Place B-spline Curve

Define Control P[oin]ts

The poles (vertices) of the control polygon are defined by data points or the vertices of the selected line string or shape. The number of poles must be greater than or equal to the order. If Closure is Open, the curve is placed between the first and last points or vertices.

Through Points

The curve passes through the points defined by the data points or the vertices of the identified line string or shape and is interpolated at each point. The curve is cubic (Order=4) with continuous second derivatives — this minimizes the curvature.

L[east]-Square[s] By Tol[erance]

The curve is approximated based on the points defined by the data points or the vertices of the identified line string or shape. The maximum deviation of the input points from the curve is adjustable using the Tolerance setting. After the approximation curve is created, the maximum deviation and the mean deviation display in the status field.

L[east]-Square[s] By Num[ber]

The sum of the squares of the distances from the data points or the vertices of the selected line string or shape to corresponding points on the curve is minimized. The control polygon has the active number of Poles.

If the number of data points or vertices is the same as the number of Poles, the curve passes through all the data points or vertices,

• If Closure is set to Open, the curve begins and ends at the first last data points, respectively.

• If Closure is set to Closed, the curve approximates all data points or vertices and need not pass through any of them, unless there are the same number as the number of Poles.

If the maximum error exceeds the Tolerance,
see footnote 86 the maximum error displays in status bar.

Catmull-Rom

Fourth-order (cubic) NURBS curve that is interpolated. Extra poles are added to closely resemble the shape defined by the data points entered, using this formula:

• Number of Poles = 3 × (Data Points - 1) + 1

Sets the manner in which the curve is generated (see large table above).

Sets the manner in which the input points are located.

• Enter Data Points
— The curve is placed by entering data points. The curve dynamically updates while new points are entered or when the pointer is moved.

• Pick Line String
— The curve is constructed based on the vertices of an identified line string or complex chain (results in open B-spline) or shape or complex shape (results in closed B-spline).

Sets whether the curve is Open or Closed. Not available if Method is Catmull-Rom.

(Method set to Define Control Pts. or L-Square By Num only) Sets the order of the equation that defines the curve (2-15).

(Method set to L-Square By Num only) Sets the number of poles (3–5000).

(Method set to L-Square By Tol. only) Sets the fitting or approximation tolerance. The distance from any one of the input data points to the curve is less than this value. The distance is computed by projecting a point to the curve.

(Method set to Through Points or L-Square By Tol and Closure set to Open only) Sets the manner in which the curve's tangency to adjacent elements is controlled.

• Automatic
— default tangent directions are automatically computed.

• Both
— starting and ending tangent directions are defined graphically.

• Start Tangent
— starting tangent direction is defined graphically.

• End Tangent
— ending tangent direction is defined graphically.

(Method set to L-Square By Tol only) Sets the manner in which the curve's beginning and ending points are located.

If On, the curve passes through the first and the last input points. Otherwise, the curve's endpoints are computed based on the Tolerance setting.