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III Penalties for Ranged Units on the Attacking Side During a Siege
Continued
The 50% damage penalty for ranged units attacking enemy units behind a fortress wall is removed if:
1) The attacking hero possesses the Golden Bow artifact;
2) The attacking hero has the Archery secondary skill;
3) The attacked enemy unit is not behind a fortress wall, i.e., it is on the fortress wall line or to the left of it;
4) The attacking unit on the attacking side is located within the castle grounds, i.e., on the fortress wall line or to the right of it;
5) The line of attack of the ranged unit is not blocked by any section of the fortress wall.
What is the line of attack, and what does it mean for it not to be blocked by any section of the fortress wall?
First, let's introduce a rectangular coordinate system, with the x-axis running from left to right and the y-axis running from top to bottom, as shown in Screenshot #1. The grid nodes will correspond to the hexes of the siege arena. In Screenshot #1, the nodes are marked with red squares.
Let's call the line of attack the segment connecting the nodes where the ranged unit and its target are located.
Note: In reality, the line of attack is not a segment, but a set of points lying on it, with a step of 0.1 along the larger dimension, but this fact does not play a significant role.
Let's call the neighborhood of a section with coordinates (X, Y) the set of points (Xi, Yi) for which the following two conditions are met:
1) [Xi] = X;
2) [Yi] = Y.
This set is a unit square (a flat figure) with two missing sides (in Screenshot #1, the green squares without the east and south sides).
Therefore, if the line of attack and the neighborhood of a section intersect (i.e., they have at least one point in common), then we will say that the section blocks the line of attack.
In Screenshot #1, the western and northern boundaries of the neighborhoods of the sections are marked in green if the section is a wall, and in blue if the section is a tower. The orange color indicates the boundaries of the neighborhood of the gate (drawbridge). Note that the neighborhood of the far right (bottom) wall consists of only one northern boundary (it is degenerate). The neighborhood of this section extends beyond the siege arena.
Thus, if you have read all this nonsense carefully :), the phrase "the line of attack of the ranged unit is not blocked by any section of the fortress wall" should now be clear to you.
Examples in Screenshot #1:
1) The ranged unit (1, 0) shoots without penalty at the unit (11, 2) only if the second section – the ranged tower – is destroyed (one hit is enough);
2) The ranged unit (1, 4) shoots without penalty at the unit (11, 0) only if the first section – the wall – is destroyed;
3) The ranged unit (1, 6) shoots without penalty at the unit (11, 4) only if the gate is destroyed or open;
4) The ranged unit (2, 2) shoots without penalty at the unit (10, 8) only if the seventh section – the wall – and the eighth section – the ranged tower – are destroyed;
5+) The ranged unit (2, 1) shoots without penalty at the unit (10, 5) even with intact walls!
Note that the line of attack of the ranged unit in this case does not intersect any neighborhood of the fortress wall sections, i.e., even in solid walls, there are gaps :) See also Screenshot #2.
Notes:
1) The fourth and sixth sections – the towers – cannot be destroyed;
2) If the ranged unit attacks multiple targets at once (liches), the penalty for each target is calculated separately.
I will provide the analytical conditions for the absence of a penalty later.
To be continued...
Continued
The 50% damage penalty for ranged units attacking enemy units behind a fortress wall is removed if:
1) The attacking hero possesses the Golden Bow artifact;
2) The attacking hero has the Archery secondary skill;
3) The attacked enemy unit is not behind a fortress wall, i.e., it is on the fortress wall line or to the left of it;
4) The attacking unit on the attacking side is located within the castle grounds, i.e., on the fortress wall line or to the right of it;
5) The line of attack of the ranged unit is not blocked by any section of the fortress wall.
What is the line of attack, and what does it mean for it not to be blocked by any section of the fortress wall?
First, let's introduce a rectangular coordinate system, with the x-axis running from left to right and the y-axis running from top to bottom, as shown in Screenshot #1. The grid nodes will correspond to the hexes of the siege arena. In Screenshot #1, the nodes are marked with red squares.
Let's call the line of attack the segment connecting the nodes where the ranged unit and its target are located.
Note: In reality, the line of attack is not a segment, but a set of points lying on it, with a step of 0.1 along the larger dimension, but this fact does not play a significant role.
Let's call the neighborhood of a section with coordinates (X, Y) the set of points (Xi, Yi) for which the following two conditions are met:
1) [Xi] = X;
2) [Yi] = Y.
This set is a unit square (a flat figure) with two missing sides (in Screenshot #1, the green squares without the east and south sides).
Therefore, if the line of attack and the neighborhood of a section intersect (i.e., they have at least one point in common), then we will say that the section blocks the line of attack.
In Screenshot #1, the western and northern boundaries of the neighborhoods of the sections are marked in green if the section is a wall, and in blue if the section is a tower. The orange color indicates the boundaries of the neighborhood of the gate (drawbridge). Note that the neighborhood of the far right (bottom) wall consists of only one northern boundary (it is degenerate). The neighborhood of this section extends beyond the siege arena.
Thus, if you have read all this nonsense carefully :), the phrase "the line of attack of the ranged unit is not blocked by any section of the fortress wall" should now be clear to you.
Examples in Screenshot #1:
1) The ranged unit (1, 0) shoots without penalty at the unit (11, 2) only if the second section – the ranged tower – is destroyed (one hit is enough);
2) The ranged unit (1, 4) shoots without penalty at the unit (11, 0) only if the first section – the wall – is destroyed;
3) The ranged unit (1, 6) shoots without penalty at the unit (11, 4) only if the gate is destroyed or open;
4) The ranged unit (2, 2) shoots without penalty at the unit (10, 8) only if the seventh section – the wall – and the eighth section – the ranged tower – are destroyed;
5+) The ranged unit (2, 1) shoots without penalty at the unit (10, 5) even with intact walls!
Note that the line of attack of the ranged unit in this case does not intersect any neighborhood of the fortress wall sections, i.e., even in solid walls, there are gaps :) See also Screenshot #2.
Notes:
1) The fourth and sixth sections – the towers – cannot be destroyed;
2) If the ranged unit attacks multiple targets at once (liches), the penalty for each target is calculated separately.
I will provide the analytical conditions for the absence of a penalty later.
To be continued...
