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author | 2024-08-02 11:46:41 +0000 | |
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committer | 2024-08-02 12:46:41 +0100 | |
commit | 94e87610c4ce9bbb1c614a61bab29c1422fed11b (patch) | |
tree | 2e06b8ce64212140e796f6077ba841b6cc678501 /vendor/github.com/golang/geo/s2/point_measures.go | |
parent | [feature] Allow import of following and blocks via CSV (#3150) (diff) | |
download | gotosocial-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
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Co-authored-by: tobi <tobi.smethurst@protonmail.com>
Diffstat (limited to 'vendor/github.com/golang/geo/s2/point_measures.go')
-rw-r--r-- | vendor/github.com/golang/geo/s2/point_measures.go | 149 |
1 files changed, 149 insertions, 0 deletions
diff --git a/vendor/github.com/golang/geo/s2/point_measures.go b/vendor/github.com/golang/geo/s2/point_measures.go new file mode 100644 index 000000000..6fa9b7ae4 --- /dev/null +++ b/vendor/github.com/golang/geo/s2/point_measures.go @@ -0,0 +1,149 @@ +// Copyright 2018 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 + +import ( + "math" + + "github.com/golang/geo/s1" +) + +// PointArea returns the area of triangle ABC. This method combines two different +// algorithms to get accurate results for both large and small triangles. +// The maximum error is about 5e-15 (about 0.25 square meters on the Earth's +// surface), the same as GirardArea below, but unlike that method it is +// also accurate for small triangles. Example: when the true area is 100 +// square meters, PointArea yields an error about 1 trillion times smaller than +// GirardArea. +// +// All points should be unit length, and no two points should be antipodal. +// The area is always positive. +func PointArea(a, b, c Point) float64 { + // This method is based on l'Huilier's theorem, + // + // tan(E/4) = sqrt(tan(s/2) tan((s-a)/2) tan((s-b)/2) tan((s-c)/2)) + // + // where E is the spherical excess of the triangle (i.e. its area), + // a, b, c are the side lengths, and + // s is the semiperimeter (a + b + c) / 2. + // + // The only significant source of error using l'Huilier's method is the + // cancellation error of the terms (s-a), (s-b), (s-c). This leads to a + // *relative* error of about 1e-16 * s / min(s-a, s-b, s-c). This compares + // to a relative error of about 1e-15 / E using Girard's formula, where E is + // the true area of the triangle. Girard's formula can be even worse than + // this for very small triangles, e.g. a triangle with a true area of 1e-30 + // might evaluate to 1e-5. + // + // So, we prefer l'Huilier's formula unless dmin < s * (0.1 * E), where + // dmin = min(s-a, s-b, s-c). This basically includes all triangles + // except for extremely long and skinny ones. + // + // Since we don't know E, we would like a conservative upper bound on + // the triangle area in terms of s and dmin. It's possible to show that + // E <= k1 * s * sqrt(s * dmin), where k1 = 2*sqrt(3)/Pi (about 1). + // Using this, it's easy to show that we should always use l'Huilier's + // method if dmin >= k2 * s^5, where k2 is about 1e-2. Furthermore, + // if dmin < k2 * s^5, the triangle area is at most k3 * s^4, where + // k3 is about 0.1. Since the best case error using Girard's formula + // is about 1e-15, this means that we shouldn't even consider it unless + // s >= 3e-4 or so. + sa := float64(b.Angle(c.Vector)) + sb := float64(c.Angle(a.Vector)) + sc := float64(a.Angle(b.Vector)) + s := 0.5 * (sa + sb + sc) + if s >= 3e-4 { + // Consider whether Girard's formula might be more accurate. + dmin := s - math.Max(sa, math.Max(sb, sc)) + if dmin < 1e-2*s*s*s*s*s { + // This triangle is skinny enough to use Girard's formula. + area := GirardArea(a, b, c) + if dmin < s*0.1*area { + return area + } + } + } + + // Use l'Huilier's formula. + return 4 * math.Atan(math.Sqrt(math.Max(0.0, math.Tan(0.5*s)*math.Tan(0.5*(s-sa))* + math.Tan(0.5*(s-sb))*math.Tan(0.5*(s-sc))))) +} + +// GirardArea returns the area of the triangle computed using Girard's formula. +// All points should be unit length, and no two points should be antipodal. +// +// This method is about twice as fast as PointArea() but has poor relative +// accuracy for small triangles. The maximum error is about 5e-15 (about +// 0.25 square meters on the Earth's surface) and the average error is about +// 1e-15. These bounds apply to triangles of any size, even as the maximum +// edge length of the triangle approaches 180 degrees. But note that for +// such triangles, tiny perturbations of the input points can change the +// true mathematical area dramatically. +func GirardArea(a, b, c Point) float64 { + // This is equivalent to the usual Girard's formula but is slightly more + // accurate, faster to compute, and handles a == b == c without a special + // case. PointCross is necessary to get good accuracy when two of + // the input points are very close together. + ab := a.PointCross(b) + bc := b.PointCross(c) + ac := a.PointCross(c) + + area := float64(ab.Angle(ac.Vector) - ab.Angle(bc.Vector) + bc.Angle(ac.Vector)) + if area < 0 { + area = 0 + } + return area +} + +// SignedArea returns a positive value for counterclockwise triangles and a negative +// value otherwise (similar to PointArea). +func SignedArea(a, b, c Point) float64 { + return float64(RobustSign(a, b, c)) * PointArea(a, b, c) +} + +// Angle returns the interior angle at the vertex B in the triangle ABC. The +// return value is always in the range [0, pi]. All points should be +// normalized. Ensures that Angle(a,b,c) == Angle(c,b,a) for all a,b,c. +// +// The angle is undefined if A or C is diametrically opposite from B, and +// becomes numerically unstable as the length of edge AB or BC approaches +// 180 degrees. +func Angle(a, b, c Point) s1.Angle { + // PointCross is necessary to get good accuracy when two of the input + // points are very close together. + return a.PointCross(b).Angle(c.PointCross(b).Vector) +} + +// TurnAngle returns the exterior angle at vertex B in the triangle ABC. The +// return value is positive if ABC is counterclockwise and negative otherwise. +// If you imagine an ant walking from A to B to C, this is the angle that the +// ant turns at vertex B (positive = left = CCW, negative = right = CW). +// This quantity is also known as the "geodesic curvature" at B. +// +// Ensures that TurnAngle(a,b,c) == -TurnAngle(c,b,a) for all distinct +// a,b,c. The result is undefined if (a == b || b == c), but is either +// -Pi or Pi if (a == c). All points should be normalized. +func TurnAngle(a, b, c Point) s1.Angle { + // We use PointCross to get good accuracy when two points are very + // close together, and RobustSign to ensure that the sign is correct for + // turns that are close to 180 degrees. + angle := a.PointCross(b).Angle(b.PointCross(c).Vector) + + // Don't return RobustSign * angle because it is legal to have (a == c). + if RobustSign(a, b, c) == CounterClockwise { + return angle + } + return -angle +} |