CubicCurve2Dpublic abstract class CubicCurve2D extends Object implements Shape, CloneableThe CubicCurve2D class defines a cubic parametric curve
segment in {@code (x,y)} coordinate space.
This class is only the abstract superclass for all objects which
store a 2D cubic curve segment.
The actual storage representation of the coordinates is left to
the subclass. |
| Fields Summary |
|---|
| private static final int | BELOW | | private static final int | LOWEDGE | | private static final int | INSIDE | | private static final int | HIGHEDGE | | private static final int | ABOVE |
| Constructors Summary |
|---|
protected CubicCurve2D()This is an abstract class that cannot be instantiated directly.
Type-specific implementation subclasses are available for
instantiation and provide a number of formats for storing
the information necessary to satisfy the various accessor
methods below.
|
| Methods Summary |
|---|
| public java.lang.Object | clone()Creates a new object of the same class as this object.
try {
return super.clone();
} catch (CloneNotSupportedException e) {
// this shouldn't happen, since we are Cloneable
throw new InternalError();
}
| | public boolean | contains(double x, double y){@inheritDoc}
if (!(x * 0.0 + y * 0.0 == 0.0)) {
/* Either x or y was infinite or NaN.
* A NaN always produces a negative response to any test
* and Infinity values cannot be "inside" any path so
* they should return false as well.
*/
return false;
}
// We count the "Y" crossings to determine if the point is
// inside the curve bounded by its closing line.
double x1 = getX1();
double y1 = getY1();
double x2 = getX2();
double y2 = getY2();
int crossings =
(Curve.pointCrossingsForLine(x, y, x1, y1, x2, y2) +
Curve.pointCrossingsForCubic(x, y,
x1, y1,
getCtrlX1(), getCtrlY1(),
getCtrlX2(), getCtrlY2(),
x2, y2, 0));
return ((crossings & 1) == 1);
| | public boolean | contains(java.awt.geom.Point2D p){@inheritDoc}
return contains(p.getX(), p.getY());
| | public boolean | contains(double x, double y, double w, double h){@inheritDoc}
if (w <= 0 || h <= 0) {
return false;
}
// Assertion: Cubic curves closed by connecting their
// endpoints form either one or two convex halves with
// the closing line segment as an edge of both sides.
if (!(contains(x, y) &&
contains(x + w, y) &&
contains(x + w, y + h) &&
contains(x, y + h))) {
return false;
}
// Either the rectangle is entirely inside one of the convex
// halves or it crosses from one to the other, in which case
// it must intersect the closing line segment.
Rectangle2D rect = new Rectangle2D.Double(x, y, w, h);
return !rect.intersectsLine(getX1(), getY1(), getX2(), getY2());
| | public boolean | contains(java.awt.geom.Rectangle2D r){@inheritDoc}
return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
| | private static int | evalCubic(double[] vals, int num, boolean include0, boolean include1, double[] inflect, double c1, double cp1, double cp2, double c2)
int j = 0;
for (int i = 0; i < num; i++) {
double t = vals[i];
if ((include0 ? t >= 0 : t > 0) &&
(include1 ? t <= 1 : t < 1) &&
(inflect == null ||
inflect[1] + (2*inflect[2] + 3*inflect[3]*t)*t != 0))
{
double u = 1 - t;
vals[j++] = c1*u*u*u + 3*cp1*t*u*u + 3*cp2*t*t*u + c2*t*t*t;
}
}
return j;
| | private static void | fillEqn(double[] eqn, double val, double c1, double cp1, double cp2, double c2)
eqn[0] = c1 - val;
eqn[1] = (cp1 - c1) * 3.0;
eqn[2] = (cp2 - cp1 - cp1 + c1) * 3.0;
eqn[3] = c2 + (cp1 - cp2) * 3.0 - c1;
return;
| | private static double | findZero(double t, double target, double[] eqn)
double slopeqn[] = {eqn[1], 2*eqn[2], 3*eqn[3]};
double slope;
double origdelta = 0;
double origt = t;
while (true) {
slope = solveEqn(slopeqn, 2, t);
if (slope == 0) {
// At a local minima - must return
return t;
}
double y = solveEqn(eqn, 3, t);
if (y == 0) {
// Found it! - return it
return t;
}
// assert(slope != 0 && y != 0);
double delta = - (y / slope);
// assert(delta != 0);
if (origdelta == 0) {
origdelta = delta;
}
if (t < target) {
if (delta < 0) return t;
} else if (t > target) {
if (delta > 0) return t;
} else { /* t == target */
return (delta > 0
? (target + java.lang.Double.MIN_VALUE)
: (target - java.lang.Double.MIN_VALUE));
}
double newt = t + delta;
if (t == newt) {
// The deltas are so small that we aren't moving...
return t;
}
if (delta * origdelta < 0) {
// We have reversed our path.
int tag = (origt < t
? getTag(target, origt, t)
: getTag(target, t, origt));
if (tag != INSIDE) {
// Local minima found away from target - return the middle
return (origt + t) / 2;
}
// Local minima somewhere near target - move to target
// and let the slope determine the resulting t.
t = target;
} else {
t = newt;
}
}
| | private static void | fixRoots(double[] res, double[] eqn)
final double EPSILON = 1E-5;
for (int i = 0; i < 3; i++) {
double t = res[i];
if (Math.abs(t) < EPSILON) {
res[i] = findZero(t, 0, eqn);
} else if (Math.abs(t - 1) < EPSILON) {
res[i] = findZero(t, 1, eqn);
}
}
| | public java.awt.Rectangle | getBounds(){@inheritDoc}
return getBounds2D().getBounds();
| | public abstract java.awt.geom.Point2D | getCtrlP1()Returns the first control point.
| | public abstract java.awt.geom.Point2D | getCtrlP2()Returns the second control point.
| | public abstract double | getCtrlX1()Returns the X coordinate of the first control point in double precision.
| | public abstract double | getCtrlX2()Returns the X coordinate of the second control point
in double precision.
| | public abstract double | getCtrlY1()Returns the Y coordinate of the first control point in double precision.
| | public abstract double | getCtrlY2()Returns the Y coordinate of the second control point
in double precision.
| | public static double | getFlatness(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2)Returns the flatness of the cubic curve specified
by the indicated control points. The flatness is the maximum distance
of a control point from the line connecting the end points.
return Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1,
ctrlx2, ctrly2, x2, y2));
| | public static double | getFlatness(double[] coords, int offset)Returns the flatness of the cubic curve specified
by the control points stored in the indicated array at the
indicated index. The flatness is the maximum distance
of a control point from the line connecting the end points.
return getFlatness(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5],
coords[offset + 6], coords[offset + 7]);
| | public double | getFlatness()Returns the flatness of this curve. The flatness is the
maximum distance of a control point from the line connecting the
end points.
return getFlatness(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
getCtrlX2(), getCtrlY2(), getX2(), getY2());
| | public static double | getFlatnessSq(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2)Returns the square of the flatness of the cubic curve specified
by the indicated control points. The flatness is the maximum distance
of a control point from the line connecting the end points.
return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1, ctrly1),
Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2, ctrly2));
| | public static double | getFlatnessSq(double[] coords, int offset)Returns the square of the flatness of the cubic curve specified
by the control points stored in the indicated array at the
indicated index. The flatness is the maximum distance
of a control point from the line connecting the end points.
return getFlatnessSq(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5],
coords[offset + 6], coords[offset + 7]);
| | public double | getFlatnessSq()Returns the square of the flatness of this curve. The flatness is the
maximum distance of a control point from the line connecting the
end points.
return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
getCtrlX2(), getCtrlY2(), getX2(), getY2());
| | public abstract java.awt.geom.Point2D | getP1()Returns the start point.
| | public abstract java.awt.geom.Point2D | getP2()Returns the end point.
| | public java.awt.geom.PathIterator | getPathIterator(java.awt.geom.AffineTransform at)Returns an iteration object that defines the boundary of the
shape.
The iterator for this class is not multi-threaded safe,
which means that this CubicCurve2D class does not
guarantee that modifications to the geometry of this
CubicCurve2D object do not affect any iterations of
that geometry that are already in process.
return new CubicIterator(this, at);
| | public java.awt.geom.PathIterator | getPathIterator(java.awt.geom.AffineTransform at, double flatness)Return an iteration object that defines the boundary of the
flattened shape.
The iterator for this class is not multi-threaded safe,
which means that this CubicCurve2D class does not
guarantee that modifications to the geometry of this
CubicCurve2D object do not affect any iterations of
that geometry that are already in process.
return new FlatteningPathIterator(getPathIterator(at), flatness);
| | private static int | getTag(double coord, double low, double high)
/*
* Determine where coord lies with respect to the range from
* low to high. It is assumed that low <= high. The return
* value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
* or ABOVE.
*/
if (coord <= low) {
return (coord < low ? BELOW : LOWEDGE);
}
if (coord >= high) {
return (coord > high ? ABOVE : HIGHEDGE);
}
return INSIDE;
| | public abstract double | getX1()Returns the X coordinate of the start point in double precision.
| | public abstract double | getX2()Returns the X coordinate of the end point in double precision.
| | public abstract double | getY1()Returns the Y coordinate of the start point in double precision.
| | public abstract double | getY2()Returns the Y coordinate of the end point in double precision.
| | public boolean | intersects(double x, double y, double w, double h){@inheritDoc}
// Trivially reject non-existant rectangles
if (w <= 0 || h <= 0) {
return false;
}
// Trivially accept if either endpoint is inside the rectangle
// (not on its border since it may end there and not go inside)
// Record where they lie with respect to the rectangle.
// -1 => left, 0 => inside, 1 => right
double x1 = getX1();
double y1 = getY1();
int x1tag = getTag(x1, x, x+w);
int y1tag = getTag(y1, y, y+h);
if (x1tag == INSIDE && y1tag == INSIDE) {
return true;
}
double x2 = getX2();
double y2 = getY2();
int x2tag = getTag(x2, x, x+w);
int y2tag = getTag(y2, y, y+h);
if (x2tag == INSIDE && y2tag == INSIDE) {
return true;
}
double ctrlx1 = getCtrlX1();
double ctrly1 = getCtrlY1();
double ctrlx2 = getCtrlX2();
double ctrly2 = getCtrlY2();
int ctrlx1tag = getTag(ctrlx1, x, x+w);
int ctrly1tag = getTag(ctrly1, y, y+h);
int ctrlx2tag = getTag(ctrlx2, x, x+w);
int ctrly2tag = getTag(ctrly2, y, y+h);
// Trivially reject if all points are entirely to one side of
// the rectangle.
if (x1tag < INSIDE && x2tag < INSIDE &&
ctrlx1tag < INSIDE && ctrlx2tag < INSIDE)
{
return false; // All points left
}
if (y1tag < INSIDE && y2tag < INSIDE &&
ctrly1tag < INSIDE && ctrly2tag < INSIDE)
{
return false; // All points above
}
if (x1tag > INSIDE && x2tag > INSIDE &&
ctrlx1tag > INSIDE && ctrlx2tag > INSIDE)
{
return false; // All points right
}
if (y1tag > INSIDE && y2tag > INSIDE &&
ctrly1tag > INSIDE && ctrly2tag > INSIDE)
{
return false; // All points below
}
// Test for endpoints on the edge where either the segment
// or the curve is headed "inwards" from them
// Note: These tests are a superset of the fast endpoint tests
// above and thus repeat those tests, but take more time
// and cover more cases
if (inwards(x1tag, x2tag, ctrlx1tag) &&
inwards(y1tag, y2tag, ctrly1tag))
{
// First endpoint on border with either edge moving inside
return true;
}
if (inwards(x2tag, x1tag, ctrlx2tag) &&
inwards(y2tag, y1tag, ctrly2tag))
{
// Second endpoint on border with either edge moving inside
return true;
}
// Trivially accept if endpoints span directly across the rectangle
boolean xoverlap = (x1tag * x2tag <= 0);
boolean yoverlap = (y1tag * y2tag <= 0);
if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
return true;
}
if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
return true;
}
// We now know that both endpoints are outside the rectangle
// but the 4 points are not all on one side of the rectangle.
// Therefore the curve cannot be contained inside the rectangle,
// but the rectangle might be contained inside the curve, or
// the curve might intersect the boundary of the rectangle.
double[] eqn = new double[4];
double[] res = new double[4];
if (!yoverlap) {
// Both y coordinates for the closing segment are above or
// below the rectangle which means that we can only intersect
// if the curve crosses the top (or bottom) of the rectangle
// in more than one place and if those crossing locations
// span the horizontal range of the rectangle.
fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly1, ctrly2, y2);
int num = solveCubic(eqn, res);
num = evalCubic(res, num, true, true, null,
x1, ctrlx1, ctrlx2, x2);
// odd counts imply the crossing was out of [0,1] bounds
// otherwise there is no way for that part of the curve to
// "return" to meet its endpoint
return (num == 2 &&
getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0);
}
// Y ranges overlap. Now we examine the X ranges
if (!xoverlap) {
// Both x coordinates for the closing segment are left of
// or right of the rectangle which means that we can only
// intersect if the curve crosses the left (or right) edge
// of the rectangle in more than one place and if those
// crossing locations span the vertical range of the rectangle.
fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx1, ctrlx2, x2);
int num = solveCubic(eqn, res);
num = evalCubic(res, num, true, true, null,
y1, ctrly1, ctrly2, y2);
// odd counts imply the crossing was out of [0,1] bounds
// otherwise there is no way for that part of the curve to
// "return" to meet its endpoint
return (num == 2 &&
getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0);
}
// The X and Y ranges of the endpoints overlap the X and Y
// ranges of the rectangle, now find out how the endpoint
// line segment intersects the Y range of the rectangle
double dx = x2 - x1;
double dy = y2 - y1;
double k = y2 * x1 - x2 * y1;
int c1tag, c2tag;
if (y1tag == INSIDE) {
c1tag = x1tag;
} else {
c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w);
}
if (y2tag == INSIDE) {
c2tag = x2tag;
} else {
c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w);
}
// If the part of the line segment that intersects the Y range
// of the rectangle crosses it horizontally - trivially accept
if (c1tag * c2tag <= 0) {
return true;
}
// Now we know that both the X and Y ranges intersect and that
// the endpoint line segment does not directly cross the rectangle.
//
// We can almost treat this case like one of the cases above
// where both endpoints are to one side, except that we may
// get one or three intersections of the curve with the vertical
// side of the rectangle. This is because the endpoint segment
// accounts for the other intersection in an even pairing. Thus,
// with the endpoint crossing we end up with 2 or 4 total crossings.
//
// (Remember there is overlap in both the X and Y ranges which
// means that the segment itself must cross at least one vertical
// edge of the rectangle - in particular, the "near vertical side"
// - leaving an odd number of intersections for the curve.)
//
// Now we calculate the y tags of all the intersections on the
// "near vertical side" of the rectangle. We will have one with
// the endpoint segment, and one or three with the curve. If
// any pair of those vertical intersections overlap the Y range
// of the rectangle, we have an intersection. Otherwise, we don't.
// c1tag = vertical intersection class of the endpoint segment
//
// Choose the y tag of the endpoint that was not on the same
// side of the rectangle as the subsegment calculated above.
// Note that we can "steal" the existing Y tag of that endpoint
// since it will be provably the same as the vertical intersection.
c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);
// Now we have to calculate an array of solutions of the curve
// with the "near vertical side" of the rectangle. Then we
// need to sort the tags and do a pairwise range test to see
// if either of the pairs of crossings spans the Y range of
// the rectangle.
//
// Note that the c2tag can still tell us which vertical edge
// to test against.
fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx1, ctrlx2, x2);
int num = solveCubic(eqn, res);
num = evalCubic(res, num, true, true, null, y1, ctrly1, ctrly2, y2);
// Now put all of the tags into a bucket and sort them. There
// is an intersection iff one of the pairs of tags "spans" the
// Y range of the rectangle.
int tags[] = new int[num+1];
for (int i = 0; i < num; i++) {
tags[i] = getTag(res[i], y, y+h);
}
tags[num] = c1tag;
Arrays.sort(tags);
return ((num >= 1 && tags[0] * tags[1] <= 0) ||
(num >= 3 && tags[2] * tags[3] <= 0));
| | public boolean | intersects(java.awt.geom.Rectangle2D r){@inheritDoc}
return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
| | private static boolean | inwards(int pttag, int opt1tag, int opt2tag)
switch (pttag) {
case BELOW:
case ABOVE:
default:
return false;
case LOWEDGE:
return (opt1tag >= INSIDE || opt2tag >= INSIDE);
case INSIDE:
return true;
case HIGHEDGE:
return (opt1tag <= INSIDE || opt2tag <= INSIDE);
}
| | public abstract void | setCurve(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2)Sets the location of the end points and control points of this curve
to the specified double coordinates.
| | public void | setCurve(double[] coords, int offset)Sets the location of the end points and control points of this curve
to the double coordinates at the specified offset in the specified
array.
setCurve(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5],
coords[offset + 6], coords[offset + 7]);
| | public void | setCurve(java.awt.geom.Point2D p1, java.awt.geom.Point2D cp1, java.awt.geom.Point2D cp2, java.awt.geom.Point2D p2)Sets the location of the end points and control points of this curve
to the specified Point2D coordinates.
setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(),
cp2.getX(), cp2.getY(), p2.getX(), p2.getY());
| | public void | setCurve(java.awt.geom.Point2D[] pts, int offset)Sets the location of the end points and control points of this curve
to the coordinates of the Point2D objects at the specified
offset in the specified array.
setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
pts[offset + 1].getX(), pts[offset + 1].getY(),
pts[offset + 2].getX(), pts[offset + 2].getY(),
pts[offset + 3].getX(), pts[offset + 3].getY());
| | public void | setCurve(java.awt.geom.CubicCurve2D c)Sets the location of the end points and control points of this curve
to the same as those in the specified CubicCurve2D.
setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
| | public static int | solveCubic(double[] eqn)Solves the cubic whose coefficients are in the eqn
array and places the non-complex roots back into the same array,
returning the number of roots. The solved cubic is represented
by the equation:
eqn = {c, b, a, d}
dx^3 + ax^2 + bx + c = 0
A return value of -1 is used to distinguish a constant equation
that might be always 0 or never 0 from an equation that has no
zeroes.
return solveCubic(eqn, eqn);
| | public static int | solveCubic(double[] eqn, double[] res)Solve the cubic whose coefficients are in the eqn
array and place the non-complex roots into the res
array, returning the number of roots.
The cubic solved is represented by the equation:
eqn = {c, b, a, d}
dx^3 + ax^2 + bx + c = 0
A return value of -1 is used to distinguish a constant equation,
which may be always 0 or never 0, from an equation which has no
zeroes.
// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
double d = eqn[3];
if (d == 0.0) {
// The cubic has degenerated to quadratic (or line or ...).
return QuadCurve2D.solveQuadratic(eqn, res);
}
double a = eqn[2] / d;
double b = eqn[1] / d;
double c = eqn[0] / d;
int roots = 0;
double Q = (a * a - 3.0 * b) / 9.0;
double R = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0;
double R2 = R * R;
double Q3 = Q * Q * Q;
a = a / 3.0;
if (R2 < Q3) {
double theta = Math.acos(R / Math.sqrt(Q3));
Q = -2.0 * Math.sqrt(Q);
if (res == eqn) {
// Copy the eqn so that we don't clobber it with the
// roots. This is needed so that fixRoots can do its
// work with the original equation.
eqn = new double[4];
System.arraycopy(res, 0, eqn, 0, 4);
}
res[roots++] = Q * Math.cos(theta / 3.0) - a;
res[roots++] = Q * Math.cos((theta + Math.PI * 2.0)/ 3.0) - a;
res[roots++] = Q * Math.cos((theta - Math.PI * 2.0)/ 3.0) - a;
fixRoots(res, eqn);
} else {
boolean neg = (R < 0.0);
double S = Math.sqrt(R2 - Q3);
if (neg) {
R = -R;
}
double A = Math.pow(R + S, 1.0 / 3.0);
if (!neg) {
A = -A;
}
double B = (A == 0.0) ? 0.0 : (Q / A);
res[roots++] = (A + B) - a;
}
return roots;
| | private static double | solveEqn(double[] eqn, int order, double t)
double v = eqn[order];
while (--order >= 0) {
v = v * t + eqn[order];
}
return v;
| | public void | subdivide(java.awt.geom.CubicCurve2D left, java.awt.geom.CubicCurve2D right)Subdivides this cubic curve and stores the resulting two
subdivided curves into the left and right curve parameters.
Either or both of the left and right objects may be the same
as this object or null.
subdivide(this, left, right);
| | public static void | subdivide(java.awt.geom.CubicCurve2D src, java.awt.geom.CubicCurve2D left, java.awt.geom.CubicCurve2D right)Subdivides the cubic curve specified by the src parameter
and stores the resulting two subdivided curves into the
left and right curve parameters.
Either or both of the left and right objects
may be the same as the src object or null.
double x1 = src.getX1();
double y1 = src.getY1();
double ctrlx1 = src.getCtrlX1();
double ctrly1 = src.getCtrlY1();
double ctrlx2 = src.getCtrlX2();
double ctrly2 = src.getCtrlY2();
double x2 = src.getX2();
double y2 = src.getY2();
double centerx = (ctrlx1 + ctrlx2) / 2.0;
double centery = (ctrly1 + ctrly2) / 2.0;
ctrlx1 = (x1 + ctrlx1) / 2.0;
ctrly1 = (y1 + ctrly1) / 2.0;
ctrlx2 = (x2 + ctrlx2) / 2.0;
ctrly2 = (y2 + ctrly2) / 2.0;
double ctrlx12 = (ctrlx1 + centerx) / 2.0;
double ctrly12 = (ctrly1 + centery) / 2.0;
double ctrlx21 = (ctrlx2 + centerx) / 2.0;
double ctrly21 = (ctrly2 + centery) / 2.0;
centerx = (ctrlx12 + ctrlx21) / 2.0;
centery = (ctrly12 + ctrly21) / 2.0;
if (left != null) {
left.setCurve(x1, y1, ctrlx1, ctrly1,
ctrlx12, ctrly12, centerx, centery);
}
if (right != null) {
right.setCurve(centerx, centery, ctrlx21, ctrly21,
ctrlx2, ctrly2, x2, y2);
}
| | public static void | subdivide(double[] src, int srcoff, double[] left, int leftoff, double[] right, int rightoff)Subdivides the cubic curve specified by the coordinates
stored in the src array at indices srcoff
through (srcoff + 7) and stores the
resulting two subdivided curves into the two result arrays at the
corresponding indices.
Either or both of the left and right
arrays may be null or a reference to the same array
as the src array.
Note that the last point in the first subdivided curve is the
same as the first point in the second subdivided curve. Thus,
it is possible to pass the same array for left
and right and to use offsets, such as rightoff
equals (leftoff + 6), in order
to avoid allocating extra storage for this common point.
double x1 = src[srcoff + 0];
double y1 = src[srcoff + 1];
double ctrlx1 = src[srcoff + 2];
double ctrly1 = src[srcoff + 3];
double ctrlx2 = src[srcoff + 4];
double ctrly2 = src[srcoff + 5];
double x2 = src[srcoff + 6];
double y2 = src[srcoff + 7];
if (left != null) {
left[leftoff + 0] = x1;
left[leftoff + 1] = y1;
}
if (right != null) {
right[rightoff + 6] = x2;
right[rightoff + 7] = y2;
}
x1 = (x1 + ctrlx1) / 2.0;
y1 = (y1 + ctrly1) / 2.0;
x2 = (x2 + ctrlx2) / 2.0;
y2 = (y2 + ctrly2) / 2.0;
double centerx = (ctrlx1 + ctrlx2) / 2.0;
double centery = (ctrly1 + ctrly2) / 2.0;
ctrlx1 = (x1 + centerx) / 2.0;
ctrly1 = (y1 + centery) / 2.0;
ctrlx2 = (x2 + centerx) / 2.0;
ctrly2 = (y2 + centery) / 2.0;
centerx = (ctrlx1 + ctrlx2) / 2.0;
centery = (ctrly1 + ctrly2) / 2.0;
if (left != null) {
left[leftoff + 2] = x1;
left[leftoff + 3] = y1;
left[leftoff + 4] = ctrlx1;
left[leftoff + 5] = ctrly1;
left[leftoff + 6] = centerx;
left[leftoff + 7] = centery;
}
if (right != null) {
right[rightoff + 0] = centerx;
right[rightoff + 1] = centery;
right[rightoff + 2] = ctrlx2;
right[rightoff + 3] = ctrly2;
right[rightoff + 4] = x2;
right[rightoff + 5] = y2;
}
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