Fix for Java's Robot.mouseMove when accounting for High DPI Screens + Mathematical error analysis for modeling how the original mouseMove function is affected.

robot-mousemove-fix.kt

/* Robot.betterMouseMove is a function that's meant to fix Robot.mouseMove when dealing with Windows's
display scaling in order to make text easier to see. The 'scaleFactor' is the actual scaling factor
as a float > 1.0f.

This is the error vector field that represents the error caused by Robot.mouseMove in which to move
in the x and y direction towards its destination. It's not that useful in hindsight, but kind of cool
that one can model the error as a mathematical function.

"Error" Vector Field: F(x, y) = f(x, y) * i + g(x, y) * j
    f(x, y) = (-x + t_x) / (width - t_x)
    g(x, y) = (-y + t_y) / (height - t_y)
    x = x coordinate of origin point
    y = y coordinate of origin point
    width = width of screen
    height = height of screen
    t_x = x coordinate of target point
    t_y = x coordinate of target point

    - Note: f(x, y) and g(x, y) will return the negative error result, which represents the
        "restoring" error quantity required to reach the target.

    -f(x, y) = actual error amount for x direction
    -g(x, y) = actual error amount for y direction

    s = scaling factor of screen (i.e. 125% => s = 1.25)
    G(x, y) = predicted output coords (as a vector)
    G(x, y) = ((-x + t_x) * s) * i + (2 * t_y) * ((-y + t_y) * s) * j
        Note: (2 * t_y) is needed to translate from cartesian coords to screen coords
*/

val Robot.defaultScaleFactor: Float
    get() = 1.0f

fun Robot.betterMouseMove(x: Int, y: Int, scaleFactor: Float = this.defaultScaleFactor) {
    val modFactor = 1 - (1 / scaleFactor)
    val origin = MouseInfo.getPointerInfo().location

    val deltaX = x - origin.x
    val deltaY = y - origin.y

    val finalX = (x - deltaX * modFactor).toInt()
    val finalY = (y - deltaY * modFactor).toInt()

    this.mouseMove(finalX, finalY)
}