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Fix docs typos in tutorial #61

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11 changes: 5 additions & 6 deletions docs/tutorial.md
Original file line number Diff line number Diff line change
Expand Up @@ -1646,11 +1646,10 @@ rotations.
The most popular technique is linear blend skinning. Each point on the shape
computes its new location as a linear combination of bone transformations:

$\mathbf{x}' = \sum\limits_{i = 1}^m w_i(\mathbf{x}) \mathbf{T}_i
\left(\begin{array}{c}\mathbf{x}_i\\1\end{array}\right),$
$\mathbf{x}' = \sum\limits_{i = 1}^m w_i(\mathbf{x}) \mathbf{T}_i \left(\begin{array}{c}\mathbf{x}\\1\end{array}\right),$

where $w_i(\mathbf{x})$ is the scalar _weight function_ of the ith bone evaluated at
$\mathbf{x}$ and $\mathbf{T}_i$ is the bone transformation as a $4 \times 3$
where $\mathbf{x}'$ and $\mathbf{x}$ are column vectors, $w_i(\mathbf{x})$ is the scalar _weight function_ of the ith bone evaluated at
$\mathbf{x}$ and $\mathbf{T}_i$ is the bone transformation as a $3 \times 4$
matrix.

This formula is embarassingly parallel (computation at one point does not
Expand All @@ -1666,8 +1665,8 @@ multiplication:
$\mathbf{X}' = \mathbf{M} \mathbf{T},$

where $\mathbf{X}'$ is $n \times 3$ stack of deformed positions as row
vectors, $\mathbf{M}$ is a $n \times m\cdot dim$ matrix containing weights and
rest positions and $\mathbf{T}$ is a $m\cdot (dim+1) \times dim$ stack of
vectors, $\mathbf{M}$ is a $n \times 4m$ matrix containing weights and
rest positions and $\mathbf{T}$ is a $4m \times 3$ stack of
transposed bone transformations.

Traditionally, the weight functions $w_j$ are painted manually by skilled
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