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2018-06-24 14:16:21 -07:00
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components/sections/matrixsplit/content.en-GB.md
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@@ -288,7 +288,7 @@ Excellent! Now we can form our new quadratic curve:
\end{bmatrix}
\]
***Brilliant***: if we want a subcurve from `t = 0` to `t = z`, we can keep the first coordinate the same (which makes sense), our control point becomes a z-ratio mixture of the original control point and the start point, and the new end point is a mixture that looks oddly similar to a [Bernstein polynomial](https://en.wikipedia.org/wiki/Bernstein_polynomial) of degree two, except it uses (z-1) rather than (1-z)... These new coordinates are actually really easy to compute directly!
***Brilliant***: if we want a subcurve from `t = 0` to `t = z`, we can keep the first coordinate the same (which makes sense), our control point becomes a z-ratio mixture of the original control point and the start point, and the new end point is a mixture that looks oddly similar to a [Bernstein polynomial](https://en.wikipedia.org/wiki/Bernstein_polynomial) of degree two. These new coordinates are actually really easy to compute directly!
Of course, that's only one of the two curves. Getting the section from `t = z` to `t = 1` requires doing this again. We first observe what we just did is actually evaluate the general interval [0,`z`], which we wrote down simplified because of that zero, but we actually evaluated this: