coordtransform | 坐标转换工具，提供WGS84，GCJ02，百度坐标系的相互转换。 | Map library

First, I have to admit I agree with generic_opto_guy:

The approach with the loop looks good, so we would need to check the math. On thing I noticed: if (oldRow > 0 && oldCol > 0 && oldRow <= oldHeight && oldCol <= oldWidth) implies you start indexing with 1. I belife that opencv starts indexing with 0.

For all that, I couldn't resist to answer. (May be, it's just an image phase of mine.)

Instead of fiddling with sin() and cos(), I would recommend to use matrix transformation. At the first glance, this might appear over-engineered but later you will recognize that it bears much more flexibility. With a transformation matrix, you can express a lot of transformations (translation, rotation, scaling, shearing, projection) as well as combining multiple transformations into one matrix.

(A teaser for what is possible: SO: How to paint / deform a QImage in 2D?)

In an image, the pixels may be addressed by 2d coordinates. Hence a 2×2 matrix comes into mind but a 2×2 matrix cannot express translations. For this, homogeneous coordinates has been introduced – a math trick to handle positions and directions in the same space by extending the dimension by one.

To make it short, a 2d position (x, y) has the homogeneous coordinates (x, y, 1).

A position transformed with a transformation matrix:

v´ = M · v.

This may or may not change the value of third component. To convert the homogeneous coordinate to 2D position again, x and y has to be divided by 3^rd component.