Package com.graphbuilder.curve

Class LagrangeCurve

java.lang.Object
com.graphbuilder.curve.Curve
com.graphbuilder.curve.ParametricCurve
com.graphbuilder.curve.LagrangeCurve
public class LagrangeCurve extends ParametricCurve

The Lagrange curve passes through the control-points specified by the group-iterator. It uses a knot-vector to control when the curve passes through each control-point. That is, if there is a knot-value for every control-point, then the curve will pass through point i when the value of t is knot[i], which is an interesting property. Figure 1 is an example of this.

In addition, when there is a knot-value for every point then the base-index should be 0, and the base-length should be n-1, where n is the size of the group-iterator.

A knot-vector with size less than n can still be used. In this case the Lagrange curve is generated in multiple sections. This approach works better when the points are roughly equally spaced. Figure 2 is an example of this.

Lagrange curves and also be closed as shown in figures 3 & 4.

Notes on the knot-vector, base-index and base-length. The size of the knot-vector specifies how many points are used for each section of the curve. The base-index specifies which point a section starts at. The base-index + base-length specify which point the section ends at. Once a section has been generated, the next section is generated starting from the end of the last section.

  • Field Details

    • knotVector

      private ValueVector knotVector

    • baseIndex

      private int baseIndex

    • baseLength

      private int baseLength

    • interpolateFirst

      private boolean interpolateFirst

    • interpolateLast

      private boolean interpolateLast

    • SHARED_DATA

      private static final ThreadLocal<LagrangeCurve.SharedData> SHARED_DATA

    • sharedData

      private final LagrangeCurve.SharedData sharedData

  • Constructor Details

    • LagrangeCurve

      public LagrangeCurve(ControlPath cp, GroupIterator gi)
      Creates a LagrangeCurve with knot vector [0, 1/3, 2/3, 1], baseIndex == 1, baseLength == 1, interpolateFirst and interpolateLast are both false. The knot vector, baseIndex and baseLength along with the control points define the shape of curve. See the appendTo method for more information.
      See Also:

  • Method Details

    • getBaseIndex

      public int getBaseIndex()
      Returns the base-index. The default value is 1.
      See Also:

    • setBaseIndex

      public void setBaseIndex(int b)
      The base-index is an index location into the knot vector such that, for each section, the curve is evaluated between [knot[baseIndex], knot[baseIndex + baseLength]].
      Throws:
      IllegalArgumentException - If base-index invalid input: '<' 0.
      See Also:

    • getBaseLength

      public int getBaseLength()
      Returns the base-length. The default value is 1.
      See Also:

    • setBaseLength

      public void setBaseLength(int b)
      The base-length along with the base-index specify the interval to evaluate each section.
      Throws:
      IllegalArgumentException - If base-length invalid input: '<'= 0.
      See Also:

    • getInterpolateFirst

      public boolean getInterpolateFirst()
      If baseIndex > 0 then the first control-points will only be interpolated if interpolate-first is set to true.
      See Also:

    • getInterpolateLast

      public boolean getInterpolateLast()
      If baseIndex + baseLength invalid input: '<' numKnots - 1 then the last control-points will only be interpolated if interpolate-last is set to true.
      See Also:

    • setInterpolateFirst

      public void setInterpolateFirst(boolean b)
      Sets the value of the interpolateFirst flag.
      See Also:

    • setInterpolateLast

      public void setInterpolateLast(boolean b)
      Sets the value of the interpolateLast flag.
      See Also:

    • getKnotVector

      public ValueVector getKnotVector()
      Returns the knot-vector for this curve.
      See Also:

    • setKnotVector

      public void setKnotVector(ValueVector v)
      Sets the knot-vector for this curve.
      Throws:
      IllegalArgumentException - If the value-vector is null.
      See Also:

    • getSampleLimit

      public int getSampleLimit()
      Returns a value of 1.
      Specified by:
      getSampleLimit in class ParametricCurve

    • eval

      protected void eval(double[] p)
      Description copied from class: ParametricCurve
      The eval method evaluates a point on a curve given a parametric value "t". The parametric value "t" is stored in the last index location of the specified double array. This value should not be changed. The dimension of the point to evaluate is p.length - 1. The result of the evaluation is placed in index locations 0 .. p.length - 2 (inclusive). The eval method should remain protected except for those curves that do no need any preparation to be done in the appendTo method.
      Specified by:
      eval in class ParametricCurve

    • L

      private double L(double t, int i)

    • appendTo

      public void appendTo(MultiPath mp)
      For the control-points to be interpolated in order, the knot-vector values should be strictly increasing, however that is not required. The requirements are the group-iterator must be in range and baseIndex + baseLength invalid input: '<' numKnots. As well, the number of points defined by the group-iterator must be >= numKnots, otherwise the curve does not have enough control-points to define itself. If any of these requirements are not met, then this method returns quietly.
      Specified by:
      appendTo in class Curve
      See Also:

    • doBCAA

      private boolean doBCAA(MultiPath mp, double t1, double t2, boolean b)

    • resetMemory

      public void resetMemory()
      Description copied from class: Curve
      Resets the shared memory to the initial state.
      Overrides:
      resetMemory in class Curve