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M_LINE(3)		     Library Functions Manual		       M_LINE(3)

NAME
     M_Line -- Agar-Math line segment / half-line structure

SYNOPSIS
     #include <agar/core.h>
     #include <agar/gui.h>
     #include <agar/math/m.h>

DESCRIPTION
     The  M_Line2  structure  describes a line segment, an Euclidean vector or a
     half-line in R^2.	An M_Line is defined by an origin point p, a  normalized
     direction	vector	d and a real length t (which can be set to M_INFINITY in
     order to express a half-line).  The structure is defined as:

     typedef struct m_line2 {
	     M_Vector2 p;
	     M_Vector2 d;
	     M_Real t;
     } M_Line2;

     Similarly, M_Line3 describes a line segment, an Euclidean vector or a half-
     line in R^3:

     typedef struct m_line3 {
	     M_Vector3 p;
	     M_Vector3 d;
	     M_Real t;
     } M_Line3;

INITIALIZATION
     M_Line2 M_LineFromPtDir2(M_Vector2 p, M_Vector2 d, M_Real t)

     M_Line3 M_LineFromPtDir3(M_Vector3 p, M_Vector3 d, M_Real t)

     M_Line2 M_LineFromPts2(M_Vector2 p1, M_Vector2 p2)

     M_Line3 M_LineFromPts3(M_Vector3 p1, M_Vector3 p2)

     M_Line2 M_LineRead2(AG_DataSource *ds)

     M_Line3 M_LineRead3(AG_DataSource *ds)

     void M_LineWrite2(AG_DataSource *ds, M_Line2 *L)

     void M_LineWrite3(AG_DataSource *ds, M_Line3 *L)

     M_Line2 M_LINE2_INITIALIZER(M_Real px, M_Real py,	M_Real	nx,  M_Real  ny,
     M_Real t)

     M_Line3  M_LINE3_INITIALIZER(M_Real  px,  M_Real  py, M_Real pz, M_Real nx,
     M_Real ny, M_Real nz, M_Real t)

     The functions M_LineFromPtDir2() and M_LineFromPtDir3() return  an  M_Line2
     or  M_Line3 describing a line segment a specified origin point p, direction
     vector d (of unit-length) and length t.  The endpoints of the line will  be
     p and (p + d*t).

     M_LineFromPts2() and M_LineFromPts3() return a line segment from two speci-
     fied endpoints p1 and p2.

     The  M_LineRead[23]()  and M_LineWrite[23]() functions read or write a line
     structure from/to an AG_DataSource(3).

     The macros M_LINE2_INITIALIZER() and M_LINE3_INITIALIZER() expand to static
     initializers for M_Line2 and M_Line3, respectively.

OPERATIONS
     M_Vector2 M_LineInitPt2(M_Line2 L)

     M_Vector2 M_LineTermPt2(M_Line2 L)

     M_Vector3 M_LineInitPt3(M_Line3 L)

     M_Vector3 M_LineTermPt3(M_Line3 L)

     void M_LineToPts2(M_Line2 L, M_Vector2 *p1, M_Vector2 *p2)

     void M_LineToPts3(M_Line3 L, M_Vector3 *p1, M_Vector3 *p2)

     void M_LineIsRay2(M_Line2 L)

     void M_LineIsRay3(M_Line3 L)

     M_Real M_LinePointSide2(M_Line2 L, M_Vector2 p)

     M_Real M_LinePointDistance2(M_Line2 L, M_Vector2 p)

     M_Real M_LinePointDistance3(M_Line3 L, M_Vector3 p)

     M_Real M_LineLineAngle2(M_Line2 L1, M_Line2 L2)

     M_Real M_LineLineAngle3(M_Line3 L1, M_Line3 L2)

     M_Line2 M_LineParallel2(M_Line2 L, M_Real offset)

     M_Line3 M_LineParallel3(M_Line3 L, M_Real offset)

     M_Line2 M_LineProject2(M_Line3 L)

     M_Line3 M_LineProject3(M_Line2 L)

     int M_LineLineIntersect2(M_Line2 L1, M_Line2 L2, M_Vector2 *x)

     int M_LineLineShortest3(M_Line3 L1, M_Line3 L2, M_Line3 *Ls)

     The M_LineInitPt[23]() routines return the initial point (i.e., the p  vec-
     tor).   M_LineTermPt[23]()  routines  return  the terminal point (i.e., p +
     d*t).  The M_LineToPts[23]() functions return the two endpoints of  line  L
     into p1 and p2.

     M_LineIsRay2() and M_LineIsRay3() evaluate to 1 of the line is defined as a
     half-line (i.e., t is M_INFINITY).

     M_LinePointSide2()  tests whether point p lies on the left (<0), is coinci-
     dent (==0), or is on the right (>0) of the line L.  The direction is deter-
     mined by the handedness of the line.

     The M_LinePointDistance2() and M_LinePointDistance3() routines compute  the
     minimal distance between a line L and a point p.

     M_LineLineAngle2() and M_LineLineAngle3() return the counterclockwise angle
     (in radians) between L1 and L2.  The angle is computed as the arc cosine of
     the dot product of the direction vectors of the two lines.

     The  M_LineParallel[23]()	functions  return a line parallel to L, with the
     specified offset amount.  The direction of the offset is determined by  the
     handedness of L.

     M_LineProject2()  computes  a  line in R^2 from the projection onto the X-Y
     plane of a specified line in R^3.	M_LineProject3() returns the  projection
     of a line in R^2 onto the X-Y plane in R^3.

     The  M_LineLineIntersect2()  function  computes the intersection point x of
     two lines in R^2.	If there is a solution, the function returns  1,  other-
     wise it returns 0.

     The  M_LineLineShortest3()  function  computes the shortest line segment Ls
     connecting two lines in R^3.  Returns 1 if there is a solution, 0 if  there
     is not.

SEE ALSO
     AG_DataSource(3),	 AG_Intro(3),  M_Circle(3),  M_Geometry(3),  M_Plane(3),
     M_Polygon(3), M_Rectangle(3), M_Sphere(3), M_Triangle(3), M_Vector(3)

HISTORY
     The M_Line structure first appeared in Agar 1.3.4.

Agar 1.7			December 21, 2022		       M_LINE(3)

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