Correct me if I'm wrong but in laymen terms, a convex hull is just an enclosed space, made up of the outermost points, that contains a set of specific points?
muminovic
The way I've heard it described visually is to imagine that all the points in your graph are like nails in a wall. A convex hull containing some set of points/nails A would be like stretching a rubber band around the nails in the set A; there's a nice gif here visualizing this (scroll to bottom) --https://www.maa.org/external_archive/joma/Volume8/Kalman/ConvexHull.html
aliceshan
The way I remember it is as "the smallest possible area that contains all the points"
aliceshan
In class, the professor gave the example that the convex hull can be useful in checking whether 2 or more curves can overlap by checking if the convex hulls overlap.
buaazhangfan
The convex hull of a finite point set S is the set of all convex combinations of its points. These points are joined together to form a Bezier polygon, and Bezier Curve is in the convex hull of this polygon
john-b-yang
I thought this Math Overflow post was pretty helpful in terms of expanding on why this property is significant: https://bit.ly/2GZ7FvH. In a nutshell, I think this property enforces why we are even able to control how the curve looks with control points.
Correct me if I'm wrong but in laymen terms, a convex hull is just an enclosed space, made up of the outermost points, that contains a set of specific points?
The way I've heard it described visually is to imagine that all the points in your graph are like nails in a wall. A convex hull containing some set of points/nails A would be like stretching a rubber band around the nails in the set A; there's a nice gif here visualizing this (scroll to bottom) --https://www.maa.org/external_archive/joma/Volume8/Kalman/ConvexHull.html
The way I remember it is as "the smallest possible area that contains all the points"
In class, the professor gave the example that the convex hull can be useful in checking whether 2 or more curves can overlap by checking if the convex hulls overlap.
The convex hull of a finite point set S is the set of all convex combinations of its points. These points are joined together to form a Bezier polygon, and Bezier Curve is in the convex hull of this polygon
I thought this Math Overflow post was pretty helpful in terms of expanding on why this property is significant: https://bit.ly/2GZ7FvH. In a nutshell, I think this property enforces why we are even able to control how the curve looks with control points.