algorithmic modeling for Rhino
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Zero is certainly larger than -2.
Chris
The sign of the principal curvature depends on the direction of the normal at the point of interest as well as the direction of the principal curve. If the normal and the curve have an opposite sense the curvature is negative.
Chris
Yeah, this makes sense, and since nothing can curve less than Curvature "0", zero has got to be the Min Principal Curvature here, no?
No. Curvature is signed based on the direction of the normal at the point of interest and the 'sense' of the curves direction so it can be less than zero. So one of the principal curvatures can be negative and therefore less than zero and also the min. principal curvature which would make zero a legitimate max. curvature. Certainly though the absolute value of the reciprocal of any radius will always be greater than zero but that's not curvature as we're talking about it here. In the case of the cylinder if the normal is pointing toward the central axis then the curvature would be positive since the curve of the cylinder and the normal have the same 'sense'. If the normal is pointing outward then the curvature would be negative since the normal and the curve of the cylinder now have opposite 'sense'. At least this is how I understand it. Playing around with the curvature component and a referenced cylinder I notice however that changing the direction of the normal from 'outside' to 'inside' has no effect on the output of the component. Swapping the uv directions however does change the sign...hmmm?
Chris
Yeah I don't get it either. It seems like the max and min curvatures should flip in the case shown in the screen shot attached.
Chris
Surfaces have a strictly defined normal vector definition. So if you flip the U direction, the V direction, or if you swap U and V the normal vector will be inverted.
Breps on the other hand have an override for the normal direction. A Brep Face is allowed to invert the normal direction of the underlying surface. This is so we can join surfaces into polysurfaces and have their normals match up without the need to flip directions and trimming curves.
I'm not sure but it could be that the current confusion stems from this brep-face-normal-override flag.
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David Rutten
david@mcneel.com
Seattle, WA
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