vulcan::geometry Namespace Reference

Functions
template<typename Scalar>
Scalar	slant_range (const Vec3< Scalar > &r_observer, const Vec3< Scalar > &r_target)
	Compute slant range (distance) between two points.
template<typename Scalar>
Vec2< Scalar >	los_angles (const Vec3< Scalar > &r_observer, const Vec3< Scalar > &r_target)
	Compute line-of-sight azimuth and elevation angles.
template<typename Scalar>
Vec2< Scalar >	los_rate (const Vec3< Scalar > &r_obs, const Vec3< Scalar > &v_obs, const Vec3< Scalar > &r_tgt, const Vec3< Scalar > &v_tgt)
	Compute line-of-sight angular rates.
template<typename Scalar>
Scalar	ray_sphere_intersection (const Vec3< Scalar > &origin, const Vec3< Scalar > &direction, const Vec3< Scalar > &center, const Scalar &radius)
	Ray-sphere intersection.
template<typename Scalar>
Scalar	ray_plane_intersection (const Vec3< Scalar > &origin, const Vec3< Scalar > &direction, const Vec3< Scalar > &plane_normal, const Vec3< Scalar > &plane_point)
	Ray-plane intersection.
template<typename Scalar>
Scalar	point_in_cone (const Vec3< Scalar > &point, const Vec3< Scalar > &apex, const Vec3< Scalar > &axis, const Scalar &half_angle)
	Check if a point lies within a cone (e.g., sensor FOV).
template<typename Scalar>
Vec3< Scalar >	project_to_plane (const Vec3< Scalar > &point, const Vec3< Scalar > &plane_normal, const Vec3< Scalar > &plane_point)
	Project a point onto a plane.
template<typename Scalar>
LLA< Scalar >	ground_track_point (const Vec3< Scalar > &r_ecef, const EarthModel &model=EarthModel::WGS84())
	Project ECEF position to ellipsoid surface (ground track point).
template<typename Scalar>
Vec3< Scalar >	ground_track_ecef (const Vec3< Scalar > &r_ecef, const EarthModel &model=EarthModel::WGS84())
	Compute ground track point and return as ECEF.

Function Documentation

ground_track_ecef()

template<typename Scalar>

Vec3< Scalar > vulcan::geometry::ground_track_ecef	(	const Vec3< Scalar > &	r_ecef,
		const EarthModel &	model = EarthModel::WGS84() )

Compute ground track point and return as ECEF.

Projects the position to the ellipsoid surface and returns the ECEF coordinates of that point.

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

r_ecef	Position in ECEF [m]
model	Earth model (default: WGS84)

Returns

ECEF position of ground track point [m]

ground_track_point()

template<typename Scalar>

LLA< Scalar > vulcan::geometry::ground_track_point	(	const Vec3< Scalar > &	r_ecef,
		const EarthModel &	model = EarthModel::WGS84() )

Project ECEF position to ellipsoid surface (ground track point).

Computes the point on the Earth's surface directly below (or above) the given ECEF position. Returns LLA with altitude set to zero.

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

r_ecef	Position in ECEF [m]
model	Earth model (default: WGS84)

Returns

LLA coordinates of ground track point (altitude = 0)

los_angles()

template<typename Scalar>

Vec2< Scalar > vulcan::geometry::los_angles	(	const Vec3< Scalar > &	r_observer,
		const Vec3< Scalar > &	r_target )

Compute line-of-sight azimuth and elevation angles.

Computes the look angles from observer to target in the observer's local coordinate frame (typically NED or ENU).

Convention:

• Azimuth: angle from +X axis, positive clockwise when viewed from above
• Elevation: angle from XY plane, positive upward

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

r_observer	Observer position [m]
r_target	Target position [m]

Returns

[azimuth, elevation] in radians

los_rate()

template<typename Scalar>

Vec2< Scalar > vulcan::geometry::los_rate	(	const Vec3< Scalar > &	r_obs,
		const Vec3< Scalar > &	v_obs,
		const Vec3< Scalar > &	r_tgt,
		const Vec3< Scalar > &	v_tgt )

Compute line-of-sight angular rates.

Computes the time derivative of LOS angles given relative positions and velocities of observer and target.

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

r_obs	Observer position [m]
v_obs	Observer velocity [m/s]
r_tgt	Target position [m]
v_tgt	Target velocity [m/s]

Returns

[azimuth_rate, elevation_rate] in rad/s

point_in_cone()

template<typename Scalar>

Scalar vulcan::geometry::point_in_cone	(	const Vec3< Scalar > &	point,
		const Vec3< Scalar > &	apex,
		const Vec3< Scalar > &	axis,
		const Scalar &	half_angle )

Check if a point lies within a cone (e.g., sensor FOV).

Determines if a point is inside a cone defined by its apex, axis direction, and half-angle. Useful for sensor field-of-view checks.

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

point	Point to test
apex	Cone apex (e.g., sensor location)
axis	Cone axis direction (should be normalized)
half_angle	Cone half-angle in radians

Returns

1.0 if point is inside cone, 0.0 otherwise (Scalar for symbolic compat)

project_to_plane()

template<typename Scalar>

Vec3< Scalar > vulcan::geometry::project_to_plane	(	const Vec3< Scalar > &	point,
		const Vec3< Scalar > &	plane_normal,
		const Vec3< Scalar > &	plane_point )

Project a point onto a plane.

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

point	Point to project
plane_normal	Plane normal (should be normalized)
plane_point	A point on the plane

Returns

Projected point on the plane

ray_plane_intersection()

template<typename Scalar>

Scalar vulcan::geometry::ray_plane_intersection	(	const Vec3< Scalar > &	origin,
		const Vec3< Scalar > &	direction,
		const Vec3< Scalar > &	plane_normal,
		const Vec3< Scalar > &	plane_point )

Ray-plane intersection.

Computes the distance along a ray to intersection with an infinite plane.

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

origin	Ray origin point
direction	Ray direction (should be normalized)
plane_normal	Plane normal vector (should be normalized)
plane_point	A point on the plane

Returns

Distance to intersection, or negative if parallel or behind

ray_sphere_intersection()

template<typename Scalar>

Scalar vulcan::geometry::ray_sphere_intersection	(	const Vec3< Scalar > &	origin,
		const Vec3< Scalar > &	direction,
		const Vec3< Scalar > &	center,
		const Scalar &	radius )

Ray-sphere intersection.

Computes the distance along a ray to the nearest intersection with a sphere. Uses the geometric solution for numerical stability.

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

origin	Ray origin point
direction	Ray direction (should be normalized)
center	Sphere center
radius	Sphere radius

Returns

Distance to nearest intersection, or negative if no intersection

slant_range()

template<typename Scalar>

Scalar vulcan::geometry::slant_range	(	const Vec3< Scalar > &	r_observer,
		const Vec3< Scalar > &	r_target )

Compute slant range (distance) between two points.

Template Parameters

Scalar

Scalar type (double or casadi::MX)

Parameters

r_observer	Observer position [m]
r_target	Target position [m]

Returns

Distance between points [m]