/libraries/libTopology/src/com/graphbuilder/curve/LagrangeCurve.java

package com.graphbuilder.curve;



/**

<p>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.



<p><center><img align="center" src="doc-files/lagrange1.gif"/></center>



<p>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.



<p>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.



<p><center><img align="center" src="doc-files/lagrange2.gif"/></center>



<p>Lagrange curves and also be closed as shown in figures 3 &amp; 4.



<p><center><img align="center" src="doc-files/lagrange3.gif"/></center>



<p><center><img align="center" src="doc-files/lagrange4.gif"/></center>



<p>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.

*/

public class LagrangeCurve extends ParametricCurve {



	private ValueVector knotVector = new ValueVector(new double[] { 0.0, 1.0 / 3.0, 2.0 / 3.0, 1.0 }, 4);

	private int baseIndex = 1;

	private int baseLength = 1;

	private boolean interpolateFirst = false;

	private boolean interpolateLast = false;



	private static double[][] pt = new double[0][];



	/**

	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 #appendTo(MultiPath)

	*/

	public LagrangeCurve(ControlPath cp, GroupIterator gi) {

		super(cp, gi);

	}



	/**

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



	@see #setBaseIndex(int)

	*/

	public int getBaseIndex() {

		return baseIndex;

	}



	/**

	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 < 0.

	@see #getBaseIndex()

	*/

	public void setBaseIndex(int b) {

		if (b < 0) throw new IllegalArgumentException("base index >= 0 required.");

		baseIndex = b;

	}



	/**

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



	@see #setBaseLength(int)

	*/

	public int getBaseLength() {

		return baseLength;

	}



	/**

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



	@throws IllegalArgumentException If base-length <= 0.

	@see #getBaseLength()

	*/

	public void setBaseLength(int b) {

		if (b <= 0) throw new IllegalArgumentException("base length > 0 required.");

		baseLength = b;

	}



	/**

	If baseIndex > 0 then the first control-points will only be interpolated if interpolate-first

	is set to true.



	@see #setInterpolateFirst(boolean)

	*/

	public boolean getInterpolateFirst() {

		return interpolateFirst;

	}



	/**

	If baseIndex + baseLength < numKnots - 1 then the last control-points will only be interpolated if

	interpolate-last is set to true.



	@see #setInterpolateLast(boolean)

	*/

	public boolean getInterpolateLast() {

		return interpolateLast;

	}



	/**

	Sets the value of the interpolateFirst flag.



	@see #getInterpolateFirst()

	*/

	public void setInterpolateFirst(boolean b) {

		interpolateFirst = b;

	}



	/**

	Sets the value of the interpolateLast flag.



	@see #getInterpolateLast()

	*/

	public void setInterpolateLast(boolean b) {

		interpolateLast = b;

	}



	/**

	Returns the knot-vector for this curve.



	@see #setKnotVector(ValueVector)

	*/

	public ValueVector getKnotVector() {

		return knotVector;

	}



	/**

	Sets the knot-vector for this curve.



	@see #getKnotVector()

	@throws IllegalArgumentException If the value-vector is null.

	*/

	public void setKnotVector(ValueVector v) {

		if (v == null)

			throw new IllegalArgumentException("Knot-vector cannot be null.");

		knotVector = v;

	}



	/**

	Returns a value of 1.

	*/

	public int getSampleLimit() {

		return 1;

	}



	protected void eval(double[] p) {

		double t = p[p.length - 1];



		int n = knotVector.size();



		for (int i = 0; i < n; i++) {

			double[] q = pt[i];

			double L = L(t, i);

			for (int j = 0; j < p.length - 1; j++)

				p[j] += q[j] * L;

		}

	}



	private double L(double t, int i) {

		double d = 1.0;



		int n = knotVector.size();



		for (int j = 0; j < n; j++) {

			double e = knotVector.get(i) - knotVector.get(j);

			if (e != 0)

				d = d * ((t - knotVector.get(j)) / e);

		}



		return d;

	}



	/**

	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.

	*/

	public void appendTo(MultiPath mp) {

		if (!gi.isInRange(0, cp.numPoints())) return;

		if (baseIndex + baseLength >= knotVector.size()) return;



		if (pt.length < knotVector.size())

			pt = new double[2 * knotVector.size()][];



		gi.set(0, 0);



		boolean b = false;



		if (baseIndex != 0 && interpolateFirst) {

			for (int i = 0; i < knotVector.size(); i++) {

				if (!gi.hasNext()) return;

				pt[i] = cp.getPoint(gi.next()).getLocation();

			}



			b = doBCAA(mp, knotVector.get(0), knotVector.get(baseIndex), b);

		}



		gi.set(0, 0);



		int last_i = 0;

		int last_j = 0;



		while (true) {

			int temp_i = gi.index_i();

			int temp_j = gi.count_j();



			int index_i = 0;

			int count_j = 0;

			int i = 0;



			int j = 0;

			for (; j < knotVector.size(); j++) {

				if (i == baseLength) {

					index_i = gi.index_i();

					count_j = gi.count_j();

				}



				if (!gi.hasNext()) break;

				pt[j] = cp.getPoint(gi.next()).getLocation();

				i++;

			}



			if (j < knotVector.size()) {

				break;

			}

			else {

				gi.set(index_i, count_j);

				last_i = temp_i;

				last_j = temp_j;

			}



			b = doBCAA(mp, knotVector.get(baseIndex), knotVector.get(baseIndex + baseLength), b);

		}



		if (baseIndex + baseLength < knotVector.size() - 1 && interpolateLast) {

			gi.set(last_i, last_j);



			for (int i = 0; i < knotVector.size(); i++) {

				if (!gi.hasNext()) {

					System.out.println("not enough points to interpolate last");

					return;

				}

				pt[i] = cp.getPoint(gi.next()).getLocation();

			}



			doBCAA(mp, knotVector.get(baseIndex + baseLength), knotVector.get(knotVector.size() - 1), b);

		}

	}



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

		if (t2 < t1) {

			double temp = t1;

			t1 = t2;

			t2 = temp;

		}



		if (!b) {

			b = true;

			double[] d = new double[mp.getDimension() + 1];

			d[mp.getDimension()] = t1;

			eval(d);



			if (connect)

				mp.lineTo(d);

			else

				mp.moveTo(d);

		}



		BinaryCurveApproximationAlgorithm.genPts(this, t1, t2, mp);



		return b;

	}



	public void resetMemory() {

		if (pt.length > 0)

			pt = new double[0][];

	}

}