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// Copyright 2005 Google Inc. All Rights Reserved.
#include "s1interval.h"
#include "base/logging.h"
S1Interval S1Interval::FromPoint(double p) {
if (p == -M_PI) p = M_PI;
return S1Interval(p, p, ARGS_CHECKED);
}
double S1Interval::GetCenter() const {
double center = 0.5 * (lo() + hi());
if (!is_inverted()) return center;
// Return the center in the range (-Pi, Pi].
return (center <= 0) ? (center + M_PI) : (center - M_PI);
}
double S1Interval::GetLength() const {
double length = hi() - lo();
if (length >= 0) return length;
length += 2 * M_PI;
// Empty intervals have a negative length.
return (length > 0) ? length : -1;
}
S1Interval S1Interval::Complement() const {
if (lo() == hi()) return Full(); // Singleton.
return S1Interval(hi(), lo(), ARGS_CHECKED); // Handles empty and full.
}
double S1Interval::GetComplementCenter() const {
if (lo() != hi()) {
return Complement().GetCenter();
} else { // Singleton.
return (hi() <= 0) ? (hi() + M_PI) : (hi() - M_PI);
}
}
bool S1Interval::FastContains(double p) const {
if (is_inverted()) {
return (p >= lo() || p <= hi()) && !is_empty();
} else {
return p >= lo() && p <= hi();
}
}
bool S1Interval::Contains(double p) const {
// Works for empty, full, and singleton intervals.
DCHECK_LE(fabs(p), M_PI);
if (p == -M_PI) p = M_PI;
return FastContains(p);
}
bool S1Interval::InteriorContains(double p) const {
// Works for empty, full, and singleton intervals.
DCHECK_LE(fabs(p), M_PI);
if (p == -M_PI) p = M_PI;
if (is_inverted()) {
return p > lo() || p < hi();
} else {
return (p > lo() && p < hi()) || is_full();
}
}
bool S1Interval::Contains(S1Interval const& y) const {
// It might be helpful to compare the structure of these tests to
// the simpler Contains(double) method above.
if (is_inverted()) {
if (y.is_inverted()) return y.lo() >= lo() && y.hi() <= hi();
return (y.lo() >= lo() || y.hi() <= hi()) && !is_empty();
} else {
if (y.is_inverted()) return is_full() || y.is_empty();
return y.lo() >= lo() && y.hi() <= hi();
}
}
bool S1Interval::InteriorContains(S1Interval const& y) const {
if (is_inverted()) {
if (!y.is_inverted()) return y.lo() > lo() || y.hi() < hi();
return (y.lo() > lo() && y.hi() < hi()) || y.is_empty();
} else {
if (y.is_inverted()) return is_full() || y.is_empty();
return (y.lo() > lo() && y.hi() < hi()) || is_full();
}
}
bool S1Interval::Intersects(S1Interval const& y) const {
if (is_empty() || y.is_empty()) return false;
if (is_inverted()) {
// Every non-empty inverted interval contains Pi.
return y.is_inverted() || y.lo() <= hi() || y.hi() >= lo();
} else {
if (y.is_inverted()) return y.lo() <= hi() || y.hi() >= lo();
return y.lo() <= hi() && y.hi() >= lo();
}
}
bool S1Interval::InteriorIntersects(S1Interval const& y) const {
if (is_empty() || y.is_empty() || lo() == hi()) return false;
if (is_inverted()) {
return y.is_inverted() || y.lo() < hi() || y.hi() > lo();
} else {
if (y.is_inverted()) return y.lo() < hi() || y.hi() > lo();
return (y.lo() < hi() && y.hi() > lo()) || is_full();
}
}
inline static double PositiveDistance(double a, double b) {
// Compute the distance from "a" to "b" in the range [0, 2*Pi).
// This is equivalent to (drem(b - a - M_PI, 2 * M_PI) + M_PI),
// except that it is more numerically stable (it does not lose
// precision for very small positive distances).
double d = b - a;
if (d >= 0) return d;
// We want to ensure that if b == Pi and a == (-Pi + eps),
// the return result is approximately 2*Pi and not zero.
return (b + M_PI) - (a - M_PI);
}
double S1Interval::GetDirectedHausdorffDistance(S1Interval const& y) const {
if (y.Contains(*this)) return 0.0; // this includes the case *this is empty
if (y.is_empty()) return M_PI; // maximum possible distance on S1
double y_complement_center = y.GetComplementCenter();
if (Contains(y_complement_center)) {
return PositiveDistance(y.hi(), y_complement_center);
} else {
// The Hausdorff distance is realized by either two hi() endpoints or two
// lo() endpoints, whichever is farther apart.
double hi_hi = S1Interval(y.hi(), y_complement_center).Contains(hi()) ?
PositiveDistance(y.hi(), hi()) : 0;
double lo_lo = S1Interval(y_complement_center, y.lo()).Contains(lo()) ?
PositiveDistance(lo(), y.lo()) : 0;
DCHECK(hi_hi > 0 || lo_lo > 0);
return max(hi_hi, lo_lo);
}
}
void S1Interval::AddPoint(double p) {
DCHECK_LE(fabs(p), M_PI);
if (p == -M_PI) p = M_PI;
if (FastContains(p)) return;
if (is_empty()) {
set_hi(p);
set_lo(p);
} else {
// Compute distance from p to each endpoint.
double dlo = PositiveDistance(p, lo());
double dhi = PositiveDistance(hi(), p);
if (dlo < dhi) {
set_lo(p);
} else {
set_hi(p);
}
// Adding a point can never turn a non-full interval into a full one.
}
}
S1Interval S1Interval::FromPointPair(double p1, double p2) {
DCHECK_LE(fabs(p1), M_PI);
DCHECK_LE(fabs(p2), M_PI);
if (p1 == -M_PI) p1 = M_PI;
if (p2 == -M_PI) p2 = M_PI;
if (PositiveDistance(p1, p2) <= M_PI) {
return S1Interval(p1, p2, ARGS_CHECKED);
} else {
return S1Interval(p2, p1, ARGS_CHECKED);
}
}
S1Interval S1Interval::Expanded(double radius) const {
DCHECK_GE(radius, 0);
if (is_empty()) return *this;
// Check whether this interval will be full after expansion, allowing
// for a 1-bit rounding error when computing each endpoint.
if (GetLength() + 2 * radius >= 2 * M_PI - 1e-15) return Full();
S1Interval result(drem(lo() - radius, 2*M_PI), drem(hi() + radius, 2*M_PI));
if (result.lo() <= -M_PI) result.set_lo(M_PI);
return result;
}
S1Interval S1Interval::Union(S1Interval const& y) const {
// The y.is_full() case is handled correctly in all cases by the code
// below, but can follow three separate code paths depending on whether
// this interval is inverted, is non-inverted but contains Pi, or neither.
if (y.is_empty()) return *this;
if (FastContains(y.lo())) {
if (FastContains(y.hi())) {
// Either this interval contains y, or the union of the two
// intervals is the Full() interval.
if (Contains(y)) return *this; // is_full() code path
return Full();
}
return S1Interval(lo(), y.hi(), ARGS_CHECKED);
}
if (FastContains(y.hi())) return S1Interval(y.lo(), hi(), ARGS_CHECKED);
// This interval contains neither endpoint of y. This means that either y
// contains all of this interval, or the two intervals are disjoint.
if (is_empty() || y.FastContains(lo())) return y;
// Check which pair of endpoints are closer together.
double dlo = PositiveDistance(y.hi(), lo());
double dhi = PositiveDistance(hi(), y.lo());
if (dlo < dhi) {
return S1Interval(y.lo(), hi(), ARGS_CHECKED);
} else {
return S1Interval(lo(), y.hi(), ARGS_CHECKED);
}
}
S1Interval S1Interval::Intersection(S1Interval const& y) const {
// The y.is_full() case is handled correctly in all cases by the code
// below, but can follow three separate code paths depending on whether
// this interval is inverted, is non-inverted but contains Pi, or neither.
if (y.is_empty()) return Empty();
if (FastContains(y.lo())) {
if (FastContains(y.hi())) {
// Either this interval contains y, or the region of intersection
// consists of two disjoint subintervals. In either case, we want
// to return the shorter of the two original intervals.
if (y.GetLength() < GetLength()) return y; // is_full() code path
return *this;
}
return S1Interval(y.lo(), hi(), ARGS_CHECKED);
}
if (FastContains(y.hi())) return S1Interval(lo(), y.hi(), ARGS_CHECKED);
// This interval contains neither endpoint of y. This means that either y
// contains all of this interval, or the two intervals are disjoint.
if (y.FastContains(lo())) return *this; // is_empty() okay here
DCHECK(!Intersects(y));
return Empty();
}
bool S1Interval::ApproxEquals(S1Interval const& y, double max_error) const {
if (is_empty()) return y.GetLength() <= max_error;
if (y.is_empty()) return GetLength() <= max_error;
return (fabs(drem(y.lo() - lo(), 2 * M_PI)) +
fabs(drem(y.hi() - hi(), 2 * M_PI))) <= max_error;
}
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