## 25. Rasterization

Rasterization is the process by which a primitive is converted to a two-dimensional image. Each discrete location of this image contains associated data such as depth, color, or other attributes.

Rasterizing a primitive begins by determining which squares of an integer grid in framebuffer coordinates are occupied by the primitive, and assigning one or more depth values to each such square. This process is described below for points, lines, and polygons.

A grid square, including its (x,y) framebuffer coordinates, z (depth), and associated data added by fragment shaders, is called a fragment. A fragment is located by its upper left corner, which lies on integer grid coordinates.

Rasterization operations also refer to a fragment’s sample locations, which are offset by fractional values from its upper left corner. The rasterization rules for points, lines, and triangles involve testing whether each sample location is inside the primitive. Fragments need not actually be square, and rasterization rules are not affected by the aspect ratio of fragments. Display of non-square grids, however, will cause rasterized points and line segments to appear fatter in one direction than the other.

We assume that fragments are square, since it simplifies antialiasing and texturing. After rasterization, fragments are processed by fragment operations.

Several factors affect rasterization, including the members of VkPipelineRasterizationStateCreateInfo and VkPipelineMultisampleStateCreateInfo.

The VkPipelineRasterizationStateCreateInfo structure is defined as:

// Provided by VK_VERSION_1_0
typedef struct VkPipelineRasterizationStateCreateInfo {
VkStructureType                            sType;
const void*                                pNext;
VkPipelineRasterizationStateCreateFlags    flags;
VkBool32                                   depthClampEnable;
VkPolygonMode                              polygonMode;
VkCullModeFlags                            cullMode;
VkFrontFace                                frontFace;
VkBool32                                   depthBiasEnable;
float                                      depthBiasConstantFactor;
float                                      depthBiasClamp;
float                                      depthBiasSlopeFactor;
float                                      lineWidth;
} VkPipelineRasterizationStateCreateInfo;
• sType is the type of this structure.

• pNext is NULL or a pointer to a structure extending this structure.

• flags is reserved for future use.

• depthClampEnable controls whether to clamp the fragment’s depth values as described in Depth Test. Enabling depth clamp will also disable clipping primitives to the z planes of the frustrum as described in Primitive Clipping.

• rasterizerDiscardEnable controls whether primitives are discarded immediately before the rasterization stage.

• polygonMode is the triangle rendering mode. See VkPolygonMode.

• cullMode is the triangle facing direction used for primitive culling. See VkCullModeFlagBits.

• frontFace is a VkFrontFace value specifying the front-facing triangle orientation to be used for culling.

• depthBiasEnable controls whether to bias fragment depth values.

• depthBiasConstantFactor is a scalar factor controlling the constant depth value added to each fragment.

• depthBiasClamp is the maximum (or minimum) depth bias of a fragment.

• depthBiasSlopeFactor is a scalar factor applied to a fragment’s slope in depth bias calculations.

• lineWidth is the width of rasterized line segments.

Valid Usage
• VUID-VkPipelineRasterizationStateCreateInfo-depthClampEnable-00782
If the depth clamping feature is not enabled, depthClampEnable must be VK_FALSE

• VUID-VkPipelineRasterizationStateCreateInfo-polygonMode-01413
If the non-solid fill modes feature is not enabled, polygonMode must be VK_POLYGON_MODE_FILL

• VUID-VkPipelineRasterizationStateCreateInfo-pointPolygons-04458
If the VK_KHR_portability_subset extension is enabled, and VkPhysicalDevicePortabilitySubsetFeaturesKHR::pointPolygons is VK_FALSE, and rasterizerDiscardEnable is VK_FALSE, polygonMode must not be VK_POLYGON_MODE_POINT.

Valid Usage (Implicit)
• VUID-VkPipelineRasterizationStateCreateInfo-sType-sType
sType must be VK_STRUCTURE_TYPE_PIPELINE_RASTERIZATION_STATE_CREATE_INFO

• VUID-VkPipelineRasterizationStateCreateInfo-pNext-pNext
pNext must be NULL

flags must be 0

• VUID-VkPipelineRasterizationStateCreateInfo-polygonMode-parameter
polygonMode must be a valid VkPolygonMode value

• VUID-VkPipelineRasterizationStateCreateInfo-cullMode-parameter
cullMode must be a valid combination of VkCullModeFlagBits values

• VUID-VkPipelineRasterizationStateCreateInfo-frontFace-parameter
frontFace must be a valid VkFrontFace value

// Provided by VK_VERSION_1_0
typedef VkFlags VkPipelineRasterizationStateCreateFlags;

VkPipelineRasterizationStateCreateFlags is a bitmask type for setting a mask, but is currently reserved for future use.

The VkPipelineMultisampleStateCreateInfo structure is defined as:

// Provided by VK_VERSION_1_0
typedef struct VkPipelineMultisampleStateCreateInfo {
VkStructureType                          sType;
const void*                              pNext;
VkPipelineMultisampleStateCreateFlags    flags;
VkSampleCountFlagBits                    rasterizationSamples;
VkBool32                                 alphaToCoverageEnable;
VkBool32                                 alphaToOneEnable;
} VkPipelineMultisampleStateCreateInfo;
• sType is the type of this structure.

• pNext is NULL or a pointer to a structure extending this structure.

• flags is reserved for future use.

• rasterizationSamples is a VkSampleCountFlagBits value specifying the number of samples used in rasterization.

• sampleShadingEnable can be used to enable Sample Shading.

• minSampleShading specifies a minimum fraction of sample shading if sampleShadingEnable is set to VK_TRUE.

• pSampleMask is a pointer to an array of VkSampleMask values used in the sample mask test.

• alphaToCoverageEnable controls whether a temporary coverage value is generated based on the alpha component of the fragment’s first color output as specified in the Multisample Coverage section.

• alphaToOneEnable controls whether the alpha component of the fragment’s first color output is replaced with one as described in Multisample Coverage.

Each bit in the sample mask is associated with a unique sample index as defined for the coverage mask. Each bit b for mask word w in the sample mask corresponds to sample index i, where i = 32 × w + b. pSampleMask has a length equal to rasterizationSamples / 32 ⌉ words.

If pSampleMask is NULL, it is treated as if the mask has all bits set to 1.

Valid Usage
If the sample rate shading feature is not enabled, sampleShadingEnable must be VK_FALSE

• VUID-VkPipelineMultisampleStateCreateInfo-alphaToOneEnable-00785
If the alpha to one feature is not enabled, alphaToOneEnable must be VK_FALSE

minSampleShading must be in the range [0,1]

Valid Usage (Implicit)
• VUID-VkPipelineMultisampleStateCreateInfo-sType-sType
sType must be VK_STRUCTURE_TYPE_PIPELINE_MULTISAMPLE_STATE_CREATE_INFO

• VUID-VkPipelineMultisampleStateCreateInfo-pNext-pNext
pNext must be NULL

flags must be 0

• VUID-VkPipelineMultisampleStateCreateInfo-rasterizationSamples-parameter
rasterizationSamples must be a valid VkSampleCountFlagBits value

If pSampleMask is not NULL, pSampleMask must be a valid pointer to an array of VkSampleMask values

// Provided by VK_VERSION_1_0
typedef VkFlags VkPipelineMultisampleStateCreateFlags;

VkPipelineMultisampleStateCreateFlags is a bitmask type for setting a mask, but is currently reserved for future use.

The elements of the sample mask array are of type VkSampleMask, each representing 32 bits of coverage information:

// Provided by VK_VERSION_1_0
typedef uint32_t VkSampleMask;

Rasterization only generates fragments which cover one or more pixels inside the framebuffer. Pixels outside the framebuffer are never considered covered in the fragment. Fragments which would be produced by application of any of the primitive rasterization rules described below but which lie outside the framebuffer are not produced, nor are they processed by any later stage of the pipeline, including any of the fragment operations.

Surviving fragments are processed by fragment shaders. Fragment shaders determine associated data for fragments, and can also modify or replace their assigned depth values.

### 25.1. Discarding Primitives Before Rasterization

Primitives are discarded before rasterization if the rasterizerDiscardEnable member of VkPipelineRasterizationStateCreateInfo is enabled. When enabled, primitives are discarded after they are processed by the last active shader stage in the pipeline before rasterization.

### 25.2. Rasterization Order

Within a subpass of a render pass instance, for a given (x,y,layer,sample) sample location, the following operations are guaranteed to execute in rasterization order, for each separate primitive that includes that sample location:

1. Fragment operations, in the order defined

2. Blending, logic operations, and color writes

Execution of these operations for each primitive in a subpass occurs in primitive order.

### 25.3. Multisampling

Multisampling is a mechanism to antialias all Vulkan primitives: points, lines, and polygons. The technique is to sample all primitives multiple times at each pixel. Each sample in each framebuffer attachment has storage for a color, depth, and/or stencil value, such that per-fragment operations apply to each sample independently. The color sample values can be later resolved to a single color (see Resolving Multisample Images and the Render Pass chapter for more details on how to resolve multisample images to non-multisample images).

Vulkan defines rasterization rules for single-sample modes in a way that is equivalent to a multisample mode with a single sample in the center of each fragment.

Each fragment includes a coverage mask with a single bit for each sample in the fragment, and a number of depth values and associated data for each sample. An implementation may choose to assign the same associated data to more than one sample. The location for evaluating such associated data may be anywhere within the fragment area including the fragment’s center location (xf,yf) or any of the sample locations. When rasterizationSamples is VK_SAMPLE_COUNT_1_BIT, the fragment’s center location must be used. The different associated data values need not all be evaluated at the same location.

It is understood that each pixel has rasterizationSamples locations associated with it. These locations are exact positions, rather than regions or areas, and each is referred to as a sample point. The sample points associated with a pixel must be located inside or on the boundary of the unit square that is considered to bound the pixel. Furthermore, the relative locations of sample points may be identical for each pixel in the framebuffer, or they may differ.

If the current pipeline includes a fragment shader with one or more variables in its interface decorated with Sample and Input, the data associated with those variables will be assigned independently for each sample. The values for each sample must be evaluated at the location of the sample. The data associated with any other variables not decorated with Sample and Input need not be evaluated independently for each sample.

A coverage mask is generated for each fragment, based on which samples within that fragment are determined to be within the area of the primitive that generated the fragment.

Single pixel fragments have one set of samples. Multi-pixel fragments defined by setting the fragment shading rate have one set of samples per pixel. Each set of samples has a number of samples determined by VkPipelineMultisampleStateCreateInfo::rasterizationSamples. Each sample in a set is assigned a unique sample index i in the range [0, rasterizationSamples).

Each sample in a fragment is also assigned a unique coverage index j in the range [0, n × rasterizationSamples), where n is the number of sets in the fragment. If the fragment contains a single set of samples, the coverage index is always equal to the sample index.

If the fragment shading rate is set, the coverage index j is determined as a function of the pixel index p, the sample index i, and the number of rasterization samples r as:

j = i + r × ((fw * fh) - 1 - p)

where the pixel index p is determined as a function of the pixel’s framebuffer location (x,y) and the fragment size (fw,fh):

px = x % fw

py = y % fh

p = px + (py * fw)

The table below illustrates the pixel index for multi-pixel fragments:

Table 28. Pixel indices - 1 wide
1x1 1x2 1x4

Table 29. Pixel indices - 2 wide
2x1 2x2 2x4

Table 30. Pixel indices - 4 wide
4x1 4x2 4x4

The coverage mask includes B bits packed into W words, defined as:

B = n × rasterizationSamples

W = ⌈B/32⌉

Bit b in coverage mask word w is 1 if the sample with coverage index j = 32*w + b is covered, and 0 otherwise.

If the standardSampleLocations member of VkPhysicalDeviceLimits is VK_TRUE, then the sample counts VK_SAMPLE_COUNT_1_BIT, VK_SAMPLE_COUNT_2_BIT, VK_SAMPLE_COUNT_4_BIT, VK_SAMPLE_COUNT_8_BIT, and VK_SAMPLE_COUNT_16_BIT have sample locations as listed in the following table, with the ith entry in the table corresponding to sample index i. VK_SAMPLE_COUNT_32_BIT and VK_SAMPLE_COUNT_64_BIT do not have standard sample locations. Locations are defined relative to an origin in the upper left corner of the fragment.

Table 31. Standard sample locations
Sample count Sample Locations

VK_SAMPLE_COUNT_1_BIT

(0.5,0.5)

VK_SAMPLE_COUNT_2_BIT

(0.75,0.75)
(0.25,0.25)

VK_SAMPLE_COUNT_4_BIT

(0.375, 0.125)
(0.875, 0.375)
(0.125, 0.625)
(0.625, 0.875)

VK_SAMPLE_COUNT_8_BIT

(0.5625, 0.3125)
(0.4375, 0.6875)
(0.8125, 0.5625)
(0.3125, 0.1875)
(0.1875, 0.8125)
(0.0625, 0.4375)
(0.6875, 0.9375)
(0.9375, 0.0625)

VK_SAMPLE_COUNT_16_BIT

(0.5625, 0.5625)
(0.4375, 0.3125)
(0.3125, 0.625)
(0.75, 0.4375)
(0.1875, 0.375)
(0.625, 0.8125)
(0.8125, 0.6875)
(0.6875, 0.1875)
(0.375, 0.875)
(0.5, 0.0625)
(0.25, 0.125)
(0.125, 0.75)
(0.0, 0.5)
(0.9375, 0.25)
(0.875, 0.9375)
(0.0625, 0.0)

The fragment shading rate strongly interacts with Multisampling, and the set of available rates for an implementation may be restricted by sample rate.

To query available shading rates, call:

// Provided by VK_KHR_fragment_shading_rate
VkPhysicalDevice                            physicalDevice,
VkPhysicalDeviceFragmentShadingRateKHR*     pFragmentShadingRates);
• physicalDevice is the handle to the physical device whose properties will be queried.

• pFragmentShadingRateCount is a pointer to an integer related to the number of fragment shading rates available or queried, as described below.

• pFragmentShadingRates is either NULL or a pointer to an array of VkPhysicalDeviceFragmentShadingRateKHR structures.

If pFragmentShadingRates is NULL, then the number of fragment shading rates available is returned in pFragmentShadingRateCount. Otherwise, pFragmentShadingRateCount must point to a variable set by the user to the number of elements in the pFragmentShadingRates array, and on return the variable is overwritten with the number of structures actually written to pFragmentShadingRates. If pFragmentShadingRateCount is less than the number of fragment shading rates available, at most pFragmentShadingRateCount structures will be written, and VK_INCOMPLETE will be returned instead of VK_SUCCESS, to indicate that not all the available fragment shading rates were returned.

The returned array of fragment shading rates must be ordered from largest fragmentSize.width value to smallest, and each set of fragment shading rates with the same fragmentSize.width value must be ordered from largest fragmentSize.height to smallest. Any two entries in the array must not have the same fragmentSize values.

For any entry in the array, the following rules also apply:

• The value of fragmentSize.width must be less than or equal to maxFragmentSize.width.

• The value of fragmentSize.width must be greater than or equal to 1.

• The value of fragmentSize.width must be a power-of-two.

• The value of fragmentSize.height must be less than or equal to maxFragmentSize.height.

• The value of fragmentSize.height must be greater than or equal to 1.

• The value of fragmentSize.height must be a power-of-two.

• The highest sample count in sampleCounts must be less than or equal to maxFragmentShadingRateRasterizationSamples.

• The product of fragmentSize.width, fragmentSize.height, and the highest sample count in sampleCounts must be less than or equal to maxFragmentShadingRateCoverageSamples.

Implementations must support at least the following shading rates:

sampleCounts fragmentSize

VK_SAMPLE_COUNT_1_BIT | VK_SAMPLE_COUNT_4_BIT

{2,2}

VK_SAMPLE_COUNT_1_BIT | VK_SAMPLE_COUNT_4_BIT

{2,1}

~0

{1,1}

If framebufferColorSampleCounts, includes VK_SAMPLE_COUNT_2_BIT, the required rates must also include VK_SAMPLE_COUNT_2_BIT.

 Note Including the {1,1} fragment size is done for completeness; it has no actual effect on the support of rendering without setting the fragment size. All sample counts are supported for this rate.
Valid Usage (Implicit)
physicalDevice must be a valid VkPhysicalDevice handle

pFragmentShadingRateCount must be a valid pointer to a uint32_t value

If the value referenced by pFragmentShadingRateCount is not 0, and pFragmentShadingRates is not NULL, pFragmentShadingRates must be a valid pointer to an array of pFragmentShadingRateCount VkPhysicalDeviceFragmentShadingRateKHR structures

Return Codes
Success
• VK_SUCCESS

• VK_INCOMPLETE

Failure
• VK_ERROR_OUT_OF_HOST_MEMORY

The VkPhysicalDeviceFragmentShadingRateKHR structure is defined as

// Provided by VK_KHR_fragment_shading_rate
VkStructureType       sType;
void*                 pNext;
VkSampleCountFlags    sampleCounts;
VkExtent2D            fragmentSize;
} VkPhysicalDeviceFragmentShadingRateKHR;
• sType is the type of this structure.

• pNext is NULL or a pointer to a structure extending this structure.

• sampleCounts is a bitmask of sample counts for which the shading rate described by fragmentSize is supported.

• fragmentSize is a VkExtent2D describing the width and height of a supported shading rate.

Valid Usage (Implicit)
sType must be VK_STRUCTURE_TYPE_PHYSICAL_DEVICE_FRAGMENT_SHADING_RATE_KHR

pNext must be NULL

Fragment shading rates can be set at three points, with the three rates combined to determine the final shading rate.

#### 25.4.1. Pipeline Fragment Shading Rate

The pipeline fragment shading rate can be set on a per-draw basis by either setting the rate in a graphics pipeline, or dynamically via vkCmdSetFragmentShadingRateKHR.

The VkPipelineFragmentShadingRateStateCreateInfoKHR structure is defined as:

// Provided by VK_KHR_fragment_shading_rate
VkStructureType                       sType;
const void*                           pNext;
VkExtent2D                            fragmentSize;
} VkPipelineFragmentShadingRateStateCreateInfoKHR;
• sType is the type of this structure.

• pNext is NULL or a pointer to a structure extending this structure.

• fragmentSize specifies a VkExtent2D structure containing the fragment size used to define the pipeline fragment shading rate for drawing commands using this pipeline.

• combinerOps specifies a VkFragmentShadingRateCombinerOpKHR value determining how the pipeline, primitive, and attachment shading rates are combined for fragments generated by drawing commands using the created pipeline.

If the pNext chain of VkGraphicsPipelineCreateInfo includes a VkPipelineFragmentShadingRateStateCreateInfoKHR structure, then that structure includes parameters that control the pipeline fragment shading rate.

If this structure is not present, fragmentSize is considered to be equal to (1,1), and both elements of combinerOps are considered to be equal to VK_FRAGMENT_SHADING_RATE_COMBINER_OP_KEEP_KHR.

Valid Usage (Implicit)
sType must be VK_STRUCTURE_TYPE_PIPELINE_FRAGMENT_SHADING_RATE_STATE_CREATE_INFO_KHR

Any given element of combinerOps must be a valid VkFragmentShadingRateCombinerOpKHR value

If a pipeline state object is created with VK_DYNAMIC_STATE_FRAGMENT_SHADING_RATE_KHR enabled, the pipeline fragment shading rate and combiner operation is set by the command:

// Provided by VK_KHR_fragment_shading_rate
VkCommandBuffer                             commandBuffer,
const VkExtent2D*                           pFragmentSize,
const VkFragmentShadingRateCombinerOpKHR    combinerOps[2]);
Valid Usage
If pipelineFragmentShadingRate is not enabled, pFragmentSize->width must be 1

If pipelineFragmentShadingRate is not enabled, pFragmentSize->height must be 1

One of pipelineFragmentShadingRate, primitiveFragmentShadingRate, or attachmentFragmentShadingRate must be enabled

If the primitiveFragmentShadingRate feature is not enabled, combinerOps[0] must be VK_FRAGMENT_SHADING_RATE_COMBINER_OP_KEEP_KHR

If the attachmentFragmentShadingRate feature is not enabled, combinerOps[1] must be VK_FRAGMENT_SHADING_RATE_COMBINER_OP_KEEP_KHR

If the fragmentSizeNonTrivialCombinerOps limit is not supported, elements of combinerOps must be either VK_FRAGMENT_SHADING_RATE_COMBINER_OP_KEEP_KHR or VK_FRAGMENT_SHADING_RATE_COMBINER_OP_REPLACE_KHR

pFragmentSize->width must be greater than or equal to 1

pFragmentSize->height must be greater than or equal to 1

pFragmentSize->width must be a power-of-two value

pFragmentSize->height must be a power-of-two value

pFragmentSize->width must be less than or equal to 4

pFragmentSize->height must be less than or equal to 4

Valid Usage (Implicit)
commandBuffer must be a valid VkCommandBuffer handle

pFragmentSize must be a valid pointer to a valid VkExtent2D structure

Any given element of combinerOps must be a valid VkFragmentShadingRateCombinerOpKHR value

commandBuffer must be in the recording state

The VkCommandPool that commandBuffer was allocated from must support graphics operations

Host Synchronization
• Host access to commandBuffer must be externally synchronized

• Host access to the VkCommandPool that commandBuffer was allocated from must be externally synchronized

Command Properties
Command Buffer Levels Render Pass Scope Supported Queue Types

Primary
Secondary

Both

Graphics

#### 25.4.2. Primitive Fragment Shading Rate

The primitive fragment shading rate can be set via the PrimitiveShadingRateKHR built-in in the last active vertex processing shader stage. The rate associated with a given primitive is sourced from the value written to PrimitiveShadingRateKHR by that primitive’s provoking vertex.

#### 25.4.3. Attachment Fragment Shading Rate

The attachment shading rate can be set by including VkFragmentShadingRateAttachmentInfoKHR in a subpass to define a fragment shading rate attachment. Each pixel in the framebuffer is assigned an attachment fragment shading rate by the corresponding texel in the fragment shading rate attachment, according to:

x' = floor(x / regionx)

y' = floor(y / regiony)

where x' and y' are the coordinates of a texel in the fragment shading rate attachment, x and y are the coordinates of the pixel in the framebuffer, and regionx and regiony are the size of the region each texel corresponds to, as defined by the shadingRateAttachmentTexelSize member of VkFragmentShadingRateAttachmentInfoKHR.

If multiview is enabled and the shading rate attachment has multiple layers, the shading rate attachment texel is selected from the layer determined by the ViewIndex built-in. If multiview is disabled, and both the shading rate attachment and the framebuffer have multiple layers, the shading rate attachment texel is selected from the layer determined by the Layer built-in. Otherwise, the texel is unconditionally selected from the first layer of the attachment.

The fragment size is encoded into the first component of the identified texel as follows:

sizew = 2((texel/4)&3)

sizeh = 2(texel&3)

where texel is the value in the first component of the identified texel, and sizew and sizeh are the width and height of the fragment size, decoded from the texel.

If no fragment shading rate attachment is specified, this size is calculated as sizew = sizeh = 1. Applications must not specify a width or height greater than 4 by this method.

The Fragment Shading Rate enumeration in SPIR-V adheres to the above encoding.

#### 25.4.4. Combining the Fragment Shading Rates

The final rate (Cxy') used for fragment shading must be one of the rates returned by vkGetPhysicalDeviceFragmentShadingRatesKHR for the sample count used by rasterization.

If any of the following conditions are met, Cxy' must be set to {1,1}:

Otherwise, each of the specified shading rates are combined and then used to derive the value of Cxy'. As there are three ways to specify shading rates, two combiner operations are specified - between the pipeline and primitive shading rates, and between the result of that and the attachment shading rate.

The equation used for each combiner operation is defined by VkFragmentShadingRateCombinerOpKHR:

// Provided by VK_KHR_fragment_shading_rate
} VkFragmentShadingRateCombinerOpKHR;
• VK_FRAGMENT_SHADING_RATE_COMBINER_OP_KEEP_KHR specifies a combiner operation of combine(Axy,Bxy) = Axy.

• VK_FRAGMENT_SHADING_RATE_COMBINER_OP_REPLACE_KHR specifies a combiner operation of combine(Axy,Bxy) = Bxy.

• VK_FRAGMENT_SHADING_RATE_COMBINER_OP_MIN_KHR specifies a combiner operation of combine(Axy,Bxy) = min(Axy,Bxy).

• VK_FRAGMENT_SHADING_RATE_COMBINER_OP_MAX_KHR specifies a combiner operation of combine(Axy,Bxy) = max(Axy,Bxy).

• VK_FRAGMENT_SHADING_RATE_COMBINER_OP_MUL_KHR specifies a combiner operation of combine(Axy,Bxy) = Axy*Bxy.

where combine(Axy,Bxy) is the combine operation, and Axy and Bxy are the inputs to the operation.

If fragmentShadingRateStrictMultiplyCombiner is VK_FALSE, using VK_FRAGMENT_SHADING_RATE_COMBINER_OP_MUL_KHR with values of 1 for both A and B in the same dimension results in the value 2 being produced for that dimension. See the definition of fragmentShadingRateStrictMultiplyCombiner for more information.

These operations are performed in a component-wise fashion.

This is used to generate a combined fragment area using the equation:

Cxy = combine(Axy,Bxy)

where Cxy is the combined fragment area result, and Axy and Bxy are the fragment areas of the fragment shading rates being combined.

Two combine operations are performed, first with Axy equal to the pipeline fragment shading rate and Bxy equal to the primitive fragment shading rate, with the combine() operation selected by combinerOps[0]. A second combination is then performed, with Axy equal to the result of the first combination and Bxy equal to the attachment fragment shading rate, with the combine() operation selected by combinerOps[1]. The result of the second combination is used as the final fragment shading rate, reported via the ShadingRateKHR built-in.

Implementations may clamp the Cxy result of each combiner operation separately, or only after the second combiner operation.

If the final combined rate is one of the rates returned by vkGetPhysicalDeviceFragmentShadingRatesKHR for the sample count used by rasterization, Cxy' = Cxy. Otherwise, Cxy' is selected from the rates returned by vkGetPhysicalDeviceFragmentShadingRatesKHR for the sample count used by rasterization. From this list of supported rates, the following steps are applied in order, to select a single value:

1. Keep only rates where Cx' ≤ Cx and Cy' ≤ Cy.

• Implementations may also keep rates where Cx' ≤ Cy and Cy' ≤ Cx.

2. Keep only rates with the highest area (Cx' × Cy').

3. Keep only rates with the lowest aspect ratio (Cx' + Cy').

4. In cases where a wide (e.g. 4x1) and tall (e.g. 1x4) rate remain, the implementation may choose either rate. However, it must choose this rate consistently for the same shading rates, and combiner operations for the lifetime of the VkDevice.

Sample shading can be used to specify a minimum number of unique samples to process for each fragment. If sample shading is enabled an implementation must provide a minimum of max(⌈ minSampleShadingFactor × totalSamples ⌉, 1) unique associated data for each fragment, where minSampleShadingFactor is the minimum fraction of sample shading. totalSamples is the value of VkPipelineMultisampleStateCreateInfo::rasterizationSamples specified at pipeline creation time. These are associated with the samples in an implementation-dependent manner. When minSampleShadingFactor is 1.0, a separate set of associated data are evaluated for each sample, and each set of values is evaluated at the sample location.

Sample shading is enabled for a graphics pipeline:

• If the interface of the fragment shader entry point of the graphics pipeline includes an input variable decorated with SampleId or SamplePosition. In this case minSampleShadingFactor takes the value 1.0.

• Else if the sampleShadingEnable member of the VkPipelineMultisampleStateCreateInfo structure specified when creating the graphics pipeline is set to VK_TRUE. In this case minSampleShadingFactor takes the value of VkPipelineMultisampleStateCreateInfo::minSampleShading.

Otherwise, sample shading is considered disabled.

### 25.6. Points

A point is drawn by generating a set of fragments in the shape of a square centered around the vertex of the point. Each vertex has an associated point size that controls the width/height of that square. The point size is taken from the (potentially clipped) shader built-in PointSize written by:

• the geometry shader, if active;

• the tessellation evaluation shader, if active and no geometry shader is active;

and clamped to the implementation-dependent point size range [pointSizeRange[0],pointSizeRange[1]]. The value written to PointSize must be greater than zero.

Not all point sizes need be supported, but the size 1.0 must be supported. The range of supported sizes and the size of evenly-spaced gradations within that range are implementation-dependent. The range and gradations are obtained from the pointSizeRange and pointSizeGranularity members of VkPhysicalDeviceLimits. If, for instance, the size range is from 0.1 to 2.0 and the gradation size is 0.1, then the sizes 0.1, 0.2, …​, 1.9, 2.0 are supported. Additional point sizes may also be supported. There is no requirement that these sizes be equally spaced. If an unsupported size is requested, the nearest supported size is used instead.

#### 25.6.1. Basic Point Rasterization

Point rasterization produces a fragment for each fragment area group of framebuffer pixels with one or more sample points that intersect a region centered at the point’s (xf,yf). This region is a square with side equal to the current point size. Coverage bits that correspond to sample points that intersect the region are 1, other coverage bits are 0. All fragments produced in rasterizing a point are assigned the same associated data, which are those of the vertex corresponding to the point. However, the fragment shader built-in PointCoord contains point sprite texture coordinates. The s and t point sprite texture coordinates vary from zero to one across the point horizontally left-to-right and vertically top-to-bottom, respectively. The following formulas are used to evaluate s and t:

where size is the point’s size; (xp,yp) is the location at which the point sprite coordinates are evaluated - this may be the framebuffer coordinates of the fragment center, or the location of a sample; and (xf,yf) is the exact, unrounded framebuffer coordinate of the vertex for the point.

### 25.7. Line Segments

Each line segment has an associated width. The line width is specified by the VkPipelineRasterizationStateCreateInfo::lineWidth property of the currently active pipeline, if the pipeline was not created with VK_DYNAMIC_STATE_LINE_WIDTH enabled.

Otherwise, the line width is set by calling vkCmdSetLineWidth:

// Provided by VK_VERSION_1_0
void vkCmdSetLineWidth(
VkCommandBuffer                             commandBuffer,
float                                       lineWidth);
• commandBuffer is the command buffer into which the command will be recorded.

• lineWidth is the width of rasterized line segments.

Valid Usage
• VUID-vkCmdSetLineWidth-lineWidth-00788
If the wide lines feature is not enabled, lineWidth must be 1.0

Valid Usage (Implicit)
• VUID-vkCmdSetLineWidth-commandBuffer-parameter
commandBuffer must be a valid VkCommandBuffer handle

• VUID-vkCmdSetLineWidth-commandBuffer-recording
commandBuffer must be in the recording state

• VUID-vkCmdSetLineWidth-commandBuffer-cmdpool
The VkCommandPool that commandBuffer was allocated from must support graphics operations

Host Synchronization
• Host access to commandBuffer must be externally synchronized

• Host access to the VkCommandPool that commandBuffer was allocated from must be externally synchronized

Command Properties
Command Buffer Levels Render Pass Scope Supported Queue Types

Primary
Secondary

Both

Graphics

Not all line widths need be supported for line segment rasterization, but width 1.0 antialiased segments must be provided. The range and gradations are obtained from the lineWidthRange and lineWidthGranularity members of VkPhysicalDeviceLimits. If, for instance, the size range is from 0.1 to 2.0 and the gradation size is 0.1, then the sizes 0.1, 0.2, …​, 1.9, 2.0 are supported. Additional line widths may also be supported. There is no requirement that these widths be equally spaced. If an unsupported width is requested, the nearest supported width is used instead.

#### 25.7.1. Basic Line Segment Rasterization

Rasterized line segments produce fragments which intersect a rectangle centered on the line segment. Two of the edges are parallel to the specified line segment; each is at a distance of one-half the current width from that segment in directions perpendicular to the direction of the line. The other two edges pass through the line endpoints and are perpendicular to the direction of the specified line segment. Coverage bits that correspond to sample points that intersect the rectangle are 1, other coverage bits are 0.

Next we specify how the data associated with each rasterized fragment are obtained. Let pr = (xd, yd) be the framebuffer coordinates at which associated data are evaluated. This may be the center of a fragment or the location of a sample within the fragment. When rasterizationSamples is VK_SAMPLE_COUNT_1_BIT, the fragment center must be used. Let pa = (xa, ya) and pb = (xb,yb) be initial and final endpoints of the line segment, respectively. Set

(Note that t = 0 at pa and t = 1 at pb. Also note that this calculation projects the vector from pa to pr onto the line, and thus computes the normalized distance of the fragment along the line.)

The value of an associated datum f for the fragment, whether it be a shader output or the clip w coordinate, must be determined using perspective interpolation:

where fa and fb are the data associated with the starting and ending endpoints of the segment, respectively; wa and wb are the clip w coordinates of the starting and ending endpoints of the segment, respectively.

Depth values for lines must be determined using linear interpolation:

z = (1 - t) za + t zb

where za and zb are the depth values of the starting and ending endpoints of the segment, respectively.

The NoPerspective and Flat interpolation decorations can be used with fragment shader inputs to declare how they are interpolated. When neither decoration is applied, perspective interpolation is performed as described above. When the NoPerspective decoration is used, linear interpolation is performed in the same fashion as for depth values, as described above. When the Flat decoration is used, no interpolation is performed, and outputs are taken from the corresponding input value of the provoking vertex corresponding to that primitive.

The above description documents the preferred method of line rasterization, and must be used when the implementation advertises the strictLines limit in VkPhysicalDeviceLimits as VK_TRUE.

When strictLines is VK_FALSE, the edges of the lines are generated as a parallelogram surrounding the original line. The major axis is chosen by noting the axis in which there is the greatest distance between the line start and end points. If the difference is equal in both directions then the X axis is chosen as the major axis. Edges 2 and 3 are aligned to the minor axis and are centered on the endpoints of the line as in Non strict lines, and each is lineWidth long. Edges 0 and 1 are parallel to the line and connect the endpoints of edges 2 and 3. Coverage bits that correspond to sample points that intersect the parallelogram are 1, other coverage bits are 0.

Samples that fall exactly on the edge of the parallelogram follow the polygon rasterization rules.

Interpolation occurs as if the parallelogram was decomposed into two triangles where each pair of vertices at each end of the line has identical attributes.

Figure 15. Non strict lines

Only when strictLines is VK_FALSE implementations may deviate from the non-strict line algorithm described above in the following ways:

#### 25.7.2. Bresenham Line Segment Rasterization

Non-strict lines may also follow these rasterization rules for non-antialiased lines.

Line segment rasterization begins by characterizing the segment as either x-major or y-major. x-major line segments have slope in the closed interval [-1,1]; all other line segments are y-major (slope is determined by the segment’s endpoints). We specify rasterization only for x-major segments except in cases where the modifications for y-major segments are not self-evident.

Ideally, Vulkan uses a diamond-exit rule to determine those fragments that are produced by rasterizing a line segment. For each fragment f with center at framebuffer coordinates xf and yf, define a diamond-shaped region that is the intersection of four half planes:

Essentially, a line segment starting at pa and ending at pb produces those fragments f for which the segment intersects Rf, except if pb is contained in Rf.

Figure 16. Visualization of Bresenham’s algorithm

To avoid difficulties when an endpoint lies on a boundary of Rf we (in principle) perturb the supplied endpoints by a tiny amount. Let pa and pb have framebuffer coordinates (xa, ya) and (xb, yb), respectively. Obtain the perturbed endpoints pa' given by (xa, ya) - (ε, ε2) and pb' given by (xb, yb) - (ε, ε2). Rasterizing the line segment starting at pa and ending at pb produces those fragments f for which the segment starting at pa' and ending on pb' intersects Rf, except if pb' is contained in Rf. ε is chosen to be so small that rasterizing the line segment produces the same fragments when δ is substituted for ε for any 0 < δ ≤ ε.

When pa and pb lie on fragment centers, this characterization of fragments reduces to Bresenham’s algorithm with one modification: lines produced in this description are "half-open," meaning that the final fragment (corresponding to pb) is not drawn. This means that when rasterizing a series of connected line segments, shared endpoints will be produced only once rather than twice (as would occur with Bresenham’s algorithm).

Implementations may use other line segment rasterization algorithms, subject to the following rules:

• The coordinates of a fragment produced by the algorithm must not deviate by more than one unit in either x or y framebuffer coordinates from a corresponding fragment produced by the diamond-exit rule.

• The total number of fragments produced by the algorithm must not differ from that produced by the diamond-exit rule by no more than one.

• For an x-major line, two fragments that lie in the same framebuffer-coordinate column must not be produced (for a y-major line, two fragments that lie in the same framebuffer-coordinate row must not be produced).

• If two line segments share a common endpoint, and both segments are either x-major (both left-to-right or both right-to-left) or y-major (both bottom-to-top or both top-to-bottom), then rasterizing both segments must not produce duplicate fragments. Fragments also must not be omitted so as to interrupt continuity of the connected segments.

The actual width w of Bresenham lines is determined by rounding the line width to the nearest integer, clamping it to the implementation-dependent lineWidthRange (with both values rounded to the nearest integer), then clamping it to be no less than 1.

Bresenham line segments of width other than one are rasterized by offsetting them in the minor direction (for an x-major line, the minor direction is y, and for a y-major line, the minor direction is x) and producing a row or column of fragments in the minor direction. If the line segment has endpoints given by (x0, y0) and (x1, y1) in framebuffer coordinates, the segment with endpoints and is rasterized, but instead of a single fragment, a column of fragments of height w (a row of fragments of length w for a y-major segment) is produced at each x (y for y-major) location. The lowest fragment of this column is the fragment that would be produced by rasterizing the segment of width 1 with the modified coordinates.

The preferred method of attribute interpolation for a wide line is to generate the same attribute values for all fragments in the row or column described above, as if the adjusted line was used for interpolation and those values replicated to the other fragments, except for FragCoord which is interpolated as usual. Implementations may instead interpolate each fragment according to the formula in Basic Line Segment Rasterization, using the original line segment endpoints.

When Bresenham lines are being rasterized, sample locations may all be treated as being at the pixel center (this may affect attribute and depth interpolation).

 Note The sample locations described above are not used for determining coverage, they are only used for things like attribute interpolation. The rasterization rules that determine coverage are defined in terms of whether the line intersects pixels, as opposed to the point sampling rules used for other primitive types. So these rules are independent of the sample locations. One consequence of this is that Bresenham lines cover the same pixels regardless of the number of rasterization samples, and cover all samples in those pixels (unless masked out or killed).

### 25.8. Polygons

A polygon results from the decomposition of a triangle strip, triangle fan or a series of independent triangles. Like points and line segments, polygon rasterization is controlled by several variables in the VkPipelineRasterizationStateCreateInfo structure.

#### 25.8.1. Basic Polygon Rasterization

The first step of polygon rasterization is to determine whether the triangle is back-facing or front-facing. This determination is made based on the sign of the (clipped or unclipped) polygon’s area computed in framebuffer coordinates. One way to compute this area is:

where and are the x and y framebuffer coordinates of the ith vertex of the n-vertex polygon (vertices are numbered starting at zero for the purposes of this computation) and i ⊕ 1 is (i + 1) mod n.

The interpretation of the sign of a is determined by the VkPipelineRasterizationStateCreateInfo::frontFace property of the currently active pipeline. Possible values are:

// Provided by VK_VERSION_1_0
typedef enum VkFrontFace {
VK_FRONT_FACE_COUNTER_CLOCKWISE = 0,
VK_FRONT_FACE_CLOCKWISE = 1,
} VkFrontFace;
• VK_FRONT_FACE_COUNTER_CLOCKWISE specifies that a triangle with positive area is considered front-facing.

• VK_FRONT_FACE_CLOCKWISE specifies that a triangle with negative area is considered front-facing.

Any triangle which is not front-facing is back-facing, including zero-area triangles.

Once the orientation of triangles is determined, they are culled according to the VkPipelineRasterizationStateCreateInfo::cullMode property of the currently active pipeline. Possible values are:

// Provided by VK_VERSION_1_0
typedef enum VkCullModeFlagBits {
VK_CULL_MODE_NONE = 0,
VK_CULL_MODE_FRONT_BIT = 0x00000001,
VK_CULL_MODE_BACK_BIT = 0x00000002,
VK_CULL_MODE_FRONT_AND_BACK = 0x00000003,
} VkCullModeFlagBits;
• VK_CULL_MODE_NONE specifies that no triangles are discarded

• VK_CULL_MODE_FRONT_BIT specifies that front-facing triangles are discarded

• VK_CULL_MODE_BACK_BIT specifies that back-facing triangles are discarded

• VK_CULL_MODE_FRONT_AND_BACK specifies that all triangles are discarded.

Following culling, fragments are produced for any triangles which have not been discarded.

// Provided by VK_VERSION_1_0
typedef VkFlags VkCullModeFlags;

VkCullModeFlags is a bitmask type for setting a mask of zero or more VkCullModeFlagBits.

The rule for determining which fragments are produced by polygon rasterization is called point sampling. The two-dimensional projection obtained by taking the x and y framebuffer coordinates of the polygon’s vertices is formed. Fragments are produced for any fragment area groups of pixels for which any sample points lie inside of this polygon. Coverage bits that correspond to sample points that satisfy the point sampling criteria are 1, other coverage bits are 0. Special treatment is given to a sample whose sample location lies on a polygon edge. In such a case, if two polygons lie on either side of a common edge (with identical endpoints) on which a sample point lies, then exactly one of the polygons must result in a covered sample for that fragment during rasterization. As for the data associated with each fragment produced by rasterizing a polygon, we begin by specifying how these values are produced for fragments in a triangle.

Barycentric coordinates are a set of three numbers, a, b, and c, each in the range [0,1], with a + b + c = 1. These coordinates uniquely specify any point p within the triangle or on the triangle’s boundary as

p = a pa + b pb + c pc

where pa, pb, and pc are the vertices of the triangle. a, b, and c are determined by:

where A(lmn) denotes the area in framebuffer coordinates of the triangle with vertices l, m, and n.

Denote an associated datum at pa, pb, or pc as fa, fb, or fc, respectively.

The value of an associated datum f for a fragment produced by rasterizing a triangle, whether it be a shader output or the clip w coordinate, must be determined using perspective interpolation:

where wa, wb, and wc are the clip w coordinates of pa, pb, and pc, respectively. a, b, and c are the barycentric coordinates of the location at which the data are produced - this must be the location of the fragment center or the location of a sample. When rasterizationSamples is VK_SAMPLE_COUNT_1_BIT, the fragment center must be used.

Depth values for triangles must be determined using linear interpolation:

z = a za + b zb + c zc

where za, zb, and zc are the depth values of pa, pb, and pc, respectively.

The NoPerspective and Flat interpolation decorations can be used with fragment shader inputs to declare how they are interpolated. When neither decoration is applied, perspective interpolation is performed as described above. When the NoPerspective decoration is used, linear interpolation is performed in the same fashion as for depth values, as described above. When the Flat decoration is used, no interpolation is performed, and outputs are taken from the corresponding input value of the provoking vertex corresponding to that primitive.

For a polygon with more than three edges, such as are produced by clipping a triangle, a convex combination of the values of the datum at the polygon’s vertices must be used to obtain the value assigned to each fragment produced by the rasterization algorithm. That is, it must be the case that at every fragment

where n is the number of vertices in the polygon and fi is the value of f at vertex i. For each i, 0 ≤ ai ≤ 1 and . The values of ai may differ from fragment to fragment, but at vertex i, ai = 1 and aj = 0 for j ≠ i.

 Note One algorithm that achieves the required behavior is to triangulate a polygon (without adding any vertices) and then treat each triangle individually as already discussed. A scan-line rasterizer that linearly interpolates data along each edge and then linearly interpolates data across each horizontal span from edge to edge also satisfies the restrictions (in this case the numerator and denominator of perspective interpolation are iterated independently, and a division is performed for each fragment).

#### 25.8.2. Polygon Mode

Possible values of the VkPipelineRasterizationStateCreateInfo::polygonMode property of the currently active pipeline, specifying the method of rasterization for polygons, are:

// Provided by VK_VERSION_1_0
typedef enum VkPolygonMode {
VK_POLYGON_MODE_FILL = 0,
VK_POLYGON_MODE_LINE = 1,
VK_POLYGON_MODE_POINT = 2,
} VkPolygonMode;
• VK_POLYGON_MODE_POINT specifies that polygon vertices are drawn as points.

• VK_POLYGON_MODE_LINE specifies that polygon edges are drawn as line segments.

• VK_POLYGON_MODE_FILL specifies that polygons are rendered using the polygon rasterization rules in this section.

These modes affect only the final rasterization of polygons: in particular, a polygon’s vertices are shaded and the polygon is clipped and possibly culled before these modes are applied.

#### 25.8.3. Depth Bias

The depth values of all fragments generated by the rasterization of a polygon can be offset by a single value that is computed for that polygon. This behavior is controlled by the depthBiasEnable, depthBiasConstantFactor, depthBiasClamp, and depthBiasSlopeFactor members of VkPipelineRasterizationStateCreateInfo, or by the corresponding parameters to the vkCmdSetDepthBias command if depth bias state is dynamic.

// Provided by VK_VERSION_1_0
void vkCmdSetDepthBias(
VkCommandBuffer                             commandBuffer,
float                                       depthBiasConstantFactor,
float                                       depthBiasClamp,
float                                       depthBiasSlopeFactor);
• commandBuffer is the command buffer into which the command will be recorded.

• depthBiasConstantFactor is a scalar factor controlling the constant depth value added to each fragment.

• depthBiasClamp is the maximum (or minimum) depth bias of a fragment.

• depthBiasSlopeFactor is a scalar factor applied to a fragment’s slope in depth bias calculations.

If depthBiasEnable is VK_FALSE at draw time, no depth bias is applied and the fragment’s depth values are unchanged.

depthBiasSlopeFactor scales the maximum depth slope of the polygon, and depthBiasConstantFactor scales the minimum resolvable difference of the depth buffer. The resulting values are summed to produce the depth bias value which is then clamped to a minimum or maximum value specified by depthBiasClamp. depthBiasSlopeFactor, depthBiasConstantFactor, and depthBiasClamp can each be positive, negative, or zero.

The maximum depth slope m of a triangle is

where (xf, yf, zf) is a point on the triangle. m may be approximated as

The minimum resolvable difference r is a parameter that depends on the depth buffer representation. It is the smallest difference in framebuffer coordinate z values that is guaranteed to remain distinct throughout polygon rasterization and in the depth buffer. All pairs of fragments generated by the rasterization of two polygons with otherwise identical vertices, but zf values that differ by r, will have distinct depth values.

For fixed-point depth buffer representations, r is constant throughout the range of the entire depth buffer. Its value is implementation-dependent but must be at most

r = 2 × 2-n

for an n-bit buffer. For floating-point depth buffers, there is no single minimum resolvable difference. In this case, the minimum resolvable difference for a given polygon is dependent on the maximum exponent, e, in the range of z values spanned by the primitive. If n is the number of bits in the floating-point mantissa, the minimum resolvable difference, r, for the given primitive is defined as

r = 2e-n

If no depth buffer is present, r is undefined.

The bias value o for a polygon is

m is computed as described above. If the depth buffer uses a fixed-point representation, m is a function of depth values in the range [0,1], and o is applied to depth values in the same range.

For fixed-point depth buffers, fragment depth values are always limited to the range [0,1] by clamping after depth bias addition is performed. Fragment depth values are clamped even when the depth buffer uses a floating-point representation.

Valid Usage
• VUID-vkCmdSetDepthBias-depthBiasClamp-00790
If the depth bias clamping feature is not enabled, depthBiasClamp must be 0.0

Valid Usage (Implicit)
• VUID-vkCmdSetDepthBias-commandBuffer-parameter
commandBuffer must be a valid VkCommandBuffer handle

• VUID-vkCmdSetDepthBias-commandBuffer-recording
commandBuffer must be in the recording state

• VUID-vkCmdSetDepthBias-commandBuffer-cmdpool
The VkCommandPool that commandBuffer was allocated from must support graphics operations

Host Synchronization
• Host access to commandBuffer must be externally synchronized

• Host access to the VkCommandPool that commandBuffer was allocated from must be externally synchronized

Command Properties
Command Buffer Levels Render Pass Scope Supported Queue Types

Primary
Secondary

Both

Graphics