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"Curve up" modeling refers to creating construction curves that define shapes, then use tools to create surfaces from the curves.
Another way of modeling is "box up" modeling, where you start with a basic shape such as a polygonal box or sphere and then add, extrude, modify, cut, delete, smooth, etc. polygons to build up the shape you want.
Curve up modeling is often associated with NURBS modeling, and box up modeling with polygons. However, Houdini can create polygonal geometry using the tools listed below.
See the Model tab on the shelf for more modeling tools.
Create a surface from profile curves
Create a surface from a mesh of U and V profile curves
Create a surface from profile curves and rail curves