LagrangeCurve.java
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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 & 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 final ThreadLocal<SharedData> SHARED_DATA = new ThreadLocal<SharedData>(){
protected SharedData initialValue() {
return new SharedData();
}
};
private final SharedData sharedData = SHARED_DATA.get();
private static class SharedData {
private 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 = sharedData.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()))
throw new IllegalArgumentException("Group iterator not in range");
if (baseIndex + baseLength >= knotVector.size())
throw new IllegalArgumentException("baseIndex + baseLength >= knotVector.size");
if (sharedData.pt.length < knotVector.size())
sharedData.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())
throw new IllegalArgumentException("Group iterator ended early");
sharedData.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;
sharedData.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;
}
sharedData.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 (sharedData.pt.length > 0)
sharedData.pt = new double[0][];
}
}