/*
* Copyright 2003-2010 Tufts University Licensed under the
* Educational Community License, Version 2.0 (the "License"); you may
* not use this file except in compliance with the License. You may
* obtain a copy of the License at
*
* http://www.osedu.org/licenses/ECL-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an "AS IS"
* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
* or implied. See the License for the specific language governing
* permissions and limitations under the License.
*/
package tufts.vue.shape;
import java.awt.geom.Rectangle2D;
import java.awt.geom.QuadCurve2D;
import java.awt.geom.CubicCurve2D;
import java.awt.geom.PathIterator;
import java.util.Vector;
public abstract class Curve {
public static final int INCREASING = 1;
public static final int DECREASING = -1;
protected int direction;
public static void insertMove(Vector curves, double x, double y) {
curves.add(new Order0(x, y));
}
public static void insertLine(Vector curves,
double x0, double y0,
double x1, double y1)
{
if (y0 < y1) {
curves.add(new Order1(x0, y0,
x1, y1,
INCREASING));
} else if (y0 > y1) {
curves.add(new Order1(x1, y1,
x0, y0,
DECREASING));
} else {
// Do not add horizontal lines
}
}
public static void insertQuad(Vector curves,
double x0, double y0,
double coords[])
{
double y1 = coords[3];
if (y0 > y1) {
Order2.insert(curves, coords,
coords[2], y1,
coords[0], coords[1],
x0, y0,
DECREASING);
} else if (y0 == y1 && y0 == coords[1]) {
// Do not add horizontal lines
return;
} else {
Order2.insert(curves, coords,
x0, y0,
coords[0], coords[1],
coords[2], y1,
INCREASING);
}
}
public static void insertCubic(Vector curves,
double x0, double y0,
double coords[])
{
double y1 = coords[5];
if (y0 > y1) {
Order3.insert(curves, coords,
coords[4], y1,
coords[2], coords[3],
coords[0], coords[1],
x0, y0,
DECREASING);
} else if (y0 == y1 && y0 == coords[1] && y0 == coords[3]) {
// Do not add horizontal lines
return;
} else {
Order3.insert(curves, coords,
x0, y0,
coords[0], coords[1],
coords[2], coords[3],
coords[4], y1,
INCREASING);
}
}
public static int crossingsForLine(double x, double y,
double x0, double y0,
double x1, double y1)
{
if (y0 > y1) {
return 0 - crossingsForLine(x, y, x1, y1, x0, y0);
}
if (y0 == y1) {
return 0;
}
if (y < y0 || y >= y1) {
return 0;
}
if (x >= x0 && x >= x1) {
return 0;
}
double t = (y - y0) / (y1 - y0);
return ((x < x0 + t * (x1 - x0)) ? 1 : 0);
}
public static int crossingsForQuad(double x, double y,
double x0, double y0,
double coords[])
{
double cx0 = coords[0];
double cy0 = coords[1];
double x1 = coords[2];
double y1 = coords[3];
if (y < y0 && y < cy0 && y < y1) {
return 0;
}
if (y >= y0 && y >= cy0 && y >= y1) {
return 0;
}
if (x >= x0 && x >= cx0 && x >= x1) {
return 0;
}
if (x < x0 && x < cx0 && x < x1) {
if (y0 < y1) {
return ((y >= y0 && y < y1) ? 1 : 0);
} else if (y1 < y0) {
return ((y >= y1 && y < y0) ? -1 : 0);
} else {
return 0;
}
}
double eqnx[] = new double[3];
double eqny[] = new double[3];
Order2.getEqn(eqnx, x0, coords[0], coords[2]);
Order2.getEqn(eqny, y0, coords[1], coords[3]);
System.arraycopy(eqny, 0, coords, 0, 3);
coords[0] -= y;
int numroots = QuadCurve2D.solveQuadratic(coords, coords);
int cross = 0;
for (int i = 0; i < numroots; i++) {
double t = coords[i];
if (t >= 0 && t <= 1) {
double v = (eqnx[2]*t + eqnx[1])*t + eqnx[0];
if (x <= v) {
v = 2*eqny[2]*t + eqny[1];
if (v > 0) {
cross++;
} else if (v < 0) {
cross--;
}
}
}
}
return cross;
}
public static int crossingsForCubic(double x, double y,
double x0, double y0,
double coords[])
{
double cx0 = coords[0];
double cy0 = coords[1];
double cx1 = coords[2];
double cy1 = coords[3];
double x1 = coords[4];
double y1 = coords[5];
if (y < y0 && y < cy0 && y < cy1 && y < y1) {
return 0;
}
if (y >= y0 && y >= cy0 && y >= cy1 && y >= y1) {
return 0;
}
if (x >= x0 && x >= cx0 && x >= cx1 && x >= x1) {
return 0;
}
if (x < x0 && x < cx0 && x < cx1 && x < x1) {
if (y0 < y1) {
return ((y >= y0 && y < y1) ? 1 : 0);
} else if (y1 < y0) {
return ((y >= y1 && y < y0) ? -1 : 0);
} else {
return 0;
}
}
double eqnx[] = new double[4];
double eqny[] = new double[4];
Order3.getEqn(eqnx, x0, coords[0], coords[2], coords[4]);
Order3.getEqn(eqny, y0, coords[1], coords[3], coords[5]);
System.arraycopy(eqny, 0, coords, 0, 4);
coords[0] -= y;
int numroots = CubicCurve2D.solveCubic(coords, coords);
int cross = 0;
for (int i = 0; i < numroots; i++) {
double t = coords[i];
if (t >= 0 && t <= 1) {
double v = ((eqnx[3]*t + eqnx[2])*t + eqnx[1])*t + eqnx[0];
if (x <= v) {
v = (3*eqny[3]*t + 2*eqny[2])*t + eqny[1];
if (v > 0) {
cross++;
} else if (v < 0) {
cross--;
}
}
}
}
return cross;
}
public static int crossingsForPath(PathIterator pi, double x, double y) {
double movx = 0;
double movy = 0;
double curx = 0;
double cury = 0;
double newx, newy;
int cross = 0;
double coords[] = new double[6];
while (!pi.isDone()) {
switch (pi.currentSegment(coords)) {
case PathIterator.SEG_MOVETO:
if (cury != movy) {
cross += Curve.crossingsForLine(x, y,
curx, cury,
movx, movy);
}
movx = curx = coords[0];
movy = cury = coords[1];
break;
case PathIterator.SEG_LINETO:
newx = coords[0];
newy = coords[1];
cross += Curve.crossingsForLine(x, y,
curx, cury,
newx, newy);
curx = newx;
cury = newy;
break;
case PathIterator.SEG_QUADTO:
newx = coords[2];
newy = coords[3];
cross += Curve.crossingsForQuad(x, y,
curx, cury,
coords);
curx = newx;
cury = newy;
break;
case PathIterator.SEG_CUBICTO:
newx = coords[4];
newy = coords[5];
cross += Curve.crossingsForCubic(x, y,
curx, cury,
coords);
curx = newx;
cury = newy;
break;
case PathIterator.SEG_CLOSE:
if (cury != movy) {
cross += Curve.crossingsForLine(x, y,
curx, cury,
movx, movy);
}
curx = movx;
cury = movy;
break;
}
pi.next();
}
if (cury != movy) {
cross += Curve.crossingsForLine(x, y,
curx, cury,
movx, movy);
}
return cross;
}
public Curve(int direction) {
this.direction = direction;
}
public final int getDirection() {
return direction;
}
public final Curve getWithDirection(int direction) {
return (this.direction == direction ? this : getReversedCurve());
}
public static double round(double v) {
//return Math.rint(v*10)/10;
return v;
}
public static double firstValidRoot(double roots[], int numroots) {
for (int i = 0; i < numroots; i++) {
double t = roots[i];
if (t >= 0 && t <= 1) {
return t;
}
}
return 0;
}
public static int orderof(double x1, double x2) {
if (x1 < x2) {
return -1;
}
if (x1 > x2) {
return 1;
}
return 0;
}
public static long signeddiffbits(double y1, double y2) {
return (Double.doubleToLongBits(y1) - Double.doubleToLongBits(y2));
}
public static long diffbits(double y1, double y2) {
return Math.abs(Double.doubleToLongBits(y1) -
Double.doubleToLongBits(y2));
}
public static double prev(double v) {
return Double.longBitsToDouble(Double.doubleToLongBits(v)-1);
}
public static double next(double v) {
return Double.longBitsToDouble(Double.doubleToLongBits(v)+1);
}
public String toString() {
return ("Curve["+
getOrder()+", "+
("("+round(getX0())+", "+round(getY0())+"), ")+
controlPointString()+
("("+round(getX1())+", "+round(getY1())+"), ")+
(direction == INCREASING ? "D" : "U")+
"]");
}
public String controlPointString() {
return "";
}
public abstract int getOrder();
public abstract double getXTop();
public abstract double getYTop();
public abstract double getXBot();
public abstract double getYBot();
public abstract double getXMin();
public abstract double getXMax();
public abstract double getX0();
public abstract double getY0();
public abstract double getX1();
public abstract double getY1();
public abstract double XforY(double y);
public abstract double TforY(double y);
public abstract double XforT(double t);
public abstract double YforT(double t);
public abstract double dXforT(double t, int deriv);
public abstract double dYforT(double t, int deriv);
public abstract double nextVertical(double t0, double t1);
public int crossingsFor(double x, double y) {
if (y >= getYTop() && y < getYBot()) {
if (x < getXMax() && (x < getXMin() || x < XforY(y))) {
return 1;
}
}
return 0;
}
public boolean accumulateCrossings(Crossings c) {
double xhi = c.getXHi();
if (getXMin() >= xhi) {
return false;
}
double xlo = c.getXLo();
double ylo = c.getYLo();
double yhi = c.getYHi();
double y0 = getYTop();
double y1 = getYBot();
double tstart, ystart, tend, yend;
if (y0 < ylo) {
if (y1 <= ylo) {
return false;
}
ystart = ylo;
tstart = TforY(ylo);
} else {
if (y0 >= yhi) {
return false;
}
ystart = y0;
tstart = 0;
}
if (y1 > yhi) {
yend = yhi;
tend = TforY(yhi);
} else {
yend = y1;
tend = 1;
}
boolean hitLo = false;
boolean hitHi = false;
while (true) {
double x = XforT(tstart);
if (x < xhi) {
if (hitHi || x > xlo) {
return true;
}
hitLo = true;
} else {
if (hitLo) {
return true;
}
hitHi = true;
}
if (tstart >= tend) {
break;
}
tstart = nextVertical(tstart, tend);
}
if (hitLo) {
c.record(ystart, yend, direction);
}
return false;
}
public abstract void enlarge(Rectangle2D r);
public Curve getSubCurve(double ystart, double yend) {
return getSubCurve(ystart, yend, direction);
}
public abstract Curve getReversedCurve();
public abstract Curve getSubCurve(double ystart, double yend, int dir);
public int compareTo(Curve that, double yrange[]) {
/*
System.out.println(this+".compareTo("+that+")");
System.out.println("target range = "+yrange[0]+"=>"+yrange[1]);
*/
double y0 = yrange[0];
double y1 = yrange[1];
y1 = Math.min(Math.min(y1, this.getYBot()), that.getYBot());
if (y1 <= yrange[0]) {
System.err.println("this == "+this);
System.err.println("that == "+that);
System.out.println("target range = "+yrange[0]+"=>"+yrange[1]);
throw new InternalError("backstepping from "+yrange[0]+" to "+y1);
}
yrange[1] = y1;
if (this.getXMax() <= that.getXMin()) {
if (this.getXMin() == that.getXMax()) {
return 0;
}
return -1;
}
if (this.getXMin() >= that.getXMax()) {
return 1;
}
// Parameter s for thi(s) curve and t for tha(t) curve
// [st]0 = parameters for top of current section of interest
// [st]1 = parameters for bottom of valid range
// [st]h = parameters for hypothesis point
// [d][xy]s = valuations of thi(s) curve at sh
// [d][xy]t = valuations of tha(t) curve at th
double s0 = this.TforY(y0);
double ys0 = this.YforT(s0);
if (ys0 < y0) {
s0 = refineTforY(s0, ys0, y0);
ys0 = this.YforT(s0);
}
double s1 = this.TforY(y1);
if (this.YforT(s1) < y0) {
s1 = refineTforY(s1, this.YforT(s1), y0);
//System.out.println("s1 problem!");
}
double t0 = that.TforY(y0);
double yt0 = that.YforT(t0);
if (yt0 < y0) {
t0 = that.refineTforY(t0, yt0, y0);
yt0 = that.YforT(t0);
}
double t1 = that.TforY(y1);
if (that.YforT(t1) < y0) {
t1 = that.refineTforY(t1, that.YforT(t1), y0);
//System.out.println("t1 problem!");
}
double xs0 = this.XforT(s0);
double xt0 = that.XforT(t0);
double scale = Math.max(Math.abs(y0), Math.abs(y1));
double ymin = Math.max(scale * 1E-14, 1E-300);
if (fairlyClose(xs0, xt0)) {
double bump = ymin;
double maxbump = Math.min(ymin * 1E13, (y1 - y0) * .1);
double y = y0 + bump;
while (y <= y1) {
if (fairlyClose(this.XforY(y), that.XforY(y))) {
if ((bump *= 2) > maxbump) {
bump = maxbump;
}
} else {
y -= bump;
while (true) {
bump /= 2;
double newy = y + bump;
if (newy <= y) {
break;
}
if (fairlyClose(this.XforY(newy), that.XforY(newy))) {
y = newy;
}
}
break;
}
y += bump;
}
if (y > y0) {
if (y < y1) {
yrange[1] = y;
}
return 0;
}
}
//double ymin = y1 * 1E-14;
if (ymin <= 0) {
System.out.println("ymin = "+ymin);
}
/*
System.out.println("s range = "+s0+" to "+s1);
System.out.println("t range = "+t0+" to "+t1);
*/
while (s0 < s1 && t0 < t1) {
double sh = this.nextVertical(s0, s1);
double xsh = this.XforT(sh);
double ysh = this.YforT(sh);
double th = that.nextVertical(t0, t1);
double xth = that.XforT(th);
double yth = that.YforT(th);
/*
System.out.println("sh = "+sh);
System.out.println("th = "+th);
*/
try {
if (findIntersect(that, yrange, ymin, 0, 0,
s0, xs0, ys0, sh, xsh, ysh,
t0, xt0, yt0, th, xth, yth)) {
break;
}
} catch (Throwable t) {
System.err.println("Error: "+t);
System.err.println("y range was "+yrange[0]+"=>"+yrange[1]);
System.err.println("s y range is "+ys0+"=>"+ysh);
System.err.println("t y range is "+yt0+"=>"+yth);
System.err.println("ymin is "+ymin);
return 0;
}
if (ysh < yth) {
if (ysh > yrange[0]) {
if (ysh < yrange[1]) {
yrange[1] = ysh;
}
break;
}
s0 = sh;
xs0 = xsh;
ys0 = ysh;
} else {
if (yth > yrange[0]) {
if (yth < yrange[1]) {
yrange[1] = yth;
}
break;
}
t0 = th;
xt0 = xth;
yt0 = yth;
}
}
double ymid = (yrange[0] + yrange[1]) / 2;
/*
System.out.println("final this["+s0+", "+sh+", "+s1+"]");
System.out.println("final y["+ys0+", "+ysh+"]");
System.out.println("final that["+t0+", "+th+", "+t1+"]");
System.out.println("final y["+yt0+", "+yth+"]");
System.out.println("final order = "+orderof(this.XforY(ymid),
that.XforY(ymid)));
System.out.println("final range = "+yrange[0]+"=>"+yrange[1]);
*/
/*
System.out.println("final sx = "+this.XforY(ymid));
System.out.println("final tx = "+that.XforY(ymid));
System.out.println("final order = "+orderof(this.XforY(ymid),
that.XforY(ymid)));
*/
return orderof(this.XforY(ymid), that.XforY(ymid));
}
public static final double TMIN = 1E-3;
public boolean findIntersect(Curve that, double yrange[], double ymin,
int slevel, int tlevel,
double s0, double xs0, double ys0,
double s1, double xs1, double ys1,
double t0, double xt0, double yt0,
double t1, double xt1, double yt1)
{
/*
String pad = " ";
pad = pad+pad+pad+pad+pad;
pad = pad+pad;
System.out.println("----------------------------------------------");
System.out.println(pad.substring(0, slevel)+ys0);
System.out.println(pad.substring(0, slevel)+ys1);
System.out.println(pad.substring(0, slevel)+(s1-s0));
System.out.println("-------");
System.out.println(pad.substring(0, tlevel)+yt0);
System.out.println(pad.substring(0, tlevel)+yt1);
System.out.println(pad.substring(0, tlevel)+(t1-t0));
*/
if (ys0 > yt1 || yt0 > ys1) {
return false;
}
if (Math.min(xs0, xs1) > Math.max(xt0, xt1) ||
Math.max(xs0, xs1) < Math.min(xt0, xt1))
{
return false;
}
// Bounding boxes intersect - back off the larger of
// the two subcurves by half until they stop intersecting
// (or until they get small enough to switch to a more
// intensive algorithm).
if (s1 - s0 > TMIN) {
double s = (s0 + s1) / 2;
double xs = this.XforT(s);
double ys = this.YforT(s);
if (s == s0 || s == s1) {
System.out.println("s0 = "+s0);
System.out.println("s1 = "+s1);
throw new InternalError("no s progress!");
}
if (t1 - t0 > TMIN) {
double t = (t0 + t1) / 2;
double xt = that.XforT(t);
double yt = that.YforT(t);
if (t == t0 || t == t1) {
System.out.println("t0 = "+t0);
System.out.println("t1 = "+t1);
throw new InternalError("no t progress!");
}
if (ys >= yt0 && yt >= ys0) {
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
s0, xs0, ys0, s, xs, ys,
t0, xt0, yt0, t, xt, yt)) {
return true;
}
}
if (ys >= yt) {
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
s0, xs0, ys0, s, xs, ys,
t, xt, yt, t1, xt1, yt1)) {
return true;
}
}
if (yt >= ys) {
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
s, xs, ys, s1, xs1, ys1,
t0, xt0, yt0, t, xt, yt)) {
return true;
}
}
if (ys1 >= yt && yt1 >= ys) {
if (findIntersect(that, yrange, ymin, slevel+1, tlevel+1,
s, xs, ys, s1, xs1, ys1,
t, xt, yt, t1, xt1, yt1)) {
return true;
}
}
} else {
if (ys >= yt0) {
if (findIntersect(that, yrange, ymin, slevel+1, tlevel,
s0, xs0, ys0, s, xs, ys,
t0, xt0, yt0, t1, xt1, yt1)) {
return true;
}
}
if (yt1 >= ys) {
if (findIntersect(that, yrange, ymin, slevel+1, tlevel,
s, xs, ys, s1, xs1, ys1,
t0, xt0, yt0, t1, xt1, yt1)) {
return true;
}
}
}
} else if (t1 - t0 > TMIN) {
double t = (t0 + t1) / 2;
double xt = that.XforT(t);
double yt = that.YforT(t);
if (t == t0 || t == t1) {
System.out.println("t0 = "+t0);
System.out.println("t1 = "+t1);
throw new InternalError("no t progress!");
}
if (yt >= ys0) {
if (findIntersect(that, yrange, ymin, slevel, tlevel+1,
s0, xs0, ys0, s1, xs1, ys1,
t0, xt0, yt0, t, xt, yt)) {
return true;
}
}
if (ys1 >= yt) {
if (findIntersect(that, yrange, ymin, slevel, tlevel+1,
s0, xs0, ys0, s1, xs1, ys1,
t, xt, yt, t1, xt1, yt1)) {
return true;
}
}
} else {
// No more subdivisions
double xlk = xs1 - xs0;
double ylk = ys1 - ys0;
double xnm = xt1 - xt0;
double ynm = yt1 - yt0;
double xmk = xt0 - xs0;
double ymk = yt0 - ys0;
double det = xnm * ylk - ynm * xlk;
if (det != 0) {
double detinv = 1 / det;
double s = (xnm * ymk - ynm * xmk) * detinv;
double t = (xlk * ymk - ylk * xmk) * detinv;
if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
s = s0 + s * (s1 - s0);
t = t0 + t * (t1 - t0);
if (s < 0 || s > 1 || t < 0 || t > 1) {
System.out.println("Uh oh!");
}
double y = (this.YforT(s) + that.YforT(t)) / 2;
if (y <= yrange[1] && y > yrange[0]) {
yrange[1] = y;
return true;
}
}
}
//System.out.println("Testing lines!");
}
return false;
}
public double refineTforY(double t0, double yt0, double y0) {
double t1 = 1;
while (true) {
double th = (t0 + t1) / 2;
if (th == t0 || th == t1) {
return t1;
}
double y = YforT(th);
if (y < y0) {
t0 = th;
yt0 = y;
} else if (y > y0) {
t1 = th;
} else {
return t1;
}
}
}
public boolean fairlyClose(double v1, double v2) {
return (Math.abs(v1 - v2) <
Math.max(Math.abs(v1), Math.abs(v2)) * 1E-10);
}
public abstract int getSegment(double coords[]);
}