New answers tagged computational-geometry
1
You can see why the sum of differences is giving a second derivative if you look at the derivative of a one-dimensional function $f$. The derivative of $f$ at $x_0$ is
$$ \frac{df}{dx}(x_0) \approx \frac{f(x_0 + dx) - f(x_0)}{dx} $$
The second derivative is then
\begin{eqnarray*}
\frac{d^2f}{dx^2}(x_0) &\approx&
\frac{df/dx(x_0) - df/dx(x_0-dx)}{...
1
As you pointed out, the problem here is the discretization/subdivision of the mesh. If your mesh was made of quadrilaterals instead of triangles, the obvious subdivision strategy would be to split each quadliteral into four equally sized smaller quadliterals:
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For any two points $P_1$ and $P_2$, Dijkstra's algorithm would yield ...
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