1 files changed, 0 insertions, 462 deletions
diff --git a/vendor/github.com/golang/geo/s1/interval.go b/vendor/github.com/golang/geo/s1/interval.go
deleted file mode 100644
index 6fea5221f..000000000
--- a/vendor/github.com/golang/geo/s1/interval.go
+++ /dev/null
@@ -1,462 +0,0 @@
-// Copyright 2014 Google Inc. All rights reserved.
-//
-// 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 s1
-
-import (
-	"math"
-	"strconv"
-)
-
-// An Interval represents a closed interval on a unit circle (also known
-// as a 1-dimensional sphere). It is capable of representing the empty
-// interval (containing no points), the full interval (containing all
-// points), and zero-length intervals (containing a single point).
-//
-// Points are represented by the angle they make with the positive x-axis in
-// the range [-π, π]. An interval is represented by its lower and upper
-// bounds (both inclusive, since the interval is closed). The lower bound may
-// be greater than the upper bound, in which case the interval is "inverted"
-// (i.e. it passes through the point (-1, 0)).
-//
-// The point (-1, 0) has two valid representations, π and -π. The
-// normalized representation of this point is π, so that endpoints
-// of normal intervals are in the range (-π, π]. We normalize the latter to
-// the former in IntervalFromEndpoints. However, we take advantage of the point
-// -π to construct two special intervals:
-//   The full interval is [-π, π]
-//   The empty interval is [π, -π].
-//
-// Treat the exported fields as read-only.
-type Interval struct {
-	Lo, Hi float64
-}
-
-// IntervalFromEndpoints constructs a new interval from endpoints.
-// Both arguments must be in the range [-π,π]. This function allows inverted intervals
-// to be created.
-func IntervalFromEndpoints(lo, hi float64) Interval {
-	i := Interval{lo, hi}
-	if lo == -math.Pi && hi != math.Pi {
-		i.Lo = math.Pi
-	}
-	if hi == -math.Pi && lo != math.Pi {
-		i.Hi = math.Pi
-	}
-	return i
-}
-
-// IntervalFromPointPair returns the minimal interval containing the two given points.
-// Both arguments must be in [-π,π].
-func IntervalFromPointPair(a, b float64) Interval {
-	if a == -math.Pi {
-		a = math.Pi
-	}
-	if b == -math.Pi {
-		b = math.Pi
-	}
-	if positiveDistance(a, b) <= math.Pi {
-		return Interval{a, b}
-	}
-	return Interval{b, a}
-}
-
-// EmptyInterval returns an empty interval.
-func EmptyInterval() Interval { return Interval{math.Pi, -math.Pi} }
-
-// FullInterval returns a full interval.
-func FullInterval() Interval { return Interval{-math.Pi, math.Pi} }
-
-// IsValid reports whether the interval is valid.
-func (i Interval) IsValid() bool {
-	return (math.Abs(i.Lo) <= math.Pi && math.Abs(i.Hi) <= math.Pi &&
-		!(i.Lo == -math.Pi && i.Hi != math.Pi) &&
-		!(i.Hi == -math.Pi && i.Lo != math.Pi))
-}
-
-// IsFull reports whether the interval is full.
-func (i Interval) IsFull() bool { return i.Lo == -math.Pi && i.Hi == math.Pi }
-
-// IsEmpty reports whether the interval is empty.
-func (i Interval) IsEmpty() bool { return i.Lo == math.Pi && i.Hi == -math.Pi }
-
-// IsInverted reports whether the interval is inverted; that is, whether Lo > Hi.
-func (i Interval) IsInverted() bool { return i.Lo > i.Hi }
-
-// Invert returns the interval with endpoints swapped.
-func (i Interval) Invert() Interval {
-	return Interval{i.Hi, i.Lo}
-}
-
-// Center returns the midpoint of the interval.
-// It is undefined for full and empty intervals.
-func (i Interval) Center() float64 {
-	c := 0.5 * (i.Lo + i.Hi)
-	if !i.IsInverted() {
-		return c
-	}
-	if c <= 0 {
-		return c + math.Pi
-	}
-	return c - math.Pi
-}
-
-// Length returns the length of the interval.
-// The length of an empty interval is negative.
-func (i Interval) Length() float64 {
-	l := i.Hi - i.Lo
-	if l >= 0 {
-		return l
-	}
-	l += 2 * math.Pi
-	if l > 0 {
-		return l
-	}
-	return -1
-}
-
-// Assumes p ∈ (-π,π].
-func (i Interval) fastContains(p float64) bool {
-	if i.IsInverted() {
-		return (p >= i.Lo || p <= i.Hi) && !i.IsEmpty()
-	}
-	return p >= i.Lo && p <= i.Hi
-}
-
-// Contains returns true iff the interval contains p.
-// Assumes p ∈ [-π,π].
-func (i Interval) Contains(p float64) bool {
-	if p == -math.Pi {
-		p = math.Pi
-	}
-	return i.fastContains(p)
-}
-
-// ContainsInterval returns true iff the interval contains oi.
-func (i Interval) ContainsInterval(oi Interval) bool {
-	if i.IsInverted() {
-		if oi.IsInverted() {
-			return oi.Lo >= i.Lo && oi.Hi <= i.Hi
-		}
-		return (oi.Lo >= i.Lo || oi.Hi <= i.Hi) && !i.IsEmpty()
-	}
-	if oi.IsInverted() {
-		return i.IsFull() || oi.IsEmpty()
-	}
-	return oi.Lo >= i.Lo && oi.Hi <= i.Hi
-}
-
-// InteriorContains returns true iff the interior of the interval contains p.
-// Assumes p ∈ [-π,π].
-func (i Interval) InteriorContains(p float64) bool {
-	if p == -math.Pi {
-		p = math.Pi
-	}
-	if i.IsInverted() {
-		return p > i.Lo || p < i.Hi
-	}
-	return (p > i.Lo && p < i.Hi) || i.IsFull()
-}
-
-// InteriorContainsInterval returns true iff the interior of the interval contains oi.
-func (i Interval) InteriorContainsInterval(oi Interval) bool {
-	if i.IsInverted() {
-		if oi.IsInverted() {
-			return (oi.Lo > i.Lo && oi.Hi < i.Hi) || oi.IsEmpty()
-		}
-		return oi.Lo > i.Lo || oi.Hi < i.Hi
-	}
-	if oi.IsInverted() {
-		return i.IsFull() || oi.IsEmpty()
-	}
-	return (oi.Lo > i.Lo && oi.Hi < i.Hi) || i.IsFull()
-}
-
-// Intersects returns true iff the interval contains any points in common with oi.
-func (i Interval) Intersects(oi Interval) bool {
-	if i.IsEmpty() || oi.IsEmpty() {
-		return false
-	}
-	if i.IsInverted() {
-		return oi.IsInverted() || oi.Lo <= i.Hi || oi.Hi >= i.Lo
-	}
-	if oi.IsInverted() {
-		return oi.Lo <= i.Hi || oi.Hi >= i.Lo
-	}
-	return oi.Lo <= i.Hi && oi.Hi >= i.Lo
-}
-
-// InteriorIntersects returns true iff the interior of the interval contains any points in common with oi, including the latter's boundary.
-func (i Interval) InteriorIntersects(oi Interval) bool {
-	if i.IsEmpty() || oi.IsEmpty() || i.Lo == i.Hi {
-		return false
-	}
-	if i.IsInverted() {
-		return oi.IsInverted() || oi.Lo < i.Hi || oi.Hi > i.Lo
-	}
-	if oi.IsInverted() {
-		return oi.Lo < i.Hi || oi.Hi > i.Lo
-	}
-	return (oi.Lo < i.Hi && oi.Hi > i.Lo) || i.IsFull()
-}
-
-// Compute distance from a to b in [0,2π], in a numerically stable way.
-func positiveDistance(a, b float64) float64 {
-	d := b - a
-	if d >= 0 {
-		return d
-	}
-	return (b + math.Pi) - (a - math.Pi)
-}
-
-// Union returns the smallest interval that contains both the interval and oi.
-func (i Interval) Union(oi Interval) Interval {
-	if oi.IsEmpty() {
-		return i
-	}
-	if i.fastContains(oi.Lo) {
-		if i.fastContains(oi.Hi) {
-			// Either oi ⊂ i, or i ∪ oi is the full interval.
-			if i.ContainsInterval(oi) {
-				return i
-			}
-			return FullInterval()
-		}
-		return Interval{i.Lo, oi.Hi}
-	}
-	if i.fastContains(oi.Hi) {
-		return Interval{oi.Lo, i.Hi}
-	}
-
-	// Neither endpoint of oi is in i. Either i ⊂ oi, or i and oi are disjoint.
-	if i.IsEmpty() || oi.fastContains(i.Lo) {
-		return oi
-	}
-
-	// This is the only hard case where we need to find the closest pair of endpoints.
-	if positiveDistance(oi.Hi, i.Lo) < positiveDistance(i.Hi, oi.Lo) {
-		return Interval{oi.Lo, i.Hi}
-	}
-	return Interval{i.Lo, oi.Hi}
-}
-
-// Intersection returns the smallest interval that contains the intersection of the interval and oi.
-func (i Interval) Intersection(oi Interval) Interval {
-	if oi.IsEmpty() {
-		return EmptyInterval()
-	}
-	if i.fastContains(oi.Lo) {
-		if i.fastContains(oi.Hi) {
-			// Either oi ⊂ i, or i and oi intersect twice. Neither are empty.
-			// In the first case we want to return i (which is shorter than oi).
-			// In the second case one of them is inverted, and the smallest interval
-			// that covers the two disjoint pieces is the shorter of i and oi.
-			// We thus want to pick the shorter of i and oi in both cases.
-			if oi.Length() < i.Length() {
-				return oi
-			}
-			return i
-		}
-		return Interval{oi.Lo, i.Hi}
-	}
-	if i.fastContains(oi.Hi) {
-		return Interval{i.Lo, oi.Hi}
-	}
-
-	// Neither endpoint of oi is in i. Either i ⊂ oi, or i and oi are disjoint.
-	if oi.fastContains(i.Lo) {
-		return i
-	}
-	return EmptyInterval()
-}
-
-// AddPoint returns the interval expanded by the minimum amount necessary such
-// that it contains the given point "p" (an angle in the range [-π, π]).
-func (i Interval) AddPoint(p float64) Interval {
-	if math.Abs(p) > math.Pi {
-		return i
-	}
-	if p == -math.Pi {
-		p = math.Pi
-	}
-	if i.fastContains(p) {
-		return i
-	}
-	if i.IsEmpty() {
-		return Interval{p, p}
-	}
-	if positiveDistance(p, i.Lo) < positiveDistance(i.Hi, p) {
-		return Interval{p, i.Hi}
-	}
-	return Interval{i.Lo, p}
-}
-
-// Define the maximum rounding error for arithmetic operations. Depending on the
-// platform the mantissa precision may be different than others, so we choose to
-// use specific values to be consistent across all.
-// The values come from the C++ implementation.
-var (
-	// epsilon is a small number that represents a reasonable level of noise between two
-	// values that can be considered to be equal.
-	epsilon = 1e-15
-	// dblEpsilon is a smaller number for values that require more precision.
-	dblEpsilon = 2.220446049e-16
-)
-
-// Expanded returns an interval that has been expanded on each side by margin.
-// If margin is negative, then the function shrinks the interval on
-// each side by margin instead. The resulting interval may be empty or
-// full. Any expansion (positive or negative) of a full interval remains
-// full, and any expansion of an empty interval remains empty.
-func (i Interval) Expanded(margin float64) Interval {
-	if margin >= 0 {
-		if i.IsEmpty() {
-			return i
-		}
-		// Check whether this interval will be full after expansion, allowing
-		// for a rounding error when computing each endpoint.
-		if i.Length()+2*margin+2*dblEpsilon >= 2*math.Pi {
-			return FullInterval()
-		}
-	} else {
-		if i.IsFull() {
-			return i
-		}
-		// Check whether this interval will be empty after expansion, allowing
-		// for a rounding error when computing each endpoint.
-		if i.Length()+2*margin-2*dblEpsilon <= 0 {
-			return EmptyInterval()
-		}
-	}
-	result := IntervalFromEndpoints(
-		math.Remainder(i.Lo-margin, 2*math.Pi),
-		math.Remainder(i.Hi+margin, 2*math.Pi),
-	)
-	if result.Lo <= -math.Pi {
-		result.Lo = math.Pi
-	}
-	return result
-}
-
-// ApproxEqual reports whether this interval can be transformed into the given
-// interval by moving each endpoint by at most ε, without the
-// endpoints crossing (which would invert the interval). Empty and full
-// intervals are considered to start at an arbitrary point on the unit circle,
-// so any interval with (length <= 2*ε) matches the empty interval, and
-// any interval with (length >= 2*π - 2*ε) matches the full interval.
-func (i Interval) ApproxEqual(other Interval) bool {
-	// Full and empty intervals require special cases because the endpoints
-	// are considered to be positioned arbitrarily.
-	if i.IsEmpty() {
-		return other.Length() <= 2*epsilon
-	}
-	if other.IsEmpty() {
-		return i.Length() <= 2*epsilon
-	}
-	if i.IsFull() {
-		return other.Length() >= 2*(math.Pi-epsilon)
-	}
-	if other.IsFull() {
-		return i.Length() >= 2*(math.Pi-epsilon)
-	}
-
-	// The purpose of the last test below is to verify that moving the endpoints
-	// does not invert the interval, e.g. [-1e20, 1e20] vs. [1e20, -1e20].
-	return (math.Abs(math.Remainder(other.Lo-i.Lo, 2*math.Pi)) <= epsilon &&
-		math.Abs(math.Remainder(other.Hi-i.Hi, 2*math.Pi)) <= epsilon &&
-		math.Abs(i.Length()-other.Length()) <= 2*epsilon)
-
-}
-
-func (i Interval) String() string {
-	// like "[%.7f, %.7f]"
-	return "[" + strconv.FormatFloat(i.Lo, 'f', 7, 64) + ", " + strconv.FormatFloat(i.Hi, 'f', 7, 64) + "]"
-}
-
-// Complement returns the complement of the interior of the interval. An interval and
-// its complement have the same boundary but do not share any interior
-// values. The complement operator is not a bijection, since the complement
-// of a singleton interval (containing a single value) is the same as the
-// complement of an empty interval.
-func (i Interval) Complement() Interval {
-	if i.Lo == i.Hi {
-		// Singleton. The interval just contains a single point.
-		return FullInterval()
-	}
-	// Handles empty and full.
-	return Interval{i.Hi, i.Lo}
-}
-
-// ComplementCenter returns the midpoint of the complement of the interval. For full and empty
-// intervals, the result is arbitrary. For a singleton interval (containing a
-// single point), the result is its antipodal point on S1.
-func (i Interval) ComplementCenter() float64 {
-	if i.Lo != i.Hi {
-		return i.Complement().Center()
-	}
-	// Singleton. The interval just contains a single point.
-	if i.Hi <= 0 {
-		return i.Hi + math.Pi
-	}
-	return i.Hi - math.Pi
-}
-
-// DirectedHausdorffDistance returns the Hausdorff distance to the given interval.
-// For two intervals i and y, this distance is defined by
-//     h(i, y) = max_{p in i} min_{q in y} d(p, q),
-// where d(.,.) is measured along S1.
-func (i Interval) DirectedHausdorffDistance(y Interval) Angle {
-	if y.ContainsInterval(i) {
-		return 0 // This includes the case i is empty.
-	}
-	if y.IsEmpty() {
-		return Angle(math.Pi) // maximum possible distance on s1.
-	}
-	yComplementCenter := y.ComplementCenter()
-	if i.Contains(yComplementCenter) {
-		return Angle(positiveDistance(y.Hi, yComplementCenter))
-	}
-
-	// The Hausdorff distance is realized by either two i.Hi endpoints or two
-	// i.Lo endpoints, whichever is farther apart.
-	hiHi := 0.0
-	if IntervalFromEndpoints(y.Hi, yComplementCenter).Contains(i.Hi) {
-		hiHi = positiveDistance(y.Hi, i.Hi)
-	}
-
-	loLo := 0.0
-	if IntervalFromEndpoints(yComplementCenter, y.Lo).Contains(i.Lo) {
-		loLo = positiveDistance(i.Lo, y.Lo)
-	}
-
-	return Angle(math.Max(hiHi, loLo))
-}
-
-// Project returns the closest point in the interval to the given point p.
-// The interval must be non-empty.
-func (i Interval) Project(p float64) float64 {
-	if p == -math.Pi {
-		p = math.Pi
-	}
-	if i.fastContains(p) {
-		return p
-	}
-	// Compute distance from p to each endpoint.
-	dlo := positiveDistance(p, i.Lo)
-	dhi := positiveDistance(i.Hi, p)
-	if dlo < dhi {
-		return i.Lo
-	}
-	return i.Hi
-}