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.Dd December 21, 2022
.Dt M_TRIANGLE 3
.Os Agar 1.7
.Sh NAME
.Nm M_Triangle
.Nd Agar-Math triangle structure
.Sh SYNOPSIS
.Bd -literal
#include <agar/core.h>
#include <agar/gui.h>
#include <agar/math/m.h>
.Ed
.Sh DESCRIPTION
.\" MANLINK(M_Triangle2)
The
.Ft M_Triangle2
structure describes a triangle in R^2 in terms of three lines:
.Bd -literal
.\" SYNTAX(c)
typedef struct m_triangle2 {
	M_Line2 a, b, c;
} M_Triangle2;
.Ed
.\" MANLINK(M_Triangle3)
.Pp
Similarly,
.Ft M_Triangle3
describes a triangle in R^3:
.Bd -literal
.\" SYNTAX(c)
typedef struct m_triangle3 {
	M_Line3 a, b, c;
} M_Triangle3;
.Ed
.Sh INITIALIZATION
.nr nS 1
.Ft M_Triangle2
.Fn M_TriangleFromLines2 "M_Line2 L1" "M_Line2 L2" "M_Line2 L3"
.Pp
.Ft M_Triangle3
.Fn M_TriangleFromLines3 "M_Line3 L1" "M_Line3 L2" "M_Line3 L3"
.Pp
.Ft M_Triangle2
.Fn M_TriangleFromPts2 "M_Vector2 a" "M_Vector2 b" "M_Vector2 c"
.Pp
.Ft M_Triangle3
.Fn M_TriangleFromPts3 "M_Vector3 a" "M_Vector3 b" "M_Vector3 c"
.Pp
.Ft M_Triangle2
.Fn M_TriangleRead2 "AG_DataSource *ds"
.Pp
.Ft M_Triangle3
.Fn M_TriangleRead3 "AG_DataSource *ds"
.Pp
.Ft void
.Fn M_TriangleWrite2 "AG_DataSource *ds" "M_Triangle2 *T"
.Pp
.Ft void
.Fn M_TriangleWrite3 "AG_DataSource *ds" "M_Triangle3 *T"
.Pp
.Ft M_Triangle2
.Fn M_TRIANGLE2_INITIALIZER "M_Vector2 a" "M_Vector2 b" "M_Vector2 c"
.Pp
.Ft M_Triangle3
.Fn M_TRIANGLE3_INITIALIZER "M_Vector3 a" "M_Vector3 b" "M_Vector3 c"
.Pp
.nr nS 0
The functions
.Fn M_TriangleFromLines2
and
.Fn M_TriangleFromLines3
return an
.Ft M_Triangle2
or
.Ft M_Triangle3
describing a triangle in terms of three lines
.Fa L1 ,
.Fa L2
and
.Fa L3 .
The three lines must be non-colinear and their endpoints must coincide.
.Pp
.Fn M_TriangleFromPts2
and
.Fn M_TriangleFromPts3
return a triangle in terms of three (non-colinear) points
.Fa a ,
.Fa b ,
.Fa c .
.Pp
The
.Fn M_TriangleRead[23]
and
.Fn M_TriangleWrite[23]
functions read or write a triangle structure from/to an
.Xr AG_DataSource 3 .
.Pp
The macros
.Fn M_TRIANGLE2_INITIALIZER
and
.Fn M_TRIANGLE3_INITIALIZER
expand to static initializers for
.Ft M_Triangle2
and
.Ft M_Triangle3 ,
respectively.
.Sh COMPUTATIONS
.nr nS 1
.Ft int
.Fn M_PointInTriangle2 "M_Triangle2 T" "M_Vector2 p"
.Pp
.nr nS 0
The
.Fn M_PointInTriangle2
routine tests (using barycentric coordinates) whether point
.Fa p
lies within the triangle
.Fa T
and returns 1 if it does, otherwise 0.
.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.