User:Naya ryo/Turret tracking visualization: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 5: / Line 5: @@
 [[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 200mm Autocannon I without any ammo or skill, tracking an orbitting object.]]
-== Title 1 ==
+== Visualization formula derivation ==
-Some very long paragraph for formula explanation and how can we visualize this.
-Some very long paragraph for formula explanation and how can we visualize this.
+It is recommended to read the [[Turret_mechanics#Hit_chance]] section beforehand, as this explanation assumes a basic understanding of turret mechanics.
+<br>
+According to the [[Turret_mechanics#Hit_Math|hit chance formula]], we have:
 :<math> \displaystyle \text{Chance to hit} = 0.5^{\displaystyle \left( \left( \frac{\text{Angular} \times 40,000 \text{ m}}{\text{Tracking} \times \text{Signature}} \right)^2 + \left(\frac{\max(0,\ \text{Distance} - \text{Optimal})}{\text{Falloff}} \right)^2\right)} </math>
+<br>
+To visualize this complex formula intuitively, we apply the following constraints to simplify the setup:
+* The attacker is stationary.
+* The target is either stationary or moving in a perfect circular orbit around the attacker.
+* The scenario takes place on a 2D plane.<references />
+First, consider the distance term.
+:<math>
+\left(\frac{\max(0,\ \text{Distance} - \text{Optimal})}{\text{Falloff}} \right)^2
+</math>
+This term shows that hit chance decreases the further the target is beyond optimal range. This relationship can be visualized along a 1D axis.
+Next, consider the tracking term:
+:<math>
+\left( \frac{\text{Angular} \times 40,000 \text{ m}}{\text{Tracking} \times \text{Signature}} \right)^2
+</math>
+We can visualize the target's orbiting motion as an arc. The length of this arc over one second represents the target’s orbital velocity. For a given orbital velocity, the angular velocity (how quickly the target moves across the turret’s aim) increases as the orbital radius (distance to the attacker) decreases:
+:<math>
+\text{Angular Velocity} = \frac{\text{Orbitting Velocity}}{\text{Orbitting Distance}}
+</math>
+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.
+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.
-Examples for parameters change and practical usage (web, TP, tracking computer etc.)
 Examples for parameters change and practical usage (web, TP, tracking computer etc.)