When units move in a straight line on the tactical map, the line on which they move is defined as a series of one-square steps. If a unit is moving more columns than rows, then the number of steps is the number of columns it moves. For example, if a unit is moving from 3-1 to 7-3, then it is moving 4 columns and 2 rows, hence its move requires four steps. If it is moving more rows than columns, then the number of steps is the number of rows. For example, if a unit is moving from 11-4 to 8-13, then it is moving 3 columns and 9 rows, so the move requires nine steps.
If the unit is moving more columns than rows, then at each step
it must move one column and less than one row. Let C be the number
of columns it moves and R be the number of rows it moves (with C
bigger than R); then the fraction of a row it must move is R/C.
Example: If the unit is moving from 3-1 to 7-3, which is 4 columns
and 2 rows, then in each step it must move 1 column and 0.5 (2/4)
rows. Its path will then be: 3-1, 4-1.5, 5-2, 6-2.5, 7-3. If the
unit is moving more row than columns, then each step must be 1 row
and C/R columns. Example: if the unit is moving from 11-4 to 8-13,
then each step is 1 row and 0.33 (3/9) columns. The path will be
11-4, 10.67-5, 10.33-6, 10-7, 9.67-8, 9.33-9, 9-10, 8.67-11,
8.33-12, 8-13.
To determine if a path is blocked by terrain, round each row or
column to the nearest integer (round 0.5 down; thus, round 2.5 to
2). In the first example above, the rounded path would be 3-1,
4-1, 5-2, 6-2, 7-3. In the second example, the rounded path would
be 11-4, 11-5, 10-6, 10-7, 10-8, 9-9, 9-10, 9-11, 8-12, 8-13. A
unit's move is blocked by terrain if:
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Whether a path is blocked by an enemy unit depends on whether the move is due N,S,E, or W, due NW, SW, SE, or NE, or some other direction.
Case 1: A move due N, S, E, or W. In this the case the move is entirely in one row or one column, for example, a move from 1-3 to 5-3 is due east along the path 1-3, 2-3, 3-3, 4-3, 5-3. This move is blocked by an enemy or neutral unit if any square of the path contains an enemy or neutral unit. Otherwise it is not blocked.
Case 2: A move due NW, SW, SE, or NE. In this case the move is on a 45-degree diagonal, and the steps are 1 row and 1 column each. Example; A move from 1-6 to 5-2 is due northeast along the path 1-6, 2-5, 3-4, 4-3, 5-2. In this case the path is blocked if any square in the path or adjacent to it contains an enemy or neutral unit. This is because the path from (say) 3-4 to 4-3 passes diagonally between 3-3 and 4-4. An enemy unit in either of those two squares can block the movement. An enemy unit at 4-5 (which touches 3-4 only diagonally) cannot block the movement.
Case 3: Any other move. In this case the move will necessarily
contain fractions in some steps along the path. Example; a unit
moving from 1-2 to 6-5, which goes 5 steps east and 3 steps south,
makes 0.6 steps south for each step east. Therefore it passes
through 2-2.6, 3-3.2, 4-3.8, 5,4.4, and 6-5. In this case, an
enemy or neutral unit blocks the path if it is in a square on the
path, rounding fractions in either direction. A unit in 3-3 can
block the path because 3-3.2 rounds down to 3-3. A unit in 3-4 can
also block the path because 3-3.2 rounds up to 3-4. If a step in
the path involves an even integer (for example, a move from 8-2 to
12-4 passes through 10-3 exactly) can be blocked only in that
square, since no rounding takes place.
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Movement from 1-1 to 5-1: Path is 2-1, 3-1, 4-1, 5-1
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Movement from 1-6 to 5-2: Path is 2-5, 3-4, 4-3, 5-2
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Movement from 1-2 to 6-5: Path is 2-2.6, 3-3.2, 4-3.8, 5-4.4, 6-5
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