Curvature: What Is It?

Gaussian Curvature = 0 kG = 0; Ridge, Valley (Isometric Folding

Gaussian Curvature kG > 0: Dome, Bowl kG < 0: Saddle

May form without fractures from horizontal sheet.

Must fracture to form from horizontal sheet.

Gaussian (k      * k       ) Curvature

min

max

Curvature - 3D

Computed for 2D tangent circles at each point on the surface Generally computed in circle normal to the surface Some curvatures:   - Maximum (kmax):      Smallest radius circle   - Minimum (kmin):     Largest radius circle, will be     perpendicular to Maximum   - Most Positive: Tangent     circle below surface         with smallest radius   - Most Negative: Tangent circle     above surface with smallest     radius   - Along Dip (kd)   - Along Strike (ks)

Curvature - 2D

Curvature is the inverse of the radius of the tangent circle at every point along the line.

Gaussian Curvature

G > 0 : Plane, ridge or valley G = 0 : Dome, basin G < 0 : Saddle