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Scott Richmond 2024-12-02 13:25:59 -05:00
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12
ch_1_intro.md
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@ -876,8 +876,10 @@ Here is the finished `cngon!`:
```
fn cngon! (n, radius) -> {
let angle = sub (inv (2), inv (n))
let angle = add (inv (4), inv (mult (2, n)))
& ^... this is equation (5), above, solving for `d`
let edge = mult (2, radius, sin (inv (mult (2, n))))
& ^... this is equation (8), above, solving for `e`
penup! ()
forward! (radius)
@ -918,7 +920,13 @@ Combine the ideas of `spingon!` with your newly constructed `cngon!`.
Design a fancier `cngon!` that fills up a polygon with textures.
Here are a few visual tips for Exercises 1.3 and 1.4:
{{Figure 13: `spincngon`s. Bottom of p. 32.}}
<img src="fig_13.1.svg" alt="Nested squares." width="400" />
<img src="fig_13.2.svg" alt="Twisty, nested nonagons." width="400" />
<img src="fig_13.3.svg" alt="Twisty, nested triangles." width="400" />
##### Figure 13: `spincngon`s.
#### Exercise 1.5
Design a Ludus function that puts polygons on the vertices of other polygons.

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<ludus>
fn ngon! (n, edge) -&gt; {
repeat n {
forward! (edge)
right! (inv (n))
}
}
fn cngon! (n, radius) -&gt; {
let angle = add (inv (4), inv (mult (2, n)))
let edge = mult (2, radius, sin (inv (mult (2, n))))
penup! ()
forward! (radius)
right! (angle)
pendown! ()
ngon! (n, edge)
left! (angle)
penup! ()
back! (radius)
pendown! ()
}
fn twisty_nonagons! (times, iter, radius, growth) -&gt; {
if gte? (iter, times) then :ok
else {
cngon! (9, radius)
right! (inv (times))
twisty_nonagons! (times, inc (iter), add (radius, growth), growth)
}
}
&amp; twisty_nonagons! (10, 0, 100, 3)
fn centre_squares! (times, radius, growth) -&gt; {
if lt? (times, 1) then :ok
else {
cngon! (4, radius)
centre_squares! (dec (times), add (radius, growth), growth)
}
}
right! (0.125)
centre_squares! (10, 100, 4)
fn twisty_triangles! (times, radius, angle, growth) -&gt; {
if lt? (times, 1) then :ok
else {
cngon! (3, radius)
right! (angle)
twisty_triangles! (dec (times), sub (radius, growth), angle, growth)
}
}
&amp; right! (inv (6))
&amp; twisty_triangles! (8, 100, inv (120), 10)
hideturtle! ()
</ludus>
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Side by Side

After

Width:  |  Height:  |  Size: 8.2 KiB

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<ludus>
fn ngon! (n, edge) -&gt; {
repeat n {
forward! (edge)
right! (inv (n))
}
}
fn cngon! (n, radius) -&gt; {
let angle = add (inv (4), inv (mult (2, n)))
let edge = mult (2, radius, sin (inv (mult (2, n))))
penup! ()
forward! (radius)
right! (angle)
pendown! ()
ngon! (n, edge)
left! (angle)
penup! ()
back! (radius)
pendown! ()
}
fn twisty_nonagons! (times, iter, radius, growth) -&gt; {
if gte? (iter, times) then :ok
else {
cngon! (9, radius)
right! (inv (times))
twisty_nonagons! (times, inc (iter), add (radius, growth), growth)
}
}
twisty_nonagons! (10, 0, 100, 3)
fn centre_squares! (times, radius, growth) -&gt; {
if lt? (times, 1) then :ok
else {
cngon! (4, radius)
centre_squares! (dec (times), add (radius, growth), growth)
}
}
&amp; right! (0.125)
&amp; centre_squares! (10, 100, 4)
fn twisty_triangles! (times, radius, angle, growth) -&gt; {
if lt? (times, 1) then :ok
else {
cngon! (3, radius)
right! (angle)
twisty_triangles! (dec (times), sub (radius, growth), angle, growth)
}
}
&amp; right! (inv (6))
&amp; twisty_triangles! (8, 100, inv (120), 10)
hideturtle! ()
</ludus>
</svg>
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<ludus>
fn ngon! (n, edge) -&gt; {
repeat n {
forward! (edge)
right! (inv (n))
}
}
fn cngon! (n, radius) -&gt; {
let angle = add (inv (4), inv (mult (2, n)))
let edge = mult (2, radius, sin (inv (mult (2, n))))
penup! ()
forward! (radius)
right! (angle)
pendown! ()
ngon! (n, edge)
left! (angle)
penup! ()
back! (radius)
pendown! ()
}
fn twisty_nonagons! (times, iter, radius, growth) -&gt; {
if gte? (iter, times) then :ok
else {
cngon! (9, radius)
right! (inv (times))
twisty_nonagons! (times, inc (iter), add (radius, growth), growth)
}
}
&amp; twisty_nonagons! (10, 0, 100, 3)
fn centre_squares! (times, radius, growth) -&gt; {
if lt? (times, 1) then :ok
else {
cngon! (4, radius)
centre_squares! (dec (times), add (radius, growth), growth)
}
}
&amp; right! (0.125)
&amp; centre_squares! (10, 100, 4)
fn twisty_triangles! (times, radius, angle, growth) -&gt; {
if lt? (times, 1) then :ok
else {
cngon! (3, radius)
right! (angle)
twisty_triangles! (dec (times), sub (radius, growth), angle, growth)
}
}
right! (inv (6))
twisty_triangles! (8, 100, inv (120), 10)
hideturtle! ()
</ludus>
</svg>
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Width:  |  Height:  |  Size: 5.6 KiB