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authorLibravatar kim <89579420+NyaaaWhatsUpDoc@users.noreply.github.com>2024-08-02 11:46:41 +0000
committerLibravatar GitHub <noreply@github.com>2024-08-02 12:46:41 +0100
commit94e87610c4ce9bbb1c614a61bab29c1422fed11b (patch)
tree2e06b8ce64212140e796f6077ba841b6cc678501 /vendor/github.com/golang/geo/s2/metric.go
parent[feature] Allow import of following and blocks via CSV (#3150) (diff)
downloadgotosocial-94e87610c4ce9bbb1c614a61bab29c1422fed11b.tar.xz
[chore] add back exif-terminator and use only for jpeg,png,webp (#3161)
* add back exif-terminator and use only for jpeg,png,webp * fix arguments passed to terminateExif() * pull in latest exif-terminator * fix test * update processed img --------- Co-authored-by: tobi <tobi.smethurst@protonmail.com>
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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)
+}