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THE FEUTEX TOOLKIT

Affine Point Transformation

Apply a two-dimensional affine map and inspect its area scale and orientation.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaX = a*x+b*y+tx; Y = c*x+d*y+ty; Area Scale = abs(a*d-b*c); Orientation = sign(a*d-b*c)
Sources and model references

Worked example

Inputs

A
2 number
B
0 number
C
0 number
D
3 number
TX
1 number
TY
-1 number
X
2 number
Y
2 number

Expected results

X
5 number
Y
5 number
Area Scale
6 number
Orientation
1 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "a": 2,
  "b": 0,
  "c": 0,
  "d": 3,
  "tx": 1,
  "ty": -1,
  "x": 2,
  "y": 2
}

Accuracy and scope

Orientation output is +1 preserving, −1 reversing, or 0 collapsed. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.