gtsocial-umbx

metric.go (6319B)

---

 // 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)
 }