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/* vector.h: operations on vectors and points. */
#ifndef VECTOR_H
#define VECTOR_H
#include "types.h"
#include "exception.h"
/* Our vectors are represented as displacements along the x and y axes. */
typedef struct
{
at_real dx, dy, dz;
} vector_type;
/* Consider a point as a vector from the origin. */
extern vector_type make_vector (const at_real_coord);
/* And a vector as a point, i.e., a displacement from the origin. */
extern at_real_coord 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 at_real magnitude (const vector_type);
extern vector_type normalize (const vector_type);
extern vector_type Vadd (const vector_type, const vector_type);
extern at_real Vdot (const vector_type, const vector_type);
extern vector_type Vmult_scalar (const vector_type, const at_real);
extern at_real Vangle (const vector_type in, const vector_type out, at_exception_type * exp);
/* 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 at_real_coord Vadd_point
(const at_real_coord, const vector_type);
#define Psubtract_vector Vsubtract_point
extern at_real_coord Vsubtract_point
(const at_real_coord, const vector_type);
/* This returns the rounded sum. */
#define IPadd_vector Vadd_int_point
extern at_coord Vadd_int_point
(const at_coord, 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 at_real_coord, const at_real_coord);
/* These are heavily used in spline fitting. */
extern at_real_coord Padd (const at_real_coord,
const at_real_coord);
extern at_real_coord Pmult_scalar (const at_real_coord, const at_real);
/* Similarly, for points with integer coordinates; here, a subtraction
operator that does return another point is useful. */
extern vector_type IPsubtract
(const at_coord, const at_coord);
extern at_coord IPsubtractP
(const at_coord, const at_coord);
extern at_coord IPadd
(const at_coord, const at_coord);
extern at_coord IPmult_scalar (const at_coord, const int);
extern at_real_coord IPmult_real
(const at_coord, const at_real);
extern at_bool IPequal (const at_coord, const at_coord);
#endif /* not VECTOR_H */
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