/* cairo - a vector graphics library with display and print output

 *

 * Copyright © 2002 University of Southern California

 *

 * This library is free software; you can redistribute it and/or

 * modify it either under the terms of the GNU Lesser General Public

 * License version 2.1 as published by the Free Software Foundation

 * (the "LGPL") or, at your option, under the terms of the Mozilla

 * Public License Version 1.1 (the "MPL"). If you do not alter this

 * notice, a recipient may use your version of this file under either

 * the MPL or the LGPL.

 *

 * You should have received a copy of the LGPL along with this library

 * in the file COPYING-LGPL-2.1; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA

 * You should have received a copy of the MPL along with this library

 * in the file COPYING-MPL-1.1

 *

 * The contents of this file are subject to the Mozilla Public License

 * Version 1.1 (the "License"); you may not use this file except in

 * compliance with the License. You may obtain a copy of the License at

 * http://www.mozilla.org/MPL/

 *

 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY

 * OF ANY KIND, either express or implied. See the LGPL or the MPL for

 * the specific language governing rights and limitations.

 *

 * The Original Code is the cairo graphics library.

 *

 * The Initial Developer of the Original Code is University of Southern

 * California.

 *

 * Contributor(s):

 *	Carl D. Worth <cworth@cworth.org>

 */

#include "cairoint.h"

#include "cairo-box-inline.h"

#include "cairo-slope-private.h"

cairo_bool_t

			  const cairo_point_t *b,

			  const cairo_point_t *c,

			  const cairo_point_t *d,

			  const cairo_box_t *box)

{

    cairo_box_t bounds;

    {

    }

    {

    }

#if 0 /* worth refining? */

    bounds.p2 = bounds.p1 = *a;

    _cairo_box_add_curve_to (&bounds, b, c, d);

    if (bounds.p2.x <= box->p1.x || bounds.p1.x >= box->p2.x ||

	bounds.p2.y <= box->p1.y || bounds.p1.y >= box->p2.y)

    {

	return FALSE;

    }

#endif

}

cairo_bool_t

		    cairo_spline_add_point_func_t add_point_func,

		    void *closure,

		    const cairo_point_t *a, const cairo_point_t *b,

		    const cairo_point_t *c, const cairo_point_t *d)

{

    /* If both tangents are zero, this is just a straight line */

    else

    else

    /* XXX if the initial, final and vector are all equal, this is just a line */

}

static cairo_status_t

			 const cairo_point_t *point,

			 const cairo_point_t *knot)

{

    cairo_point_t *prev;

    cairo_slope_t slope;

}

static void

{

static void

{

    cairo_point_t ab, bc, cd;

    cairo_point_t abbc, bccd;

    cairo_point_t final;

/* Return an upper bound on the error (squared) that could result from

 * approximating a spline as a line segment connecting the two endpoints. */

static double

{

    double bdx, bdy, berr;

    double cdx, cdy, cerr;

    /* We are going to compute the distance (squared) between each of the b

     * and c control points and the segment a-b. The maximum of these two

     * distances will be our approximation error. */

	/* Intersection point (px):

	 *     px = p1 + u(p2 - p1)

	 *     (p - px) ∙ (p2 - p1) = 0

	 * Thus:

	 *     u = ((p - p1) ∙ (p2 - p1)) / ∥p2 - p1∥²;

	 */

	double dx, dy, u, v;

	    /* bdx -= 0;

	     * bdy -= 0;

	     */

	} else {

	}

	    /* cdx -= 0;

	     * cdy -= 0;

	     */

	} else {

	}

    }

    else

}

static cairo_status_t

			      double tolerance_squared,

			      cairo_spline_t *result)

{

    cairo_spline_knots_t s2;

    cairo_status_t status;

}

cairo_status_t

{

    cairo_spline_knots_t s1;

    cairo_status_t status;

}

/* Note: this function is only good for computing bounds in device space. */

cairo_status_t

		     void *closure,

		     const cairo_point_t *p0, const cairo_point_t *p1,

		     const cairo_point_t *p2, const cairo_point_t *p3)

{

    double x0, x1, x2, x3;

    double y0, y1, y2, y3;

    double a, b, c;

    double t[4];

    cairo_status_t status;

    /* The spline can be written as a polynomial of the four points:

     *

     *   (1-t)³p0 + 3t(1-t)²p1 + 3t²(1-t)p2 + t³p3

     *

     * for 0≤t≤1.  Now, the X and Y components of the spline follow the

     * same polynomial but with x and y replaced for p.  To find the

     * bounds of the spline, we just need to find the X and Y bounds.

     * To find the bound, we take the derivative and equal it to zero,

     * and solve to find the t's that give the extreme points.

     *

     * Here is the derivative of the curve, sorted on t:

     *

     *   3t²(-p0+3p1-3p2+p3) + 2t(3p0-6p1+3p2) -3p0+3p1

     *

     * Let:

     *

     *   a = -p0+3p1-3p2+p3

     *   b =  p0-2p1+p2

     *   c = -p0+p1

     *

     * Gives:

     *

     *   a.t² + 2b.t + c = 0

     *

     * With:

     *

     *   delta = b*b - a*c

     *

     * the extreme points are at -c/2b if a is zero, at (-b±√delta)/a if

     * delta is positive, and at -b/a if delta is zero.

     */

#define ADD(t0) \

    { \

	double _t0 = (t0); \

	if (0 < _t0 && _t0 < 1) \

	    t[t_num++] = _t0; \

    }

#define FIND_EXTREMES(a,b,c) \

    { \

	if (a == 0) { \

	    if (b != 0) \

		ADD (-c / (2*b)); \

	} else { \

	    double b2 = b * b; \

	    double delta = b2 - a * c; \

	    if (delta > 0) { \

		cairo_bool_t feasible; \

		double _2ab = 2 * a * b; \

		/* We are only interested in solutions t that satisfy 0<t<1 \

		 * here.  We do some checks to avoid sqrt if the solutions \

		 * are not in that range.  The checks can be derived from: \

		 * \

		 *   0 < (-b±√delta)/a < 1 \

		 */ \

		if (_2ab >= 0) \

		    feasible = delta > b2 && delta < a*a + b2 + _2ab; \

		else if (-b / a >= 1) \

		    feasible = delta < b2 && delta > a*a + b2 + _2ab; \

		else \

		    feasible = delta < b2 || delta < a*a + b2 + _2ab; \

	        \

		if (unlikely (feasible)) { \

		    double sqrt_delta = sqrt (delta); \

		    ADD ((-b - sqrt_delta) / a); \

		    ADD ((-b + sqrt_delta) / a); \

		} \

	    } else if (delta == 0) { \

		ADD (-b / a); \

	    } \

	} \

    }

    /* Find X extremes */

    /* Find Y extremes */

	cairo_point_t p;

	double x, y;

        double t_1_0, t_0_1;

        double t_2_0, t_0_2;

        double t_3_0, t_2_1_3, t_1_2_3, t_0_3;

        /* Bezier polynomial */

    }

}