Convex hull

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Create a convex hull for a given set of points. The convex hull is a polygon with shortest perimeter that encloses a set of points. As a visual analogy, consider a set of points as nails in a board. The convex hull of the points would be like a rubber band stretched around the outermost nails.

screenshot

Use case

A convex hull can be useful in collision detection. For example, when charting the position of two yacht fleets (with each vessel represented by a point), if their convex hulls have been precomputed, it is efficient to first check if their convex hulls intersect before computing their proximity point-by-point.

How to use the sample

Tap on the map to add points. Click "Convex hull" button to generate the convex hull of those points. Click the "Reset" button to start over.

How it works

  1. Create an input geometry such as a Multipoint object.
  2. Use GeometryEngine::convexHull(inputGeometry)to create a new Geometry object representing the convex hull of the input points. The returned geometry will either be a Point, Polyline, or Polygon based on the number of input points.

Relevant API

  • Geometry
  • GeometryEngine

Tags

convex hull, geometry, spatial analysis

Sample Code

ConvexHull.cppConvexHull.cppConvexHull.hConvexHull.qml
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// [WriteFile Name=ConvexHull, Category=Geometry]
// [Legal]
// Copyright 2020 Esri.

// Licensed 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.
// [Legal]

#ifdef PCH_BUILD
#include "pch.hpp"
#endif // PCH_BUILD

#include "ConvexHull.h"

#include "GeometryEngine.h"
#include "Graphic.h"
#include "GraphicsOverlay.h"
#include "Map.h"
#include "MapQuickView.h"
#include "MultipointBuilder.h"
#include "PointCollection.h"
#include "SimpleFillSymbol.h"
#include "SimpleMarkerSymbol.h"

using namespace Esri::ArcGISRuntime;

ConvexHull::ConvexHull(QObject* parent /* = nullptr */):
  QObject(parent),
  m_map(new Map(BasemapStyle::ArcGISTopographic, this))
{
  setupGraphics();
}

ConvexHull::~ConvexHull() = default;

void ConvexHull::init()
{
  // Register the map view for QML
  qmlRegisterType<MapQuickView>("Esri.Samples", 1, 0, "MapView");
  qmlRegisterType<ConvexHull>("Esri.Samples", 1, 0, "ConvexHullSample");
}

MapQuickView* ConvexHull::mapView() const
{
  return m_mapView;
}

void ConvexHull::displayConvexHull()
{
  if (m_inputsGraphic->geometry().isEmpty())
    return;

  // normalizing the geometry before performing geometric operations
  const Geometry normalizedPoints = GeometryEngine::normalizeCentralMeridian(m_inputsGraphic->geometry());
  const Geometry convexHull = GeometryEngine::convexHull(normalizedPoints);

  // change the symbol based on the returned geometry type
  if (convexHull.geometryType() == GeometryType::Point)
  {
    m_convexHullGraphic->setSymbol(m_markerSymbol);
  }
  else if (convexHull.geometryType() == GeometryType::Polyline)
  {
    m_convexHullGraphic->setSymbol(m_lineSymbol);
  }
  else if (convexHull.geometryType() == GeometryType::Polygon)
  {
    m_convexHullGraphic->setSymbol(m_fillSymbol);
  }
  else
  {
    qWarning("Not a valid geometry.");
  }

  m_convexHullGraphic->setGeometry(convexHull);
}

void ConvexHull::clearGraphics()
{
  if (m_multipointBuilder)
    m_multipointBuilder->points()->removeAll();
  if (m_inputsGraphic)
    m_inputsGraphic->setGeometry(Geometry());
  if (m_convexHullGraphic)
    m_convexHullGraphic->setGeometry(Geometry());
}

void ConvexHull::setupGraphics()
{
  // graphics overlay to show clicked points and convex hull
  m_graphicsOverlay = new GraphicsOverlay(this);

  // create a graphic to show clicked points
  m_markerSymbol = new SimpleMarkerSymbol(SimpleMarkerSymbolStyle::Circle, Qt::red, 10, this);
  m_inputsGraphic = new Graphic(this);
  m_inputsGraphic->setSymbol(m_markerSymbol);
  m_graphicsOverlay->graphics()->append(m_inputsGraphic);

  // create a graphic to display the convex hull
  m_convexHullGraphic = new Graphic(this);
  m_graphicsOverlay->graphics()->append(m_convexHullGraphic);

  // create a graphic to show the convex hull
  m_lineSymbol = new SimpleLineSymbol(SimpleLineSymbolStyle::Solid, Qt::blue, 3, this);
  m_fillSymbol = new SimpleFillSymbol(SimpleFillSymbolStyle::Null, Qt::transparent, m_lineSymbol, this);
}

void ConvexHull::getInputs()
{
  // show clicked points on MapView
  connect(m_mapView, &MapQuickView::mouseClicked, this, [this](QMouseEvent& e)
  {
    e.accept();

    const Point clickedPoint = m_mapView->screenToLocation(e.x(), e.y());
    m_multipointBuilder->points()->addPoint(clickedPoint);
    m_inputsGraphic->setGeometry(m_multipointBuilder->toGeometry());
  });
}

// Set the view (created in QML)
void ConvexHull::setMapView(MapQuickView* mapView)
{
  if (!mapView || mapView == m_mapView)
    return;

  m_mapView = mapView;
  m_mapView->setMap(m_map);

  // wait for map to load before creating multipoint builder
  connect(m_map, &Map::doneLoading, this, [this](Error e){
    if (!e.isEmpty())
    {
      qDebug() << e.message() << e.additionalMessage();
      return;
    }

    if (m_map->loadStatus() == LoadStatus::FailedToLoad)
    {
      qWarning( "Failed to load map.");
      return;
    }

    m_multipointBuilder = new MultipointBuilder(m_map->spatialReference(), this);
  });

  getInputs();

  m_mapView->graphicsOverlays()->append(m_graphicsOverlay);
  emit mapViewChanged();
}

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