Polygons are made up of triangles. They are the simplest form of something you model with normally.
Nurbs, are made up of points that describe curves. The curves form a mesh. The curves are calculated based on the points.. so like no matter how close you get to a curve it will always be smooth. So Nurbs are basically guide lines.. and the calculations decide how to make it out of triangles.. This is why with nurbs you can change the quality of them. Ei tell it to make it out of more triangles than what it was, so that the object appears even smoother..
This might give you some idea.. I'm sure there are others out there that can explain it better than me..
NURBS (nonuniform rational B-splines) are mathematical representations of 2- or 3-dimensional objects, which can be standard shapes (such as a cone) or free-form shapes (such as a car). NURBS are used in computer graphics and the CAD/CAM industry and have come to be regarded as a standard way to create and represent complex objects.
Polys by geometry are planes bound by straight lines...I couldn't find anything else to describe them.
Most people after some experience using Maya, know what to use for what and why.....which I am sure our 3D guru's can answer
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