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For "Porcupine Curvature Analysis", i can give you an example. For example you are creating route for electrical cable. And let's say route can not have a radius lower than X value. If you apply "Porcupine Curvature Analysis" on that curve (route), you can see the minimum radius value. And your design will be on safe zone.
And this information from google. It may be example for "Surface Curvature Analysis"
-->Surface curvature plays a key role in selecting a cutting size to avoid gouging in CAM system. Tool size can be selected from the critical curvature. Minimum curvature radius equals largest tool radius, represents contour map of tool radius distribution mapped on the surface model.
-->Graphical display of curvature values can be useful to indicate error cutting areas which require modification of the machining program, beside the calculation of the value of cutter size required for machining.