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Difference between revisions of "SCI/FreeSCI/Pathfinding/Implementation"
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to a point that is in the barred area of a polygon, because that would make that point unreachable. First we strengthen Assumption 2 as follows: | to a point that is in the barred area of a polygon, because that would make that point unreachable. First we strengthen Assumption 2 as follows: | ||
;Assumption 3 : Let <i>P</i> be the polygon set. For all points <i>p ∈ ℚ<sup>2</sup></i> that lie on an edge of one of the polygons in <i>P</i>, there is at least one point <i>p′ ∈ ℤ<sup>2</sup></i> at distance <i>< √2</i> from <i>p</i> that is not strictly contained in the barred area of any polygon in <i>P</i>. | ;<span id="anchor_name">Assumption 3</span> : Let <i>P</i> be the polygon set. For all points <i>p ∈ ℚ<sup>2</sup></i> that lie on an edge of one of the polygons in <i>P</i>, there is at least one point <i>p′ ∈ ℤ<sup>2</sup></i> at distance <i>< √2</i> from <i>p</i> that is not strictly contained in the barred area of any polygon in <i>P</i>. | ||
This means that besides intersecting polygons, we also exclude polygons that are very close together. It would be very hard to manoeuvre Ego between two | This means that besides intersecting polygons, we also exclude polygons that are very close together. It would be very hard to manoeuvre Ego between two | ||
such polygons with the directional keys on the keyboard. We therefore believe that the input polygon set will not contain polygons that are very close together. | such polygons with the directional keys on the keyboard. We therefore believe that the input polygon set will not contain polygons that are very close together. | ||