1 / 14

2D Convex Hull in

2D Convex Hull in. Pierre Alliez. http://www.cgal.org. Outline. Definitions Convex hull in CGAL Interface Extreme points Subsequences of hull points Convexity Checking Exercise. Definitions.

gannon-burns
Télécharger la présentation

2D Convex Hull in

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2D Convex Hull in Pierre Alliez http://www.cgal.org

  2. Outline • Definitions • Convex hull in CGAL • Interface • Extreme points • Subsequences of hull points • Convexity Checking • Exercise

  3. Definitions • A subset S IR2 is convex if for any two points p and q in the set the line segment with endpoints p and q is contained in S. • The convex hull of a set S is the smallest convex set containing S. • The convex hull of a set of points Pis a convex polygon with vertices in P.

  4. Definitions • A point in P is an extreme point (with respect to P) if it is a vertex of the convex hull of P. • A point set is said to be strongly convex if it consists of only extreme points.

  5. Convex Hull in CGAL 5 algorithms to compute the counterclockwise sequence of extreme points for a 2D point set. 1 6 5 2 4 3

  6. Convex Hull in CGAL n input points with h extreme points Algorithms: • [Bykat 78] O(nh) output-sensitive • [Akl & Toussaint] O(nlogn) worst case • [Graham-Andrew] O(nlogn) • [Jarvis 73] O(nh) • [Eddy] O(nh)

  7. Interface template <class InputIterator, class OutputIterator> OutputIterator convex_hull_2(InputIterator first, InputIterator beyond, OutputIterator result, Traits ch_traits = Default_traits) generates the counterclockwise sequence of extreme points of the points in the range [first,beyond). The resulting sequence is placed starting at position result, and the past-the-end iterator for the resulting sequence is returned (it is not specified at which point the cyclic sequence of extreme points is cut into a linear sequence).

  8. Interface template <class InputIterator, class OutputIterator> OutputIterator convex_hull_2(InputIterator first, InputIterator beyond, OutputIterator result,Traits ch_traits = Default_traits) InputIterator::value_type OutputIterator::value_type Traits contains types and functions: Traits::Point_2, Traits::Less_xy_2, Traits::Less_yx_2, Traits::Leftturn_2. Traits::Point_2

  9. Default... #include <CGAL/Cartesian.h> #include <CGAL/convex_hull_2.h> #include <list> typedef CGAL::Cartesian<double> kernel; typedefkernel::Point_2 Point; std::list<Point> points; std::list<Point> hull; points.push_back(Point(0,0)); points.push_back(Point(0,1)); // ... CGAL::convex_hull_2(points.begin(), points.end(), std::inserter(hull,hull.begin()));

  10. Graham-Andrew #include <CGAL/Cartesian.h> #include <CGAL/graham_andrew.h> #include <list> typedef CGAL::Cartesian<double> kernel; typedefkernel::Point_2 Point; std::list<Point> points; std::list<Point> hull; points.push_back(Point(0,0)); points.push_back(Point(0,1)); // ... CGAL::ch_graham_andrew(points.begin(), points.end(), std::inserter(hull,hull.begin()));

  11. Extreme Points • North, South, East, West and combinations. N E W S

  12. SubSequences of Hull Points 2 • Lower Hull • Upper Hull 1 4 1 3 2

  13. Convexity Checking #include <CGAL/convexity_check_2.h> template <class ForwardIterator, class Traits> boolis_ccw_strongly_convex_2 ( ForwardIterator first, ForwardIterator beyond, Traits ch_traits = Default_traits) returns true iff the point elements in [first,beyond) form a counterclockwise-oriented strongly convex polygon.

  14. Exercise

More Related