# Bias, Dualbias

Applies to: Curves

Summary: Meshes a curve with node spacing biased toward one or both curve ends.

Syntax:

Curve <range> Scheme Bias

Curve <range> Scheme Bias {Factor|First_Delta|Fraction} <double> [Start Vertex <range>] [preview]

Curve <range> Scheme Dualbias {Factor|First_Delta|Fraction} <double> [preview]

Curve <range> Scheme Bias Fine Size <double>
{Coarse Size <double> | Factor <double>} [Start Vertex <range>] [preview]

Curve <range> Scheme Dualbias Fine Size <double>
{Coarse Size <double> | Factor <double>} [preview]

Curve <range> Scheme Multi_bias Start <size>
[Fraction <value> <size>]... End <size>
[Start Vertex <id>][Respect_intervals][preview]

Related Commands:

Curve <range> Reverse Bias

Set Maximum Interval <int>

The main differences between scheme bias and stretch are the following: scheme stretch does not use strict geometric series for node placement. If you specify scheme bias or dualbias using the "fine size" form, the interval count will be hard-set to a value that fills in the curve.

Auto Bias

When using the command 'curve <range> scheme bias' with no additional parameters, an auto setting will be enabled by default for tet and tri meshing. This scheme honors sizes at a curve's vertices and that vertex size will be used to create a biased edge mesh. For example, two volumes with different sizes set on the volumes are merged. The size at the vertices (averaged from sizes on the parent entities) will be used to create the biased edge mesh.

A user can set a size on a vertex with the following command:

Vertex <id> Size <size>

More Discussion:

The Bias and DualBias schemes space the curve mesh unequally, placing more nodes towards (or away from) the ends of the curve according to a geometric progression. The ratio of successive edges is the "factor," which may be greater than or less than one. For bias, the series starts at the first vertex of the curve, or the "start vertex" if specified. For dualbias, the series starts at both ends of the curve and meets in the middle.

The command behaves differently depending on which set of parameters are specified. There are three basic variables: the interval count, the bias factor, or the first edge size. The curve length is a given, fixed quantity. The user can specify any two of these variables, and the third will be automatically determined.

If the "{Factor|First_Delta|Fraction}" form is specified, then the interval count is taken as a given. The interval count is whatever was specified previously by an interval count or size command (see Interval Assignment). If "Factor" is specified, then the first edge size will be automatically chosen so that the geometric progression of edges "fit" onto the curve. If "first_delta" is specified, then the first edge length is exactly that absolute value, and the "factor" is automatically chosen. If "fraction" is specified, then the first edge length is the curve length times that fraction, and again the "factor" is automatically chosen.

If the "fine size" is specified, then the first edge length is exactly that absolute value. If the "factor" is specified, then the interval count is automatically chosen. If an approximate coarse size is specified, then this also determines the factor, and again the interval count is automatically chosen. If a surface sizing function type bias is used, then the curves of the surface are sized using similar formulas.

If no start or end vertex is specified, the curve's start vertex is used as the starting point of the bias. (A curve's start vertex can be identified by listing the curve from the "CUBIT>" prompt.)

If a curve needs to have its nodes distributed towards the opposite end, it can be easily edited using the reverse bias command. Reversing the curve bias using this command is equivalent to setting a bias factor equal to the inverse of the original bias factor. Reversing the bias can be performed on both meshed and unmeshed curves.

The maximum interval setting allows the user to set a maximum number of intervals on any bias curve. This value is doubled for a curve with a dualbias scheme. It can be easy to accidentally specify a very large number of intervals and this setting allows the user to place an upper limit the number of intervals.

The preview option will allow the user to preview mesh size and distribution on the curve before meshing.

The following figure shows the result of meshing edges with equal, bias and dualbias schemes.

### Multi Bias

The multi-bias scheme allows several biases to be created on a single curve by specifying desired sizes at multiple locations along the curve (see Figure 1 below). The "start" and "end" sizes must be specified, and any number of fraction-size pairs may be specified, where the fraction value is between 0 - 1. If "Start Vertex" is given, the specified vertex is considered to have the fraction value of 0, with the opposite vertex having the fraction value of 1. If "respect_intervals" is not specified, the scheme will choose an appropriate number of intervals for the curve based on the given sizes.

### Figure 1. Curve with scheme multi_bias.

If the "respect_intervals" option is given, the multi-bias scheme will try to get as close to the desired sizes as possible, but will always respect the number of intervals set on the curve and adjust sizing as necessary (see Figure 2).

### Figure 2. Same curve as in Figure 1, but with the respect_intervals option. Note the areas of relatively dense mesh correspond to the dense mesh in the original.