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5f0141ca4c
Changes made in dsp/fourier/internal/fftpack break the formatting used there, so these are reverted. There will be complaints in CI. [git-generate] gofmt -w . go generate gonum.org/v1/gonum/blas go generate gonum.org/v1/gonum/blas/gonum go generate gonum.org/v1/gonum/unit go generate gonum.org/v1/gonum/unit/constant go generate gonum.org/v1/gonum/graph/formats/dot go generate gonum.org/v1/gonum/graph/formats/rdf go generate gonum.org/v1/gonum/stat/card git checkout -- dsp/fourier/internal/fftpack
98 lines
2.7 KiB
Go
98 lines
2.7 KiB
Go
// Copyright ©2022 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package r2
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import "math"
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// Triangle represents a triangle in 2D space and
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// is composed by 3 vectors corresponding to the position
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// of each of the vertices.
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type Triangle [3]Vec
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// Centroid returns the intersection of the three medians of the triangle
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// as a point in space.
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func (t Triangle) Centroid() Vec {
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return Scale(1.0/3.0, Add(Add(t[0], t[1]), t[2]))
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}
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// Area returns the surface area of the triangle.
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func (t Triangle) Area() float64 {
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// Heron's Formula, see https://en.wikipedia.org/wiki/Heron%27s_formula.
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// Also see William M. Kahan (24 March 2000). "Miscalculating Area and Angles of a Needle-like Triangle"
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// for more discussion. https://people.eecs.berkeley.edu/~wkahan/Triangle.pdf.
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a, b, c := t.orderedLengths()
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A := (c + (b + a)) * (a - (c - b))
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A *= (a + (c - b)) * (c + (b - a))
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return math.Sqrt(A) / 4
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}
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// orderedLengths returns the lengths of the sides of the triangle such that
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// a ≤ b ≤ c.
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func (t Triangle) orderedLengths() (a, b, c float64) {
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s1, s2, s3 := t.sides()
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l1 := Norm(s1)
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l2 := Norm(s2)
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l3 := Norm(s3)
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// sort-3
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if l2 < l1 {
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l1, l2 = l2, l1
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}
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if l3 < l2 {
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l2, l3 = l3, l2
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if l2 < l1 {
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l1, l2 = l2, l1
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}
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}
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return l1, l2, l3
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}
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// sides returns vectors for each of the sides of t.
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func (t Triangle) sides() (Vec, Vec, Vec) {
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return Sub(t[1], t[0]), Sub(t[2], t[1]), Sub(t[0], t[2])
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}
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// IsDegenerate returns true if all of triangle's vertices are
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// within tol distance of its longest side.
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func (t Triangle) IsDegenerate(tol float64) bool {
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sides := [3]Vec{Sub(t[1], t[0]), Sub(t[2], t[1]), Sub(t[0], t[2])}
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len2 := [3]float64{Norm2(sides[0]), Norm2(sides[1]), Norm2(sides[2])}
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longLen := len2[0]
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longIdx := 0
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if len2[1] > longLen {
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longLen = len2[1]
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longIdx = 1
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}
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if len2[2] > longLen {
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longIdx = 2
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}
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// calculate vertex distance from longest side
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ln := line{t[longIdx], t[(longIdx+1)%3]}
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dist := ln.distance(t[(longIdx+2)%3])
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return dist <= tol
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}
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// line is an infinite 3D line
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// defined by two points on the line.
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type line [2]Vec
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// vecOnLine takes a value between 0 and 1 to linearly
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// interpolate a point on the line.
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//
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// vecOnLine(0) returns l[0]
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// vecOnLine(1) returns l[1]
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func (l line) vecOnLine(t float64) Vec {
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lineDir := Sub(l[1], l[0])
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return Add(l[0], Scale(t, lineDir))
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}
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// distance returns the minimum euclidean distance of point p to the line.
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func (l line) distance(p Vec) float64 {
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// https://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html
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p1 := l[0]
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p2 := l[1]
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num := math.Abs((p2.X-p1.X)*(p1.Y-p.Y) - (p1.X-p.X)*(p2.Y-p1.Y))
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return num / math.Hypot(p2.X-p1.X, p2.Y-p1.Y)
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}
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