I have a point on a 2D coordinate plane. There is an imaginary circle around some other origin point, and I need two expressions (one for each axis) to find the nearest point from my first coordinates that is on that circle's perimeter. Like this:

when green flag clicked
set [radius v] to (100)
set [origin x v] to [0]
set [origin y v] to [0]
set [x v] to [100]
set [y v] to [100]
go to x: [expression 1] y: [expression 2]
set [x v] to (x position)
set [y v] to (x position)

The nearest point will always be on a line from the current position to the centre of the circle which is presumably known. (Extend the line if within the circle.)

You can just point towards the centre, go to that point, turn 180 degrees and move R steps where R is the radius. You may want to save the direction the sprite was pointing before doing all this so you can then point it in that direction again.

deck26 wrote:

The nearest point will always be on a line from the current position to the centre of the circle which is presumably known. (Extend the line if within the circle.)

You can just point towards the centre, go to that point, turn 180 degrees and move R steps where R is the radius. You may want to save the direction the sprite was pointing before doing all this so you can then point it in that direction again.

It's a good idea, but I would have to make a point towards 0, 0 expression and use multiple blocks, and I'm trying to make everything fit in one expression.

Place a hidden sprite at the centre of the circle and you can easily just point to that/

This should work for you.

So, you're just wanting to find a third point (?).

Sorry for changing the variable names but this should do it:

when @greenFlag clicked
set [R v] to [100]
set [Cx v] to [20]
set [Cy v] to [-20]
set [Px v] to [200]
set [Py v] to [-150]
set [m v] to ([sqrt v] of ((((Px) - (Cx)) * ((Px) - (Cx))) + (((Py) - (Cy)) * ((Py) - (Cy))))::operators)
set [Ix v] to ((Cx) + ((R) * (((Px) - (Cx)) / (m))))
set [Iy v] to ((Cy) + ((R) * (((Py) - (Cy)) / (m))))
go to x\: (Ix) y\: (Iy)

as a single expression

go to x\: ((Cx) + ((R) * (((Px) - (Cx)) / ([sqrt v] of ((((Px) - (Cx)) * ((Px) - (Cx))) + (((Py) - (Cy)) * ((Py) - (Cy))))::operators)))) y\: ((Cy) + ((R) * (((Py) - (Cy)) / ([sqrt v] of ((((Px) - (Cx)) * ((Px) - (Cx))) + (((Py) - (Cy)) * ((Py) - (Cy))))::operators))))

I don't know if any of these already work for you, but if not, here's how I would do it: (assuming my mental algebra is up to code)
Assuming that

(r)

is your circle's radius,

(cX)

(cY)

are its center coordinates,

(pX)

(pY)

are your other point's coordinates, then

set [closestPointX v] to ((cX) + ((r) * ([cos v] of ([atan v] of ([abs v] of (((pX) - (cX)) / ((pY) - (cY)))::operators)::operators)::operators)))
set [closestPointY v] to ((cY) + ((r) * ([sin v] of ([atan v] of ([abs v] of (((pX) - (cX)) / ((pY) - (cY)))::operators)::operators)::operators)))

should work. (I think) This is the most compact way I could come up with to write it.

This is based on some math I learned while trying to make a soft-body physics engine, and some notes from my college algebra class.