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Tenshou
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I don't understand what a convex hull is and what it does. does anyone think they can explain what exactly it is?
Tenshou said:Thank you micromass, I think I get it... I think I understand that the two points should be a line segment, 3 points a triangle and 4 a tetrahedron. I just don't get why those are convex sets, is it because the dimension of the line segment(or the other stuff) is equal to the dimension of the plane that it sits in? Why isn't a circle a convex hull or a square? are they convex sets?
A convex hull is a geometric shape that contains all points within a set, while also being the smallest possible shape to do so. It can be thought of as the outer boundary or envelope of a set of points.
The most common way to calculate a convex hull is by using the "gift wrapping" algorithm, also known as the Jarvis march. This algorithm starts at the leftmost point and wraps an imaginary string around the points, creating the convex hull. Other algorithms, such as Graham's scan and Quickhull, can also be used.
Convex hulls have various applications in different fields such as computer graphics, image processing, robotics, and operations research. They are used to determine the boundary of an area or shape and can also be used for collision detection in computer simulations.
A convex hull is a shape that contains all points within a set, while a concave hull is a shape that contains the points and also has indentations or "dents". In other words, a concave hull is not a continuously smooth boundary like a convex hull.
Yes, a convex hull can be applied to any set of points, regardless of whether they represent geometric or non-geometric data. However, the shape may not have a clear interpretation in non-geometric cases.