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| R2012a Documentation → Symbolic Math Toolbox | |
Learn more about Symbolic Math Toolbox |
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plot::hull computes the convex hull of a list of points in arbitrary dimension.
Call:
plot::hull(L)
Parameters:
|
L: |
a list of points, which are given as lists of real values |
Return Value:
a list of simplices of dimension one less than that of the points in L, given as lists of lists of floating point values.
Dependencies:
Although plot::hull accepts and returns floating point values, the actual computations take place in hardware floating points and are therefore not affected by the value of DIGITS.
Details:
plot::hull computes the convex hull of a list of points in any dimension, i.e., the smallest convex region containing all the points. Such a region is bounded by simplices (straight lines in the plane, triangles in 3D) and it is these simplices which plot::hull returns.
Example 1
We generate a list of random points and compute their convex hull:
X := stats::uniformRandom(0, 20):
l := [[X(), X()] $ i = 1..10]:
h := plot::hull(l):
The convex hull is returned as lists of lists, as accepted by plot::Polygon2d:
h[1]
![[[17.58320254, 18.38769696], [3.063130321, 19.89625562]]](hull_images/math0.png){kind=small}
plot(plot::PointList2d(l),
plot::Polygon2d(t) $ t in h,
Closed, PointSize=2)
Example 2
The convex hull of a list of points in 3D is also easy to visualize:
l := [[x, y, z] $ y = z..x $ z = -x..x $ x = 0..10]:
h := plot::hull(l):
plot(plot::PointList3d(l, PointSize=1),
plot::Polygon3d(t) $ t in h,
Closed, Filled, FillColor=RGB::LightOrange.[0.6])
Background:
plot::hull uses qhull from the Geometry Center of the University of Minnesota, cf. www.qhull.org.
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