Drag+Drop with physical behaviour

Question

I'd like to implement a dragging feature where users can drag objects around the workspace. That of course is the easy bit. The hard bit is to try and make it a physically correct drag which incorporates rotation due to torque moments (imagine dragging a book around on a table using only one finger, how does it rotate as you drag?).

Does anyone know where I can find explanations on how to code this (2D only, rectangles only, no friction required)?

Much obliged, David

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EDIT:

I wrote a small app (with clearly erroneous behaviour) that I hope will convey what I'm looking for much better than words could. C# (VS 2008) source and compiled exe here

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EDIT 2:

Adjusted the example project to give acceptable behaviour. New source (and compiled exe) is available here. Written in C# 2008. I provide this code free of any copyright, feel free to use/modify/whatever. No need to inform me or mention me.

Answer 1

This would seem to be a basic physics problem.

You would need to know where the click, and that will tell you if they are pushing or pulling, so, though you are doing this in 2D, your calculations will need to be in 3D, and your awareness of where they clicked will be in 3D.

Each item will have properties, such as mass, and perhaps information for air resistance, since the air will help to provide the motion.

You will also need to react differently based on how fast the user is moving the mouse.

So, they may be able to move the 2 ton weight faster than is possible, and you will just need to adapt to that, as the user will not be happy if the object being dragged is slower than the mouse pointer.

Answer 2

Which language?

Here's a bunch of 2d transforms in C

Answer 3

Torque is just the applied force projected perpendicular to a vector between the point where the force is applied and the centroid of the object. So, if you pull perpendicular to the diameter, the torque is equal to the applied force. If you pull directly away from the centroid, the torque is zero.

You'd typically want to do this by modeling a spring connecting the original mouse-down point to the current position of the mouse (in object-local coordinates). Using a spring and some friction smooths out the motions of the mouse a bit.

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I've heard good things about Chipmunk as a 2D physics package:

http://code.google.com/p/chipmunk-physics/

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Okay, It's getting late, and I need to sleep. But here are some starting points. You can either do all the calculations in one coordinate space, or you can define a coordinate space per object. In most animation systems, people use coordinate spaces per object, and use transformation matrices to convert, because it makes the math easier.

The basic sequence of calculations is:

1. On mouse-down, you do your hit-test, and store the coordinates of the event (in the object coordinate space).

2. When the mouse moves, you create a vector representing the distance moved.

3. The force exterted by the spring is k * M, where M is the amount of distance between that initial mouse-down point from step 1, and the current mouse position. k is the spring constant of the spring.

4. Project that vector onto two direction vectors, starting from the initial mouse-down point. One direction is towards the center of the object, the other is 90 degrees from that.

5. The force projected towards the center of the object will move it towards the mouse cursor, and the other force is the torque around the axis. How much the object accelerates is dependent on its mass, and the rotational acceleration is dependent on angular momentum.

6. The friction and viscosity of the medium the object is moving in causes drag, which simply reduces the motion of the object over time.

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Or, maybe you just want to fake it. In that case, just store the (x,y) location of the rectangle, and its current rotation, phi. Then, do this:

1. Capture the mouse-down location in world coordinates
2. When the mouse moves, move the box according to the change in mouse position
3. Calculate the angle between the mouse and the center of the object (atan2 is useful here), and between the center of the object and the initial mouse-down point. Add the difference between the two angles to the rotation of the rectangle.