/*
# vector.h: operations on vectors and points.
#
# Copyright (C) 1992, 2011 Free Software Foundation, Inc.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
*/


#ifndef VECTOR_H
#define VECTOR_H

#include "types.h"


/* Our vectors are represented as displacements along the x and y axes.  */

typedef struct
{
  real dx, dy;
} vector_type;


/* Consider a point as a vector from the origin.  */
extern const vector_type make_vector (const real_coordinate_type);

/* And a vector as a point, i.e., a displacement from the origin.  */
extern const real_coordinate_type vector_to_point (const vector_type);


/* Definitions for these common operations can be found in any decent
   linear algebra book, and most calculus books.  */

extern const real magnitude (const vector_type);
extern const vector_type normalize (const vector_type);

extern const vector_type Vadd (const vector_type, const vector_type);
extern const real Vdot (const vector_type, const vector_type);
extern const vector_type Vmult_scalar (const vector_type, const real);
extern const real Vangle (const vector_type in, const vector_type out);

/* These operations could have been named `P..._vector' just as well as
   V..._point, so we may as well allow both names.  */
#define Padd_vector Vadd_point
extern const real_coordinate_type Vadd_point
  (const real_coordinate_type, const vector_type);

#define Psubtract_vector Vsubtract_point
extern const real_coordinate_type Vsubtract_point
  (const real_coordinate_type, const vector_type);

/* This returns the rounded sum.  */
#define IPadd_vector Vadd_int_point
extern const coordinate_type Vadd_int_point
  (const coordinate_type, const vector_type);

/* Take the absolute value of both components.  */
extern const vector_type Vabs (const vector_type);



/* Operations on points with real coordinates.  It is not orthogonal,
   but more convenient, to have the subtraction operator return a
   vector, and the addition operator return a point.  */
extern const vector_type Psubtract
  (const real_coordinate_type, const real_coordinate_type);

/* These are heavily used in spline fitting, so we define them as macros
   instead of functions.  */
#define Padd(rc1, rc2)							\
  ((real_coordinate_type) { (rc1).x + (rc2).x, (rc1).y + (rc2).y })
#define Pmult_scalar(rc, r)						\
  ((real_coordinate_type) { (rc).x * (r), (rc).y * (r) })

#if 0
extern const real_coordinate_type Padd (real_coordinate_type,
                                        real_coordinate_type);
extern const real_coordinate_type Pmult_scalar (real_coordinate_type, real);
#endif

/* Similarly, for points with integer coordinates; here, a subtraction
   operator that does return another point is useful.  */
extern const vector_type IPsubtract
  (const coordinate_type, const coordinate_type);
extern const coordinate_type IPsubtractP
  (const coordinate_type, const coordinate_type);
extern const coordinate_type IPadd
  (const coordinate_type, const coordinate_type);
extern const coordinate_type IPmult_scalar (const coordinate_type, const int);
extern const real_coordinate_type IPmult_real
  (const coordinate_type, const real);
extern const boolean IPequal (const coordinate_type, const coordinate_type);

#endif /* not VECTOR_H */