GiftWrapping.kt

/*
 * Copyright (c) 2017 Kotlin Algorithm Club
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */

package io.uuddlrlrba.ktalgs.geometry.convexhull

import io.uuddlrlrba.ktalgs.datastructures.Stack
import io.uuddlrlrba.ktalgs.geometry.Point

class GiftWrapping: ConvexHullAlgorithm {
    override fun convexHull(points: Array<Point>): Collection<Point> {
        if (points.size < 3) throw IllegalArgumentException("there must be at least 3 points")

        val hull = Stack<Point>()

        // Find the leftmost point
        var l = 0
        points.indices
                .asSequence()
                .filter { points[it].x < points[l].x }
                .forEach { l = it }

        // Start from leftmost point, keep moving counterclockwise
        // until reach the start point again.  This loop runs O(h)
        // times where h is number of points in result or output.
        var p = l
        var q: Int
        do {
            // Add current point to result
            hull.push(points[p])

            // Search for a point 'q' such that orientation(p, x,
            // q) is counterclockwise for all points 'x'. The idea
            // is to keep track of last visited most counterclock-
            // wise point in q. If any point 'i' is more counterclock-
            // wise than q, then update q.
            q = ( p+ 1) % points.size
            points.indices
                    .asSequence()
                    .filter { Point.orientation(points[p], points[it], points[q]) < 0 }
                    .forEach { q = it }

            // Now q is the most counterclockwise with respect to p
            // Set p as q for next iteration, so that q is added to
            // result 'hull'
            p = q

        } while (p != l)  // While we don't come to first point

        return hull
    }
}