# Tagged Questions

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In the euclidean plane I want a smooth curve $\gamma (t)$ which satisfy:$$\gamma (0)=(0,0)\quad\quad \gamma '(0)=(1,0)\quad\quad n\in \mathbb{N}\land n\neq 1\Rightarrow \gamma ^{(n)}(0)=(0,0)\\\gamma ... 0answers 22 views ### Given a numerical curvature, compute the shape of the function Given a numerical curvature, I want to accurately compute the shape of the function. Let s be the arc-length along a curve of total length L which is divided into N-1 segments. I am given 1) ... 0answers 268 views ### Surface integral for a scalar function defined on a discrete surface Imagine a polyhedral, discrete surface embedded in \mathbb{R}^3. Its faces are all triangles. For each vertex, one can compute the discrete mean and Gaussian curvatures and evaluate the sum of ... 1answer 118 views ### Find the Frenet frame Consider the following space curve:$$ \gamma(x)=(e^x\cos(x), e^x\sin(x), e^x). $$My main goal is to find the Frenet Frame T,N,B. So far I have found the arc-length using the following formula:$$ ...
I've been struggling with this one for about $3$ weeks: What is the integral of a $\mathbb{R}^3$ curve with respect to its curvature? I though about approaching it with the Ferret-S formulas, and ...