An affine transform can move, scale or shear coordinates. The mapped position needs the matrix and reference axes beside it.
Retain the mapping direction
An affine coordinate mapping combines a linear transformation with a translation. Its matrix, origin and mapping direction define how an input point becomes an output point. A changed output coordinate is not automatically motion of the physical object; it can follow a changed representation or coordinate reference. Primary reference: OpenCV affine mapping and translation.
For an original worksheet, identify which coordinates are input and which are output. Keep the axes, units and matrix coefficients with the result. Pixel resampling is a separate image operation, so a point mapping alone does not completely define how output intensities will be produced.
Map a fictional point
Use the invented equations x′ = 2x + y + 5 and y′ = y − 3. The point (4,6) maps to (19,3). A neighboring point (5,6) maps to (21,3), so their horizontal separation changes from 1 to 2 under the stated mapping.
The extra five and minus three translate the reference without changing that separation; the linear coefficients control its scaling and shear. These are defined teaching coordinates, not a measured pack displacement or a claimed image-calibration transform. No interpolation result is inferred from these point values.
Review representation changes
Prepare an original table listing each input point, mapped point and matrix revision. If two images use different transformed references, bring corresponding points into an expressly common definition before comparing their numerical locations. Preserve the original observations so the mapping can be reconstructed.
This guide gives no HM alignment accuracy or universal correction matrix. Its reader decision is whether a reported displacement belongs to a stated coordinate transform or an observed scene change. Transformation direction and point identity must survive the comparison before a physical motion claim is made.
Customer Questions
Where does the fictional point (4,6) map?
To (19,3).
Does translation alone change point separation?
No, under the defined affine mapping.
Does the point mapping specify image interpolation?
No. That operation needs its own definition.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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