TRAJECTORY: cubic Hermite spline dead reckoning and movement simulation for 2D/3D

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

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Data Structure Documentation

TRAJECTORY

struct TRAJECTORY

structure holding all data for trajectory interpolation / extrapolation

Examples

ex_iso_astar.c, and ex_trajectory.c.

Definition at line 82 of file n_trajectory.h.

Collaboration diagram for TRAJECTORY:

Data Fields
PHYSICS	current	current computed state at current_time
int	current_segment	index of the currently loaded segment (points[i] -> points[i+1]), -1 if none
double	current_time	last computed time
double	duration	duration = end_time - start_time
PHYSICS	end	state at trajectory end (terminal known state)
double	end_time	timestamp of end state
VECTOR3D	m0	Hermite tangent at start for position (start.speed * duration)
VECTOR3D	m0_orient	Hermite tangent at start for orientation (start.angular_speed * duration)
VECTOR3D	m1	Hermite tangent at end for position (end.speed * duration)
VECTOR3D	m1_orient	Hermite tangent at end for orientation (end.angular_speed * duration)
int	mode	current computation mode: TRAJECTORY_INTERP, TRAJECTORY_EXTRAP, or TRAJECTORY_BEFORE
int	nb_components	number of components to process: TRAJECTORY_2D (2) or TRAJECTORY_3D (3)
int	nb_points	number of waypoints in the points array
int	nb_points_allocated	allocated capacity of the points array
TRAJECTORY_POINT *	points	array of waypoints for multi-point paths (NULL if single segment)
PHYSICS	start	state at trajectory start (initial known state)
double	start_time	timestamp of start state

TRAJECTORY_POINT

struct TRAJECTORY_POINT

a single waypoint in a multi-point trajectory path

Definition at line 74 of file n_trajectory.h.

Collaboration diagram for TRAJECTORY_POINT:

Data Fields
PHYSICS	state	physics state (position, speed, etc.) at this waypoint
double	time_val	timestamp of this waypoint

Macro Definition Documentation

TRAJECTORY_2D

#define TRAJECTORY_2D   2

use 2 components (x,y) for trajectory computation

Examples

ex_iso_astar.c, and ex_trajectory.c.

Definition at line 69 of file n_trajectory.h.

TRAJECTORY_3D

#define TRAJECTORY_3D   3

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

Examples

ex_trajectory.c.

Definition at line 71 of file n_trajectory.h.

TRAJECTORY_BEFORE

#define TRAJECTORY_BEFORE   3

trajectory is extrapolating before the start state using quadratic motion

Examples

ex_trajectory.c.

Definition at line 66 of file n_trajectory.h.

TRAJECTORY_EXTRAP

#define TRAJECTORY_EXTRAP   2

trajectory is extrapolating beyond the end state using quadratic motion

Examples

ex_trajectory.c.

Definition at line 64 of file n_trajectory.h.

TRAJECTORY_INTERP

#define TRAJECTORY_INTERP   1

trajectory is interpolating along the cubic Hermite spline between start and end

Examples

ex_trajectory.c.

Definition at line 62 of file n_trajectory.h.

Function Documentation

trajectory_add_point()

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)

add a waypoint to the multi-point path (times must be strictly increasing)

Waypoints must be added in strictly increasing chronological order. When 2+ waypoints exist, trajectory_compute and trajectory_get_* functions automatically find and interpolate the correct segment.

Parameters

traj	The trajectory
state	The physics state at this waypoint
time_val	The timestamp of this waypoint (must be > previous point's time)

Returns

TRUE or FALSE

Definition at line 616 of file n_trajectory.c.

References __n_assert, current_segment, LOG_ERR, n_log, nb_points, nb_points_allocated, points, Realloc, TRAJECTORY_POINT::state, TRAJECTORY_POINT::time_val, and trajectory_load_segment().

Referenced by demo_dead_reckoning(), init_3d(), and rebuild_2d_trajectory().

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trajectory_clear_points()

int trajectory_clear_points

(

TRAJECTORY *

traj

)

clear all waypoints from the multi-point path

clear all waypoints from the multi-point path

Keeps the allocated memory for reuse. Resets start/end/duration.

Parameters

traj	The trajectory

Returns

TRUE or FALSE

Definition at line 655 of file n_trajectory.c.

References __n_assert, current_segment, duration, end, end_time, nb_points, start, and start_time.

Referenced by rebuild_2d_trajectory().

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trajectory_compute()

int trajectory_compute	(	TRAJECTORY *	traj,
		double	time_val
	)

compute full state (position, speed, acceleration, orientation) at given time

compute full state (position, speed, acceleration, orientation) at given time

Parameters

traj	The trajectory
time_val	The time at which to compute the state

Returns

TRUE or FALSE

Definition at line 329 of file n_trajectory.c.

References __n_assert, PHYSICS::acceleration, PHYSICS::angular_acceleration, PHYSICS::angular_speed, current, current_time, duration, end, end_time, hermite_d2h00(), hermite_d2h01(), hermite_d2h10(), hermite_d2h11(), hermite_dh00(), hermite_dh01(), hermite_dh10(), hermite_dh11(), hermite_h00(), hermite_h01(), hermite_h10(), hermite_h11(), m0, m0_orient, m1, m1_orient, mode, nb_components, PHYSICS::orientation, PHYSICS::position, PHYSICS::speed, start, start_time, TRAJECTORY_BEFORE, TRAJECTORY_EXTRAP, TRAJECTORY_INTERP, and trajectory_load_segment().

Referenced by draw_2d_panel(), draw_3d_panel(), main(), and update_3d_logic().

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trajectory_delete()

void trajectory_delete

(

TRAJECTORY **

traj

)

free a trajectory

free a trajectory

Parameters

traj	Pointer to the TRAJECTORY pointer to free

Definition at line 234 of file n_trajectory.c.

References __n_assert, and Free.

Referenced by demo_dead_reckoning(), main(), and reset_2d().

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trajectory_distance()

double trajectory_distance	(	TRAJECTORY *	traj,
		double	time_a,
		double	time_b,
		int	steps
	)

distance along the trajectory between two times

distance along the trajectory between two times

Parameters

traj	The trajectory
time_a	Start time
time_b	End time
steps	Number of integration steps (higher = more precise, 100 is usually enough)

Returns

The approximate distance, or -1.0 on error

Definition at line 678 of file n_trajectory.c.

References __n_assert, nb_components, and trajectory_get_position().

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trajectory_get_acceleration()

int trajectory_get_acceleration	(	TRAJECTORY *	traj,
		double	time_val,
		VECTOR3D	out
	)

compute only acceleration at given time, stores result in out

compute only acceleration at given time, stores result in out

Parameters

traj	The trajectory
time_val	The time at which to compute
out	VECTOR3D to store the result

Returns

TRUE or FALSE

Definition at line 526 of file n_trajectory.c.

References __n_assert, PHYSICS::acceleration, duration, end, end_time, hermite_d2h00(), hermite_d2h01(), hermite_d2h10(), hermite_d2h11(), m0, m1, nb_components, PHYSICS::position, start, start_time, and trajectory_load_segment().

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trajectory_get_orientation()

int trajectory_get_orientation	(	TRAJECTORY *	traj,
		double	time_val,
		VECTOR3D	out
	)

compute only orientation at given time, stores result in out

compute only orientation at given time, stores result in out

Parameters

traj	The trajectory
time_val	The time at which to compute
out	VECTOR3D to store the result

Returns

TRUE or FALSE

Definition at line 568 of file n_trajectory.c.

References __n_assert, PHYSICS::angular_acceleration, PHYSICS::angular_speed, duration, end, end_time, hermite_h00(), hermite_h01(), hermite_h10(), hermite_h11(), m0_orient, m1_orient, nb_components, PHYSICS::orientation, start, start_time, and trajectory_load_segment().

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trajectory_get_position()

int trajectory_get_position	(	TRAJECTORY *	traj,
		double	time_val,
		VECTOR3D	out
	)

compute only position at given time, stores result in out

compute only position at given time, stores result in out

This is a lightweight version of trajectory_compute that only computes position.

Parameters

traj	The trajectory
time_val	The time at which to compute
out	VECTOR3D to store the result

Returns

TRUE or FALSE

Definition at line 435 of file n_trajectory.c.

References __n_assert, PHYSICS::acceleration, duration, end, end_time, hermite_h00(), hermite_h01(), hermite_h10(), hermite_h11(), m0, m1, nb_components, PHYSICS::position, PHYSICS::speed, start, start_time, and trajectory_load_segment().

Referenced by demo_dead_reckoning(), draw_full_path_2d(), draw_full_path_3d(), and trajectory_distance().

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trajectory_get_speed()

int trajectory_get_speed	(	TRAJECTORY *	traj,
		double	time_val,
		VECTOR3D	out
	)

compute only speed at given time, stores result in out

compute only speed at given time, stores result in out

Parameters

traj	The trajectory
time_val	The time at which to compute
out	VECTOR3D to store the result

Returns

TRUE or FALSE

Definition at line 480 of file n_trajectory.c.

References __n_assert, PHYSICS::acceleration, duration, end, end_time, hermite_dh00(), hermite_dh01(), hermite_dh10(), hermite_dh11(), m0, m1, nb_components, PHYSICS::position, PHYSICS::speed, start, start_time, and trajectory_load_segment().

Referenced by demo_dead_reckoning().

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trajectory_new()

TRAJECTORY * trajectory_new

(

int

nb_components

)

allocate a new trajectory for 2D or 3D use

allocate a new trajectory for 2D or 3D use

Parameters

nb_components

TRAJECTORY_2D (2) or TRAJECTORY_3D (3)

Returns

A new TRAJECTORY or NULL on error

Definition at line 206 of file n_trajectory.c.

References __n_assert, current_segment, current_time, duration, end_time, LOG_ERR, Malloc, mode, n_log, nb_components, nb_points, nb_points_allocated, points, start_time, TRAJECTORY_2D, TRAJECTORY_3D, and TRAJECTORY_BEFORE.

Referenced by demo_dead_reckoning(), init_3d(), and reset_2d().

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trajectory_set_end()

int trajectory_set_end	(	TRAJECTORY *	traj,
		const PHYSICS *	state,
		double	time_val
	)

set the terminal state and time of the trajectory, recomputes Hermite tangents

set the terminal state and time of the trajectory, recomputes Hermite tangents

Recomputes the Hermite tangent vectors.

Parameters

traj	The trajectory to configure
state	The physics state at the end point
time_val	The timestamp of this state (must be > start_time)

Returns

TRUE or FALSE

Definition at line 270 of file n_trajectory.c.

References __n_assert, duration, end, end_time, LOG_ERR, n_log, start_time, and trajectory_compute_tangents().

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trajectory_set_start()

int trajectory_set_start	(	TRAJECTORY *	traj,
		const PHYSICS *	state,
		double	time_val
	)

set the initial state and time of the trajectory

set the initial state and time of the trajectory

Parameters

traj	The trajectory to configure
state	The physics state at the start point
time_val	The timestamp of this state

Returns

TRUE or FALSE

Definition at line 247 of file n_trajectory.c.

References __n_assert, duration, end_time, start, start_time, and trajectory_compute_tangents().

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trajectory_update()

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)

shift: old end becomes new start, set a new end state (for continuous dead reckoning updates)

The previous end state becomes the new start state, and the new state becomes the end. This is the core function for continuous dead reckoning: call it each time a new network update arrives to create a smooth spline from the current endpoint to the new one.

Parameters

traj	The trajectory to update
new_end	The new physics state received (e.g. from a network packet)
time_val	The timestamp of the new state

Returns

TRUE or FALSE

Definition at line 298 of file n_trajectory.c.

References __n_assert, duration, end, end_time, LOG_ERR, n_log, start, start_time, and trajectory_compute_tangents().

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