three-dimensional point

Collaboration diagram for three-dimensional point:

Data Structures
struct	a_point3
	instance structure for three-dimensional point More...

Macros
#define	A_POINT3_C(x, y, z)
#define	a_point3_c(x)
#define	a_point3_(_, x)

Typedefs
typedef struct a_point3	a_point3

Functions
void	a_vector3_set (a_vector3 *ctx, a_point3 const *p, a_point3 const *q)
	set a 3D vector as the difference from point p to point q.
void	a_point3_val (a_point3 const *ctx, a_real *x, a_real *y, a_real *z)
	get the cartesian coordinates of a 3D point.
void	a_point3_set_val (a_point3 *ctx, a_real x, a_real y, a_real z)
	set the cartesian coordinates of a 3D point.
void	a_point3_cyl (a_point3 const *ctx, a_real *rho, a_real *theta, a_real *z)
	get the cylindrical coordinates of a 3D point.
void	a_point3_set_cyl (a_point3 *ctx, a_real rho, a_real theta, a_real z)
	set the cylindrical coordinates of a 3D point.
void	a_point3_sph (a_point3 const *ctx, a_real *rho, a_real *theta, a_real *alpha)
	get the spherical coordinates of a 3D point.
void	a_point3_set_sph (a_point3 *ctx, a_real rho, a_real theta, a_real alpha)
	set the spherical coordinates of a 3D point.
void	a_point3_add (a_point3 const *lhs, a_vector3 const *rhs, a_point3 *res)
	add a 3D vector to a 3D point.
void	a_point3_sub (a_point3 const *lhs, a_vector3 const *rhs, a_point3 *res)
	subtract a 3D vector from a 3D point.
void	a_point3_mul (a_point3 const *lhs, a_real rhs, a_point3 *res)
	multiplie a 3D point by a scalar.
void	a_point3_div (a_point3 const *lhs, a_real rhs, a_point3 *res)
	divide a 3D point by a scalar.
void	a_point3_pos (a_point3 const *ctx, a_vector3 *res)
	convert it into a vector from the origin to the point.
void	a_point3_neg (a_point3 const *ctx, a_vector3 *res)
	convert it into a vector from the point to the origin.
a_real	a_point3_dist (a_point3 const *lhs, a_point3 const *rhs)
	compute the distance between two 3D points.
a_real	a_point3_dist2 (a_point3 const *lhs, a_point3 const *rhs)
	compute the squared distance between two 3D points.
a_real	a_point3_mindist (a_point3 const *ctx, a_point3 const *i_p, a_size i_n, a_point3 *o_p, a_size *o_i)
	compute the minimum distance from a reference point to a point set.
a_real	a_point3_maxdist (a_point3 const *ctx, a_point3 const *i_p, a_size i_n, a_point3 *o_p, a_size *o_i)
	compute the maximum distance from a reference point to a point set.
int	a_point3_cmpxy (a_point3 const *lhs, a_point3 const *rhs)
	compare two 3D points primarily by X, then by Y, and finally by Z.
int	a_point3_cmpyx (a_point3 const *lhs, a_point3 const *rhs)
	compare two 3D points primarily by Y, then by X, and finally by Z.
void	a_vector3::set (a_point3 const &p, a_point3 const &q)
	set a 3D vector as the difference from point p to point q.

Detailed Description

Macro Definition Documentation

a_point3_

#define a_point3_	(		_,
			x )

Value:

a_cast_s(a_point3 _, x)

A_POINT3_C

#define A_POINT3_C	(		x,
			y,
			z )

Value:

{a_real_c(x), a_real_c(y), a_real_c(z)}

constructs a three-dimensional point from cartesian coordinate

a_point3_c

#define a_point3_c

(

x

)

Value:

a_cast_s(a_point3, x)

static cast to three-dimensional point

Function Documentation

a_point3_cmpxy()

int a_point3_cmpxy	(	a_point3 const *	lhs,
		a_point3 const *	rhs )

compare two 3D points primarily by X, then by Y, and finally by Z.

Parameters

[in]	lhs	is left-hand side 3D point
[in]	rhs	is right-hand side 3D point

Returns

relationship between 3D points

Return values

>0	if lhs is greater than rhs
<0	if lhs is less than rhs
0	if lhs is equal to rhs

a_point3_cmpyx()

int a_point3_cmpyx	(	a_point3 const *	lhs,
		a_point3 const *	rhs )

compare two 3D points primarily by Y, then by X, and finally by Z.

Parameters

[in]	lhs	is left-hand side 3D point
[in]	rhs	is right-hand side 3D point

Returns

relationship between 3D points

Return values

>0	if lhs is greater than rhs
<0	if lhs is less than rhs
0	if lhs is equal to rhs

a_point3_dist()

a_real a_point3_dist	(	a_point3 const *	lhs,
		a_point3 const *	rhs )

compute the distance between two 3D points.

In three-dimensional space, let point \(p\) have coordinates \((p_x,p_y,p_z)\) and let point \(q\) have coordinates \((q_x,q_y,q_z)\). Then the distance between \(p\) and \(q\) is given by:

\[ d(p,q)=\sqrt{(p_x-q_x)^2+(p_y-q_y)^2+(p_z-q_z)^2} \]

Parameters

[in]	lhs	is left-hand side 3D point
[in]	rhs	is right-hand side 3D point

Returns

the distance between two 3D points

a_point3_dist2()

a_real a_point3_dist2	(	a_point3 const *	lhs,
		a_point3 const *	rhs )

compute the squared distance between two 3D points.

In three-dimensional space, let point \(p\) have coordinates \((p_x,p_y,p_z)\) and let point \(q\) have coordinates \((q_x,q_y,q_z)\). Then the squared distance between \(p\) and \(q\) is given by:

\[ d(p,q)^2=(p_x-q_x)^2+(p_y-q_y)^2+(p_z-q_z)^2 \]

Parameters

[in]	lhs	is left-hand side 3D point
[in]	rhs	is right-hand side 3D point

Returns

the squared distance between two 3D points

a_point3_maxdist()

a_real a_point3_maxdist	(	a_point3 const *	ctx,
		a_point3 const *	i_p,
		a_size	i_n,
		a_point3 *	o_p,
		a_size *	o_i )

compute the maximum distance from a reference point to a point set.

Parameters

[in]	ctx	points to the reference point
[in]	i_p	points to the points in memory
[in]	i_n	number of the points in memory
[out]	o_p	stores the farthest point; may be NULL
[out]	o_i	stores the index of the farthest point; may be NULL

Returns

the maximum distance from a reference point to a point set

Return values

-inf

failure

a_point3_mindist()

a_real a_point3_mindist	(	a_point3 const *	ctx,
		a_point3 const *	i_p,
		a_size	i_n,
		a_point3 *	o_p,
		a_size *	o_i )

compute the minimum distance from a reference point to a point set.

Parameters

[in]	ctx	points to the reference point
[in]	i_p	points to the points in memory
[in]	i_n	number of the points in memory
[out]	o_p	stores the nearest point; may be NULL
[out]	o_i	stores the index of the nearest point; may be NULL

Returns

the minimum distance from a reference point to a point set

Return values

+inf

failure

set()

void a_vector3::set ( a_point3 const & p, a_point3 const & q )

inline

set a 3D vector as the difference from point p to point q.

See also

a_vector3_set