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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 */