API for server-side 3D rendering [closed]

Question

I'm working on an application that needs to quickly render simple 3D scenes on the server, and then return them as a JPEG via HTTP. Basically, I want to be able to simply include a dynamic 3D scene in an HTML page, by doing something like:

<img src="http://www.myserver.com/renderimage?scene=1&x=123&y=123&z=123">

My question is about what technologies to use to do the rendering. In a desktop application I would quite naturally use DirectX, but I'm afraid it might not be ideal for a server-side application that would be creating images for dozens or even hundreds of users in tandem. Does anyone have any experience with this? Is there a 3D API (preferably freely available) that would be ideal for this application? Is it better to write a software renderer from scratch?

My main concerns about using DirectX or OpenGL, is whether it will function well in a virtualized server environment, and whether it makes sense with typical server hardware (over which I have little control).