User Guide
User Guide
User Guide

Evaluate Curve

Use it!

Used to graphically and numerically evaluate the attributes of a B-spline curve (tangents, curvatures, and inflection points) at given locations on the curve. There are five ways to define locations on a curve.

Computed points and tangents, which are placed as elements in the design, can be used as reference points or reference lines for other purposes. Curvature displays indicate the slopes change as you traverse the B-spline. Flatter curves thus are indicated graphically with shorter lines. For example, straight lines have zero curvatures.

Below is an example of Evaluate Curve results specifying node points. Note that the number of node points is equal to the number of knots.

Tool Settings for Evaluate Curve

  

By changing the number of points, the data may be viewed in a variety of pictorial formats.

This B-spline curve is identical to the one displayed in the table of tool setting descriptions. Note that increasing the number of points in the Curvature Plot and changing the Curvature Plot Scale, this image clearly shows the first derivative.

  
Tool SettingEffect
Location(s) Input By

Sets the manner in which the locations on the surface are defined.

  • Enter Data Point
    • — Interactively define a single location on the curve.
  • Parameter
    • — Using the Parameter Value setting, the value, which must be in the range 0–1, specifies the location from the domain to map to the displayed object. Within MicroStation, the domain is from 0.0 to 1.0.
  • Node Points
    • — These are the points on the curve calculated by evaluating it at the knots parameters. Node points represent the joints between the Bézier segments of a B-spline composed of Bézier segments separated by knots.
  • Dist[ance] Along Curve
    • — Using the Dist From Start setting, you can extract an attribute at a particular distance along the curve.
  • (%) Dist[ance] Along Curve
    • — Using the Dist From Start(%) setting, the value is a percentage of the total length of the curve. For example, to extract the tangent direction of a curve at its middle point, set Dist. From Start(%) to 50 (for 50% of the distance of the total curve length).
  • Point Array
    • — Using the Number of Points setting, the value is the number of evenly spaced locations on the curve. For example, to evaluate at 20 evenly spaced locations on the curve, set Number of Points to 20.
Tangent Plot Scale

Sets the scale factor applied to the magnitude display. If set to 1.0, the extracted tangent is the true derivative vector — that is, the tangent direction with the magnitude.

Curvature Plot Scale

Sets the scale factor applied to the line segments that represent curvature vectors in Curvature Plot output. If set to 1.0, the true curvature vector is displayed. The curvature value is the length of this vector. The radius of curvature is equal to one divided by the curvature. For a straight line, the radius of curvature is infinity since its curvature is zero.

Perpendicular Circle Radius

Sets the radius of the perpendicular circles in Perpendicular Circles output.

Parameter Value

Sets the parameter value applicable to the Parameter option for defining locations on the curve; see Location(s) Input By above.

Dist[ance] From Start

Sets the distance value applicable to the Dist Along Curve option for defining locations on the curve; see Location(s) Input By above.

Dist[ance] From Start(%)

Sets the distance value applicable to the (%) Dist Along Curve option for defining locations on the curve; see Location(s) Input By above.

Number of Points

Sets the numeric value applicable to the Point Array option for defining locations on the curve; see Location(s) Input By above.

[Compute] Points

If on, the points on the curve at which evaluation is performed are displayed in the output.

[Compute] Tangents

If on, the curve's tangents are computed.

[Compute] Curvature Plot

If on, the curve's curvature plot is computed.

[Compute] Inflection Points

If on, the curve's inflection points are computed. Inflection points are where the curve changes concavity.

[Compute] Perpendicular Circles

If on, the curve's perpendicular circles are computed.

To evaluate a B-spline curve
  1. Select the Evaluate Curve tool.

  2. Identify the curve.
    If Location(s) Input By is set to Enter Data Point, this data point also determines the location on the curve at which to evaluate.

  3. Accept the curve.
    The curve is evaluated, and the desired attributes are computed and output.

Key-in: EVALUATE CURVE

This tool can also be used to evaluate lines, arcs, and ellipses.