/*

    ......... 2015 Ivan Mahonin

    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 of the License, 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 <http://www.gnu.org/licenses/>.

*/

using System;

using System.Drawing;

namespace Contours {

    public static class Geometry {

        public enum IntersectionType {

            None,

            Cross,

            Identical,

            Inverted,

            Touch_a0,

            Touch_a1,

            Touch_b0,

            Touch_b1,

            Touch_a0_b0,

            Touch_a0_b1,

            Touch_a1_b0,

            Touch_a1_b1,

            Along_a0_b0_a1_b1,

            Along_a0_b0_b1_a1,

            Along_a0_b1_a1_b0,

            Along_a0_b1_b0_a1,

            Along_b0_a0_a1_b1,

            Along_b0_a0_b1_a1,

            Along_b1_a0_a1_b0,

            Along_b1_a0_b0_a1

        }

        // Compare to points place at line base0-base1

        public static int comparePointsAtLine(Point a0, Point a1, Point base0, Point base1) {

            if (base0.X < base1.X && a0.X < a1.X) return -1;

            if (base0.X < base1.X && a1.X < a0.X) return  1;

            if (base1.X < base0.X && a0.X < a1.X) return  1;

            if (base1.X < base0.X && a1.X < a0.X) return -1;

            if (base0.Y < base1.Y && a0.Y < a1.Y) return -1;

            if (base0.Y < base1.Y && a1.Y < a0.Y) return  1;

            if (base1.Y < base0.Y && a0.Y < a1.Y) return  1;

            if (base1.Y < base0.Y && a1.Y < a0.Y) return -1;

            return 0;

        }

        public static bool isPointAtLine(Point p, Point p0, Point p1) {

            if (p == p0 || p == p1)

                return true;

            if (p0 == p1)

                return false;

            if ((long)(p.Y-p0.Y)*(long)(p1.X-p0.X) != (long)(p.X-p0.X)*(long)(p1.Y-p0.Y))

                return false;

            if (p1.X > p0.X)

                return p.X >= p0.X && p.X <= p1.X;

            if (p1.X < p0.X)

                return p.X >= p1.X && p.X <= p0.X;

            if (p1.Y > p0.Y)

                return p.Y >= p0.Y && p.Y <= p1.Y;

            //if (p1.Y < p0.Y)

                return p.Y >= p1.Y && p.Y <= p0.Y;

        }

        public static IntersectionType findIntersection(Point a0, Point a1, Point b0, Point b1, out Point c) {

            c = new Point(0, 0);

            Point da = new Point(a1.X - a0.X, a1.Y - a0.Y);

            Point db = new Point(b1.X - b0.X, b1.Y - b0.Y);

            if (a0.X == b0.X && a0.Y == b0.Y && a1.X == b1.X && a1.Y == b1.Y)

                return IntersectionType.Identical;

            if (a0.X == b1.X && a0.Y == b1.Y && a1.X == b0.X && a1.Y == b0.Y)

                return IntersectionType.Inverted;

            long divider = (long)da.X*(long)db.Y - (long)db.X*(long)da.Y;

            if (divider == 0) {

                if ((long)da.X*(long)(b0.Y - a0.Y) != (long)da.Y*(long)(b0.X - a0.X))

                    return IntersectionType.None;

                int a0b0 = comparePointsAtLine(a0, b0, a0, a1);

                int a0b1 = comparePointsAtLine(a0, b1, a0, a1);

                int a1b0 = comparePointsAtLine(a1, b0, a0, a1);

                int a1b1 = comparePointsAtLine(a1, b1, a0, a1);

                int b0b1 = comparePointsAtLine(b0, b1, a0, a1);

                int b0a0 = -a0b0;

                int b0a1 = -a1b0;

                int b1a0 = -a0b1;

                int b1a1 = -a1b1;

                int b1b0 = -b0b1;

                // a0a1b0b1

                if (a1b0 == 0 && b0b1 <= 0)

                    return IntersectionType.Touch_a1_b0;

                // a0a1b1b0

                if (a1b1 == 0 && b1b0 <= 0)

                    return IntersectionType.Touch_a1_b1;

                // b0b1a0a1

                if (b0b1 <= 0 && b1a0 == 0)

                    return IntersectionType.Touch_a0_b1;

                // b1b0a0a1

                if (b1b0 <= 0 && b0a0 == 0)

                    return IntersectionType.Touch_a0_b0;

                if (a0b0 <= 0 && b0a1 <= 0 && a1b1 <= 0)

                    return IntersectionType.Along_a0_b0_a1_b1;

                if (a0b0 <= 0 && b0b1 <= 0 && b1a1 <= 0)

                    return IntersectionType.Along_a0_b0_b1_a1;

                if (a0b1 <= 0 && b1a1 <= 0 && a1b0 <= 0)

                    return IntersectionType.Along_a0_b1_a1_b0;

                if (a0b1 <= 0 && b1b0 <= 0 && b0a1 <= 0)

                    return IntersectionType.Along_a0_b1_b0_a1;

                if (b0a0 <= 0 && /*  a0a1  */ a1b1 <= 0)

                    return IntersectionType.Along_b0_a0_a1_b1;

                if (b0a0 <= 0 && a0b1 <= 0 && b1a1 <= 0)

                    return IntersectionType.Along_b0_a0_b1_a1;

                if (b1a0 <= 0 && /*  a0a1  */ a1b0 <= 0)

                    return IntersectionType.Along_b1_a0_a1_b0;

                if (b1a0 <= 0 && a0b0 <= 0 && b0a1 <= 0)

                    return IntersectionType.Along_b1_a0_b0_a1;

                return IntersectionType.None;

            }

            if (a0.X == b0.X && a0.Y == b0.Y)

                return IntersectionType.Touch_a0_b0;

            if (a0.X == b1.X && a0.Y == b1.Y)

                return IntersectionType.Touch_a0_b1;

            if (a1.X == b0.X && a1.Y == b0.Y)

                return IntersectionType.Touch_a1_b0;

            if (a1.X == b1.X && a1.Y == b1.Y)

                return IntersectionType.Touch_a1_b1;

            long numeratorX = (long)da.X*((long)b1.Y*(long)b0.X - (long)b0.Y*(long)b1.X)

                            - (long)db.X*((long)a1.Y*(long)a0.X - (long)a0.Y*(long)a1.X);

            long numeratorY = (long)db.Y*((long)a1.X*(long)a0.Y - (long)a0.X*(long)a1.Y)

                            - (long)da.Y*((long)b1.X*(long)b0.Y - (long)b0.X*(long)b1.Y);

            Point p = new Point((int)(numeratorX/divider), (int)(numeratorY/divider));

            if ( comparePointsAtLine(p, a0, a0, a1) < 0

              || comparePointsAtLine(p, a1, a0, a1) > 0

              || comparePointsAtLine(p, b0, b0, b1) < 0

              || comparePointsAtLine(p, b1, b0, b1) > 0 )

                return IntersectionType.None;

            if (p.X == a0.X && p.Y == a0.Y)

                return IntersectionType.Touch_a0;

            if (p.X == a1.X && p.Y == a1.Y)

                return IntersectionType.Touch_a1;

            if (p.X == b0.X && p.Y == b0.Y)

                return IntersectionType.Touch_b0;

            if (p.X == b1.X && p.Y == b1.Y)

                return IntersectionType.Touch_b1;

            c = p;

            return IntersectionType.Cross;

        }

        public static bool isCCW(Point a, Point b, Point c) {

            long d = (long)a.X*(long)c.Y - (long)a.Y*(long)c.X;

            // angle AC < 180 deg

            if (d > 0)

                return (long)a.X*(long)b.Y >= (long)a.Y*(long)b.X

                    && (long)c.X*(long)b.Y <= (long)c.Y*(long)b.X;

            // angle AC > 180 deg

            if (d < 0)

                return (long)a.X*(long)b.Y >= (long)a.Y*(long)b.X

                    || (long)c.X*(long)b.Y <= (long)c.Y*(long)b.X;

            // angle AC == 180 deg

            if ((a.X >= 0) != (c.X >= 0) || (a.Y >= 0) != (c.Y >= 0))

                return (long)a.X*(long)b.Y >= (long)a.Y*(long)b.X;

            // angle AC == 0 deg

            return true;

        }

        public static bool isCCW(Point center, Point a, Point b, Point c) {

            return isCCW(

                new Point(a.X - center.X, a.Y - center.Y),

                new Point(b.X - center.X, b.Y - center.Y),

                new Point(c.X - center.X, c.Y - center.Y) );

        }

        public static void makeLongestLine(Point p0, ref Point p1) {

            int MaxValue = int.MaxValue >> 1;

            Point direction = new Point(p1.X - p0.X, p1.Y - p0.Y);

            int amplifierX =

                direction.X > 0 ? (MaxValue - p0.X)/direction.X + 1

              : direction.X < 0 ? (MaxValue + p0.X)/(-direction.X) + 1

              : int.MaxValue;

            int amplifierY =

                direction.Y > 0 ? (MaxValue - p0.Y)/direction.Y + 1

              : direction.Y < 0 ? (MaxValue + p0.Y)/(-direction.Y) + 1

              : int.MaxValue;

            int amplifier = Math.Min(amplifierX, amplifierY);

            p1 = new Point(

                    p0.X + direction.X*amplifier,

                    p0.Y + direction.Y*amplifier );

        }

    }

}