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Bezierinfo CI
2021-04-19 18:36:24 +00:00
parent c990a4f48d
commit a4511d217d
35 changed files with 3661 additions and 1676 deletions
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5
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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
2 2
B + B = r
x y

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌───────────────────────┐
╭ 1 │ 2 2
erf (θ, k) = | \| │B (t,θ,k) + B (t,θ,k) - r\|dt
╯ 0 ⟍│ x y

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ ┌───────┐ ╮
│ ╭ 1 │ 2 2 │ d
│ | \| │B + B - r\|dt │ ── = 0
╰ ╯ 0 ⟍│ x y ╯ dt

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ \pi ╮ 4 ╭ \pi ╮ 4 ┌─┐
f│ ─── │ = ─ · tan│ ─── │ = ─(⟍│2 -1) ≅ 0.55228474983[...]
╰ 2 ╯ 3 ╰ 8 ╯ 3

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
start= (r, 0)
control = (r, 0.55228 · r)
1
control = (0.55228 · r, r)
2
end= (0, r)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
3c + 4sin(θ)) - 3k · cos(θ) θ
────────────────────────────= sin(─)
8 2
╭ θ ╮
3k + 4sin(θ)) - 3k · cos(θ)= 8sin│ ─ │
╰ 2 ╯
╭ θ ╮
3k - 3k · cos(θ)= 8sin│ ─ │ - 4sin(θ)
╰ 2 ╯
╭ ╭ θ ╮ ╮
3k (1 - cos(θ))= 4 │ 2sin│ ─ │ - sin(θ) │
╰ ╰ 2 ╯ ╯
θ
2sin(─) - sin(θ)
2
3k= 4 · ────────────────
1 - cos(θ)
╭ θ ╮
2sin│ ─ │ - sin(θ)
4 ╰ 2 ╯
k= ─ · ──────────────────
3 1 - cos(θ)

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
┌───────┐
│ 2 2
\| │B + B - r\| = 0, t ∈[0,1]
⟍│ x y

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
start= (r, 0)
control = (r, k)
1
control = r · (cos(θ) + k · sin(θ), sin(θ) - k · cos(θ))
2
end= r · (cos(θ), sin(θ))

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
P + P
2 3
y y k + sin(θ) - k · cos(θ)
A = ───────── = ────────────────────────
y 2 2
1
A + ─P k + sin(θ) - k · cos(θ)
y 2 2 ──────────────────────── + ─
y 2 2 2k + sin(θ) + k · cos(θ)
e = ───────── = ──────────────────────────── = ─────────────────────────
1 2 2 4
y
k
A + mid(P , P ) A + sin(θ) - ─ cos(θ)
y 4 3 y 2 k + 3sin(θ) 2k · cos(θ)
e = ───────────────── = ────────────────────── = ────────────────────────
2 2 2 4
y
e + e
1 2
y y 3k + 4sin(θ) - 3k · cos(θ)
B = ───────── = ───────────────────────────
y 2 8

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
4 ╭ θ ╮
k = f(θ) = ─ tan│ ─ │
3 ╰ 4 ╯

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
╭ θ ╮
2sin│ ─ │ - sin(θ)
4 ╰ 2 ╯
k= ─ · ──────────────────
3 1 - cos(θ)
╭ ╭ θ ╮ ╮
│ 2sin│ ─ │ │
4 │ ╰ 2 ╯ sin(θ) │
k= ─ · │ ────────── - ────────── │
3 ╰ 1 - cos(θ) 1 - cos(θ) ╯
4 ╭ ╭ θ ╮ ╭ θ ╮ ╮
k= ─ · │ csc│ ─ │ - cot│ ─ │ │
3 ╰ ╰ 2 ╯ ╰ 2 ╯ ╯
4 ╭ θ ╮
k= ─ · tan│ ─ │
3 ╰ 4 ╯

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\setmainfont[Ligatures=TeX]TeX Gyre Pagella \setmathfontTeX Gyre Pagella Math
P = (1, 0)
1
P = (1, c)
2
P = P + k · (sin(θ), -cos(θ))
3 4
P = (cos(θ), sin(θ))
4