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Isocline Curve

Find a direction V with a shortest 0° isocline curve

Approach

Isoline curve is constructed given a reference vector V and an angle A such that the angle between the surface normal anywhere on the curve and V is (pi/2 - A).

In our case, the angle A = 0 and the 0° isocline is a curve with normals perpendicular to a given V. We are looking for the V with shortest isocline.

Assuming a closed differentiable surface in mesh representation, get all the faces that have a normal close enough to perpendicular to the given vector and try to connect them in a non-trivial loop. The shortest path of edges in that loop approximates the isocline for given direction. Estimate its length then find V with shortest isocline length.

Requirements

Tested with Python 3.10.11 and openmesh 1.24.3

pip install openmesh

Run an example

python find_isocline.py examples/bob_isotropic.obj

Bob isocline

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Find a direction a with a shortest 0° isocline curve

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