query: Convex and concave regions of a closed curve
positive_passages.docid: 147274
positive_passages.text: Can I get the curvature at any point of a random curve?
negative_passages.docid: 146519
negative_passages.text: gaussian and mean curvatures
negative_passages.docid: 61481
negative_passages.text: Continuously Differentiable Curves in $\mathbb{R}^{d}$ and their Lebesgue Measure
negative_passages.docid: 101690
negative_passages.text: Is linear function convex or concave?
negative_passages.docid: 66151
negative_passages.text: Solving inequality for convex functions.
negative_passages.docid: 140383
negative_passages.text: Concave implies subadditive
negative_passages.docid: 132911
negative_passages.text: Determining if there can be smooth closed geodesic given its curvature
negative_passages.docid: 72255
negative_passages.text: Parametric curve on cylinder surface
negative_passages.docid: 105488
negative_passages.text: Finding the curvature and normal vector for an arclength curve
negative_passages.docid: 106075
negative_passages.text: Shading a region where an inequality is satisfied
negative_passages.docid: 5667
negative_passages.text: Marking points of intersection between two curves
negative_passages.docid: 105506
negative_passages.text: Finding the Total Curvature of Plane Curves
negative_passages.docid: 64084
negative_passages.text: Existence of a simple closed curve which is not null-homotopic
negative_passages.docid: 14077
negative_passages.text: Finding a Concave Hull
negative_passages.docid: 154012
negative_passages.text: A simple curve of positive area
negative_passages.docid: 71960
negative_passages.text: How to determine the equation and length of this curve consistently formed by the intersection of Circles
negative_passages.docid: 66494
negative_passages.text: Curvature of a curve on a sphere