Functions/Subroutines
double precision function, dimension(3)	find_zero_position (x1, x2, phi1, phi2)
	Find the position of the point where phi is zero, given linear approximation.

double precision function, dimension(3)	project_point_on_sphere (x, c, r)

double precision function, dimension(3)	slerp (p0, p1, theta, t)

double precision function	compute_cos_angle (v1, v2)
	Compute the cosinus of the angle between two vectors v1 and v2.

double precision function	compute_sinangle (v1, v2)
	Compute the sinus of the angle between two vectors v1 and v2.

double precision function, dimension(3)	find_position_sphere (x, orig, dist, normal, x_radius, min_cos_angle, effective_cos_angle, is_debug)
	Find the position of the point in the surface with spherical approximation.

double precision function, dimension(3)	find_position_plane (x, orig, dist, normal, max_dist, effective_dist, is_debug)

double precision function, dimension(3)	restrain_descent (x1, x2, max_step)
	Restrain the advance from x1 towards x2 up to max_step.

double precision function, dimension(3)	compute_best_point_with_angles (x1, theta1, x2, theta2)
	Return the interpolated point between x1 and x2, given respective angles by linear interpolation between theta1 and theta2. In practice, compute the interpolation parameter \( \alpha \in [0,1]\) such that \( \theta( \alpha ) = \theta_1 + (\theta_2 - \theta_1) \alpha \). We search for \( alpha = 0 \). Finaly, the result is \( X(\alpha) = X_1 + \alpha (X_2 - X_1) \).

Function/Subroutine Documentation

◆ compute_best_point_with_angles()

double precision function, dimension(3) mod_geo_tools::compute_best_point_with_angles	(	double precision, dimension(3), intent(in)	x1,
		double precision, intent(in)	theta1,
		double precision, dimension(3), intent(in)	x2,
		double precision, intent(in)	theta2 )

Return the interpolated point between x1 and x2, given respective angles by linear interpolation between theta1 and theta2. In practice, compute the interpolation parameter \( \alpha \in [0,1]\) such that \( \theta( \alpha ) = \theta_1 + (\theta_2 - \theta_1) \alpha \). We search for \( alpha = 0 \). Finaly, the result is \( X(\alpha) = X_1 + \alpha (X_2 - X_1) \).

Note: We do not go beyond [x1,x2] for stability reasons. In consequence, if both angles are of the same sign, simply conserve the smallest one (in absolute value).; We try to minimize the value of the angle (i.e. closer to 0).; If theta2=theta1, return x1.

◆ compute_cos_angle()

double precision function mod_geo_tools::compute_cos_angle	(	double precision, dimension(:), intent(in)	v1,
		double precision, dimension(:), intent(in)	v2 )

Compute the cosinus of the angle between two vectors v1 and v2.

Note: the vectors are not necessarily normalized

◆ compute_sinangle()

double precision function mod_geo_tools::compute_sinangle	(	double precision, dimension(:), intent(in)	v1,
		double precision, dimension(:), intent(in)	v2 )

Compute the sinus of the angle between two vectors v1 and v2.

Note: the vectors are not necessarily normalized

◆ find_position_plane()

double precision function, dimension(3) mod_geo_tools::find_position_plane	(	double precision, dimension(3), intent(in)	x,
		double precision, dimension(3), intent(in)	orig,
		double precision, intent(in)	dist,
		double precision, dimension(3), intent(in)	normal,
		double precision, intent(in)	max_dist,
		double precision, intent(out)	effective_dist,
		logical, intent(in), optional	is_debug )

◆ find_position_sphere()

double precision function, dimension(3) mod_geo_tools::find_position_sphere	(	double precision, dimension(3), intent(in)	x,
		double precision, dimension(3), intent(in)	orig,
		double precision, intent(in)	dist,
		double precision, dimension(3), intent(in)	normal,
		double precision, intent(in)	x_radius,
		double precision, intent(in)	min_cos_angle,
		double precision, intent(out)	effective_cos_angle,
		logical, intent(in), optional	is_debug )

Find the position of the point in the surface with spherical approximation.

x_radius[in]: the signed radius to the sphere (x_radius=R=1/curvature) at x such that the center of the sphere is \( x_c = x - R n \).

◆ find_zero_position()

double precision function, dimension(3) mod_geo_tools::find_zero_position	(	double precision, dimension(3), intent(in)	x1,
		double precision, dimension(3), intent(in)	x2,
		double precision, intent(in)	phi1,
		double precision, intent(in)	phi2 )

Find the position of the point where phi is zero, given linear approximation.

◆ project_point_on_sphere()

double precision function, dimension(3) mod_geo_tools::project_point_on_sphere	(	double precision, dimension(3), intent(in)	x,
		double precision, dimension(3), intent(in)	c,
		double precision, intent(in)	r )

◆ restrain_descent()

double precision function, dimension(3) mod_geo_tools::restrain_descent	(	double precision, dimension(3), intent(in)	x1,
		double precision, dimension(3), intent(in)	x2,
		double precision, intent(in)	max_step )

Restrain the advance from x1 towards x2 up to max_step.

Parameters

x1	the starting point.
x2	the end point.
max_step	the maximum distance to travel from x1 to x2

Note: if the distance between x1 and x2 is less than max_step, hence the result is x2

◆ slerp()

double precision function, dimension(3) mod_geo_tools::slerp	(	double precision, dimension(3), intent(in)	p0,
		double precision, dimension(3), intent(in)	p1,
		double precision, intent(in)	theta,
		double precision, intent(in)	t )

Functions/Subroutines