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.Dd December 21, 2022
.Dt M_PLANE 3
.Os Agar 1.7
.Sh NAME
.Nm M_Line
.Nd Agar-Math plane structure
.Sh SYNOPSIS
.Bd -literal
#include <agar/core.h>
#include <agar/gui.h>
#include <agar/math/m.h>
.Ed
.Sh DESCRIPTION
The
.Ft M_Plane
structure describes a plane in R^3 (Ax+By+Cz+D=0):
.Bd -literal
.\" SYNTAX(c)
typedef struct m_plane {
	M_Vector3 n;		/* Normal vector */
	M_Real d;		/* Distance to origin */
} M_Plane;
.Ed
.Pp
The plane satisfies the equation A(n.x) + B(n.y) + C(n.z) = d.
.Sh INITIALIZATION
.nr nS 1
.Ft M_Plane
.Fn M_PlaneFromPts "M_Vector3 p1" "M_Vector p2" "M_Vector p3"
.Pp
.Ft M_Plane
.Fn M_PlaneFromParallel "M_Plane P" "M_Real d"
.Pp
.Ft M_Plane
.Fn M_PlaneRead "AG_DataSource *ds"
.Pp
.Ft void
.Fn M_PlaneWrite "AG_DataSource *ds" "M_Plane *P"
.Pp
.Ft M_Plane
.Fn M_PLANE_INITIALIZER "M_Real a" "M_Real b" "M_Real c" "M_Real d"
.Pp
.nr nS 0
The
.Fn M_PlaneFromPts
function returns a plane from three (non-colinear) points
.Fa p1 ,
.Fa p2
and
.Fa p3 .
.Fn M_PlaneFromParallel
returns the parallel plane at distance
.Fa d
from the specified plane
.Fa P .
.Pp
The
.Fn M_PlaneRead
and
.Fn M_PlaneWrite
functions read or write a plane structure from/to an
.Xr AG_DataSource 3 .
.Pp
The macro
.Fn M_PLANE_INITIALIZER
expands to a static initializer for a
.Ft M_Plane
from the coefficients of the plane equation
.Fa a ,
.Fa b ,
.Fa c ,
.Fa d .
.Sh TESTS
.nr nS 1
.Ft M_Real
.Fn M_PlaneVectorAngle "M_Plane P" "M_Vector3 v"
.Pp
.nr nS 0
The
.Fn M_PlaneVectorAngle
function computes the angle between the plane and specified vector,
in radians.
.Sh SEE ALSO
.Xr AG_DataSource 3 ,
.Xr AG_Intro 3 ,
.Xr M_Circle 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.