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m Update some minor terms and descriptions. |
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To visualize this complex formula intuitively, we apply the following constraints to simplify the setup: | To visualize this complex formula intuitively, we apply the following constraints to simplify the setup: | ||
* The attacker is stationary. | * The attacker is stationary.<ref group=Note>If the attacker is moving, we can treat it as stationary by adding its velocity to the target instead. This doesn't change the relative motion.</ref> | ||
* The target is either stationary or moving in a perfect circular orbit around the attacker. | * The target is either stationary or moving in a perfect circular orbit around the attacker. | ||
* The scenario takes place on a 2D plane.< | * The scenario takes place on a 2D plane.<ref group=Note>This can be easily generalized to 3D.</ref> | ||
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This term shows that hit chance decreases the further the target is beyond optimal range. This relationship can be visualized along a 1D axis. | This term shows that hit chance decreases the further the target is beyond optimal range. This relationship can be visualized along a 1D axis. | ||
[[File:Turret tracking visualization.png|thumb|alt=The heatmap of hit chance, from a stationary 200mm Autocannon I without any ammo or skill, tracking an orbitting object at a distance of 5000 meter and 1380m/s speed, is 60.55%.|The heatmap of hit chance, from a stationary | [[File:Turret tracking visualization.png|thumb|alt=The heatmap of hit chance, from a stationary 200mm Autocannon I without any ammo or skill, tracking an orbitting object at a distance of 5000 meter and 1380m/s speed, is 60.55%.|The heatmap of hit chance, from a stationary attacker, tracking an orbitting object. <br> | ||
Note that the orbitting velocity (orange arrow arc) lies within the yellow area of the heatmap, which represents mediocre hit chance.]] | |||
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\text{Angular Velocity} = \frac{\text{Orbitting Velocity}}{\text{Orbitting Distance}} | \text{Angular Velocity} = \frac{\text{Orbitting Velocity}}{\text{Orbitting Distance}} | ||
</math> | </math> | ||
This means | This means, the closer the target is while orbiting at the same speed, the harder it is for the turret to track. | ||
From this, we can interpret the turret's tracking stat as a kind of '''"maximum allowable angular velocity"''' it can handle. Visually, this forms a 2D cone shape where hit chance remains high within the cone and falls off outside of it. | From this, we can interpret the turret's tracking stat as a kind of '''"maximum allowable angular velocity"''' it can handle. Visually, this forms a 2D cone shape where hit chance remains high within the cone and falls off outside of it. | ||
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By combining the 1D distance-based falloff term with the 2D angular velocity-based tracking cone, we can visualize the hit chance on a 2D plane using a heatmap. | By combining the 1D distance-based falloff term with the 2D angular velocity-based tracking cone, we can visualize the hit chance on a 2D plane using a heatmap. | ||
== Title for some examples ? == | == Title for some examples ? == | ||
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