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diff --git a/vendor/github.com/golang/geo/s2/metric.go b/vendor/github.com/golang/geo/s2/metric.go
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-// Copyright 2015 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 s2
-
-// This file implements functions for various S2 measurements.
-
-import "math"
-
-// A Metric is a measure for cells. It is used to describe the shape and size
-// of cells. They are useful for deciding which cell level to use in order to
-// satisfy a given condition (e.g. that cell vertices must be no further than
-// "x" apart). You can use the Value(level) method to compute the corresponding
-// length or area on the unit sphere for cells at a given level. The minimum
-// and maximum bounds are valid for cells at all levels, but they may be
-// somewhat conservative for very large cells (e.g. face cells).
-type Metric struct {
- // Dim is either 1 or 2, for a 1D or 2D metric respectively.
- Dim int
- // Deriv is the scaling factor for the metric.
- Deriv float64
-}
-
-// Defined metrics.
-// Of the projection methods defined in C++, Go only supports the quadratic projection.
-
-// Each cell is bounded by four planes passing through its four edges and
-// the center of the sphere. These metrics relate to the angle between each
-// pair of opposite bounding planes, or equivalently, between the planes
-// corresponding to two different s-values or two different t-values.
-var (
- MinAngleSpanMetric = Metric{1, 4.0 / 3}
- AvgAngleSpanMetric = Metric{1, math.Pi / 2}
- MaxAngleSpanMetric = Metric{1, 1.704897179199218452}
-)
-
-// The width of geometric figure is defined as the distance between two
-// parallel bounding lines in a given direction. For cells, the minimum
-// width is always attained between two opposite edges, and the maximum
-// width is attained between two opposite vertices. However, for our
-// purposes we redefine the width of a cell as the perpendicular distance
-// between a pair of opposite edges. A cell therefore has two widths, one
-// in each direction. The minimum width according to this definition agrees
-// with the classic geometric one, but the maximum width is different. (The
-// maximum geometric width corresponds to MaxDiag defined below.)
-//
-// The average width in both directions for all cells at level k is approximately
-// AvgWidthMetric.Value(k).
-//
-// The width is useful for bounding the minimum or maximum distance from a
-// point on one edge of a cell to the closest point on the opposite edge.
-// For example, this is useful when growing regions by a fixed distance.
-var (
- MinWidthMetric = Metric{1, 2 * math.Sqrt2 / 3}
- AvgWidthMetric = Metric{1, 1.434523672886099389}
- MaxWidthMetric = Metric{1, MaxAngleSpanMetric.Deriv}
-)
-
-// The edge length metrics can be used to bound the minimum, maximum,
-// or average distance from the center of one cell to the center of one of
-// its edge neighbors. In particular, it can be used to bound the distance
-// between adjacent cell centers along the space-filling Hilbert curve for
-// cells at any given level.
-var (
- MinEdgeMetric = Metric{1, 2 * math.Sqrt2 / 3}
- AvgEdgeMetric = Metric{1, 1.459213746386106062}
- MaxEdgeMetric = Metric{1, MaxAngleSpanMetric.Deriv}
-
- // MaxEdgeAspect is the maximum edge aspect ratio over all cells at any level,
- // where the edge aspect ratio of a cell is defined as the ratio of its longest
- // edge length to its shortest edge length.
- MaxEdgeAspect = 1.442615274452682920
-
- MinAreaMetric = Metric{2, 8 * math.Sqrt2 / 9}
- AvgAreaMetric = Metric{2, 4 * math.Pi / 6}
- MaxAreaMetric = Metric{2, 2.635799256963161491}
-)
-
-// The maximum diagonal is also the maximum diameter of any cell,
-// and also the maximum geometric width (see the comment for widths). For
-// example, the distance from an arbitrary point to the closest cell center
-// at a given level is at most half the maximum diagonal length.
-var (
- MinDiagMetric = Metric{1, 8 * math.Sqrt2 / 9}
- AvgDiagMetric = Metric{1, 2.060422738998471683}
- MaxDiagMetric = Metric{1, 2.438654594434021032}
-
- // MaxDiagAspect is the maximum diagonal aspect ratio over all cells at any
- // level, where the diagonal aspect ratio of a cell is defined as the ratio
- // of its longest diagonal length to its shortest diagonal length.
- MaxDiagAspect = math.Sqrt(3)
-)
-
-// Value returns the value of the metric at the given level.
-func (m Metric) Value(level int) float64 {
- return math.Ldexp(m.Deriv, -m.Dim*level)
-}
-
-// MinLevel returns the minimum level such that the metric is at most
-// the given value, or maxLevel (30) if there is no such level.
-//
-// For example, MinLevel(0.1) returns the minimum level such that all cell diagonal
-// lengths are 0.1 or smaller. The returned value is always a valid level.
-//
-// In C++, this is called GetLevelForMaxValue.
-func (m Metric) MinLevel(val float64) int {
- if val < 0 {
- return maxLevel
- }
-
- level := -(math.Ilogb(val/m.Deriv) >> uint(m.Dim-1))
- if level > maxLevel {
- level = maxLevel
- }
- if level < 0 {
- level = 0
- }
- return level
-}
-
-// MaxLevel returns the maximum level such that the metric is at least
-// the given value, or zero if there is no such level.
-//
-// For example, MaxLevel(0.1) returns the maximum level such that all cells have a
-// minimum width of 0.1 or larger. The returned value is always a valid level.
-//
-// In C++, this is called GetLevelForMinValue.
-func (m Metric) MaxLevel(val float64) int {
- if val <= 0 {
- return maxLevel
- }
-
- level := math.Ilogb(m.Deriv/val) >> uint(m.Dim-1)
- if level > maxLevel {
- level = maxLevel
- }
- if level < 0 {
- level = 0
- }
- return level
-}
-
-// ClosestLevel returns the level at which the metric has approximately the given
-// value. The return value is always a valid level. For example,
-// AvgEdgeMetric.ClosestLevel(0.1) returns the level at which the average cell edge
-// length is approximately 0.1.
-func (m Metric) ClosestLevel(val float64) int {
- x := math.Sqrt2
- if m.Dim == 2 {
- x = 2
- }
- return m.MinLevel(x * val)
-}