How do Guassian, Minimum, and Maximum Curvature values relate to real world units?


#1

Hi,
I am analyzing surfaces that are being panelized for a facade - they have been generated and rebuilt using D-Loft to create seemingly developable surfaces.

  1. I need to be able to analyze/describe how much of the panelized surface is actually developable to a material tolerance and how much has slight gaussian curvature.
  2. I need to describe in real world buildable terms the amount of curvature per panel for the single curved unrollable panels (ie it is bent 11 mm over 1000m, etc.)

My model is in meters (please tell me if I should change to mm). If my model is in meters can someone explain to me what the values for gaussian curvature mean and how it relates to real world units and the same for max and min principal curvature values (im assuming this is what describes the actual range of degree of curvature?

Thank you!
Tyson


(Pascal Golay) #2

Hi Tyson - Curvature is 1/radius of curvature, in model units. Any units will do, but you need to know what that minimum radius is.

-Pascal


(David Cockey) #3

Gaussian curvature is K1 * K2 where K1 and K2 are the principal curvatures and equal to 1/radii of curvatures in the principal directions. So Gaussain curvature has units of 1/length^2. If millimeters are the length unit then Gaussian curvature has units of 1/mm^2. If meters are used then Gaussian curvature has units of 1/m^2. So the numeric value for the Gaussian curvature of a surface will be 1,000,000 larger if meters are used rather than millimeters.