Collaboration diagram for two-dimensional point:

Data Structures
struct	a_point2
	instance structure for two-dimensional point More...

Macros
#define	A_POINT2_C(x, y)
#define	a_point2_c(x)
#define	a_point2_(_, x)

Typedefs
typedef struct a_point2	a_point2

Functions
void	a_vector2_set (a_vector2 ctx, a_point2 const p, a_point2 const *q)
	set a 2D vector as the difference from point p to point q.
void	a_point2_val (a_point2 const ctx, a_real x, a_real *y)
	get the cartesian coordinates of a 2D point.
void	a_point2_set_val (a_point2 *ctx, a_real x, a_real y)
	set the cartesian coordinates of a 2D point.
void	a_point2_pol (a_point2 const ctx, a_real rho, a_real *theta)
	get the polar coordinates of a 2D point.
void	a_point2_set_pol (a_point2 *ctx, a_real rho, a_real theta)
	set the polar coordinates of a 2D point.
void	a_point2_add (a_point2 const lhs, a_vector2 const rhs, a_point2 *res)
	add a 2D vector to a 2D point.
void	a_point2_sub (a_point2 const lhs, a_vector2 const rhs, a_point2 *res)
	subtract a 2D vector from a 2D point.
void	a_point2_mul (a_point2 const lhs, a_real rhs, a_point2 res)
	multiplie a 2D point by a scalar.
void	a_point2_div (a_point2 const lhs, a_real rhs, a_point2 res)
	divide a 2D point by a scalar.
void	a_point2_pos (a_point2 const ctx, a_vector2 res)
	convert it into a vector from the origin to the point.
void	a_point2_neg (a_point2 const ctx, a_vector2 res)
	convert it into a vector from the point to the origin.
a_real	a_point2_norm (a_point2 const *ctx)
	compute the magnitude of a 2D point.
a_real	a_point2_norm2 (a_point2 const *ctx)
	compute the squared magnitude of a 2D point.
a_real	a_point2_dist (a_point2 const lhs, a_point2 const rhs)
	compute the distance between two 2D points.
a_real	a_point2_dist2 (a_point2 const lhs, a_point2 const rhs)
	compute the squared distance between two 2D points.
a_real	a_point2_mindist (a_point2 const ctx, a_point2 const i_p, a_size i_n, a_point2 o_p, a_size o_i)
	compute the minimum distance from a reference point to a point set.
a_real	a_point2_maxdist (a_point2 const ctx, a_point2 const i_p, a_size i_n, a_point2 o_p, a_size o_i)
	compute the maximum distance from a reference point to a point set.
void	a_point2_lerp (a_point2 const lhs, a_point2 const rhs, a_real val, a_point2 *res)
	compute linear interpolation (LERP) between two 2D points.
a_real	a_point2_tricir (a_point2 const p1, a_point2 const p2, a_point2 const p3, a_point2 pc)
	compute the circumcenter and circumradius of a triangle defined by three 2D points.
a_real	a_point2_tricir2 (a_point2 const p1, a_point2 const p2, a_point2 const p3, a_point2 pc)
	compute the circumcenter and squared circumradius of a triangle defined by three 2D points.
int	a_point2_cmpx (a_point2 const lhs, a_point2 const rhs)
	compare two 2D points primarily by X-coordinate, then by Y-coordinate.
int	a_point2_cmpy (a_point2 const lhs, a_point2 const rhs)
	compare two 2D points primarily by Y-coordinate, then by X-coordinate.
void	a_vector2::set (a_point2 const &p, a_point2 const &q)
	set a 2D vector as the difference from point p to point q.

Detailed Description

Macro Definition Documentation

◆ a_point2_

#define a_point2_	(		_,
			x )

Value:

a_cast_s(a_point2 _, x)

a_point2

instance structure for two-dimensional point

Definition point2.h:264

◆ A_POINT2_C

#define A_POINT2_C	(		x,
			y )

Value:

{a_real_c(x), a_real_c(y)}

a_real_c

#define a_real_c(x)

static cast to floating-point number

Definition a.h:1009

constructs a two-dimensional point from cartesian coordinate

◆ a_point2_c

#define a_point2_c ( x )

Value:

a_cast_s(a_point2, x)

static cast to two-dimensional point

Function Documentation

◆ a_point2_cmpx()

int a_point2_cmpx	(	a_point2 const *	lhs,
		a_point2 const *	rhs )

compare two 2D points primarily by X-coordinate, then by Y-coordinate.

Parameters

[in]	lhs	is left-hand side 2D point
[in]	rhs	is right-hand side 2D point

Returns: relationship between 2D 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_point2_cmpy()

int a_point2_cmpy	(	a_point2 const *	lhs,
		a_point2 const *	rhs )

compare two 2D points primarily by Y-coordinate, then by X-coordinate.

Parameters

[in]	lhs	is left-hand side 2D point
[in]	rhs	is right-hand side 2D point

Returns: relationship between 2D 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_point2_dist()

a_real a_point2_dist	(	a_point2 const *	lhs,
		a_point2 const *	rhs )

compute the distance between two 2D points.

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

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

Parameters

[in]	lhs	is left-hand side 2D point
[in]	rhs	is right-hand side 2D point

Returns: the distance between two 2D points

◆ a_point2_dist2()

a_real a_point2_dist2	(	a_point2 const *	lhs,
		a_point2 const *	rhs )

compute the squared distance between two 2D points.

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

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

Parameters

[in]	lhs	is left-hand side 2D point
[in]	rhs	is right-hand side 2D point

Returns: the squared distance between two 2D points

◆ a_point2_lerp()

void a_point2_lerp	(	a_point2 const *	lhs,
		a_point2 const *	rhs,
		a_real	val,
		a_point2 *	res )

compute linear interpolation (LERP) between two 2D points.

Let \(\vec{a}\) and \(\vec{b}\) be two 2D points and let \(t\) be the interpolation factor. Then the linear interpolation \(\vec{p}\) between \(\vec{a}\) and \(\vec{b}\) is given by:

\[ \vec{p} = \vec{a} + (\vec{b} - \vec{a}) * t \]

Parameters

[in]	lhs	points to the starting point
[in]	rhs	points to the ending point
[in]	val	is the interpolation factor
[out]	res	stores the interpolated point

◆ a_point2_maxdist()

a_real a_point2_maxdist	(	a_point2 const *	ctx,
		a_point2 const *	i_p,
		a_size	i_n,
		a_point2 *	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_point2_mindist()

a_real a_point2_mindist	(	a_point2 const *	ctx,
		a_point2 const *	i_p,
		a_size	i_n,
		a_point2 *	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

◆ a_point2_norm()

a_real a_point2_norm ( a_point2 const * ctx )

compute the magnitude of a 2D point.

In two-dimensional space, a point \(\vec{p}\) with coordinates \((x,y)\) has a magnitude defined as:

\[ \|\vec{p}\|=\sqrt{x^2+y^2} \]

Parameters

[in] ctx points to the input point

Returns: the magnitude of the point

◆ a_point2_norm2()

a_real a_point2_norm2 ( a_point2 const * ctx )

compute the squared magnitude of a 2D point.

In two-dimensional space, a point \(\vec{p}\) with coordinates \((x,y)\) has a squared magnitude defined as:

\[ \|\vec{p}\|^2=x^2+y^2 \]

Parameters

[in] ctx points to the input point

Returns: the squared magnitude of the point

◆ a_point2_tricir()

a_real a_point2_tricir	(	a_point2 const *	p1,
		a_point2 const *	p2,
		a_point2 const *	p3,
		a_point2 *	pc )

compute the circumcenter and circumradius of a triangle defined by three 2D points.

Parameters

[in]	p1	is the first 2D point on circle
[in]	p2	is the second 2D point on circle
[in]	p3	is the third 2D point on circle
[out]	pc	stores the circumcenter

Returns: the circumradius

Return values

0	if points are collinear

See also: a_point2_tricir2

◆ a_point2_tricir2()

a_real a_point2_tricir2	(	a_point2 const *	p1,
		a_point2 const *	p2,
		a_point2 const *	p3,
		a_point2 *	pc )

compute the circumcenter and squared circumradius of a triangle defined by three 2D points.

Solves for center (x,y) where distances to all three points are equal:

\[ (x_1-x)^2+(y_1-y)^2=(x_2-x)^2+(y_2-y)^2=(x_3-x)^2+(y_3-y)^2 \]

This simplifies to:

\begin{cases} 2(x_2−x_1)dx + 2(y_2−y_1)dy = (x_2-x_1)^2 + (y_2-y_1)^2 \\ 2(x_3−x_1)dx + 2(y_3−y_1)dy = (x_3-x_1)^2 + (y_3-y_1)^2 \end{cases}

Where

\begin{aligned} dx &= x - x_1 \\ dy &= y - y_1 \end{aligned}

Matrix form:

\[ 2\begin{bmatrix} x_{21}&y_{21} \\ x_{31}&y_{31} \end{bmatrix} \begin{bmatrix} dx\\dy \end{bmatrix} =\begin{bmatrix} b_{21} \\ b_{31} \end{bmatrix} \]

Where

\begin{aligned} x_{ji}&=x_j-x_i \\ y_{ji}&=y_j-y_i \\ b_{ji}&=x_{ji}^2+y_{ji}^2 \end{aligned}

Explicit Solution (Cramer's Rule):

\begin{aligned} dx=\frac{b_{21}y_{31}-y_{21}b_{31}}{2(x_{21}y_{31}-y_{21}x_{31})} \\ dy=\frac{x_{21}b_{31}-b_{21}x_{31}}{2(x_{21}y_{31}-y_{21}x_{31})} \end{aligned}

Radius (r):

\[ r = \sqrt{dx^2+dy^2} \]

Parameters

[in]	p1	is the first 2D point on circle
[in]	p2	is the second 2D point on circle
[in]	p3	is the third 2D point on circle
[out]	pc	stores the circumcenter

Returns: the squared circumradius

Return values

0	if points are collinear

◆ set()

void a_vector2::set	(	a_point2 const &	p,
		a_point2 const &	q )

inline

set a 2D vector as the difference from point p to point q.

See also: a_vector2_set

Data Structures

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

◆ a_point2_

◆ A_POINT2_C

◆ a_point2_c

Function Documentation

◆ a_point2_cmpx()

◆ a_point2_cmpy()

◆ a_point2_dist()

◆ a_point2_dist2()

◆ a_point2_lerp()

◆ a_point2_maxdist()

◆ a_point2_mindist()

◆ a_point2_norm()

◆ a_point2_norm2()

◆ a_point2_tricir()

◆ a_point2_tricir2()

◆ set()