Shared Angle Solver

Shared Angle Solver

The two places an angle is solved

Builder:  ZeroDistanceYds(R)  →  SolveAngle(R, 0) → zero_angle
Inverse:  range R             →  SolveAngle(R, 0) → θ* → adjustment = θ* − zero_angle

Both are the same mathematical problem: find θ with

f(θ) = y(R; θ) − optic − impact = 0

(source/solve_angle.hpp, source/lob_builder.cpp, source/lob_solve.cpp). Historically a ballistics library might have two implementations — one for zero and one for inverse — and they can diverge subtly in tolerance, bounds, jump handling, or iteration cap.

One solver

lob factors the iteration into source/solve_angle.hpp:

• FastInverseAngle(θ, f, R) = atan(tan θ − f/R) — geometric one-step.
• SolveAngle(ctx, R, impact, seed, tol) — fixed-point over FastInverseAngle, tol = 0.01 MOA, ±45°, ≤10 iterations, NaN on unreachable.

Both call sites use it:

• BuildZeroAngle seeds with the vacuum parabola 0.5·g·R/v0² clamped to ±45° (source/lob_builder.cpp).
• LobSolveInverse seeds with FastInverseAngle(zero_angle, forward_residual, R) (source/lob_solve.cpp) and calls the same SolveAngle. The comment // Seed represents mechanical launch angle. SolveAngle adds aerodynamic_jump internally records the subtlety that both paths add jump inside fire_to_target/SolveStep, not outside.

Why sharing matters

• Consistency: the zero that zeros the rifle and the adjustments that assume that zero are computed with identical tolerance, bounds and jump handling — otherwise a rifle zeroed with one solver would be off by the other's bias.
• Maintenance: a fix to bounds or convergence (e.g. the ±45° clamp) applies to both features at once; test/source/solve_angle_test.cpp cross-checks FastInverse vs SolveAngle and BuilderZeroAngleTest cross-checks builder vs SolveAngle.
• Diff size: one guard in the shared function is a smaller, safer diff than a guard in every caller.

Validation of sharing

• SolveAngle round-trips heights −3…+3 in at 300 yd to ±0.1 in (test/source/solve_angle_test.cpp).
• Builder zero matches a direct SolveAngle call to 1e-6 MOA (test/source/solve_angle_test.cpp).
• Iterative inverse vs one-step FastInverse agree within 0.1 MOA even with non-zero aerodynamic_jump (test/source/lob_inverse_test.cpp).