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* this list of conditions and the following disclaimer.
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* this list of conditions and the following disclaimer in the documentation
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* used to endorse or promote products derived from this software without
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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 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()))
throw new
IllegalArgumentException("Group iterator not in range");
if (
baseIndex +
baseLength >=
knotVector.
size())
throw new
IllegalArgumentException("baseIndex + baseLength >= knotVector.size");
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())
throw new
IllegalArgumentException("Group iterator ended early");
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][];
}
}