformationMatrix=([MeasureScaleX]*Cos([MeasureAngle]));(-1*[MeasureScaleX]*Sin([MeasureAngle]));(Sin([MeasureAngle]));(Cos([MeasureAngle]));[MeasureFinalTX];[MeasureFinalTY]
AntiAlias=1
DynamicVariables=1

I rewrote more measures, please take a look at the above code and tell me if it is what you need.

[AndrewBot88]

I'm using the documentation because I assume that is the most recently updated. According to it, the syntax is

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TransformationMatrix={scale x};{skew x};{skew y};{scale y};{move x};{move y}

Then I take a look at the guide, which uses this matrix (as mentioned)

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a  c  tx
b  d  ty
0  0  1

and says

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a is used to scale the x value
d is used to scale the y value
c is used to skew the x value
b is used to skew the y value

Matched up to the documentation syntax: a=scale x;c=skew x;b=skew y;d=scale y;tx=move x;ty=move y.

So it would be a;c;b;d;tx;ty not a;b;c;d;tx;ty as you've said.

[eclectic-tech]

The 'layman' term has a typo ... that needs to be corrected ...

It should be

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TransformationMatrix={scale x};{skew y};{skew x};{scale y};{move x};{move y}

I apologize for this because I inadvertently switch the terms when I suggested this ... my bad!

[balala]

Code: Select all

a  c  tx
b  d  ty
0  0  1

With this matrix, the order of the elements should be TransformationMatrix=a;b;c;d;tx;ty. I can assure you this is the correct order.
But finally does my code work?

[AndrewBot88]

The 'layman' term has a typo ... that needs to be corrected ...

It should be

Code: Select all

TransformationMatrix={scale x};{skew y};{skew x};{scale y};{move x};{move y}

I apologize for this because I inadvertently switch the terms when I suggested this ... my bad!

That would explain it!

But finally does my code work?

Yes it does, thank you!

[balala]

You're welcome.