Vulkan-Docs/doc/specs/vulkan/chapters/vertexpostproc.txt

// Copyright (c) 2015-2017 The Khronos Group Inc.
// Copyright notice at https://www.khronos.org/registry/speccopyright.html

[[vertexpostproc]]
= Fixed-Function Vertex Post-Processing

After programmable vertex processing, the following fixed-function
operations are applied to vertices of the resulting primitives:

ifdef::VK_NV_viewport_swizzle[]
  * Viewport swizzle (see <<vertexpostproc-viewport-swizzle,Viewport
    Swizzle>>)
endif::VK_NV_viewport_swizzle[]
  * Flatshading (see <<vertexpostproc-flatshading,Flatshading>>).
  * Primitive clipping, including client-defined half-spaces (see
    <<vertexpostproc-clipping,Primitive Clipping>>).
  * Shader output attribute clipping (see
    <<vertexpostproc-clipping-shader-outputs,Clipping Shader Outputs>>).
ifdef::VK_NV_clip_space_w_scaling[]
  * Clip space W scaling (see <<vertexpostproc-viewportwscaling,Controlling
    Viewport W Scaling>>).
endif::VK_NV_clip_space_w_scaling[]
  * Perspective division on clip coordinates (see
    <<vertexpostproc-coord-transform,Coordinate Transformations>>).
  * Viewport mapping, including depth range scaling (see
    <<vertexpostproc-viewport,Controlling the Viewport>>).
  * Front face determination for polygon primitives (see
    <<primsrast-polygons-basic,Basic Polygon Rasterization>>).

ifdef::editing-notes[]
[NOTE]
.editing-note
====
TODO:Odd that this one link to a different chapter is in this list.
====
endif::editing-notes[]

Next, rasterization is performed on primitives as described in chapter
<<primsrast,Rasterization>>.

ifdef::VK_NV_viewport_swizzle[]
[[vertexpostproc-viewport-swizzle]]
== Viewport Swizzle

Each primitive sent to a given viewport has a swizzle and optional negation
applied to its clip coordinates.
The swizzle that is applied depends on the viewport index, and is controlled
by the sname:VkPipelineViewportSwizzleStateCreateInfoNV pipeline state:

include::../api/structs/VkPipelineViewportSwizzleStateCreateInfoNV.txt[]

  * pname:sType is the type of this structure.
  * pname:pNext is `NULL` or a pointer to an extension-specific structure.
  * pname:flags is reserved for future use.
  * pname:viewportCount is the number of viewport swizzles used by the
    pipeline.
  * pname:pViewportSwizzles is a pointer to an array of
    slink:VkViewportSwizzleNV structures, defining the viewport swizzles.

.Valid Usage
****
  * [[VUID-VkPipelineViewportSwizzleStateCreateInfoNV-viewportCount-01215]] pname:viewportCount must: match the pname:viewportCount set in
    sname:VkPipelineViewportStateCreateInfo
****

include::../validity/structs/VkPipelineViewportSwizzleStateCreateInfoNV.txt[]

The sname:VkPipelineViewportSwizzleStateCreateInfoNV state is set by adding
an instance of this structure to the pname:pNext chain of an instance of the
sname:VkPipelineViewportStateCreateInfo structure and setting the graphics
pipeline state with flink:vkCreateGraphicsPipelines.

Each viewport specified from 0 to pname:viewportCount - 1 has its x,y,z,w
swizzle state set to the corresponding pname:x, pname:y, pname:z and pname:w
in the slink:VkViewportSwizzleNV structure.
Each component is of type elink:VkViewportCoordinateSwizzleNV, which
determines the type of swizzle for that component.
The value of pname:x computes the new x component of the position as:

    if (x == VK_VIEWPORT_COORDINATE_SWIZZLE_POSITIVE_X_NV) x' = x; if (x ==
    VK_VIEWPORT_COORDINATE_SWIZZLE_NEGATIVE_X_NV) x' = -x; if (x ==
    VK_VIEWPORT_COORDINATE_SWIZZLE_POSITIVE_Y_NV) x' = y; if (x ==
    VK_VIEWPORT_COORDINATE_SWIZZLE_NEGATIVE_Y_NV) x' = -y; if (x ==
    VK_VIEWPORT_COORDINATE_SWIZZLE_POSITIVE_Z_NV) x' = z; if (x ==
    VK_VIEWPORT_COORDINATE_SWIZZLE_NEGATIVE_Z_NV) x' = -z; if (x ==
    VK_VIEWPORT_COORDINATE_SWIZZLE_POSITIVE_W_NV) x' = w; if (x ==
    VK_VIEWPORT_COORDINATE_SWIZZLE_NEGATIVE_W_NV) x' = -w;

Similar selections are performed for the pname:y, pname:z, and pname:w
coordinates.
This swizzling is applied before clipping and perspective divide.
If the swizzle for an active viewport index is not specified, the swizzle
for pname:x is ename:VK_VIEWPORT_COORDINATE_SWIZZLE_POSITIVE_X_NV, pname:y
is ename:VK_VIEWPORT_COORDINATE_SWIZZLE_POSITIVE_Y_NV, pname:z is
ename:VK_VIEWPORT_COORDINATE_SWIZZLE_POSITIVE_Z_NV and pname:w is
ename:VK_VIEWPORT_COORDINATE_SWIZZLE_POSITIVE_W_NV.

Viewport swizzle parameters are specified by setting the pname:pNext pointer
of sname:VkGraphicsPipelineCreateInfo to point to an instance of
sname:VkPipelineViewportSwizzleStateCreateInfoNV.
slink:VkPipelineViewportSwizzleStateCreateInfoNV uses
sname:VkViewportSwizzleNV to set the viewport swizzle parameters.

// refBegin VkViewportSwizzleNV Structure specifying a viewport swizzle

The sname:VkViewportSwizzleNV structure is defined as:

include::../api/structs/VkViewportSwizzleNV.txt[]

  * pname:x is the swizzle operation to apply to the x component of the
    primitive
  * pname:y is the swizzle operation to apply to the y component of the
    primitive
  * pname:z is the swizzle operation to apply to the z component of the
    primitive
  * pname:w is the swizzle operation to apply to the w component of the
    primitive

include::../validity/structs/VkViewportSwizzleNV.txt[]

The ename:VkViewportCoordinateSwizzleNV enum is defined as:

include::../api/enums/VkViewportCoordinateSwizzleNV.txt[]

endif::VK_NV_viewport_swizzle[]

[[vertexpostproc-flatshading]]
== Flat Shading

_Flat shading_ a vertex output attribute means to assign all vertices of the
primitive the same value for that output.

The output values assigned are those of the _provoking vertex_ of the
primitive.
The provoking vertex depends on the primitive topology, and is generally the
"`first`" vertex of the primitive.
For primitives not processed by tessellation or geometry shaders, the
provoking vertex is selected from the input vertices according to the
following table.

<<<

[[provoking-vertex-selection]]
.Provoking vertex selection
[align="center",cols="75%,25%"]
|====
| Primitive type of primitive [eq]#i#                       | Provoking vertex number
| ename:VK_PRIMITIVE_TOPOLOGY_POINT_LIST                    | [eq]#i#
| ename:VK_PRIMITIVE_TOPOLOGY_LINE_LIST                     | [eq]#2 i#
| ename:VK_PRIMITIVE_TOPOLOGY_LINE_STRIP                    | [eq]#i#
| ename:VK_PRIMITIVE_TOPOLOGY_TRIANGLE_LIST                 | [eq]#3 i#
| ename:VK_PRIMITIVE_TOPOLOGY_TRIANGLE_STRIP                | [eq]#i#
| ename:VK_PRIMITIVE_TOPOLOGY_TRIANGLE_FAN                  | [eq]#i + 1#
| ename:VK_PRIMITIVE_TOPOLOGY_LINE_LIST_WITH_ADJACENCY      | [eq]#4 i + 1#
| ename:VK_PRIMITIVE_TOPOLOGY_LINE_STRIP_WITH_ADJACENCY     | [eq]#i + 1#
| ename:VK_PRIMITIVE_TOPOLOGY_TRIANGLE_LIST_WITH_ADJACENCY  | [eq]#6 i#
| ename:VK_PRIMITIVE_TOPOLOGY_TRIANGLE_STRIP_WITH_ADJACENCY | [eq]#2 i#
|====

.Caption
****
The <<provoking-vertex-selection,Provoking vertex selection>> table defines
the output values used for flat shading the i^th^ primitive generated by
drawing commands with the indicated primitive type, derived from the
corresponding values of the vertex whose index is shown in the table.
Primitives and vertices are numbered starting from zero.
****

Flat shading is applied to those vertex attributes that
<<interfaces-iointerfaces-matching,match>> fragment input attributes which
are decorated as code:Flat.

If a geometry shader is active, the output primitive topology is either
points, line strips, or triangle strips, and the selection of the provoking
vertex behaves according to the corresponding row of the table.
If a tessellation evaluation shader is active and a geometry shader is not
active, the provoking vertex is undefined but must: be one of the vertices
of the primitive.


[[vertexpostproc-clipping]]
== Primitive Clipping

Primitives are culled against the _cull volume_ and then clipped to the
_clip volume_.
In clip coordinates, the _view volume_ is defined by:

[latexmath]
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
\begin{array}{c}
-w_c \leq x_c \leq w_c \\
-w_c \leq y_c \leq w_c \\
0 \leq z_c \leq w_c
\end{array}
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

This view volume can: be further restricted by as many as
sname:VkPhysicalDeviceLimits::pname:maxClipDistances client-defined
half-spaces.

The cull volume is the intersection of up to
sname:VkPhysicalDeviceLimits::pname:maxCullDistances client-defined
half-spaces (if no client-defined cull half-spaces are enabled, culling
against the cull volume is skipped).

A shader must: write a single cull distance for each enabled cull half-space
to elements of the code:CullDistance array.
If the cull distance for any enabled cull half-space is negative for all of
the vertices of the primitive under consideration, the primitive is
discarded.
Otherwise the primitive is clipped against the clip volume as defined below.

The clip volume is the intersection of up to
sname:VkPhysicalDeviceLimits::pname:maxClipDistances client-defined
half-spaces with the view volume (if no client-defined clip half-spaces are
enabled, the clip volume is the view volume).

A shader must: write a single clip distance for each enabled clip half-space
to elements of the code:ClipDistance array.
Clip half-space [eq]#i# is then given by the set of points satisfying the
inequality

  :: [eq]#c~i~(**P**) {geq} 0#

where [eq]#c~i~(**P**)# is the clip distance [eq]#i# at point [eq]#**P**#.
For point primitives, [eq]#c~i~(**P**)# is simply the clip distance for the
vertex in question.
For line and triangle primitives, per-vertex clip distances are interpolated
using a weighted mean, with weights derived according to the algorithms
described in sections <<primsrast-lines-basic,Basic Line Segment
Rasterization>> and <<primsrast-polygons-basic,Basic Polygon
Rasterization>>, using the perspective interpolation equations.

The number of client-defined clip and cull half-spaces that are enabled is
determined by the explicit size of the built-in arrays code:ClipDistance and
code:CullDistance, respectively, declared as an output in the interface of
the entry point of the final shader stage before clipping.

Depth clamping is enabled or disabled via the pname:depthClampEnable enable
of the sname:VkPipelineRasterizationStateCreateInfo structure.
If depth clamping is enabled, the plane equation

  :: [eq]#0 {leq} z~c~ {leq} w~c~#

(see the clip volume definition above) is ignored by view volume clipping
(effectively, there is no near or far plane clipping).

If the primitive under consideration is a point or line segment, then
clipping passes it unchanged if its vertices lie entirely within the clip
volume.

If a point's vertex lies outside of the clip volume, the entire primitive
may: be discarded.

If either of a line segment's vertices lie outside of the clip volume, the
line segment may: be clipped, with new vertex coordinates computed for each
vertex that lies outside the clip volume.
A clipped line segment endpoint lies on both the original line segment and
the boundary of the clip volume.

This clipping produces a value, [eq]#0 {leq} t {leq} 1#, for each clipped
vertex.
If the coordinates of a clipped vertex are [eq]#**P**# and the original
vertices' coordinates are [eq]#**P**~1~# and [eq]#**P**~2~#, then [eq]#t# is
given by

  :: [eq]#**P** = t **P**~1~ + (1-t) **P**~2~#.

ifdef::editing-notes[]
[NOTE]
.editing-note
====
This is weird - it gives **P**, not t.
====
endif::editing-notes[]

[eq]#t# is used to clip vertex output attributes as described in
<<vertexpostproc-clipping-shader-outputs,Clipping Shader Outputs>>.

If the primitive is a polygon, it passes unchanged if every one of its edges
lie entirely inside the clip volume, and it is discarded if every one of its
edges lie entirely outside the clip volume.
If the edges of the polygon intersect the boundary of the clip volume, the
intersecting edges are reconnected by new edges that lie along the boundary
of the clip volume - in some cases requiring the introduction of new
vertices into a polygon.

If a polygon intersects an edge of the clip volume's boundary, the clipped
polygon must: include a point on this boundary edge.

Primitives rendered with user-defined half-spaces must: satisfy a
complementarity criterion.
Suppose a series of primitives is drawn where each vertex [eq]#i# has a
single specified clip distance [eq]#d~i~# (or a number of similarly
specified clip distances, if multiple half-spaces are enabled).
Next, suppose that the same series of primitives are drawn again with each
such clip distance replaced by [eq]#-d~i~# (and the graphics pipeline is
otherwise the same).
In this case, primitives must: not be missing any pixels, and pixels must:
not be drawn twice in regions where those primitives are cut by the clip
planes.


[[vertexpostproc-clipping-shader-outputs]]
== Clipping Shader Outputs

Next, vertex output attributes are clipped.
The output values associated with a vertex that lies within the clip volume
are unaffected by clipping.
If a primitive is clipped, however, the output values assigned to vertices
produced by clipping are clipped.

Let the output values assigned to the two vertices [eq]#**P**~1~# and
[eq]#**P**~2~# of an unclipped edge be [eq]#**c**~1~# and [eq]#**c**~2~#.
The value of [eq]#t# (see <<vertexpostproc-clipping,Primitive Clipping>>)
for a clipped point [eq]#**P**# is used to obtain the output value
associated with [eq]#**P**# as

  :: [eq]#**c** = t **c**~1~ + (1-t) **c**~2~#.

(Multiplying an output value by a scalar means multiplying each of _x_, _y_,
_z_, and _w_ by the scalar.)

Since this computation is performed in clip space before division by
[eq]#w~c~#, clipped output values are perspective-correct.

Polygon clipping creates a clipped vertex along an edge of the clip volume's
boundary.
This situation is handled by noting that polygon clipping proceeds by
clipping against one half-space at a time.
Output value clipping is done in the same way, so that clipped points always
occur at the intersection of polygon edges (possibly already clipped) with
the clip volume's boundary.

For vertex output attributes whose matching fragment input attributes are
decorated with code:NoPerspective, the value of [eq]#t# used to obtain the
output value associated with [eq]#**P**# will be adjusted to produce results
that vary linearly in framebuffer space.

Output attributes of integer or unsigned integer type must: always be flat
shaded.
Flat shaded attributes are constant over the primitive being rasterized (see
<<primsrast-lines-basic,Basic Line Segment Rasterization>> and
<<primsrast-polygons-basic,Basic Polygon Rasterization>>), and no
interpolation is performed.
The output value [eq]#**c**# is taken from either [eq]#**c**~1~# or
[eq]#**c**~2~#, since flat shading has already occurred and the two values
are identical.

ifdef::VK_NV_clip_space_w_scaling[]
include::VK_NV_clip_space_w_scaling/vertexpostproc.txt[]
endif::VK_NV_clip_space_w_scaling[]

[[vertexpostproc-coord-transform]]
== Coordinate Transformations

_Clip coordinates_ for a vertex result from shader execution, which yields a
vertex coordinate code:Position.

Perspective division on clip coordinates yields _normalized device
coordinates_, followed by a _viewport_ transformation (see
<<vertexpostproc-viewport,Controlling the Viewport>>) to convert these
coordinates into _framebuffer coordinates_.

If a vertex in clip coordinates has a position given by

[latexmath]
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
\left(\begin{array}{c}
x_c \\
y_c \\
z_c \\
w_c
\end{array}\right)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

then the vertex's normalized device coordinates are
[latexmath]
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
\left(
        \begin{array}{c}
                x_d \\
                y_d \\
                z_d
        \end{array}
\right) =
\left(
        \begin{array}{c}
                \frac{x_c}{w_c} \\
                \frac{y_c}{w_c} \\
                \frac{z_c}{w_c}
        \end{array}
\right)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


[[vertexpostproc-viewport]]
== Controlling the Viewport

The viewport transformation is determined by the selected viewport's width
and height in pixels, [eq]#p~x~# and [eq]#p~y~#, respectively, and its
center [eq]#(o~x~, o~y~)# (also in pixels), as well as its depth range min
and max determining a depth range scale value [eq]#p~z~# and a depth range
bias value [eq]#o~z~# (defined below).
The vertex's framebuffer coordinates [eq]#(x~f~, y~f~, z~f~)# are given by

  :: [eq]#x~f~ = (p~x~ / 2) x~d~ + o~x~#
  :: [eq]#y~f~ = (p~y~ / 2) y~d~ + o~y~#
  :: [eq]#z~f~ = p~z~ {times} z~d~ + o~z~#

Multiple viewports are available, numbered zero up to
sname:VkPhysicalDeviceLimits::pname:maxViewports minus one.
The number of viewports used by a pipeline is controlled by the
pname:viewportCount member of the sname:VkPipelineViewportStateCreateInfo
structure used in pipeline creation.

// refBegin VkPipelineViewportStateCreateInfo Structure specifying parameters of a newly created pipeline viewport state

The sname:VkPipelineViewportStateCreateInfo structure is defined as:

include::../api/structs/VkPipelineViewportStateCreateInfo.txt[]

  * pname:sType is the type of this structure.
  * pname:pNext is `NULL` or a pointer to an extension-specific structure.
  * pname:flags is reserved for future use.
  * pname:viewportCount is the number of viewports used by the pipeline.
  * pname:pViewports is a pointer to an array of slink:VkViewport
    structures, defining the viewport transforms.
    If the viewport state is dynamic, this member is ignored.
  * pname:scissorCount is the number of <<fragops-scissor,scissors>> and
    must: match the number of viewports.
  * pname:pScissors is a pointer to an array of sname:VkRect2D structures
    which define the rectangular bounds of the scissor for the corresponding
    viewport.
    If the scissor state is dynamic, this member is ignored.

.Valid Usage
****
  * [[VUID-VkPipelineViewportStateCreateInfo-viewportCount-01216]] If the <<features-features-multiViewport,multiple viewports>> feature is
    not enabled, pname:viewportCount must: be `1`
  * [[VUID-VkPipelineViewportStateCreateInfo-scissorCount-01217]] If the <<features-features-multiViewport,multiple viewports>> feature is
    not enabled, pname:scissorCount must: be `1`
  * [[VUID-VkPipelineViewportStateCreateInfo-viewportCount-01218]] pname:viewportCount must: be between `1` and
    sname:VkPhysicalDeviceLimits::pname:maxViewports, inclusive
  * [[VUID-VkPipelineViewportStateCreateInfo-scissorCount-01219]] pname:scissorCount must: be between `1` and
    sname:VkPhysicalDeviceLimits::pname:maxViewports, inclusive
  * [[VUID-VkPipelineViewportStateCreateInfo-scissorCount-01220]] pname:scissorCount and pname:viewportCount must: be identical
****

include::../validity/structs/VkPipelineViewportStateCreateInfo.txt[]

ifndef::VK_NV_viewport_array2[]
If a geometry shader is active and has an output variable decorated with
code:ViewportIndex, the viewport transformation uses the viewport
corresponding to the value assigned to code:ViewportIndex taken from an
implementation-dependent vertex of each primitive.
If code:ViewportIndex is outside the range zero to pname:viewportCount minus
one for a primitive, or if the geometry shader did not assign a value to
code:ViewportIndex for all vertices of a primitive due to flow control, the
results of the viewport transformation of the vertices of such primitives
are undefined.
If no geometry shader is active, or if the geometry shader does not have an
output decorated with code:ViewportIndex, the viewport numbered zero is used
by the viewport transformation.
endif::VK_NV_viewport_array2[]
ifdef::VK_NV_viewport_array2[]
A _vertex processing stage_ may direct each primitive to zero or more
viewports.
The destination viewports for a primitive are selected by the last active
vertex processing stage that has an output variable decorated with
code:ViewportIndex (selecting a single viewport) or code:ViewportMaskNV
(selecting multiple viewports).
The viewport transform uses the viewport corresponding to either the value
assigned to code:ViewportIndex or one of the bits set in
code:ViewportMaskNV, and taken from an implementation-dependent vertex of
each primitive.
If code:ViewportIndex or any of the bits in code:ViewportMaskNV are outside
the range zero to pname:viewportCount minus one for a primitive, or if the
last active vertex processing stage did not assign a value to either
code:ViewportIndex or code:ViewportMaskNV for all vertices of a primitive
due to flow control, the results of the viewport transformation of the
vertices of such primitives are undefined.
If the last vertex processing stage does not have an output decorated with
code:ViewportIndex or code:ViewportMask, the viewport numbered zero is used
by the viewport transformation.
endif::VK_NV_viewport_array2[]

A single vertex can: be used in more than one individual primitive, in
primitives such as ename:VK_PRIMITIVE_TOPOLOGY_TRIANGLE_STRIP.
In this case, the viewport transformation is applied separately for each
primitive.

// refBegin vkCmdSetViewport Set the viewport on a command buffer

If the bound pipeline state object was not created with the
ename:VK_DYNAMIC_STATE_VIEWPORT dynamic state enabled, viewport
transformation parameters are specified using the pname:pViewports member of
sname:VkPipelineViewportStateCreateInfo in the pipeline state object.
If the pipeline state object was created with the
ename:VK_DYNAMIC_STATE_VIEWPORT dynamic state enabled, the viewport
transformation parameters are dynamically set and changed with the command:

include::../api/protos/vkCmdSetViewport.txt[]

  * pname:commandBuffer is the command buffer into which the command will be
    recorded.
  * pname:firstViewport is the index of the first viewport whose parameters
    are updated by the command.
  * pname:viewportCount is the number of viewports whose parameters are
    updated by the command.
  * pname:pViewports is a pointer to an array of slink:VkViewport structures
    specifying viewport parameters.

The viewport parameters taken from element [eq]#i# of pname:pViewports
replace the current state for the viewport index [eq]#pname:firstViewport
{plus} i#, for [eq]#i# in [eq]#[0, pname:viewportCount)#.

.Valid Usage
****
  * [[VUID-vkCmdSetViewport-None-01221]] The currently bound graphics pipeline must: have been created with the
    ename:VK_DYNAMIC_STATE_VIEWPORT dynamic state enabled
  * [[VUID-vkCmdSetViewport-firstViewport-01222]] pname:firstViewport must: be less than
    sname:VkPhysicalDeviceLimits::pname:maxViewports
  * [[VUID-vkCmdSetViewport-firstViewport-01223]] The sum of pname:firstViewport and pname:viewportCount must: be between
    `1` and sname:VkPhysicalDeviceLimits::pname:maxViewports, inclusive
  * [[VUID-vkCmdSetViewport-firstViewport-01224]] If the <<features-features-multiViewport,multiple viewports>> feature is
    not enabled, pname:firstViewport must: be `0`
  * [[VUID-vkCmdSetViewport-viewportCount-01225]] If the <<features-features-multiViewport,multiple viewports>> feature is
    not enabled, pname:viewportCount must: be `1`
  * [[VUID-vkCmdSetViewport-pViewports-01226]] pname:pViewports must: be a pointer to an array of pname:viewportCount
    valid sname:VkViewport structures
****

include::../validity/protos/vkCmdSetViewport.txt[]

Both slink:VkPipelineViewportStateCreateInfo and flink:vkCmdSetViewport use
sname:VkViewport to set the viewport transformation parameters.

// refBegin VkViewport Structure specifying a viewport

The sname:VkViewport structure is defined as:

include::../api/structs/VkViewport.txt[]

  * pname:x and pname:y are the viewport's upper left corner [eq]#(x,y)#.
  * pname:width and pname:height are the viewport's width and height,
    respectively.
  * pname:minDepth and pname:maxDepth are the depth range for the viewport.
    It is valid for pname:minDepth to be greater than or equal to
    pname:maxDepth.

The framebuffer depth coordinate [eq]#pname:z~f~# may: be represented using
either a fixed-point or floating-point representation.
However, a floating-point representation must: be used if the depth/stencil
attachment has a floating-point depth component.
If an [eq]#m#-bit fixed-point representation is used, we assume that it
represents each value latexmath:[\frac{k}{2^m - 1}], where [eq]#k {elem} {
0, 1, ..., 2^m^-1 }#, as [eq]#k# (e.g. 1.0 is represented in binary as a
string of all ones).

The viewport parameters shown in the above equations are found from these
values as

  :: [eq]#o~x~ = pname:x + pname:width / 2#
  :: [eq]#o~y~ = pname:y + pname:height / 2#
  :: [eq]#o~z~ = pname:minDepth#
  :: [eq]#p~x~ = pname:width#
  :: [eq]#p~y~ = pname:height#
  :: [eq]#p~z~ = pname:maxDepth - pname:minDepth#.

ifdef::VK_KHR_maintenance1[]
The application can: specify a negative term for pname:height, which has the
effect of negating the y coordinate in clip space before performing the
transform.
When using a negative pname:height, the application should: also adjust the
pname:y value to point to the lower left corner of the viewport instead of
the upper left corner.
Using the negative pname:height allows the application to avoid having to
negate the y component of the code:Position output from the last vertex
processing stage in shaders that also target other graphics APIs.
endif::VK_KHR_maintenance1[]

The width and height of the <<features-limits-maxViewportDimensions,
implementation-dependent maximum viewport dimensions>> must: be greater than
or equal to the width and height of the largest image which can: be created
and attached to a framebuffer.

The floating-point viewport bounds are represented with an
<<features-limits-viewportSubPixelBits,implementation-dependent precision>>.

.Valid Usage
****
  * [[VUID-VkViewport-width-01227]] pname:width must: be greater than `0.0` and less than or equal to
    sname:VkPhysicalDeviceLimits::pname:maxViewportDimensions[0]
ifndef::VK_KHR_maintenance1[]
  * [[VUID-VkViewport-height-01228]] pname:height must: be greater than `0.0` and less than or equal to
    sname:VkPhysicalDeviceLimits::pname:maxViewportDimensions[1]
endif::VK_KHR_maintenance1[]
ifdef::VK_KHR_maintenance1[]
  * [[VUID-VkViewport-height-01229]] pname:height must: be greater than or equal to
    -sname:VkPhysicalDeviceLimits::pname:maxViewportDimensions[1] and less
    than or equal to
    sname:VkPhysicalDeviceLimits::pname:maxViewportDimensions[1]
endif::VK_KHR_maintenance1[]
ifdef::VK_AMD_negative_viewport_height[]
  * [[VUID-VkViewport-height-01230]] If the VK_AMD_negative_viewport_height extension is enabled,
    pname:height can: also be negative.
endif::VK_AMD_negative_viewport_height[]
  * [[VUID-VkViewport-x-01231]] pname:x and pname:y must: each be between pname:viewportBoundsRange[0]
    and pname:viewportBoundsRange[1], inclusive
  * [[VUID-VkViewport-x-01232]] pname:x + pname:width must: be less than or equal to
    pname:viewportBoundsRange[1]
  * [[VUID-VkViewport-y-01233]] pname:y + pname:height must: be less than or equal to
    pname:viewportBoundsRange[1]
  * [[VUID-VkViewport-minDepth-01234]] pname:minDepth must: be between `0.0` and `1.0`, inclusive
  * [[VUID-VkViewport-maxDepth-01235]] pname:maxDepth must: be between `0.0` and `1.0`, inclusive
****

include::../validity/structs/VkViewport.txt[]