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/*
* Copyright (c) 2017 by Gerrit Grunwald
*
* Licensed under the Apache 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.apache.org/licenses/LICENSE-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 eu.hansolo.fx.geometry.tools;
import java.util.Arrays;
public abstract class AbstractSegment implements Segment {
static final double eps = 1 / (1L << 48);
static final double tol = 4.0 * eps;
public static int solveLine(double a, double b, double[] roots) {
if (a == 0) {
if (b != 0) { return 0; }
roots[0] = 0;
return 1;
}
roots[0] = -b / a;
return 1;
}
public static int solveQuad(double a, double b, double c, double[] roots) {
if (a == 0) { return solveLine(b, c, roots); }
double det = b * b - 4 * a * c;
if (Math.abs(det) <= tol * b * b) {
roots[0] = -b / (2 * a);
return 1;
}
if (det < 0) { return 0; }
// Two real roots
det = Math.sqrt(det);
double w = -(b + matchSign(det, b));
roots[0] = (2 * c) / w;
roots[1] = w / (2 * a);
return 2;
}
public static double matchSign(double a, double b) {
if (b < 0) return (a < 0) ? a : -a;
return (a > 0) ? a : -a;
}
public static int solveCubic(double a3, double a2, double a1, double a0, double[] roots) {
double[] dRoots = {0, 0};
int dCnt = solveQuad(3 * a3, 2 * a2, a1, dRoots);
double[] yVals = {0, 0, 0, 0};
double[] tVals = {0, 0, 0, 0};
int yCnt = 0;
yVals[yCnt] = a0;
tVals[yCnt++] = 0;
double r;
switch (dCnt) {
case 1:
r = dRoots[0];
if ((r > 0) && (r < 1)) {
yVals[yCnt] = ((a3 * r + a2) * r + a1) * r + a0;
tVals[yCnt++] = r;
}
break;
case 2:
if (dRoots[0] > dRoots[1]) {
double t = dRoots[0];
dRoots[0] = dRoots[1];
dRoots[1] = t;
}
r = dRoots[0];
if ((r > 0) && (r < 1)) {
yVals[yCnt] = ((a3 * r + a2) * r + a1) * r + a0;
tVals[yCnt++] = r;
}
r = dRoots[1];
if ((r > 0) && (r < 1)) {
yVals[yCnt] = ((a3 * r + a2) * r + a1) * r + a0;
tVals[yCnt++] = r;
}
break;
default:
break;
}
yVals[yCnt] = a3 + a2 + a1 + a0;
tVals[yCnt++] = 1.0;
int ret = 0;
for (int i = 0; i < yCnt - 1; i++) {
double y0 = yVals[i], t0 = tVals[i];
double y1 = yVals[i + 1], t1 = tVals[i + 1];
if ((y0 < 0) && (y1 < 0)) continue;
if ((y0 > 0) && (y1 > 0)) continue;
if (y0 > y1) { // swap so y0 < 0 and y1 > 0
double t;
t = y0;
y0 = y1;
y1 = t;
t = t0;
t0 = t1;
t1 = t;
}
if (-y0 < tol * y1) {
roots[ret++] = t0;
continue;
}
if (y1 < -tol * y0) {
roots[ret++] = t1;
i++;
continue;
}
double epsZero = tol * (y1 - y0);
int cnt;
for (cnt = 0; cnt < 20; cnt++) {
double dt = t1 - t0;
double dy = y1 - y0;
// double t = (t0+t1)/2;
// double t= t0+Math.abs(y0/dy)*dt;
// This tends to make sure that we come up
// a little short each time this generaly allows
// you to eliminate as much of the range as possible
// without overshooting (in which case you may eliminate
// almost nothing).
double t = t0 + (Math.abs(y0 / dy) * 99 + .5) * dt / 100;
double v = ((a3 * t + a2) * t + a1) * t + a0;
if (Math.abs(v) < epsZero) {
roots[ret++] = t;
break;
}
if (v < 0) {
t0 = t;
y0 = v;
} else {
t1 = t;
y1 = v;
}
}
if (cnt == 20) roots[ret++] = (t0 + t1) / 2;
}
return ret;
}
protected abstract int findRoots(double y, double[] roots);
public Segment.SplitResults split(double y) {
double[] roots = {0, 0, 0};
int numSol = findRoots(y, roots);
if (numSol == 0) return null; // No split
Arrays.sort(roots, 0, numSol);
double[] segs = new double[numSol + 2];
int numSegments = 0;
segs[numSegments++] = 0;
for (int i = 0; i < numSol; i++) {
double r = roots[i];
if (r <= 0.0) continue;
if (r >= 1.0) break;
if (segs[numSegments - 1] != r) segs[numSegments++] = r;
}
segs[numSegments++] = 1.0;
if (numSegments == 2) return null;
// System.err.println("Y: " + y + "#Seg: " + numSegments +
// " Seg: " + this);
Segment[] parts = new Segment[numSegments];
double pT = 0.0;
int pIdx = 0;
boolean firstAbove = false, prevAbove = false;
for (int i = 1; i < numSegments; i++) {
// System.err.println("Segs: " + segs[i-1]+", "+segs[i]);
parts[pIdx] = getSegment(segs[i - 1], segs[i]);
Point pt = parts[pIdx].eval(0.5);
// System.err.println("Pt: " + pt);
if (pIdx == 0) {
pIdx++;
firstAbove = prevAbove = (pt.y < y);
continue;
}
boolean above = (pt.y < y);
if (prevAbove == above) {
// Merge segments
parts[pIdx - 1] = getSegment(pT, segs[i]);
} else {
pIdx++;
pT = segs[i - 1];
prevAbove = above;
}
}
if (pIdx == 1) return null;
Segment[] below, above;
if (firstAbove) {
above = new Segment[(pIdx + 1) / 2];
below = new Segment[pIdx / 2];
} else {
above = new Segment[pIdx / 2];
below = new Segment[(pIdx + 1) / 2];
}
int ai = 0, bi = 0;
for (int i = 0; i < pIdx; i++) {
if (firstAbove) { above[ai++] = parts[i]; } else below[bi++] = parts[i];
firstAbove = !firstAbove;
}
return new SplitResults(below, above);
}
public Segment splitBefore(double t) {
return getSegment(0.0, t);
}
public Segment splitAfter(double t) {
return getSegment(t, 1.0);
}
}