algorithm - Finding a stable placement of an irregular (non-convex) shape -


Looking at an image of a 2-dimensional irregular (non-convex) shape, how do I calculate all these methods Can it be stable on a flat surface? For example, if the size is a perfect square rectangular, then there will definitely be 4 ways in which it is static. On the other hand, there is no fixed orientation in each division or every point is a constant orientation.

EDIT: This is a nice little game (be careful, addictive game) which seems close to what I want. Notice that you cut a piece of wood, it falls on the ground and happens in a steady way.

Edit: In the end, calculate the approach I have taken, the center of mass and calculate the convex hull (using OpenCVY), and then loop through the upper pair. If the scale of the center falls on the top of the line made of the upper part of 2, then it is considered stable, and no, no. First of all, its mass (CM) is a stable position in which the Chief Minister will send you higher

If the hull is a polygon, then a steady state In which the shape is resting on one side of the sides, and the chief minister is not directly on the side (directly on the middle point of the side, just above it If the hull is the cue (if the shape decreases, the hull is touching), they should be given special treatment. If the shape becomes stable after sitting on the curved edges, then the CM straight curve Is above the lowest point, and at that point the radius of the curve is higher than the height, for example:

  1. A rectangle, the hull is only rectangular, and the chief is in the center. Is stable.
  2. a rectangle with sides is hollow, but the corners are still intact. The hull is still basically rectangular, and the chief is to be used to close it. All the four sides of the hull are still stable (i.e., I resize the shape on any two corners).
  3. A cycle is in the center center, the hull circle is no stable condition, since the radius of the curve is always the height of the chief Are equal. Give it a little touch, and this will be the roll.
  4. An oval center is in the center, the hull is the size. Now there are two stable positions
  5. A semicolon CM is somewhere on the axis of the symmetry, the hull shape is two fixed position
  6. A narrow semicircular crescent hull is a semicircle, the chief is out of shape (but inside the hull). Two fixed position

(The oval position marked with X is unstable, because curvature is less than the distance from the mass of the center.)


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