Build a website with a moving graphic

This will be a table hire company website. I need the functionality built for this phase of the website. So basically a front page with some navigation to future pages. Graphics & logos I will incorporate in phase 2. The main item this website should have is an app that generates different shapes, based on 2 initial shapes. I have a 'Rectangle' and a 6th of a donut. see images. I want the website user to be able to move these two shapes about in plan view. The app should know which two edges connect. The shapes can be used to create different shaped tables. Once you look at the attached images you'll get the idea. What I need from you: The website with the foundation setup for future pages. One page which launches the Table making app. The app to have intelligence so it knows when the two selected shapes touch. The two shapes should then snap into the correct position adjacent to one another.' The user can then add another shape to the existing shapes on the planner' The app should know when the shape is closed. The user has to create a complete loop. Once the complete loop is created the app will list how many of the two different shapes where used. With the provision to pass this info back to me. (This will evolve) So put simply I need the app to allow the end user create any shape possible using the 2 shapes provided in the images. But the shape needs to be a closed loop by the end of their planning. This needs to work Ipads, pc's, tablets & smart phones.