diff --git a/docs/tutorial.md b/docs/tutorial.md index cb7d3716a..ad905e3ac 100644 --- a/docs/tutorial.md +++ b/docs/tutorial.md @@ -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 @@ -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