## 15.7. Unnormalized Texel Coordinate Operations

### 15.7.1. (u,v,w,a) to (i,j,k,l,n) Transformation And Array Layer Selection

The unnormalized texel coordinates are transformed to integer texel coordinates relative to the selected mipmap level.

The layer index l is computed as:

\begin{align*} l & = \operatorname{clamp}( \operatorname{RNE}(a), 0, layerCount - 1 ) + baseArrayLayer \end{align*}

where `layerCount` is the number of layers in the image subresource range of the image view, `baseArrayLayer` is the first layer from the subresource range, and where:

\begin{align*} \operatorname{RNE}(a) & = \begin{cases} \operatorname{roundTiesToEven}(a) & \textrm{preferred, from IEEE Std 754-2008 Floating-Point Arithmetic} \\ \left \lfloor a + \frac{1}{2} \right \rfloor & \textrm{alternative} \end{cases} \end{align*}

The sample index n is assigned the value zero.

Nearest filtering (`VK_FILTER_NEAREST`) computes the integer texel coordinates that the unnormalized coordinates lie within:

\begin{align*} i & = \left \lfloor u \right \rfloor \\ j & = \left \lfloor v \right \rfloor \\ k & = \left \lfloor w \right \rfloor \end{align*}

Linear filtering (`VK_FILTER_LINEAR`) computes a set of neighboring coordinates which bound the unnormalized coordinates. The integer texel coordinates are combinations of $i_0\textrm{ or }i_1,j_0\textrm{ or }j_1,k_0\textrm{ or }k_1$ , as well as weights $\alpha, \beta, and \gamma$ .

\begin{align*} i_{0} & = \left \lfloor u - \frac{1}{2} \right \rfloor & i_{1} & = i_{0} + 1 \\ j_{0} & = \left \lfloor v - \frac{1}{2} \right \rfloor & j_{1} & = j_{0} + 1 \\ k_{0} & = \left \lfloor w - \frac{1}{2} \right \rfloor & k_{1} & = k_{0} + 1 \\ \\ \alpha & = \operatorname{frac} \left ( u - \frac{1}{2} \right ) \\ \beta & = \operatorname{frac} \left ( v - \frac{1}{2} \right ) \\ \gamma & = \operatorname{frac} \left ( w - \frac{1}{2} \right ) \end{align*}

If the image instruction includes a $ConstOffset$ operand, the constant offsets $(\Delta_{i},\Delta_{j},\Delta_{k})$ are added to $(i,j,k)$ components of the integer texel coordinates.