Trajectory interpolation and dead reckoning for 2D/3D networked simulations. More...

#include "n_3d.h"

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Data Structures
struct	TRAJECTORY
	structure holding all data for trajectory interpolation / extrapolation More...

struct	TRAJECTORY_POINT
	a single waypoint in a multi-point trajectory path More...

Macros
#define	TRAJECTORY_2D 2
	use 2 components (x,y) for trajectory computation

#define	TRAJECTORY_3D 3
	use 3 components (x,y,z) for trajectory computation

#define	TRAJECTORY_BEFORE 3
	trajectory is extrapolating before the start state using quadratic motion

#define	TRAJECTORY_EXTRAP 2
	trajectory is extrapolating beyond the end state using quadratic motion

#define	TRAJECTORY_INTERP 1
	trajectory is interpolating along the cubic Hermite spline between start and end

Functions
int	trajectory_add_point (TRAJECTORY traj, const PHYSICS state, double time_val)
	add a waypoint to the multi-point path (times must be strictly increasing)

int	trajectory_clear_points (TRAJECTORY *traj)
	clear all waypoints from the multi-point path

int	trajectory_compute (TRAJECTORY *traj, double time_val)
	compute full state (position, speed, acceleration, orientation) at given time

void	trajectory_delete (TRAJECTORY **traj)
	free a trajectory

double	trajectory_distance (TRAJECTORY *traj, double time_a, double time_b, int steps)
	distance along the trajectory between two times

int	trajectory_get_acceleration (TRAJECTORY *traj, double time_val, VECTOR3D out)
	compute only acceleration at given time, stores result in out

int	trajectory_get_orientation (TRAJECTORY *traj, double time_val, VECTOR3D out)
	compute only orientation at given time, stores result in out

int	trajectory_get_position (TRAJECTORY *traj, double time_val, VECTOR3D out)
	compute only position at given time, stores result in out

int	trajectory_get_speed (TRAJECTORY *traj, double time_val, VECTOR3D out)
	compute only speed at given time, stores result in out

TRAJECTORY *	trajectory_new (int nb_components)
	allocate a new trajectory for 2D or 3D use

int	trajectory_set_end (TRAJECTORY traj, const PHYSICS state, double time_val)
	set the terminal state and time of the trajectory, recomputes Hermite tangents

int	trajectory_set_start (TRAJECTORY traj, const PHYSICS state, double time_val)
	set the initial state and time of the trajectory

int	trajectory_update (TRAJECTORY traj, const PHYSICS new_end, double time_val)
	shift: old end becomes new start, set a new end state (for continuous dead reckoning updates)

Detailed Description

Trajectory interpolation and dead reckoning for 2D/3D networked simulations.

Implementation of the "Defeating Lag With Cubic Splines" approach (GameDev.net Article 914 by Nicholas Van Caldwell) combined with cubic Hermite spline interpolation and quadratic extrapolation.

The API provides smooth movement prediction for networked games and local simulations by:

Using cubic Hermite spline interpolation between two known states (matching position and velocity at both endpoints)
Quadratic extrapolation beyond the known interval using velocity and acceleration
Smooth orientation interpolation using the same Hermite approach

Works for both 2D (xy) and 3D (xyz) coordinate systems.

Time units are user-defined: as long as position, speed, acceleration, and time values use consistent units, the math works. For example:

position in pixels, speed in pixels/sec, accel in pixels/sec^2, time in sec
position in meters, speed in m/usec, accel in m/usec^2, time in usec

Author: Castagnier Mickael

Version: 1.0

Date: 28/02/2026

Definition in file n_trajectory.h.

Data Structures

Macros

Functions

Detailed Description