Projectile Lead Intercept Angle Estimate

Solve stable constant-velocity 2D projectile interception within explicit caller horizon, preserving unreachable/time-censored cases as false/−1/empty point; angle zero is sentinel when absent or already coincident. No gravity, acceleration or collision geometry.

Description

Projectile interception solves for a future target position reachable at a constant projectile speed.

Projectile interception solves for a future target position reachable at a constant projectile speed. The earliest admissible root matters.^[1]

Enter two-component relative position/velocity bounded by absolute 1000000, positive speed≤1000000 and nonnegative horizon. Solve the quadratic with a stable root construction and linear/coincident cases; choose the earliest finite nonnegative root within horizon. Return time, angle and intercept point, or false with time−1, angle 0 and empty point.

When to use Projectile Lead Intercept Angle Estimate

Use Projectile Lead Intercept Angle Estimate when you need to evaluate the supplied records under the calculation and evidence rules below. No gravity, acceleration, obstacle collision or shooter velocity conversion is modeled.

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.

How to use Projectile Lead Intercept Angle Estimate and understand its results

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
Enter relativeTargetPosition, targetVelocity, projectileSpeed, callerMaximumInterceptSeconds using the field table and calculation rules, then run the tool.
Read interceptFound, interceptTimeSeconds, leadAngleDegrees, relativeInterceptCoordinates. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
relativeTargetPosition	Relative target position	list of number	Required
targetVelocity	Target velocity	list of number	Required
projectileSpeed	Projectile speed	number	Required
callerMaximumInterceptSeconds	Caller maximum intercept seconds	number	Required

(v·v−s²)t²+2(p·v)t+p·p=0

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
interceptFound	Intercept found	boolean
interceptTimeSeconds	Intercept time seconds	number
leadAngleDegrees	Lead angle degrees	number
relativeInterceptCoordinates	Relative intercept coordinates	list of number

json

{
  "input": {
    "relativeTargetPosition": [
      100,
      0
    ],
    "targetVelocity": [
      0,
      0
    ],
    "projectileSpeed": 10,
    "callerMaximumInterceptSeconds": 20
  },
  "output": {
    "interceptFound": true,
    "interceptTimeSeconds": 10,
    "leadAngleDegrees": 0,
    "relativeInterceptCoordinates": [
      100,
      0
    ]
  }
}

Limitations and assumptions

No gravity, acceleration, obstacle collision or shooter velocity conversion is modeled.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Numeric lists are limited to 10,000 entries; string lists to 128 strings of at most 128 characters each. The rules above may impose smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Enemy FOV Cone Detection Angle Check: A planar field of view combines angular and range gates with caller line-of-sight evidence. A coincident target has zero angular offset. For a complementary task, use Boss Leash Range Reset Distance Check: A boss leash compares current distance with a caller boundary. Whether equality resets is an explicit policy.

References

Projectile Lead Intercept Angle Estimate — tool.io

Similar or alternative tools

Enemy FOV Cone Detection Angle Check
A planar field of view combines angular and range gates with caller line-of-sight evidence. A coincident target has zero angular offset.
Boss Leash Range Reset Distance Check
A boss leash compares current distance with a caller boundary. Whether equality resets is an explicit policy.