Fit SOP
Summary
The Fit SOP fits a Spline curve to a sequence of points or a Spline surface to an m X n mesh of points.
Any type of face or surface represents a valid input. The Fit SOP looks only at the control vertices (CVs) of the primitives, treating the CVs as data points to run the fit through. For example, if a cubic NURBS surface and a mesh have the same number of rows and columns and identical points, they will yield an identical fit because the Spline bases of the input NURBS surface are ignored.
The Fit SOP generates two types of outputs: primitives that roughly follow the path of the data points without necessarily going through the data points; and primitives that touch all the data points. The first type, known as "approximation", is used primarily to extract a lean, smooth shape from a heavy data set, lending itself well to data reduction. The second type, known as "interpolation", often serves as a smoothing tool for paths that must go through specified target positions.
Contents
Parameters  Fit Page
This is the main page of the SOP. Its purpose is to specify the type of fitting and the characteristics of the output primitive.
Method /method
 Specifies one of two fitting styles: approximation or interpolation. Each style has a number of parameters that are accessible from the respective folder. For more information see the Approximation and Interpolation pages below.
Primitive Type /type
 The output of the Fit SOP is a NURBS or Bzier primitive. All input faces are fitted to Spline curves, and all input surfaces are fitted to spline surfaces. The resulting shapes are identical whether created as NURBS or as Bzier primitives.
Connectivity /surftype
 This option is used to select the type of surface, when using a Mesh Primitive Type.
 Rows  Creates horizontal lines.
 Columns  Creates vertical lines.
 Rows & Cols  Both Rows and Columns. Looks like Quads in wire frame display, but all polygons are open (if the primitive type is polygon).
 Triangles  Build the grid with Triangles.
 Quadrilaterals  Generates sides composed of quadrilaterals (default).
 Alternating Triangles  Generates triangles that are opposed; similar to the Triangles option.
U Order /orderu
 If the input is a face, this is the order of the Spline curve to be generated. If the input is a surface, this is the order of the fitted spline surface in the U parametric direction.
V Order /orderv
If the input is a surface, this is the order of the fitted Spline surface in the V parametric direction. The V order is irrelevant if the input is a face.
Parameters  Approximation Page
Approximation fitting is used primarily to generate a lean, smooth shape from a dense data set. The result is a primitive that approximates the positions and attributes of the data points but does not necessarily touch these points. The only points the fitted curve or surface goes through are the endpoints of the data set. If the fitted primitive is required to go through all the points, fitting by interpolation is the answer.
The approximation fit is capable of producing very reasonable shapes with far fewer control vertices than the number of data points. Although the result is unlikely to match the original shape identically, it can come very close to it, depending on the parameters it is set to. For this reason, approximation fitting is often used as a data reduction tool and performs best when the size of the data set is large.
The fitted primitives are generated open or wrapped based on the "open" property of the inputs. For best results, the input primitives should be open.
Tolerance /tol
 This is the primary precision factor in approximation fitting. The smaller the tolerance, the closer the fit and the higher the number of generated vertices. If a small tolerance causes unwanted twists or contortions in the fitted primitive, it may help to vary the Spline order and/or enable the Multiple Knots flag.
Smoothness /smooth
 For a set tolerance, the smoothness factor allows for more or less roundness in the generated shape. If this parameter is zero, it does not mean that the fit will be sharp. It simply indicates that no additional smoothing is required past the level of smoothness already achieved with the given tolerance.
U / V Multiple Knots /multipleu /multiplev
 Sometimes the data set has sharp bends that must be preserved in the fitted shape. In this case, inserting multiple knots in the areas of sharp curvature will usually produce the right effect. Sometimes, however, the simulated sharpness induces unwanted twists immediately before or after the corner. Lowering the Spline order and/or reducing the tolerance may help diminish this sideeffect.
Parameters  Interpolation Page
Interpolation fitting is used primarily to generate a shape that goes through (i.e. interpolates) a complete set of data points and their attributes. As opposed to approximation fitting, interpolation thrives on small data sets. Moreover, unlike the approximation method, this one does not produce a leaner structure than the input it fits. In certain cases it even generates a higher CV count than its input. For this reason, the use of interpolation fitting should be limited to those cases where point interpolation is paramount, such as building precise animation paths.
Scope /scope
 Scope establishes the interpolation method.
 Global  Global interpolation take the whole data set into account at once and generates exactly as many CVs as data points is it given.
 Local  Local interpolation takes a more geometric approach, building the curve or surface one span at a time, using only local data at each step. The local method generates more CVs than the number of data points it is given, but it usually yields a tighter fit than the global method. The local approach is also less computationally expensive than the global one, and handles cusps and local perturbations better. Local interpolation is available only for curves.
 Breakpoints  Breakpoint interpolation is a variant of global interpolation that satisfies the requirement that the locations of data points coincide with the breakpoints of the generated curve. The breakpoints of a Spline curve are the image of the Spline basis on the curve. Breakpoint interpolation is available only for curves.
U Data Parameter /dataparmu
 Specifies the parameterization of the data in the U direction (the only direction if the input is a curve). The data parameterization can be uniform, chord length, or centripetal.
 Uniform Uniform parameterization uses equally spaced parameter values. It works best when the geometry is very regular. When the data is unevenly spaced, this approach can produce very unintuitive shapes, and is not recommended.
 Chord Length Chord length computes the parameterization of the data based on the relative distances between successive data points. It is the most commonly used approach because is tends to produce the most accurate results.
 Centripetal Centripetal parameterization is similar to chord length, but yields better results when the data has very sharp corners.
V Data Parameter /dataparmv
 V data parameterization is identical to U data parameterization, but it affects the V direction when the input is a surface. It is not used when the input is a face.
U Wrap /closeu
 This menu determines whether the fitted curve should be closed, or whether the fitted surface should be wrapped in the U parametric direction. The options are to open (Off), close (On), or inherit the closure type from the input primitive.
V Wrap /closev
 This menu determines whether the fitted surface should be wrapped in the V parametric direction. The options are to open (Off), close (On), or inherit the closure type from the input primitive. V Wrap is ignored when the input is a face.
Fit Corners /corners
 Specifies whether corners in the data should be preserved when doing local curve interpolation.
