XeLaTeX interpration of LaTeX for localization

components/sections/explanation/content.en-GB.md

@@ -54,22 +54,22 @@ If they have a highest order term <i>x³</i> they're called "cubic" polynomials,
 Bézier curves are polynomials of <i>t</i>, rather than <i>x</i>, with the value for <i>t</i> fixed being between 0 and 1, with coefficients <i>a</i>, <i>b</i> etc. taking the "binomial" form, which sounds fancy but is actually a pretty simple description for mixing values:
 
 \[
-\begin{align*}
+\begin{aligned}
   linear &= (1-t) + t \\
   square &= (1-t)^2 + 2 \cdot (1-t) \cdot t + t^2 \\
   cubic &= (1-t)^3 + 3 \cdot (1-t)^2 \cdot t + 3 \cdot (1-t) \cdot t^2 + t^3
-\end{align*}
+\end{aligned}
 \]
 
 I know what you're thinking: that doesn't look too simple, but if we remove <i>t</i> and add in "times one", things suddenly look pretty easy. Check out these binomial terms:
 
 \[
-\begin{align*}
-  linear &= \hskip{2.5em} 1 + 1 \\
-  square &= \hskip{1.7em} 1 + 2 + 1\\
-  cubic &= \hskip{0.85em} 1 + 3 + 3 + 1\\
+\begin{aligned}
+  linear &= \hspace{2.5em} 1 + 1 \\
+  square &= \hspace{1.7em} 1 + 2 + 1\\
+  cubic &= \hspace{0.85em} 1 + 3 + 3 + 1\\
   hypercubic &= 1 + 4 + 6 + 4 + 1
-\end{align*}
+\end{aligned}
 \]
 
 Notice that 2 is the same as 1+1, and 3 is 2+1 and 1+2, and 6 is 3+3... As you can see, each time we go up a dimension, we simply start and end with 1, and everything in between is just "the two numbers above it, added together". Now <i>that's</i> easy to remember.
@@ -77,11 +77,11 @@ Notice that 2 is the same as 1+1, and 3 is 2+1 and 1+2, and 6 is 3+3... As you c
 There's an equally simple way to figure out how the polynomial terms work: if we rename <i>(1-t)</i> to <i>a</i> and <i>t</i> to <i>b</i>, and remove the weights for a moment, we get this:
 
 \[
-\begin{align*}
+\begin{aligned}
   linear &= BLUE[a] + RED[b] \\
   square &= BLUE[a] \cdot BLUE[a] + BLUE[a] \cdot RED[b] + RED[b] \cdot RED[b] \\
   cubic &= BLUE[a] \cdot BLUE[a] \cdot BLUE[a] + BLUE[a] \cdot BLUE[a] \cdot RED[b] + BLUE[a] \cdot RED[b] \cdot RED[b] + RED[b] \cdot RED[b] \cdot RED[b]\\
-\end{align*}
+\end{aligned}
 \]
 
 It's basically just a sum of "every combination of <i>a</i> and <i>b</i>", progressively replacing <i>a</i>'s with <i>b</i>'s after every + sign. So that's actually pretty simple too. So now you know binomial polynomials, and just for completeness I'm going to show you the generic function for this:

components/sections/explanation/content.ja-JP.md

@@ -54,22 +54,22 @@
 ベジエ曲線は<i>x</i>の多項式ではなく、<i>t</i>の多項式です。<i>t</i>の値は0から1までの間に制限され、その係数<i>a</i>、<i>b</i>などは「二項係数」の形をとります。というと複雑そうに聞こえますが、実際には値を組み合わせて、とてもシンプルに記述できます。
 
 \[
-\begin{align*}
+\begin{aligned}
   linear &= (1-t) + t \\
   square &= (1-t)^2 + 2 \cdot (1-t) \cdot t + t^2 \\
   cubic &= (1-t)^3 + 3 \cdot (1-t)^2 \cdot t + 3 \cdot (1-t) \cdot t^2 + t^3
-\end{align*}
+\end{aligned}
 \]
 
 「そこまでシンプルには見えないよ」と思っていることでしょう。しかし仮に、<i>t</i>を取り去って係数に1を掛けることにしてしまえば、急激に簡単になります。これが二項係数部分の項です。
 
 \[
-\begin{align*}
-  linear &= \hskip{2.5em} 1 + 1 \\
-  square &= \hskip{1.7em} 1 + 2 + 1\\
-  cubic &= \hskip{0.85em} 1 + 3 + 3 + 1\\
+\begin{aligned}
+  linear &= \hspace{2.5em} 1 + 1 \\
+  square &= \hspace{1.7em} 1 + 2 + 1\\
+  cubic &= \hspace{0.85em} 1 + 3 + 3 + 1\\
   hypercubic &= 1 + 4 + 6 + 4 + 1
-\end{align*}
+\end{aligned}
 \]
 
 2は1+1に等しく、3は2+1や1+2に等しく、6は3+3に等しく、……ということに注目してください。見てわかるように、先頭と末尾は単に1になっていますが、中間はどれも次数が増えるたびに「上の2つの数を足し合わせた」ものになっています。<i>これなら</i>覚えやいですね。
@@ -77,11 +77,11 @@
 多項式部分の項がどうなっているのか、同じぐらい簡単な方法で考えることができます。仮に、<i>(1-t)</i>を<i>a</i>に、<i>t</i>を<i>b</i>に書き換え、さらに重みを一旦削除してしまえば、このようになります。
 
 \[
-\begin{align*}
+\begin{aligned}
   linear &= BLUE[a] + RED[b] \\
   square &= BLUE[a] \cdot BLUE[a] + BLUE[a] \cdot RED[b] + RED[b] \cdot RED[b] \\
   cubic &= BLUE[a] \cdot BLUE[a] \cdot BLUE[a] + BLUE[a] \cdot BLUE[a] \cdot RED[b] + BLUE[a] \cdot RED[b] \cdot RED[b] + RED[b] \cdot RED[b] \cdot RED[b]\\
-\end{align*}
+\end{aligned}
 \]
 
 これは要するに、「<i>a</i>と<i>b</i>のすべての組み合わせ」の単なる和です。プラスが出てくるたびに、<i>a</i>を<i>b</i>へと1つずつ置き換えていけばよいのです。こちらも本当に単純です。さて、これで「二項係数多項式」がわかりました。完璧を期するため、この関数の一般の形を示しておきます。

components/sections/explanation/content.zh-CN.md

@@ -54,22 +54,22 @@
 贝塞尔曲线不是x的多项式，它是<i>t</i>的多项式，<i>t</i>的值被限制在0和1之间，并且含有<i>a</i>，<i>b</i>等参数。它采用了二次项的形式，听起来很神奇但实际上就是混合不同值的简单描述：
 
 \[
-\begin{align*}
+\begin{aligned}
   linear &= (1-t) + t \\
   square &= (1-t)^2 + 2 \cdot (1-t) \cdot t + t^2 \\
   cubic &= (1-t)^3 + 3 \cdot (1-t)^2 \cdot t + 3 \cdot (1-t) \cdot t^2 + t^3
-\end{align*}
+\end{aligned}
 \]
 
 我明白你在想什么：这看起来并不简单，但如果我们拿掉<i>t</i>并让系数乘以1，事情就会立马简单很多，看看这些二次项：
 
 \[
-\begin{align*}
-  linear &= \hskip{2.5em} 1 + 1 \\
-  square &= \hskip{1.7em} 1 + 2 + 1\\
-  cubic &= \hskip{0.85em} 1 + 3 + 3 + 1\\
+\begin{aligned}
+  linear &= \hspace{2.5em} 1 + 1 \\
+  square &= \hspace{1.7em} 1 + 2 + 1\\
+  cubic &= \hspace{0.85em} 1 + 3 + 3 + 1\\
   hypercubic &= 1 + 4 + 6 + 4 + 1
-\end{align*}
+\end{aligned}
 \]
 
 需要注意的是，2与1+1相同，3相当于2+1或1+2，6相当于3+3...如你所见，每次我们增加一个维度，只要简单地将头尾置为1，中间的操作都是“将上面的两个数字相加”。现在就能很容易地记住了。
@@ -77,11 +77,11 @@
 还有一个简单的办法可以弄清参数项怎么工作的：如果我们将<i>(1-t)</i>重命名为<i>a</i>，将<i>t</i>重命名为<i>b</i>，暂时把权重删掉，可以得到这个：
 
 \[
-\begin{align*}
+\begin{aligned}
   linear &= BLUE[a] + RED[b] \\
   square &= BLUE[a] \cdot BLUE[a] + BLUE[a] \cdot RED[b] + RED[b] \cdot RED[b] \\
   cubic &= BLUE[a] \cdot BLUE[a] \cdot BLUE[a] + BLUE[a] \cdot BLUE[a] \cdot RED[b] + BLUE[a] \cdot RED[b] \cdot RED[b] + RED[b] \cdot RED[b] \cdot RED[b]\\
-\end{align*}
+\end{aligned}
 \]
 
 基本上它就是“每个<i>a</i>和<i>b</i>结合项”的和，在每个加号后面逐步的将<i>a</i>换成<i>b</i>。因此这也很简单。现在你已经知道了二次多项式，为了叙述的完整性，我将给出一般方程：