======NURBS Surfaces Concepts======

> **Summary:** //Basic concepts of NURBS surface geometry//

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One of the main geometry concepts that comes up often when modeling with Rhino is [[rhino:nurbs|NURBS]] curves and surfaces.  Non-Uniform Rational Basis Spline (NURBS) is an accurate mathematical representation of curves and surfaces. The shape of the surface is defined by a number of control points and the degree of that surface in each one of the two directions (u- and v-directions). Refer to Rhino Help Glossary for more details.

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[[rhino:nurbs|NURBS]] surfaces can be trimmed or untrimmed. Think of trimmed surfaces as using an underlying [[rhino:nurbs|NURBS]] surface and closed curves to cut a specific shape of that surface. Each surface has one closed curve that define the outer border (//OuterLoop//) and as many non-intersecting closed inner curves that define holes (//InnerLoops//). We refer to a surface with outer loop that is the same as that of its underlying [[rhino:nurbs|NURBS]] surface and that has no holes as **untrimmed surface**.

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The surface on the left is untrimmed. The one on the right is the same surface trimmed with an elliptical hole. Note that the [[rhino:nurbs|NURBS]] structure of the surface doesn’t change when trimming.

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A polysurface consists of more than one surface joined together. Each of the surfaces has its own u- and v-direction. Thus, paneling using uv-directions may not continue the paneling pattern across the polysurface edges. Paneling commands can either use surface uv-directions or follow a specified direction.

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