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Fix typo in matrixsplit (#102)

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Masaya Nakamura
2017-04-25 00:30:46 +09:00
committed by Mike Kamermans
parent c812ab3aec
commit 9f8a97cc78
1 changed files with 2 additions and 2 deletions
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4
components/sections/matrixsplit/content.en-GB.md
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@@ -37,7 +37,7 @@ and
\end{bmatrix}
\]
Let's say we want to split the curve at some point `t = z`, forming two new (obviously smaller) Bézier curves. To find the coordinates for these two Bézier curves, we can use the matrix representation and some linear algebra. First, we split out the the actual "point on the curve" information as a new matrix multiplication:
Let's say we want to split the curve at some point `t = z`, forming two new (obviously smaller) Bézier curves. To find the coordinates for these two Bézier curves, we can use the matrix representation and some linear algebra. First, we split out the actual "point on the curve" information as a new matrix multiplication:
\[
B(t) =
@@ -290,7 +290,7 @@ Excellent! Now we can form our new quadratic curve:
***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 of degree two, except it uses (z-1) rather than (1-z)... 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 what we just did is actually evaluate the general interval [0,`z`], which we wrote down simplified becuase of that zero, but we actually evaluated this:
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 becuase of that zero, but we actually evaluated this:
\[
B(t) =