I have seen the use of the > operator for the geometry of the -rescale option for ImageMagick, which basically ensures that the longer axis is scaled down to the desired length. What I am looking for is similar, but for the shorter axis. Also, > apparently prevents any upscaling, which is not what I want.

Let me explain with an example:

• The desired size of an image is given as X, let’s say 512 pixels.
• An image with resolution 1920×1080 would be scaled down to (roughly) 910×512, because y is the shorter axis, therefore it gets rescaled to 512, and x scales down accordingly, preserving aspect ratio
• An image with resolution 1000×3000 would be scaled down to 512×1536, because x is the shorter axis, therefore it gets rescaled to 512, and y scales down accordingly, preserving aspect ratio
• An image with resolution 600×300 would be scaled up to 1024×512, because y is the shorter axis, therefore it gets rescaled to 512, and x scales up accordingly, preserving aspect ratio

Is there an existing command or syntax in ImageMagick that I can use to accomplish this?