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 Summary

Fields

Modifier and Type	Field and Description
private int	baseIndex
private int	baseLength
private boolean	interpolateFirst
private boolean	interpolateLast
private ValueVector	knotVector
private static double[][]	pt

Fields inherited from class com.graphbuilder.curve.Curve

connect, cp, gi

Constructor Summary

Constructors

Constructor and Description
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.

Method Summary

Modifier and Type	Method and Description
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.
private boolean	doBCAA(MultiPath mp, double t1, double t2, boolean b)
protected void	eval(double[] p) The eval method evaluates a point on a curve given a parametric value "t".
int	getBaseIndex() Returns the base-index.
int	getBaseLength() Returns the base-length.
boolean	getInterpolateFirst() If baseIndex > 0 then the first control-points will only be interpolated if interpolate-first is set to true.
boolean	getInterpolateLast() If baseIndex + baseLength < numKnots - 1 then the last control-points will only be interpolated if interpolate-last is set to true.
ValueVector	getKnotVector() Returns the knot-vector for this curve.
int	getSampleLimit() Returns a value of 1.
private double	L(double t, int i)
void	resetMemory() Resets the shared memory to the initial state.
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]].
void	setBaseLength(int b) The base-length along with the base-index specify the interval to evaluate each section.
void	setInterpolateFirst(boolean b) Sets the value of the interpolateFirst flag.
void	setInterpolateLast(boolean b) Sets the value of the interpolateLast flag.
void	setKnotVector(ValueVector v) Sets the knot-vector for this curve.

Methods inherited from class com.graphbuilder.curve.Curve

getConnect, getControlPath, getGroupIterator, setConnect, setControlPath, setGroupIterator

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

knotVector

private ValueVector knotVector

baseIndex

private int baseIndex

baseLength

private int baseLength

interpolateFirst

private boolean interpolateFirst

interpolateLast

private boolean interpolateLast

pt

private static double[][] pt

Constructor Detail

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:

appendTo(MultiPath)

Method Detail

getBaseIndex

public int getBaseIndex()

Returns the base-index. The default value is 1.

See Also:

setBaseIndex(int)

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:

java.lang.IllegalArgumentException - If base-index < 0.

See Also:

getBaseIndex()

getBaseLength

public int getBaseLength()

Returns the base-length. The default value is 1.

See Also:

setBaseLength(int)

setBaseLength

public void setBaseLength(int b)

The base-length along with the base-index specify the interval to evaluate each section.

Throws:

java.lang.IllegalArgumentException - If base-length <= 0.

See Also:

getBaseLength()

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:

setInterpolateFirst(boolean)

getInterpolateLast

public boolean getInterpolateLast()

If baseIndex + baseLength < numKnots - 1 then the last control-points will only be interpolated if interpolate-last is set to true.

See Also:

setInterpolateLast(boolean)

setInterpolateFirst

public void setInterpolateFirst(boolean b)

Sets the value of the interpolateFirst flag.

See Also:

getInterpolateFirst()

setInterpolateLast

public void setInterpolateLast(boolean b)

Sets the value of the interpolateLast flag.

See Also:

getInterpolateLast()

getKnotVector

public ValueVector getKnotVector()

Returns the knot-vector for this curve.

See Also:

setKnotVector(ValueVector)

setKnotVector

public void setKnotVector(ValueVector v)

Sets the knot-vector for this curve.

Throws:

java.lang.IllegalArgumentException - If the value-vector is null.

See Also:

getKnotVector()

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 < 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:

MultiPath, BinaryCurveApproximationAlgorithm

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