`omath::unity_engine::PredEngineTrait` — projectile prediction trait

Header: omath/engines/unity_engine/traits/pred_engine_trait.hpp Namespace: omath::unity_engine Purpose: provide Unity Engine-specific projectile and target prediction for ballistic calculations

Summary

PredEngineTrait implements engine-specific helpers for projectile prediction:

predict_projectile_position – computes where a projectile will be after time seconds
predict_target_position – computes where a moving target will be after time seconds
calc_vector_2d_distance – horizontal distance (X/Z plane, ignoring Y)
get_vector_height_coordinate – extracts vertical coordinate (Y in Unity Engine)
calc_viewpoint_from_angles – computes aim point given pitch angle
calc_direct_pitch_angle – pitch angle to look from origin to target
calc_direct_yaw_angle – yaw angle to look from origin to target

These methods satisfy the PredEngineTraitConcept required by generic projectile prediction algorithms.

API

namespace omath::unity_engine {

class PredEngineTrait final {
public:
  // Predict projectile position after `time` seconds
  static constexpr Vector3<float>
  predict_projectile_position(const projectile_prediction::Projectile& projectile,
                             float pitch, float yaw, float time,
                             float gravity) noexcept;

  // Predict target position after `time` seconds
  static constexpr Vector3<float>
  predict_target_position(const projectile_prediction::Target& target,
                         float time, float gravity) noexcept;

  // Compute horizontal (2D) distance
  static float
  calc_vector_2d_distance(const Vector3<float>& delta) noexcept;

  // Get vertical coordinate (Y in Unity Engine)
  static constexpr float
  get_vector_height_coordinate(const Vector3<float>& vec) noexcept;

  // Compute aim point from angles
  static Vector3<float>
  calc_viewpoint_from_angles(const projectile_prediction::Projectile& projectile,
                            Vector3<float> predicted_target_position,
                            std::optional<float> projectile_pitch) noexcept;

  // Compute pitch angle to look at target
  static float
  calc_direct_pitch_angle(const Vector3<float>& origin,
                         const Vector3<float>& view_to) noexcept;

  // Compute yaw angle to look at target
  static float
  calc_direct_yaw_angle(const Vector3<float>& origin,
                       const Vector3<float>& view_to) noexcept;
};

} // namespace omath::unity_engine

Projectile prediction

auto pos = PredEngineTrait::predict_projectile_position(
  projectile,    // initial position, speed, gravity scale
  pitch_deg,     // launch pitch (positive = up)
  yaw_deg,       // launch yaw
  time,          // time in seconds
  gravity        // gravity constant (e.g., 9.81 m/s²)
);

Computes:

Forward vector from pitch/yaw (using forward_vector)
Initial velocity: forward * launch_speed
Position after time: origin + velocity*time - 0.5*gravity*gravityScale*time² (Y component only)

Note: Negative pitch in forward_vector convention → positive pitch looks up.

Target prediction

auto pos = PredEngineTrait::predict_target_position(
  target,   // position, velocity, airborne flag
  time,     // time in seconds
  gravity   // gravity constant
);

Simple linear extrapolation plus gravity if target is airborne:

predicted = origin + velocity * time
if (airborne)
  predicted.y -= 0.5 * gravity * time²

Distance & height helpers

calc_vector_2d_distance(delta) → sqrt(delta.x² + delta.z²) (horizontal distance)
get_vector_height_coordinate(vec) → vec.y (vertical coordinate in Unity Engine)

Used to compute ballistic arc parameters.

Aim angle calculation

calc_direct_pitch_angle(origin, target) → pitch in degrees to look from origin to target
Formula: asin(Δy / distance) converted to degrees (direction normalized first)
Positive = looking up, negative = looking down
calc_direct_yaw_angle(origin, target) → yaw in degrees to look from origin to target
Formula: atan2(Δx, Δz) converted to degrees (direction normalized first)
Horizontal rotation around Y-axis

Viewpoint from angles

auto aim_point = PredEngineTrait::calc_viewpoint_from_angles(
  projectile,
  predicted_target_pos,
  optional_pitch_deg
);

Computes where to aim in 3D space given a desired pitch angle. Uses horizontal distance and tan(pitch) to compute height offset. Result has adjusted Y coordinate.

Conventions

Coordinate system: Y-up (height increases with Y)
Angles: pitch in [-90°, +90°], yaw in [-180°, +180°]
Gravity: applied downward along -Y axis
Pitch convention: +90° = straight up, -90° = straight down

Usage example

using namespace omath::unity_engine;
using namespace omath::projectile_prediction;

Projectile proj{
  .m_origin = {0, 2, 0},
  .m_launch_speed = 50.0f,
  .m_gravity_scale = 1.0f
};

Target tgt{
  .m_origin = {20, 2, 15},
  .m_velocity = {1, 0, 0.5f},
  .m_is_airborne = false
};

float gravity = 9.81f;
float time = 0.5f;

// Predict where target will be
auto target_pos = PredEngineTrait::predict_target_position(tgt, time, gravity);

// Compute aim angles
float pitch = PredEngineTrait::calc_direct_pitch_angle(proj.m_origin, target_pos);
float yaw   = PredEngineTrait::calc_direct_yaw_angle(proj.m_origin, target_pos);

// Predict projectile position with those angles
auto proj_pos = PredEngineTrait::predict_projectile_position(proj, pitch, yaw, time, gravity);

omath::unity_engine::PredEngineTrait — projectile prediction trait