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Geometry.java
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Geometry.java
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import java.util.*;
public class Geometry {
/**
* Convex polygon
*
* n = x.length - 1
* x[n] == x[0]
*/
static void sliceWithEachIntegerLine(int[] x, int[] y) {
int n = x.length - 1;
int xmin = Integer.MAX_VALUE;
int xmax = Integer.MIN_VALUE;
for (int i = 0; i < n; i++) {
xmin = Math.min(xmin, x[i]);
xmax = Math.max(xmax, x[i]);
}
int i = 0;
while (x[i] != xmin) {
i++;
}
int j = i;
if (j == 0) j = n;
double slope1 = (y[i + 1] - y[i]) * 1.0 / (x[i + 1] - x[i]);
double slope2 = (y[j - 1] - y[j]) * 1.0 / (x[j - 1] - x[j]);
for (int t = xmin; t <= xmax; t++) {
if (t < xmax) {
while (x[i + 1] <= t) {
i++;
if (i == n) {
i = 0;
}
slope1 = (y[i + 1] - y[i]) * 1.0 / (x[i + 1] - x[i]);
}
while (x[j - 1] <= t) {
j--;
if (j == 0) {
j = n;
}
slope2 = (y[j - 1] - y[j]) * 1.0 / (x[j - 1] - x[j]);
}
}
double y1 = y[i] + (t - x[i]) * slope1;
double y2 = y[j] + (t - x[j]) * slope2;
if (y1 > y2) {
double p = y1; y1 = y2; y2 = p;
}
double yFrom = Math.ceil(y1);
double yTo = Math.floor(y2) + 1;
System.err.println(yFrom + ".." + yTo);
}
}
static void sortByPolarAngle(Point[] array, final Point origin) {
Arrays.sort(array, new Comparator<Point>() {
@Override
public int compare(Point a, Point b) {
int qA = quarterOrAxis(a.x - origin.x, a.y - origin.y);
int qB = quarterOrAxis(b.x - origin.x, b.y - origin.y);
int res = Integer.compare(qA, qB);
if (res == 0) {
res = orientation(origin, b, a);
}
if (res != 0) {
return res;
}
return Long.compare(a.x * 1L * a.x + a.y * 1L * a.y, b.x * 1L * b.x + b.y * 1L * b.y);
}
});
}
static void scan180DegreeSpans(Point[] array, Point origin) {
sortByPolarAngle(array, origin);
for (int j = 0, k = 0; j < array.length; j++) {
for (k = Math.max(k, j + 1);; k++) {
if (k == j + array.length) {
break;
}
if (orientation(origin, array[j], array[k % array.length]) < 0) {
break;
}
}
System.err.println("Span size: " + (j + array.length - k));
System.err.println(array[j] + ".." + array[k % array.length]);
}
}
static long area(long xA, long yA, long xB, long yB, long xC, long yC) {
return Math.abs(
xA * yB - xB * yA +
xB * yC - xC * yB +
xC * yA - xA * yC
);
}
static int orientation(Point a, Point b, Point c) {
return orientation(a.x, a.y, b.x, b.y, c.x, c.y);
}
static int orientation(long xA, long yA, long xB, long yB, long xC, long yC) {
return Long.signum(
xA * yB - xB * yA +
xB * yC - xC * yB +
xC * yA - xA * yC
);
}
static int orientation3D(int x0, int y0, int z0, int x1, int y1, int z1, int x2, int y2, int z2, int x3, int y3, int z3) {
long a0 = x1 - x0;
long a1 = x2 - x0;
long a2 = x3 - x0;
long b0 = y1 - y0;
long b1 = y2 - y0;
long b2 = y3 - y0;
long c0 = z1 - z0;
long c1 = z2 - z0;
long c2 = z3 - z0;
long det =
a0 * b1 * c2 - a0 * b2 * c1 +
a1 * b2 * c0 - a1 * b0 * c2 +
a2 * b0 * c1 - a2 * b1 * c0;
return Long.signum(det);
}
static boolean above(int x0, int y0, int z0, int x1, int y1, int z1, int x2, int y2, int z2, int x3, int y3, int z3) {
int ori2d = orientation(x0, y0, x1, y1, x2, y2);
int ori3d = orientation3D(x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3);
return ori2d == ori3d;
}
static int quarterOrAxis(int x, int y) {
if (y == 0) {
if (x == 0) {
return -1;
}
return x > 0 ? 0 : 4;
}
if (x == 0) {
return y > 0 ? 2 : 6;
}
if (y > 0) {
return x > 0 ? 1 : 3;
}
return x > 0 ? 7 : 5;
}
static boolean insideTriangleNonStrict(int[] xs, int[] ys, int x, int y) {
int o0 = orientation(xs[0], ys[0], xs[1], ys[1], x, y);
int o1 = orientation(xs[1], ys[1], xs[2], ys[2], x, y);
int o2 = orientation(xs[2], ys[2], xs[0], ys[0], x, y);
int oMin = Math.min(Math.min(o0, o1), o2);
int oMax = Math.max(Math.max(o0, o1), o2);
return oMin * oMax != -1;
}
static boolean insideTriangleStrict(int[] xs, int[] ys, int x, int y) {
int o0 = orientation(xs[0], ys[0], xs[1], ys[1], x, y);
int o1 = orientation(xs[1], ys[1], xs[2], ys[2], x, y);
int o2 = orientation(xs[2], ys[2], xs[0], ys[0], x, y);
return Math.abs(o0 + o1 + o2) == 3;
}
static boolean betWeenStrictly(int x0, int x1, int x2) {
return (x0 < x2) ? (x0 < x1 && x1 < x2) : (x0 > x1 && x1 > x2);
}
static boolean pointOnSegmentStrict(int x, int y, int x0, int y0, int x1, int y1) {
if (orientation(x, y, x0, y0, x1, y1) != 0) {
return false;
}
return betWeenStrictly(x0, x, x1) || betWeenStrictly(y0, y, y1);
}
static boolean segmentsIntersectStrictlyNonParrallel(
int x0, int y0, int x1, int y1, int x2, int y2, int x3, int y3) {
return orientation(x0, y0, x1, y1, x2, y2) * orientation(x0, y0, x1, y1, x3, y3) == -1
&& orientation(x2, y2, x3, y3, x0, y0) * orientation(x2, y2, x3, y3, x1, y1) == -1;
}
static boolean linearSegmentsIntersectNonStricly(int a, int b, int c, int d) {
return Math.max(Math.min(a, b), Math.min(c, d)) <= Math.min(Math.max(a, b), Math.max(c, d));
}
static boolean segmentsIntersectNonStricly(int x0, int y0, int x1, int y1, int x2, int y2, int x3, int y3) {
return linearSegmentsIntersectNonStricly(x0, x1, x2, x3) && linearSegmentsIntersectNonStricly(y0, y1, y2, y3) &&
orientation(x0, y0, x1, y1, x2, y2) * orientation(x0, y0, x1, y1, x3, y3) <= 0 &&
orientation(x2, y2, x3, y3, x0, y0) * orientation(x2, y2, x3, y3, x1, y1) <= 0;
}
class Point {
int x, y;
public Point(int x, int y) {
this.x = x;
this.y = y;
}
}
}