I have the following set of 2D data points:

```
data1 =
{
{21,557, 801,607}, {5.84689, 800,425}, {50,9284, 770.49},
{46.4516, 750.192}, {32.9808, 671.931}, {48.8067, 673.198},
{3.59394, 671.167}, {18.1513, 671.949}, {64.1628, 670.801},
{13.1805, 652.588}, {55.6619, 651.298}, {26.9262, 650.35},
{41.4876, 650.752}, {5.45129, 635.602}, {20.3858, 633.391},
{64.1931, 632.506}, {33.9168, 631.006}, {58.7559, 613.401},
{36.0045, 612.007}, {23.5348, 608.289}, {54.6781, 598.251},
{26.4914, 548.723}, {65.0549, 531.442}, {82.9996, 514.631},
{74.4132, 479.425}, {58.3295, 458.015}, {27.1816, 413.334}
}
```

I would like to apply `ScalingTransform`

, `Translation Transform`

and `Rotation Transform`

to find the most suitable to transform `data1`

in `data2`

, in which:

```
data2 =
{
{1530.03, 790.2}, {1514.13, 789.}, {1559.17, 758.9}
{1554.5, 738.5}, {1540.5, 660.237}, {1556.15, 661.154},
{1511.34, 659.395}, {1525.63, 660.167}, {1572.13, 658.656},
{1520.66, 640.844}, {1562.55, 639.132}, {1533.79, 638.607}
{1548.37, 638.933}, {1512.62, 623.985}, {1526.88, 621.69},
{1571.44, 620.556}, {1540.44, 618.794}, {1565.69, 601.532},
{1543.06, 600.093}, {1530.22, 596.423}, {1560.9, 586.053},
{1532.93, 536.587}, {1571.9, 519.25}, {1590.15, 501.882}
{1580.39, 467.111}, {1564.73, 445.615}, {1532.8, 400.935}
}
```

The corresponding points of `data1`

that should be converted into `data2`

are already sorted and at the same position of the lists.

I use the following name:

```
s = ScalingTransform[{sx, sy}, {psx, psy}];
t = TranslationTransform[{vecx, vecy}];
r = RotationTransform[theta, {prx, pry}];
```

The combined transformation for each point `{x, y}`

from `data1`

is:

```
combined transformation = s.t.r;
```

and finally:

```
kombinierteTransformation[{x, y}] =
{sx (prx (-Cos[theta]) + prx + pry sin[theta]) + psx (-sx) + psx +
sx x Cos[theta] - sx y Sin[theta] + sx vecx,
sy (- (prx Sin[theta]) + pry (-Cos[theta]) + Prey) + Psy (-sy) + Psy +
sy x sin[theta] + sy y Cos[theta] + sy vecy}
```

The adjustment parameters are: `sx, sy, vecx, vecy, theta`

,

The scale is centered at the point `{psx, psy}`

and the 2d rotation is around the point `{prx, pry}`

,

I would hire `{psx, psy} = {1, 1}`

and `{prx, pry} = {1, 1}`

,

**How can I transform myself? **`data1`

best in `data2`

and how can I determine the appropriate parameters and their errors?