/* Copyright (C) 2001-2021 Artifex Software, Inc.
   All Rights Reserved.

   This software is provided AS-IS with no warranty, either express or
   implied.

   This software is distributed under license and may not be copied,
   modified or distributed except as expressly authorized under the terms
   of the license contained in the file LICENSE in this distribution.

   Refer to licensing information at http://www.artifex.com or contact
   Artifex Software, Inc.,  1305 Grant Avenue - Suite 200, Novato,
   CA 94945, U.S.A., +1(415)492-9861, for further information.
*/


/* pggeom.c */
/* HP-GL/2 geometry routines */

#include "stdio_.h"
#include "pggeom.h"
#include "gxfarith.h"           /* for gs_sincos */

/* HAS most of these computations require more error checking */

/* ------ Lines, angles, arcs, and chords ------ */

/* compute the angle between 0 and 2*PI given the slope */
double
hpgl_compute_angle(double dx, double dy)
{
    double alpha = atan2(dy, dx);

    return (alpha < 0 ? alpha + M_PI * 2.0 : alpha);
}

/* compute the center of an arc given 3 points on the arc */
int
hpgl_compute_arc_center(double x1, double y1, double x2, double y2,
                        double x3, double y3, double * pcx, double * pcy)
{
    double px2, py2, dx2, dy2, px3, py3, dx3, dy3;
    double denom, t2;

    /*
     * The center is the intersection of the perpendicular bisectors
     * of the 3 chords.  Any two will do for the computation.
     * (For greatest numerical stability, we should probably choose
     * the two outside chords, but this is a refinement that we will
     * leave for the future.)
     * We define each bisector by a line with the equations
     *      xi = pxi + ti * dxi
     *      yi = pyi + ti * dyi
     * where i is 2 or 3.
     */

#define compute_bisector(px, py, dx, dy, xa, ya, xb, yb)\
  (px = (xa + xb) / 2, py = (ya + yb) / 2,\
   dx = (ya - yb), dy = (xb - xa) /* 90 degree rotation (either way is OK) */)

    compute_bisector(px2, py2, dx2, dy2, x1, y1, x2, y2);
    compute_bisector(px3, py3, dx3, dy3, x1, y1, x3, y3);

#undef compute_bisector

    /*
     * Now find the intersections by solving for t2 or t3:
     *      px2 + t2 * dx2 = px3 + t3 * dx3
     *      py2 + t2 * dy2 = py3 + t3 * dy3
     * i.e., in standard form,
     *      t2 * dx2 - t3 * dx3 = px3 - px2
     *      t2 * dy2 - t3 * dy3 = py3 - py2
     * The solution of
     *      a*x + b*y = c
     *      d*x + e*y = f
     * is
     *      denom = a*e - b*d
     *      x = (c*e - b*f) / denom
     *      y = (a*f - c*d) / denom
     */
    denom = dx3 * dy2 - dx2 * dy3;
    if (fabs(denom) < 1.0e-6)
        return -1;              /* degenerate */

    t2 = ((px3 - px2) * (-dy3) - (-dx3) * (py3 - py2)) / denom;
    *pcx = px2 + t2 * dx2;
    *pcy = py2 + t2 * dy2;
    return 0;
}

/* compute the coordinates of a point on an arc */
int
hpgl_compute_arc_coords(double radius, double center_x, double center_y,
                        double angle, double * px, double * py)
{
    gs_sincos_t sincos;

    gs_sincos_degrees(angle, &sincos);
    *px = radius * sincos.cos + center_x;
    *py = radius * sincos.sin + center_y;
    return 0;
}

/* given a start point, angle (degrees) and magnitude of a vector
   compute its endpoints */
int
hpgl_compute_vector_endpoints(double magnitude, double x, double y,
                              double angle_degrees, double * endx,
                              double * endy)
{
    return hpgl_compute_arc_coords(magnitude, x, y,
                                   angle_degrees, endx, endy);
}
