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add videos in stereo.2

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queue-miscreant 2025-07-22 03:28:17 -05:00
parent 8fb3ddad8f
commit 94dee54cdb
2 changed files with 25 additions and 8 deletions
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2
posts/stereo/2/anim.py
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@ -34,7 +34,7 @@ def bindfig(fig):
class SympyAnimationWrapper: class SympyAnimationWrapper:
""" """
Context manager for binding a figurebinfoinfoinfoinfoinfoinfo Context manager for binding a figure for animation.
""" """
def __init__(self, filename: Path | str): def __init__(self, filename: Path | str):
self._filename = filename if isinstance(filename, Path) else Path(filename) self._filename = filename if isinstance(filename, Path) else Path(filename)

31
posts/stereo/2/index.qmd
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@ -44,7 +44,7 @@ def generate_os(amt):
yield ret yield ret
ret = (ret * o).expand().cancel().simplify() ret = (ret * o).expand().cancel().simplify()
os = list(generate_os(10)) os = list(generate_os(11))
cs = [sympy.re(i).simplify() for i in os] cs = [sympy.re(i).simplify() for i in os]
ss = [sympy.im(i).simplify() for i in os] ss = [sympy.im(i).simplify() for i in os]
``` ```
@ -365,9 +365,7 @@ will plot a $p/1$ polar rose as t ranges over $(-\infty, \infty)$.
```{python} ```{python}
#| echo: false #| echo: false
#| fig-cap: | #| output: false
#| p/1 polar roses as rational curves.
#| Since *t* never reaches infinity, a bite appears to be taken out of the graphs near (-1, 0).
@dataclass @dataclass
class Rose: class Rose:
@ -384,7 +382,7 @@ class Rose:
) )
def animate_roses(filename: str, arguments: list[Rose], interval=200): def animate_roses(filename: str, arguments: list[Rose], interval=500):
with SympyAnimationWrapper(filename) as animate: with SympyAnimationWrapper(filename) as animate:
@animate(list(range(len(arguments))), interval=interval) @animate(list(range(len(arguments))), interval=interval)
def ret(fr): def ret(fr):
@ -408,6 +406,13 @@ animate_roses(
) )
``` ```
::: {#fig-polar-roses-1}
{{< video "./polar_roses_1.mp4" >}}
p/1 polar roses as rational curves.
Since *t* never reaches infinity, a bite appears to be taken out of the graphs near (-1, 0)."
:::
$q = 1$ happens to match the subscript *c* term of *x* and *s* term of *y*, so one might wonder $q = 1$ happens to match the subscript *c* term of *x* and *s* term of *y*, so one might wonder
whether the other polar curves can be obtained by allowing it to vary as well. whether the other polar curves can be obtained by allowing it to vary as well.
And you'd be right. And you'd be right.
@ -420,7 +425,7 @@ will plot a $p/q$ polar rose as t ranges over $(-\infty, \infty)$.
```{python} ```{python}
#| echo: false #| echo: false
#| fig-cap: p/q polar roses as rational curves #| output: false
animate_roses( animate_roses(
"polar_roses_2.mp4", "polar_roses_2.mp4",
@ -431,6 +436,11 @@ animate_roses(
) )
``` ```
::: {#fig-polar-roses-2}
{{< video "./polar_roses_2.mp4" >}}
p/q polar roses as rational curves
:::
Just as with the prior calculus examples, doubling all subscripts of *c* and *s* will Just as with the prior calculus examples, doubling all subscripts of *c* and *s* will
only require *t* to range over $(-1, 1)$, which removes the ugly bite mark. only require *t* to range over $(-1, 1)$, which removes the ugly bite mark.
@ -700,7 +710,7 @@ Indeed, the sequence of curves with parametrization $R_n(t) = 2nt$ approximate t
```{python} ```{python}
#| echo: false #| echo: false
#| fig-cap: Approximations to the Archimedean spiral #| output: false
with SympyAnimationWrapper("approximate_archimedes.mp4") as animate: with SympyAnimationWrapper("approximate_archimedes.mp4") as animate:
@animate(list(range(10)), interval=500) @animate(list(range(10)), interval=500)
@ -734,6 +744,13 @@ with SympyAnimationWrapper("approximate_archimedes.mp4") as animate:
ret.save() # type: ignore ret.save() # type: ignore
``` ```
::: {#fig-approx-archimedes}
{{< video ./approximate_archimedes.mp4 >}}
Approximations to the Archimedean spiral
:::
Since R necessarily defines a rational curve, the curves will never be equal, Since R necessarily defines a rational curve, the curves will never be equal,
just as any stretching of $c_n$ will never exactly become cosine. just as any stretching of $c_n$ will never exactly become cosine.