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May 22, 2024 · Concavity provides valuable insights into how a function curves, distinguishing between concave upward and concave downward shapes, while points of inflection mark locations where the curvature changes sign.
- Convex and Concave Functions
Examples of Concave Functions. Some examples of concave...
- Convex and Concave Functions
Jul 30, 2019 · Here is a github repo on finding the concave hull for a set of points using python. My recommendation to you is the following. Create a set of points using the endpoints of each line. Then use the linked to code to generate a concave hull for these points, with some guess for the value of alpha.
Sep 22, 2024 · Examples of Concave Functions. Some examples of concave functions are: g(x) = - x 2; g(x) = log x; g(x) = -e x; Graphical Representation of Concave Functions. Mathematically, a function f(x) is concave if for any two points x 1 and x 2 and any λ ∈ [0, 1], the following inequality holds: f(λx 1 + (1 − λ)x 2) ≥ λf(x 1) + (1 − λ)f(x 2 ...
Apr 12, 2024 · Inflection Point is a point of the function where the concavity of the function changes. Learn more about inflection point along with methods to find the inflection point of a function in this article.
Mar 3, 2024 · The one-liner function is_concave_convex_hull leverages scipy.spatial.ConvexHull to quickly determine if the given points form a concave polygon. The comparison of vertex count to points count is a clever shortcut and computationally efficient, assuming the use of this third-party library.
A simple (but non-obvious) computational geometry algorithm for determining convexity is to check that every triplet of consecutive vertices is CCW. This takes just a few lines of Python geometry code (assuming that the points are provided in counterclockwise order—if points is in clockwise order, you’ll want all triplets to be clockwise):
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The mathematical definition of a function being concave between points $x_1$ and $x_2$ is the following: $\lambda f(x_1)+(1-\lambda)f(x_2) \leq f(\lambda x_1+(1-\lambda)x_2)$, for any $0 \leq \lambda \leq 1$. Can someone give a detailed, intuitive explanation of this theorem?
