Edited by Jacob T. Schwartz, Micha Sharir, John Hopcroft

TJ211.4, P57, 1987

- Jacob T. Schwartz and Micha Sharir, On the Piano Movers' Problem I. The Case of a Two-Dimensional Rigid Polygonal Body Moving Amidst Polygonal Barriers
- In moving a body which is a line segment or "ladder" among obstacles consisting of polyhedral walls from a starting position to a goal position, either find a continuous motion connecting the two positions or show that no such motion exists.
- Jacob T. Schwartz and Micha Sharir, On the Piano Movers' Problem II. General Techniques for Computing Topological Properties of Real Algebraic Manifolds
- Extends the discussion of part I to include bodies which may be hinged (that is, they may allow motion around various joints).
- Jacob T. Schwartz and Micha Sharir, On the Piano Movers' Problem III. Coordinating the Motion of Several Independent Bodies: The Special Case of Circular Bodies Moving Amidst Polygonal Barriers
- Extends the discussion of part I to 2-dimensional circular bodies which avoid collision with the walls and with each other.
- Micha Sharir and Elka Ariel-Sheffi, On the Piano Movers' Problem IV. Various Decomposable Two-Dimensional Motion Planning Problems
- Addresses various special problems involving arbitrarily many degrees of freedom which have relatively simple solutions by the techniques of determing the non-critical regions and using a connectivity graph.
- Jacob T. Schwartz and Micha Sharir, On the Piano Movers' Problem V. The Case of a Rod Moving in Three-Dimensional Space Amidst Polyhedral Obstacles
- Addresses some 3-dimensional special cases, principally the motion of a rod moving among polyhedral obstacles.

- Learn about Micha Sharir
- Learn about Jacob T Schwartz
*Report by Eric Johnson, CPSC 643, Fall 1996* - Eric's Home Page