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.Dd December 21, 2022
.Dt M_CIRCLE 3
.Os Agar 1.7
.Sh NAME
.Nm M_Circle
.Nd Agar-Math circle structure
.Sh SYNOPSIS
.Bd -literal
#include <agar/core.h>
#include <agar/gui.h>
#include <agar/math/m.h>
.Ed
.Sh DESCRIPTION
.\" MANLINK(M_Circle2)
.\" IMAGE(/widgets/VG_Circle.png, "A circle")
The
.Ft M_Circle2
structure describes a circle in R^2 in terms of an origin point
.Va p
and radius
.Va r :
.Bd -literal
.\" SYNTAX(c)
typedef struct m_circle2 {
	M_Vector2 p;
	M_Real r;
} M_Circle2;
.Ed
.\" MANLINK(M_Circle3)
.Pp
Similarly,
.Ft M_Circle3
describes a circle in R^3:
.Bd -literal
.\" SYNTAX(c)
typedef struct m_circle3 {
	M_Vector3 p;
	M_Real r;
} M_Circle3;
.Ed
.Sh INITIALIZATION
.nr nS 1
.Ft M_Circle2
.Fn M_CircleFromPt "M_Vector2 p" "M_Real r"
.Pp
.Ft M_Circle2
.Fn M_CircleRead2 "AG_DataSource *ds"
.Pp
.Ft M_Circle3
.Fn M_CircleRead3 "AG_DataSource *ds"
.Pp
.Ft void
.Fn M_CircleWrite2 "AG_DataSource *ds" "M_Circle2 *C"
.Pp
.Ft void
.Fn M_CircleWrite3 "AG_DataSource *ds" "M_Circle3 *C"
.Pp
.Ft M_Circle2
.Fn M_CIRCLE2_INITIALIZER "M_Real x" "M_Real y" "M_Real r"
.Pp
.Ft M_Circle3
.Fn M_CIRCLE3_INITIALIZER "M_Real x" "M_Real y" "M_Real z" "M_Real r"
.Pp
.nr nS 0
The
.Fn M_CircleFromPt
function returns a
.Ft M_Circle2
describing a circle of radius
.Fa r
centered at point
.Ft p .
.Pp
The
.Fn M_CircleRead[23]
and
.Fn M_CircleWrite[23]
functions read or write a circle structure from/to an
.Xr AG_DataSource 3 .
.Pp
The macros
.Fn M_CIRCLE2_INITIALIZER
and
.Fn M_CIRCLE3_INITIALIZER
expand to static initializers for
.Ft M_Circle2
and
.Ft M_Circle3 ,
respectively.
.Sh COMPUTATIONS
.nr nS 1
.Ft M_Real
.Fn M_CirclePointDistance2 "M_Circle2 C" "M_Vector2 p"
.Pp
.Ft M_GeomSet2
.Fn M_IntersectCircleCircle2 "M_Circle2 C1" "M_Circle2 C2"
.Pp
.Ft M_GeomSet2
.Fn M_IntersectCircleLine2 "M_Circle2 C" "M_Line2 L"
.Pp
.nr nS 0
The
.Fn M_CirclePointDistance2
routine computes the minimal distance between a circle
.Fa C
and a point
.Fa p .
.Pp
.Fn M_IntersectCircleCircle2
computes the intersection of two circles in R^2 and returns an
.Xr M_GeomSet2 3
describing the intersection.
The returned set may be:
.Bl -bullet -compact
.It
Two points.
.It
One point (circles are tangent up to machine precision).
.It
A circle (circles are equivalent).
.It
The empty set.
.El
.Pp
The
.Fn M_IntersectCircleCircle2
function computes the intersection of a circle and a line in R^2.
The returned set may be:
.Bl -bullet -compact
.It
Two points.
.It
One point (line is tangent up to machine precision).
.It
The empty set.
.El
.Sh SEE ALSO
.Xr AG_DataSource 3 ,
.Xr AG_Intro 3 ,
.Xr M_Geometry 3 ,
.Xr M_Plane 3 ,
.Xr M_Polygon 3 ,
.Xr M_Rectangle 3 ,
.Xr M_Sphere 3 ,
.Xr M_Triangle 3 ,
.Xr M_Vector 3
.Sh HISTORY
The
.Nm
structure first appeared in Agar 1.3.4.