[GitHub] [commons-geometry] darkma773r commented on a diff in pull request #218: Refactor hull

["darkma773r (via GitHub)" <gi...@apache.org>]

darkma773r commented on code in PR #218:
URL: https://github.com/apache/commons-geometry/pull/218#discussion_r1278700931


##########
commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/twod/hull/ConvexHull2D.java:
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@@ -0,0 +1,475 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (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.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.geometry.euclidean.twod.hull;
+
+import java.util.ArrayList;
+import java.util.Collection;
+import java.util.Collections;
+import java.util.Iterator;
+import java.util.List;
+
+import org.apache.commons.geometry.core.ConvexHull;
+import org.apache.commons.geometry.euclidean.EuclideanCollections;
+import org.apache.commons.geometry.euclidean.twod.ConvexArea;
+import org.apache.commons.geometry.euclidean.twod.Lines;
+import org.apache.commons.geometry.euclidean.twod.Vector2D;
+import org.apache.commons.geometry.euclidean.twod.path.LinePath;
+import org.apache.commons.numbers.core.Precision;
+
+/**
+ * This class represents a convex hull in two-dimensional Euclidean space.
+ */
+public final class ConvexHull2D implements ConvexHull<Vector2D> {
+
+    /** Vertices for the convex hull, in order. */
+    private final List<Vector2D> vertices;
+
+    /** Polyline path for the convex hull. */
+    private final LinePath path;
+
+    /** Simple constructor; no validation is performed.
+     * @param vertices the vertices of the convex hull; callers are responsible for ensuring that
+     *      the given vertices are in order, unique, and define a convex hull.
+     * @param precision precision context used to compare floating point numbers
+     */
+    ConvexHull2D(final Collection<Vector2D> vertices, final Precision.DoubleEquivalence precision) {
+        this.vertices = Collections.unmodifiableList(new ArrayList<>(vertices));
+        this.path = buildHullPath(vertices, precision);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public List<Vector2D> getVertices() {
+        return vertices;
+    }
+
+    /** Get a path defining the convex hull. The path will contain
+     * <ul>
+     *      <li>zero segments if the hull consists of only a single point,</li>
+     *      <li>one segment if the hull consists of two points,</li>
+     *      <li>three or more segments defining a closed loop if the hull consists of more than
+     *          two non-collinear points.</li>
+     * </ul>
+     * @return polyline path defining the convex hull
+     */
+    public LinePath getPath() {
+        return path;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public ConvexArea getRegion() {
+        return path.isClosed() ?
+                ConvexArea.convexPolygonFromPath(path) :
+                null;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public String toString() {
+        final StringBuilder sb = new StringBuilder();
+        sb.append(getClass().getSimpleName())
+            .append("[vertices= ")
+            .append(getVertices())
+            .append(']');
+
+        return sb.toString();
+    }
+
+    /** Build a polyline representing the path for a convex hull.
+     * @param vertices convex hull vertices
+     * @param precision precision context used to compare floating point values
+     * @return path for the convex hull defined by the given vertices
+     */
+    private static LinePath buildHullPath(final Collection<Vector2D> vertices,
+            final Precision.DoubleEquivalence precision) {
+        if (vertices.size() < 2) {
+            return LinePath.empty();
+        }
+
+        final boolean closeLoop = vertices.size() > 2;
+
+        return LinePath.builder(precision)
+                .appendVertices(vertices)
+                .build(closeLoop);
+    }
+
+    /** Class used to build convex hulls. The builder is based on the Akl-Toussaint
+     * heuristic to construct the hull. The heuristic is based on the idea of a
+     * convex quadrilateral, which is formed by four points with the lowest and
+     * highest x / y coordinates. Any point that lies inside this quadrilateral can
+     * not be part of the convex hull and can thus be safely discarded before
+     * generating the convex hull itself.
+     * <p>
+     * The complexity of the operation is O(n), and may greatly improve the time it
+     * takes to construct the convex hull afterwards, depending on the point
+     * distribution.
+     *
+     * @see <a href=
+     *      "http://en.wikipedia.org/wiki/Convex_hull_algorithms#Akl-Toussaint_heuristic">
+     *      Akl-Toussaint heuristic (Wikipedia)</a>
+     */
+    public static final class Builder {
+
+        /** Corner of quadrilateral with minimal x coordinate. */
+        private Vector2D minX;
+
+        /** Corner of quadrilateral with maximal x coordinate. */
+        private Vector2D maxX;
+
+        /** Corner of quadrilateral with minimal y coordinate. */
+        private Vector2D minY;
+
+        /** Corner of quadrilateral with maximal y coordinate. */
+        private Vector2D maxY;
+
+        /** Collection of all remaining candidates for a convex hull. */
+        private final Collection<Vector2D> candidates;
+
+        /** A precision context for comparing points. */
+        private final Precision.DoubleEquivalence precision;
+
+        /** Indicates if collinear points on the hull shall be present in the output.
+         * If {@code false}, only the extreme points are added to the hull.
+         */
+        private final boolean includeCollinearPoints;
+
+        /** Return a {@link Builder} instance configured with the given precision
+         * context. The precision context is used when comparing points.
+         *
+         * @param builderPrecision       precision context to use when building a convex
+         *                               hull from raw vertices; may be null if raw
+         *                               vertices are not used.
+         * @param includeCollinearPoints whether collinear points shall be added as hull
+         *                               vertices
+         */
+        public Builder(final boolean includeCollinearPoints, final Precision.DoubleEquivalence builderPrecision) {
+            this.precision = builderPrecision;
+            this.includeCollinearPoints = includeCollinearPoints;
+            candidates = EuclideanCollections.pointSet2D(builderPrecision);
+        }
+
+        /** Appends the given point to a collection of possible hull points, if and only
+         * if the given point is outside of a constructed quadrilateral of extreme properties.
+         *
+         * @param point a given point.
+         * @return this instance.
+         */
+        public Builder append(Vector2D point) {
+
+            // Checks if the given point supersedes one of the corners.
+            checkCorners(point);
+
+            // Only proceed if the quadrilateral is complete.
+            if (candidates.size() < 4) {
+                return this;
+            }
+
+            final List<Vector2D> quadrilateral = buildQuadrilateral(minY, maxX, maxY, minX);

Review Comment:
   I agree with at least caching the quadrilateral. @agoss94, I'm not sure what to picture yet for your counting approach. Can you explain that a bit more?



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