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/* vector.h: operations on vectors and points.
*
* Copyright (C) 1992 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, 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 <https://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 vector_type make_vector (const real_coordinate_type);
/* And a vector as a point, i.e., a displacement from the origin. */
extern 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 real magnitude (const vector_type);
extern vector_type normalize (const vector_type);
extern vector_type Vadd (const vector_type, const vector_type);
extern real Vdot (const vector_type, const vector_type);
extern vector_type Vmult_scalar (const vector_type, const real);
extern 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 real_coordinate_type Vadd_point
(const real_coordinate_type, const vector_type);
#define Psubtract_vector Vsubtract_point
extern real_coordinate_type Vsubtract_point
(const real_coordinate_type, const vector_type);
/* This returns the rounded sum. */
#define IPadd_vector Vadd_int_point
extern coordinate_type Vadd_int_point
(const coordinate_type, const vector_type);
/* Take the absolute value of both components. */
extern 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 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) })
/* Similarly, for points with integer coordinates; here, a subtraction
operator that does return another point is useful. */
extern vector_type IPsubtract
(const coordinate_type, const coordinate_type);
extern coordinate_type IPsubtractP
(const coordinate_type, const coordinate_type);
extern coordinate_type IPadd
(const coordinate_type, const coordinate_type);
extern coordinate_type IPmult_scalar (const coordinate_type, const int);
extern real_coordinate_type IPmult_real
(const coordinate_type, const real);
extern boolean IPequal (const coordinate_type, const coordinate_type);
#endif /* not VECTOR_H */
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