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Copyright (c) 2015-2017 Khronos Group. This work is licensed under a // Creative Commons Attribution 4.0 International License; see // http://creativecommons.org/licenses/by/4.0/ [[textures]] = Image Operations == Image Operations Overview Image Operations are steps performed by SPIR-V image instructions, where those instructions which take an code:OpTypeImage (representing a sname:VkImageView) or code:OpTypeSampledImage (representing a (sname:VkImageView, sname:VkSampler) pair) and texel coordinates as operands, and return a value based on one or more neighboring texture elements (_texels_) in the image. [NOTE] .Note ================== Texel is a term which is a combination of the words texture and element. Early interactive computer graphics supported texture operations on textures, a small subset of the image operations on images described here. The discrete samples remain essentially equivalent, however, so we retain the historical term texel to refer to them. ================== SPIR-V Image Instructions include the following functionality: * code:OpImageSample* and code:OpImageSparseSample* read one or more neighboring texels of the image, and <> the texel values based on the state of the sampler. ** Instructions with code:ImplicitLod in the name <> the LOD used in the sampling operation based on the coordinates used in neighboring fragments. ** Instructions with code:ExplicitLod in the name <> the LOD used in the sampling operation based on additional coordinates. ** Instructions with code:Proj in the name apply homogeneous <> to the coordinates. * code:OpImageFetch and code:OpImageSparseFetch return a single texel of the image. No sampler is used. * code:OpImage*code:Gather and code:OpImageSparse*code:Gather read neighboring texels and <> of each. * code:OpImageRead (and code:OpImageSparseRead) and code:OpImageWrite read and write, respectively, a texel in the image. No sampler is used. * Instructions with code:Dref in the name apply <> on the texel values. * Instructions with code:Sparse in the name additionally return a <> code. === Texel Coordinate Systems Images are addressed by _texel coordinates_. There are three _texel coordinate systems_: * normalized texel coordinates [eq]#[0.0, 1.0]# * unnormalized texel coordinates [eq]#[0.0, width / height / depth)# * integer texel coordinates [eq]#[0, width / height / depth)# SPIR-V code:OpImageFetch, code:OpImageSparseFetch, code:OpImageRead, code:OpImageSparseRead, and code:OpImageWrite instructions use integer texel coordinates. Other image instructions can: use either normalized or unnormalized texel coordinates (selected by the pname:unnormalizedCoordinates state of the sampler used in the instruction), but there are <> on what operations, image state, and sampler state is supported. Normalized coordinates are logically <> to unnormalized as part of image operations, and <> are only performed on normalized coordinates. The array layer coordinate is always treated as unnormalized even when other coordinates are normalized. Normalized texel coordinates are referred to as [eq]#(s,t,r,q,a)#, with the coordinates having the following meanings: * [eq]#s#: Coordinate in the first dimension of an image. * [eq]#t#: Coordinate in the second dimension of an image. * [eq]#r#: Coordinate in the third dimension of an image. ** [eq]#(s,t,r)# are interpreted as a direction vector for Cube images. * [eq]#q#: Fourth coordinate, for homogeneous (projective) coordinates. * [eq]#a#: Coordinate for array layer. The coordinates are extracted from the SPIR-V operand based on the dimensionality of the image variable and type of instruction. For code:Proj instructions, the components are in order (s, [t,] [r,] q) with t and r being conditionally present based on the code:Dim of the image. For non-code:Proj instructions, the coordinates are (s [,t] [,r] [,a]), with t and r being conditionally present based on the code:Dim of the image and a being conditionally present based on the code:Arrayed property of the image. Projective image instructions are not supported on code:Arrayed images. Unnormalized texel coordinates are referred to as [eq]#(u,v,w,a)#, with the coordinates having the following meanings: * [eq]#u#: Coordinate in the first dimension of an image. * [eq]#v#: Coordinate in the second dimension of an image. * [eq]#w#: Coordinate in the third dimension of an image. * [eq]#a#: Coordinate for array layer. Only the [eq]#u# and [eq]#v# coordinates are directly extracted from the SPIR-V operand, because only 1D and 2D (non-code:Arrayed) dimensionalities support unnormalized coordinates. The components are in order [eq]#(u [,v])#, with [eq]#v# being conditionally present when the dimensionality is 2D. When normalized coordinates are converted to unnormalized coordinates, all four coordinates are used. Integer texel coordinates are referred to as [eq]#(i,j,k,l,n)#, and the first four in that order have the same meanings as unnormalized texel coordinates. They are extracted from the SPIR-V operand in order [eq]#(i, [,j], [,k], [,l])#, with [eq]#j# and [eq]#k# conditionally present based on the code:Dim of the image, and l conditionally present based on the code:Arrayed property of the image. n is the sample index and is taken from the code:Sample image operand. For all coordinate types, unused coordinates are assigned a value of zero. [[textures-texel-coordinate-systems-diagrams]] image::images/vulkantexture0.png[align="center",title="Texel Coordinate Systems",{fullimagewidth}] The Texel Coordinate Systems - For the example shown of an 8{times}4 texel two dimensional image. * Normalized texel coordinates: ** The [eq]#s# coordinate goes from 0.0 to 1.0, left to right. ** The [eq]#t# coordinate goes from 0.0 to 1.0, top to bottom. * Unnormalized texel coordinates: ** The [eq]#u# coordinate goes from -1.0 to 9.0, left to right. The [eq]#u# coordinate within the range 0.0 to 8.0 is within the image, otherwise it is within the border. ** The [eq]#v# coordinate goes from -1.0 to 5.0, top to bottom. The [eq]#v# coordinate within the range 0.0 to 4.0 is within the image, otherwise it is within the border. * Integer texel coordinates: ** The [eq]#i# coordinate goes from -1 to 8, left to right. The [eq]#i# coordinate within the range 0 to 7 addresses texels within the image, otherwise it addresses a border texel. ** The [eq]#j# coordinate goes from -1 to 5, top to bottom. The [eq]#j# coordinate within the range 0 to 3 addresses texels within the image, otherwise it addresses a border texel. * Also shown for linear filtering: ** Given the unnormalized coordinates [eq]#(u,v)#, the four texels selected are [eq]#i~0~j~0~#, [eq]#i~1~j~0~#, [eq]#i~0~j~1~#, and [eq]#i~1~j~1~#. ** The weights [eq]#{alpha}# and [eq]#{beta}#. ** Given the offset [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~#, the four texels selected by the offset are [eq]#i~0~j'~0~#, [eq]#i~1~j'~0~#, [eq]#i~0~j'~1~#, and [eq]#i~1~j'~1~#. ifdef::VK_KHR_sampler_ycbcr_conversion[] [NOTE] .Note ==== For formats with reduced-resolution channels, [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~# are relative to the resolution of the highest-resolution channel, and therefore may be divided by two relative to the unnormalized coordinate space of the lower-resolution channels. ==== endif::VK_KHR_sampler_ycbcr_conversion[] image::images/vulkantexture1.png[align="center",title="Texel Coordinate Systems",{fullimagewidth}] The Texel Coordinate Systems - For the example shown of an 8{times}4 texel two dimensional image. * Texel coordinates as above. Also shown for nearest filtering: ** Given the unnormalized coordinates [eq]#(u,v)#, the texel selected is [eq]#ij#. ** Given the offset [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~#, the texel selected by the offset is [eq]#ij'#. == Conversion Formulas ifdef::editing-notes[] [NOTE] .editing-note ================== (Bill) These Conversion Formulas will likely move to Section 2.7 Fixed-Point Data Conversions (RGB to sRGB and sRGB to RGB) and section 2.6 Numeric Representation and Computation (RGB to Shared Exponent and Shared Exponent to RGB) ================== endif::editing-notes[] [[textures-RGB-sexp]] === RGB to Shared Exponent Conversion An RGB color [eq]#(red, green, blue)# is transformed to a shared exponent color [eq]#(red~shared~, green~shared~, blue~shared~, exp~shared~)# as follows: First, the components [eq]#(red, green, blue)# are clamped to [eq]#(red~clamped~, green~clamped~, blue~clamped~)# as: :: [eq]#red~clamped~ = max(0, min(sharedexp~max~, red))# :: [eq]#green~clamped~ = max(0, min(sharedexp~max~, green))# :: [eq]#blue~clamped~ = max(0, min(sharedexp~max~, blue))# Where: [latexmath] +++++++++++++++++++ \begin{aligned} N & = 9 & \text{number of mantissa bits per component} \\ B & = 15 & \text{exponent bias} \\ E_{max} & = 31 & \text{maximum possible biased exponent value} \\ sharedexp_{max} & = \frac{(2^N-1)}{2^N} \times 2^{(E_{max}-B)} \end{aligned} +++++++++++++++++++ [NOTE] .Note ================== [eq]#NaN#, if supported, is handled as in <> minNum() and maxNum(). That is the result is a [eq]#NaN# is mapped to zero. ================== The largest clamped component, [eq]#max~clamped~# is determined: :: [eq]#max~clamped~ = max(red~clamped~, green~clamped~, blue~clamped~)# A preliminary shared exponent [eq]#exp'# is computed: [latexmath] +++++++++++++++++++ \begin{aligned} exp' = \begin{cases} \left \lfloor \log_2(max_{clamped}) \right \rfloor + (B+1) & \text{for}\ max_{clamped} > 2^{-(B+1)} \\ 0 & \text{for}\ max_{clamped} \leq 2^{-(B+1)} \end{cases} \end{aligned} +++++++++++++++++++ The shared exponent [eq]#exp~shared~# is computed: [latexmath] +++++++++++++++++++ \begin{aligned} max_{shared} = \left \lfloor { \frac{max_{clamped}}{2^{(exp'-B-N)}} + \frac{1}{2} } \right \rfloor \end{aligned} +++++++++++++++++++ [latexmath] +++++++++++++++++++ \begin{aligned} exp_{shared} = \begin{cases} exp' & \text{for}\ 0 \leq max_{shared} < 2^N \\ exp'+1 & \text{for}\ max_{shared} = 2^N \end{cases} \end{aligned} +++++++++++++++++++ Finally, three integer values in the range [eq]#0# to [eq]#2^N^# are computed: [latexmath] +++++++++++++++++++ \begin{aligned} red_{shared} & = \left \lfloor { \frac{red_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \\ green_{shared} & = \left \lfloor { \frac{green_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \\ blue_{shared} & = \left \lfloor { \frac{blue_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \end{aligned} +++++++++++++++++++ [[textures-sexp-RGB]] === Shared Exponent to RGB A shared exponent color [eq]#(red~shared~, green~shared~, blue~shared~, exp~shared~)# is transformed to an RGB color [eq]#(red, green, blue)# as follows: :: latexmath:[red = red_{shared} \times {2^{(exp_{shared}-B-N)}}] :: latexmath:[green = green_{shared} \times {2^{(exp_{shared}-B-N)}}] :: latexmath:[blue = blue_{shared} \times {2^{(exp_{shared}-B-N)}}] Where: :: [eq]#N = 9# (number of mantissa bits per component) :: [eq]#B = 15# (exponent bias) == Texel Input Operations _Texel input instructions_ are SPIR-V image instructions that read from an image. _Texel input operations_ are a set of steps that are performed on state, coordinates, and texel values while processing a texel input instruction, and which are common to some or all texel input instructions. They include the following steps, which are performed in the listed order: * <> ** <> ** <> ** <> ** <> * <> * <> * <> * <> * <> ifdef::VK_KHR_sampler_ycbcr_conversion[] * <> * <> endif::VK_KHR_sampler_ycbcr_conversion[] For texel input instructions involving multiple texels (for sampling or gathering), these steps are applied for each texel that is used in the instruction. Depending on the type of image instruction, other steps are conditionally performed between these steps or involving multiple coordinate or texel values. ifdef::VK_KHR_sampler_ycbcr_conversion[] If <> is implicit, <> instead takes place during chroma reconstruction, before <> occurs. endif::VK_KHR_sampler_ycbcr_conversion[] [[textures-input-validation]] === Texel Input Validation Operations _Texel input validation operations_ inspect instruction/image/sampler state or coordinates, and in certain circumstances cause the texel value to be replaced or become undefined. There are a series of validations that the texel undergoes. [[textures-operation-validation]] ==== Instruction/Sampler/Image View Validation There are a number of cases where a SPIR-V instruction can: mismatch with the sampler, the image view, or both. There are a number of cases where the sampler can: mismatch with the image view. In such cases the value of the texel returned is undefined. These cases include: * The sampler pname:borderColor is an integer type and the image view pname:format is not one of the elink:VkFormat integer types or a stencil component of a depth/stencil format. * The sampler pname:borderColor is a float type and the image view pname:format is not one of the elink:VkFormat float types or a depth component of a depth/stencil format. * The sampler pname:borderColor is one of the opaque black colors (ename:VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK or ename:VK_BORDER_COLOR_INT_OPAQUE_BLACK) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not ename:VK_COMPONENT_SWIZZLE_IDENTITY. * The elink:VkImageLayout of any subresource in the image view does not match that specified in slink:VkDescriptorImageInfo::pname:imageLayout used to write the image descriptor. * If the instruction is code:OpImageRead or code:OpImageSparseRead and the pname:shaderStorageImageReadWithoutFormat feature is not enabled, or the instruction is code:OpImageWrite and the pname:shaderStorageImageWriteWithoutFormat feature is not enabled, then the SPIR-V Image Format must: be <> with the image view's pname:format. * The sampler pname:unnormalizedCoordinates is ename:VK_TRUE and any of the <> are violated. * The SPIR-V instruction is one of the code:OpImage*code:Dref* instructions and the sampler pname:compareEnable is ename:VK_FALSE * The SPIR-V instruction is not one of the code:OpImage*code:Dref* instructions and the sampler pname:compareEnable is ename:VK_TRUE * The SPIR-V instruction is one of the code:OpImage*code:Dref* instructions and the image view pname:format is not one of the depth/stencil formats with a depth component, or the image view aspect is not ename:VK_IMAGE_ASPECT_DEPTH_BIT. * The SPIR-V instruction's image variable's properties are not compatible with the image view: ** Rules for pname:viewType: *** ename:VK_IMAGE_VIEW_TYPE_1D must: have code:Dim = 1D, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_2D must: have code:Dim = 2D, code:Arrayed = 0. *** ename:VK_IMAGE_VIEW_TYPE_3D must: have code:Dim = 3D, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_CUBE must: have code:Dim = Cube, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_1D_ARRAY must: have code:Dim = 1D, code:Arrayed = 1, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_2D_ARRAY must: have code:Dim = 2D, code:Arrayed = 1. *** ename:VK_IMAGE_VIEW_TYPE_CUBE_ARRAY must: have code:Dim = Cube, code:Arrayed = 1, code:MS = 0. ** If the image was created with slink:VkImageCreateInfo::pname:samples equal to ename:VK_SAMPLE_COUNT_1_BIT, the instruction must: have code:MS = 0. ** If the image was created with slink:VkImageCreateInfo::pname:samples not equal to ename:VK_SAMPLE_COUNT_1_BIT, the instruction must: have code:MS = 1. ifdef::VK_KHR_sampler_ycbcr_conversion[] Only code:OpImageSample* and code:OpImageSparseSample* can: be used with a sampler that enables <>. code:OpImageFetch, code:OpImageSparseFetch, code:OpImage*code:Gather, and code:OpImageSparse*code:Gather must: not be used with a sampler that enables <>. The code:ConstOffset and code:Offset operands must: not be used with a sampler that enables <>. endif::VK_KHR_sampler_ycbcr_conversion[] [[textures-integer-coordinate-validation]] ==== Integer Texel Coordinate Validation Integer texel coordinates are validated against the size of the image level, and the number of layers and number of samples in the image. For SPIR-V instructions that use integer texel coordinates, this is performed directly on the integer coordinates. For instructions that use normalized or unnormalized texel coordinates, this is performed on the coordinates that result after <> to integer texel coordinates. If the integer texel coordinates do not satisfy all of the conditions :: [eq]#0 {leq} i < w~s~# :: [eq]#0 {leq} j < h~s~# :: [eq]#0 {leq} k < d~s~# :: [eq]#0 {leq} l < layers# :: [eq]#0 {leq} n < samples# where: :: [eq]#w~s~ =# width of the image level :: [eq]#h~s~ =# height of the image level :: [eq]#d~s~ =# depth of the image level :: [eq]#layers =# number of layers in the image :: [eq]#samples =# number of samples per texel in the image then the texel fails integer texel coordinate validation. There are four cases to consider: . Valid Texel Coordinates + * If the texel coordinates pass validation (that is, the coordinates lie within the image), + then the texel value comes from the value in image memory. . Border Texel + * If the texel coordinates fail validation, and * If the read is the result of an image sample instruction or image gather instruction, and * If the image is not a cube image, + then the texel is a border texel and <> is performed. . Invalid Texel + * If the texel coordinates fail validation, and * If the read is the result of an image fetch instruction, image read instruction, or atomic instruction, + then the texel is an invalid texel and <> is performed. . Cube Map Edge or Corner + Otherwise the texel coordinates lie on the borders along the edges and corners of a cube map image, and <> is performed. [[textures-cubemapedge]] ==== Cube Map Edge Handling If the texel coordinates lie on the borders along the edges and corners of a cube map image, the following steps are performed. Note that this only occurs when using ename:VK_FILTER_LINEAR filtering within a mip level, since ename:VK_FILTER_NEAREST is treated as using ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. * Cube Map Edge Texel + ** If the texel lies along the border in either only [eq]#i# or only [eq]#j# + then the texel lies along an edge, so the coordinates [eq]#(i,j)# and the array layer [eq]#l# are transformed to select the adjacent texel from the appropriate neighboring face. * Cube Map Corner Texel + ** If the texel lies along the border in both [eq]#i# and [eq]#j# + then the texel lies at a corner and there is no unique neighboring face from which to read that texel. The texel should: be replaced by the average of the three values of the adjacent texels in each incident face. However, implementations may: replace the cube map corner texel by other methods, subject to the constraint that if the three available samples have the same value, the replacement texel also has that value. [[textures-sparse-validation]] ==== Sparse Validation If the texel reads from an unbound region of a sparse image, the texel is a _sparse unbound texel_, and processing continues with <>. ifdef::VK_KHR_sampler_ycbcr_conversion[] [[textures-layout-validation]] ==== Layout Validation If all planes of a _disjoint_ _multi-planar_ image are not in the same <> when the image is sampled with <>, the result of texel reads is undefined. endif::VK_KHR_sampler_ycbcr_conversion[] [[textures-format-conversion]] === Format Conversion Texels undergo a format conversion from the elink:VkFormat of the image view to a vector of either floating point or signed or unsigned integer components, with the number of components based on the number of components present in the format. * Color formats have one, two, three, or four components, according to the format. * Depth/stencil formats are one component. The depth or stencil component is selected by the pname:aspectMask of the image view. Each component is converted based on its type and size (as defined in the <> section for each elink:VkFormat), using the appropriate equations in <>, <>, <>, <>, and <>. Signed integer components smaller than 32 bits are sign-extended. If the image format is sRGB, the color components are first converted as if they are UNORM, and then sRGB to linear conversion is applied to the R, G, and B components as described in the "sRGB EOTF" section of the <>. The A component, if present, is unchanged. If the image view format is block-compressed, then the texel value is first decoded, then converted based on the type and number of components defined by the compressed format. [[textures-texel-replacement]] === Texel Replacement A texel is replaced if it is one (and only one) of: * a border texel, * an invalid texel, or * a sparse unbound texel. Border texels are replaced with a value based on the image format and the pname:borderColor of the sampler. The border color is: [[textures-border-replacement-color]] .Border Color [eq]#B# [options="header",cols="60%,40%"] |==== | Sampler pname:borderColor | Corresponding Border Color | ename:VK_BORDER_COLOR_FLOAT_TRANSPARENT_BLACK | [eq]#B = (0.0, 0.0, 0.0, 0.0)# | ename:VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK | [eq]#B = (0.0, 0.0, 0.0, 1.0)# | ename:VK_BORDER_COLOR_FLOAT_OPAQUE_WHITE | [eq]#B = (1.0, 1.0, 1.0, 1.0)# | ename:VK_BORDER_COLOR_INT_TRANSPARENT_BLACK | [eq]#B = (0, 0, 0, 0)# | ename:VK_BORDER_COLOR_INT_OPAQUE_BLACK | [eq]#B = (0, 0, 0, 1)# | ename:VK_BORDER_COLOR_INT_OPAQUE_WHITE | [eq]#B = (1, 1, 1, 1)# |==== [NOTE] .Note ==== The names etext:VK_BORDER_COLOR_*\_TRANSPARENT_BLACK, etext:VK_BORDER_COLOR_*\_OPAQUE_BLACK, and etext:VK_BORDER_COLOR_*_OPAQUE_WHITE are meant to describe which components are zeros and ones in the vocabulary of compositing, and are not meant to imply that the numerical value of ename:VK_BORDER_COLOR_INT_OPAQUE_WHITE is a saturating value for integers. ==== This is substituted for the texel value by replacing the number of components in the image format [[textures-border-replacement-table]] .Border Texel Components After Replacement [width="80%",options="header"] |==== | Texel Aspect or Format | Component Assignment | Depth aspect | [eq]#D = B~r~# | Stencil aspect | [eq]#S = B~r~# | One component color format | [eq]#C~r~ = B~r~# | Two component color format | [eq]#C~rg~ = (B~r~,B~g~)# | Three component color format| [eq]#C~rgb~ = (B~r~,B~g~,B~b~)# | Four component color format | [eq]#C~rgba~ = (B~r~,B~g~,B~b~,B~a~)# |==== If the read operation is from a buffer resource, and the pname:robustBufferAccess feature is enabled, an invalid texel is replaced as described <>. If the pname:robustBufferAccess feature is not enabled, the value of an invalid texel is undefined. ifdef::editing-notes[] [NOTE] .editing-note ================== (Bill) This is not currently catching this significant case. For opImageFetch, which fetches from an *image* not a buffer, the result is defined if pname:robustBufferAccess is enabled. ================== endif::editing-notes[] If the slink:VkPhysicalDeviceSparseProperties::pname:residencyNonResidentStrict property is ename:VK_TRUE, a sparse unbound texel is replaced with 0 or 0.0 values for integer and floating-point components of the image format, respectively. If pname:residencyNonResidentStrict is ename:VK_FALSE, the read must: be safe, but the value of the sparse unbound texel is undefined. [[textures-depth-compare-operation]] === Depth Compare Operation If the image view has a depth/stencil format, the depth component is selected by the pname:aspectMask, and the operation is a code:Dref instruction, a depth comparison is performed. The value of the result [eq]#D# is [eq]#1.0# if the result of the compare operation is [eq]#true#, and [eq]#0.0# otherwise. The compare operation is selected by the pname:compareOp member of the sampler. [latexmath] +++++++++++++++++++ \begin{aligned} D & = 1.0 & \begin{cases} D_{\textit{ref}} \leq D & \text{for LEQUAL} \\ D_{\textit{ref}} \geq D & \text{for GEQUAL} \\ D_{\textit{ref}} < D & \text{for LESS} \\ D_{\textit{ref}} > D & \text{for GREATER} \\ D_{\textit{ref}} = D & \text{for EQUAL} \\ D_{\textit{ref}} \neq D & \text{for NOTEQUAL} \\ \textit{true} & \text{for ALWAYS} \\ \textit{false} & \text{for NEVER} \end{cases} \\ D & = 0.0 & \text{otherwise} \end{aligned} +++++++++++++++++++ where, in the depth comparison: :: [eq]#D~ref~ = shaderOp.D~ref~# (from optional: SPIR-V operand) :: [eq]#D# (texel depth value) [[textures-conversion-to-rgba]] === Conversion to RGBA The texel is expanded from one, two, or three to four components based on the image base color: [[textures-texel-color-rgba-conversion-table]] .Texel Color After Conversion To RGBA [options="header"] |==== | Texel Aspect or Format | RGBA Color | Depth aspect | [eq]#C~rgba~ = (D,0,0,one)# | Stencil aspect | [eq]#C~rgba~ = (S,0,0,one)# | One component color format | [eq]#C~rgba~ = (C~r~,0,0,one)# | Two component color format | [eq]#C~rgba~ = (C~rg~,0,one)# | Three component color format| [eq]#C~rgba~ = (C~rgb~,one)# | Four component color format | [eq]#C~rgba~ = C~rgba~# |==== where [eq]#one = 1.0f# for floating-point formats and depth aspects, and [eq]#one = 1# for integer formats and stencil aspects. [[textures-component-swizzle]] === Component Swizzle ifndef::VK_KHR_sampler_ycbcr_conversion[] All texel input instructions apply a _swizzle_ based on the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkImageViewCreateInfo structure for the image being read. endif::VK_KHR_sampler_ycbcr_conversion[] ifdef::VK_KHR_sampler_ycbcr_conversion[] All texel input instructions apply a _swizzle_ based on: * the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkImageViewCreateInfo structure for the image being read if <> is not enabled, and * the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkSamplerYcbcrConversionCreateInfoKHR structure for the <> if sampler Y'C~B~C~R~ conversion is enabled. endif::VK_KHR_sampler_ycbcr_conversion[] The swizzle can: rearrange the components of the texel, or substitute zero and one for any components. It is defined as follows for the R component, and operates similarly for the other components. [latexmath] +++++++++++++++++++ \begin{aligned} C'_{rgba}[R] & = \begin{cases} C_{rgba}[R] & \text{for RED swizzle} \\ C_{rgba}[G] & \text{for GREEN swizzle} \\ C_{rgba}[B] & \text{for BLUE swizzle} \\ C_{rgba}[A] & \text{for ALPHA swizzle} \\ 0 & \text{for ZERO swizzle} \\ one & \text{for ONE swizzle} \\ C_{rgba}[R] & \text{for IDENTITY swizzle} \end{cases} \end{aligned} +++++++++++++++++++ where: [latexmath] +++++++++++++++++++ \begin{aligned} C_{rgba}[R] & \text{is the RED component} \\ C_{rgba}[G] & \text{is the GREEN component} \\ C_{rgba}[B] & \text{is the BLUE component} \\ C_{rgba}[A] & \text{is the ALPHA component} \\ one & = 1.0\text{f} & \text{for floating point components} \\ one & = 1 & \text{for integer components} \end{aligned} +++++++++++++++++++ For each component this is applied to, the ename:VK_COMPONENT_SWIZZLE_IDENTITY swizzle selects the corresponding component from [eq]#C~rgba~#. If the border color is one of the etext:VK_BORDER_COLOR_*_OPAQUE_BLACK enums and the elink:VkComponentSwizzle is not ename:VK_COMPONENT_SWIZZLE_IDENTITY for all components (or the <>), the value of the texel after swizzle is undefined. [[textures-sparse-residency]] === Sparse Residency code:OpImageSparse* instructions return a structure which includes a _residency code_ indicating whether any texels accessed by the instruction are sparse unbound texels. This code can: be interpreted by the code:OpImageSparseTexelsResident instruction which converts the residency code to a boolean value. ifdef::VK_KHR_sampler_ycbcr_conversion[] [[textures-chroma-reconstruction]] === Chroma Reconstruction In some color models, the color representation is defined in terms of monochromatic light intensity (often called "luma") and color differences relative to this intensity, often called "chroma". It is common for color models other than RGB to represent the chroma channels at lower spatial resolution than the luma channel. This approach is used to take advantage of the eye's lower spatial sensitivity to color compared with its sensitivity to brightness. Less commonly, the same approach is used with additive color, since the green channel dominates the eye's sensitivity to light intensity and the spatial sensitivity to color introduced by red and blue is lower. Lower-resolution channels are "downsampled" by resizing them to a lower spatial resolution than the channel representing luminance. The process of reconstructing a full color value for texture access involves accessing both chroma and luma values at the same location. To generate the color accurately, the values of the lower-resolution channels at the location of the luma samples must be reconstructed from the lower-resolution sample locations, an operation known here as "chroma reconstruction" irrespective of the actual color model. The location of the chroma samples relative to the luma coordinates is determined by the pname:xChromaOffset and pname:yChromaOffset members of the slink:VkSamplerYcbcrConversionCreateInfoKHR structure used to create the sampler Y'C~B~C~R~ conversion. The following diagrams show the relationship between unnormalized (_u_,_v_) coordinates and (_i_,_j_) integer texel positions in the luma channel (shown in black, with circles showing integer sample positions) and the texel coordinates of reduced-resolution chroma channels, shown as crosses in red. [NOTE] .Note ==== If the chroma values are reconstructed at the locations of the luma samples by means of interpolation, chroma samples from outside the image bounds are needed; these are determined according to <>. These diagrams represent this by showing the bounds of the "chroma texel" extending beyond the image bounds, and including additional chroma sample positions where required for interpolation. The limits of a sample for etext:NEAREST sampling is shown as a grid. ==== image::images/chromasamples_422_cosited.svg[align="center",title="422 downsampling, xChromaOffset=COSITED_EVEN",width="400"] image::images/chromasamples_422_midpoint.svg[align="center",title="422 downsampling, xChromaOffset=MIDPOINT",width="400"] image::images/chromasamples_420_xcosited_ycosited.svg[align="center",title="420 downsampling, xChromaOffset=COSITED_EVEN, yChromaOffset=COSITED_EVEN",width="400"] image::images/chromasamples_420_xmidpoint_ycosited.svg[align="center",title="420 downsampling, xChromaOffset=MIDPOINT, yChromaOffset=COSITED_EVEN",width="400"] image::images/chromasamples_420_xcosited_ymidpoint.svg[align="center",title="420 downsampling, xChromaOffset=COSITED_EVEN, yChromaOffset=MIDPOINT",width="400"] image::images/chromasamples_420_xmidpoint_ymidpoint.svg[align="center",title="420 downsampling, xChromaOffset=MIDPOINT, yChromaOffset=MIDPOINT",width="400"] Reconstruction is implemented in one of two ways: If the format of the image that is to be sampled sets ename:VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT_KHR, or the sname:VkSamplerYcbcrConversionCreateInfoKHR's pname:forceExplicitReconstruction is set to ename:VK_TRUE, reconstruction is performed as an explicit step independent of filtering, described in the <> section. If the format of the image that is to be sampled does not set ename:VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT_KHR and if the sname:VkSamplerYcbcrConversionCreateInfoKHR's pname:forceExplicitReconstruction is set to ename:VK_FALSE, reconstruction is performed as an implicit part of filtering prior to color model conversion, with no separate post-conversion texel filtering step, as described in the <> section. [[textures-explicit-reconstruction]] ==== Explicit Reconstruction * If the pname:chromaFilter member of the slink:VkSamplerYcbcrConversionCreateInfoKHR structure is ename:VK_FILTER_NEAREST: ** If the format's R and B channels are reduced in resolution in just width by a factor of two relative to the G channel (i.e. this is a "etext:_422" format), the latexmath:[\tau_{ijk}[level\]] values accessed by <> are reconstructed as follows: + [latexmath] ++++++++++++++ \begin{aligned} \tau_R'(i, j) & = \tau_R(\lfloor{i\times 0.5}\rfloor, j)[level] \\ \tau_B'(i, j) & = \tau_B(\lfloor{i\times 0.5}\rfloor, j)[level] \end{aligned} ++++++++++++++ ** If the format's R and B channels are reduced in resolution in width and height by a factor of two relative to the G channel (i.e. this is a "etext:_420" format), the latexmath:[\tau_{ijk}[level\]] values accessed by <> are reconstructed as follows: + [latexmath] ++++++++++++++ \begin{aligned} \tau_R'(i, j) & = \tau_R(\lfloor{i\times 0.5}\rfloor, \lfloor{j\times 0.5}\rfloor)[level] \\ \tau_B'(i, j) & = \tau_B(\lfloor{i\times 0.5}\rfloor, \lfloor{j\times 0.5}\rfloor)[level] \end{aligned} ++++++++++++++ + [NOTE] .Note ==== pname:xChromaOffset and pname:yChromaOffset have no effect if pname:chromaFilter is ename:VK_FILTER_NEAREST for explicit reconstruction. ==== * If the pname:chromaFilter member of the slink:VkSamplerYcbcrConversionCreateInfoKHR structure is ename:VK_FILTER_LINEAR: ** If the format's R and B channels are reduced in resolution in just width by a factor of two relative to the G channel (i.e. this is a "422" format): *** If pname:xChromaOffset is ename:VK_CHROMA_LOCATION_COSITED_EVEN_KHR: + [latexmath] +++++ \tau_{RB}'(i,j) = \begin{cases} \tau_{RB}(\lfloor{i\times 0.5}\rfloor,j)[level], & 0.5 \times i = \lfloor{0.5 \times i}\rfloor\\ 0.5\times\tau_{RB}(\lfloor{i\times 0.5}\rfloor,j)[level] + \\ 0.5\times\tau_{RB}(\lfloor{i\times 0.5}\rfloor + 1,j)[level], & 0.5 \times i \neq \lfloor{0.5 \times i}\rfloor \end{cases} +++++ + *** If pname:xChromaOffset is ename:VK_CHROMA_LOCATION_MIDPOINT_KHR: + [latexmath] +++++ \tau_{RB}(i,j)' = \begin{cases} 0.25 \times \tau_{RB}(\lfloor{i\times 0.5}\rfloor - 1,j)[level] + \\ 0.75 \times \tau_{RB}(\lfloor{i\times 0.5}\rfloor,j)[level], & 0.5 \times i = \lfloor{0.5 \times i}\rfloor\\ 0.75 \times \tau_{RB}(\lfloor{i\times 0.5}\rfloor,j)[level] + \\ 0.25 \times \tau_{RB}(\lfloor{i\times 0.5}\rfloor + 1,j)[level], & 0.5 \times i \neq \lfloor{0.5 \times i}\rfloor \end{cases} +++++ ** If the format's R and B channels are reduced in resolution in width and height by a factor of two relative to the G channel (i.e. this is a "420" format), a similar relationship applies. Due to the number of options, these formulae are expressed more concisely as follows: + [width="30%",options="header",cols="5,1"] |========== | pname:xChromaOffset | δ~i~ | etext:COSITED_EVEN | 0 | etext:MIDPOINT | 0.5 |========== + [width="30%",options="header",cols="5,1"] |========== | pname:yChromaOffset | δ~j~ | etext:COSITED_EVEN | 0 | etext:MIDPOINT | 0.5 |========== + [latexmath] +++++ \begin{aligned} \tau_{RB}'(i,j) = &\\ &\tau_{RB}(\lfloor 0.5\times(i-\delta_i)\rfloor, \lfloor 0.5\times(j-\delta_j)\rfloor)[level] && \times (1 - (0.5\times(i-\delta_i) - \lfloor 0.5\times(i-\delta_i)\rfloor)) && \times (1 - (0.5\times(j-\delta_j) - \lfloor 0.5\times(j-\delta_j)\rfloor)) +\\ &\tau_{RB}(1+\lfloor 0.5\times(i-\delta_i)\rfloor, \lfloor 0.5\times(j-\delta_j)\rfloor)[level] && \times (0.5\times(i-\delta_i) - \lfloor 0.5\times(i-\delta_i)\rfloor) && \times (1 - (0.5\times(j-\delta_j) - \lfloor 0.5\times(j-\delta_j)\rfloor)) +\\ &\tau_{RB}(\lfloor 0.5\times(i-\delta_i)\rfloor, 1+\lfloor 0.5\times(j-\delta_j)\rfloor)[level] && \times (1 - (0.5\times(i-\delta_i) - \lfloor 0.5\times(i-\delta_i)\rfloor)) && \times (0.5\times(j-\delta_j) - \lfloor 0.5\times(j-\delta_j)\rfloor) +\\ &\tau_{RB}(1+\lfloor 0.5\times(i-\delta_i)\rfloor, 1+\lfloor 0.5\times(j-\delta_j)\rfloor)[level] && \times (0.5\times(i-\delta_i) - \lfloor 0.5\times(i-\delta_i)\rfloor) && \times (0.5\times(j-\delta_j) - \lfloor 0.5\times(j-\delta_j)\rfloor) \end{aligned} +++++ [NOTE] ====== In the case where the texture itself is bilinearly interpolated as described in <>, thus requiring four full-color samples for the filtering operation, and where the reconstruction of these samples uses bilinear interpolation in the chroma channels due to pname:chromaFilter=ename:VK_FILTER_LINEAR, up to nine chroma samples may be required, depending on the sample location. ====== [[textures-implict-reconstruction]] ==== Implicit Reconstruction Implicit reconstruction takes place by the samples being interpolated, as required by the filter settings of the sampler, except that pname:chromaFilter takes precedence for the chroma samples. The sample coordinates are adjusted by the downsample factor of the channel (such that, for example, the sample coordinates are divided by two if the channel has a downsample factor of two relative to the luma channel): [latexmath] ++++++ \begin{aligned} u_{RB}' (422/420) &= \begin{cases} 0.5\times (u + 0.5), & \textrm{xChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5\times u, & \textrm{xChromaOffset = MIDPOINT} \end{cases} \\ v_{RB}' (420) &= \begin{cases} 0.5\times (v + 0.5), & \textrm{yChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5\times v, & \textrm{yChromaOffset = MIDPOINT} \end{cases} \end{aligned} ++++++ [[textures-sampler-YCbCr-conversion]] === Sampler Y'C~B~C~R~ Conversion Sampler Y'C~B~C~R~ conversion performs the following operations, which an implementation may: combine into a single mathematical operation: * <> * <> [[textures-sampler-YCbCr-conversion-rangeexpand]] ==== Sampler Y'C~B~C~R~ Range Expansion Sampler Y'C~B~C~R~ range expansion is applied to color channel values after all texel input operations which are not specific to sampler Y'C~B~C~R~ conversion. For example, the input values to this stage have been converted using the normal <> rules. Sampler Y'C~B~C~R~ range expansion is not applied if pname:ycbcrModel is ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY_KHR. That is, the shader receives the vector C'~rgba~ as output by the Component Swizzle stage without further modification. For other values of pname:ycbcrModel, range expansion is applied to the texel channel values output by the <> defined by the pname:components member of slink:VkSamplerYcbcrConversionCreateInfoKHR. Range expansion applies independently to each channel of the image. For the purposes of range expansion and Y'C~B~C~R~ model conversion, the R and B channels contain color difference (chroma) values and the G channel contains luma. The A channel is not modified by sampler Y'C~B~C~R~ range expansion. The range expansion to be applied is defined by the pname:ycbcrRange member of the sname:VkSamplerYcbcrConversionCreateInfoKHR structure: * If pname:ycbcrRange is ename:VK_SAMPLER_YCBCR_RANGE_ITU_FULL_KHR, the following transformations are applied: + [latexmath] +++++++++++++++++++ \begin{aligned} Y' &= C'_{rgba}[G] \\ C_B &= C'_{rgba}[B] - {{2^{(n-1)}}\over{(2^n) - 1}} \\ C_R &= C'_{rgba}[R] - {{2^{(n-1)}}\over{(2^n) - 1}} \end{aligned} +++++++++++++++++++ + [NOTE] .Note ==== These formulae correspond to the "full range" encoding in the <>. Should any future amendments be made to the ITU specifications from which these equations are derived, the formulae used by Vulkan may: also be updated to maintain parity. ==== * If pname:ycbcrRange is ename:VK_SAMPLER_YCBCR_RANGE_ITU_NARROW_KHR, the following transformations are applied: + [latexmath] +++++++++++++++++++ \begin{aligned} Y' &= {{C'_{rgba}[G] \times (2^n-1) - 16\times 2^{n-8}}\over{219\times 2^{n-8}}} \\ C_B &= {{C'_{rgba}[B] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \\ C_R &= {{C'_{rgba}[R] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \end{aligned} +++++++++++++++++++ + [NOTE] .Note ==== These formulae correspond to the "narrow range" encoding in the <>. ==== * _n_ is the bit-depth of the channels in the format. The precision of the operations performed during range expansion must: be at least that of the source format. An implementation may: clamp the results of these range expansion operations such that Y' falls in the range [0,1], and/or such that C~B~ and C~R~ fall in the range [-0.5,0.5]. [[textures-sampler-YCbCr-conversion-modelconversion]] ==== Sampler Y'C~B~C~R~ Model Conversion The range-expanded values are converted between color models, according to the color model conversion specified in the pname:ycbcrModel member: ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY_KHR:: The color channels are not modified by the color model conversion since they are assumed already to represent the desired color model in which the shader is operating; Y'C~B~C~R~ range expansion is also ignored. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_IDENTITY_KHR:: The color channels are not modified by the color model conversion and are assumed to be treated as though in Y'C~B~C~R~ form both in memory and in the shader; Y'C~B~C~R~ range expansion is applied to the channels as for other Y'C~B~C~R~ models, with the vector (C~R~,Y',C~B~,A) provided to the shader. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_709_KHR:: The color channels are transformed from a Y'C~B~C~R~ representation to an R'G'B' representation as described in the "BT.709 Y'C~B~C~R~ conversion" section of the <>. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_601_KHR:: The color channels are transformed from a Y'C~B~C~R~ representation to an R'G'B' representation as described in the "BT.601 Y'C~B~C~R~ conversion" section of the <>. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_2020_KHR:: The color channels are transformed from a Y'C~B~C~R~ representation to an R'G'B' representation as described in the "BT.2020 Y'C~B~C~R~ conversion" section of the <>. In this operation, each output channel is dependent on each input channel. An implementation may: clamp the R'G'B' results of these conversions to the range [0,1]. The precision of the operations performed during model conversion must: be at least that of the source format. The alpha channel is not modified by these model conversions. [NOTE] .Note ==== Sampling operations in a non-linear color space can introduce color and intensity shifts at sharp transition boundaries. To avoid this issue, the technically precise color correction sequence described in the "Introduction to Color Conversions" chapter of the <> may be performed as follows: * Calculate the <> corresponding to the desired sample position. * For a pname:minFilter/pname:magFilter of ename:VK_FILTER_NEAREST: . Calculate (_i_,_j_) for the sample location as described under the "nearest filtering" formulae in <> . Calculate the normalized texel coordinates corresponding to these integer coordinates. . Sample using <> at this location. * For a pname:minFilter/pname:magFilter of ename:VK_FILTER_LINEAR: . Calculate (_i~[0,1]~_,_j~[0,1]~_) for the sample location as described under the "linear filtering" formulae in <> . Calculate the normalized texel coordinates corresponding to these integer coordinates. . Sample using <> at each of these locations. . Convert the non-linear AR'G'B' outputs of the Y'C~B~C~R~ conversions to linear ARGB values as described in the "Transfer Functions" chapter of the <>. . Interpolate the linear ARGB values using the [eq]#{alpha}# and [eq]#{beta}# values described in the "linear filtering" section of <> and the equations in <>. The additional calculations and, especially, additional number of sampling operations in the ename:VK_FILTER_LINEAR case can be expected to have a performance impact compared with using the outputs directly; since the variation from "correct" results are subtle for most content, the application author should determine whether a more costly implementation is strictly necessary. Note that if pname:chromaFilter and pname:minFilter/pname:magFilter are both ename:VK_FILTER_NEAREST, these operations are redundant and sampling using <> at the desired sample coordinates will produce the "correct" results without further processing. ==== endif::VK_KHR_sampler_ycbcr_conversion[] == Texel Output Operations _Texel output instructions_ are SPIR-V image instructions that write to an image. _Texel output operations_ are a set of steps that are performed on state, coordinates, and texel values while processing a texel output instruction, and which are common to some or all texel output instructions. They include the following steps, which are performed in the listed order: * <> ** <> ** <> ** <> * <> [[textures-output-validation]] === Texel Output Validation Operations _Texel output validation operations_ inspect instruction/image state or coordinates, and in certain circumstances cause the write to have no effect. There are a series of validations that the texel undergoes. [[textures-format-validation]] ==== Texel Format Validation If the image format of the code:OpTypeImage is not compatible with the sname:VkImageView's pname:format, the effect of the write on the image view's memory is undefined, but the write must: not access memory outside of the image view. [[textures-output-coordinate-validation]] === Integer Texel Coordinate Validation The integer texel coordinates are validated according to the same rules as for texel input <>. If the texel fails integer texel coordinate validation, then the write has no effect. [[textures-output-sparse-validation]] === Sparse Texel Operation If the texel attempts to write to an unbound region of a sparse image, the texel is a sparse unbound texel. In such a case, if the slink:VkPhysicalDeviceSparseProperties::pname:residencyNonResidentStrict property is ename:VK_TRUE, the sparse unbound texel write has no effect. If pname:residencyNonResidentStrict is ename:VK_FALSE, the effect of the write is undefined but must: be safe. In addition, the write may: have a side effect that is visible to other image instructions, but must: not be written to any device memory allocation. [[textures-output-format-conversion]] === Texel Output Format Conversion Texels undergo a format conversion from the floating point, signed, or unsigned integer type of the texel data to the elink:VkFormat of the image view. Any unused components are ignored. Each component is converted based on its type and size (as defined in the <> section for each elink:VkFormat), using the appropriate equations in <> and <>. == Derivative Operations SPIR-V derivative instructions include code:OpDPdx, code:OpDPdy, code:OpDPdxFine, code:OpDPdyFine, code:OpDPdxCoarse, and code:OpDPdyCoarse. Derivative instructions are only available in a fragment shader. image::images/vulkantexture2.png[align="center",title="Implicit Derivatives",{fullimagewidth}] Derivatives are computed as if there is a 2{times}2 neighborhood of fragments for each fragment shader invocation. These neighboring fragments are used to compute derivatives with the assumption that the values of P in the neighborhood are piecewise linear. It is further assumed that the values of P in the neighborhood are locally continuous, therefore derivatives in non-uniform control flow are undefined. [latexmath] +++++++++++++++++++ \begin{aligned} dPdx_{i_1,j_0} & = dPdx_{i_0,j_0} & = P_{i_1,j_0} - P_{i_0,j_0} \\ dPdx_{i_1,j_1} & = dPdx_{i_0,j_1} & = P_{i_1,j_1} - P_{i_0,j_1} \\ \\ dPdy_{i_0,j_1} & = dPdy_{i_0,j_0} & = P_{i_0,j_1} - P_{i_0,j_0} \\ dPdy_{i_1,j_1} & = dPdy_{i_1,j_0} & = P_{i_1,j_1} - P_{i_1,j_0} \end{aligned} +++++++++++++++++++ The code:Fine derivative instructions must: return the values above, for a group of fragments in a 2{times}2 neighborhood. Coarse derivatives may: return only two values. In this case, the values should: be: [latexmath] +++++++++++++++++++ \begin{aligned} dPdx & = \begin{cases} dPdx_{i_0,j_0} & \text{preferred}\\ dPdx_{i_0,j_1} \end{cases} \\ dPdy & = \begin{cases} dPdy_{i_0,j_0} & \text{preferred}\\ dPdy_{i_1,j_0} \end{cases} \end{aligned} +++++++++++++++++++ code:OpDPdx and code:OpDPdy must: return the same result as either code:OpDPdxFine or code:OpDPdxCoarse and either code:OpDPdyFine or code:OpDPdyCoarse, respectively. Implementations must: make the same choice of either coarse or fine for both code:OpDPdx and code:OpDPdy, and implementations should: make the choice that is more efficient to compute. ifdef::VK_KHR_sampler_ycbcr_conversion[] For multi-planar formats, the derivatives are computed based on the plane with the largest dimensions. endif::VK_KHR_sampler_ycbcr_conversion[] [[textures-normalized-operations]] == Normalized Texel Coordinate Operations If the image sampler instruction provides normalized texel coordinates, some of the following operations are performed. [[textures-projection]] === Projection Operation For code:Proj image operations, the normalized texel coordinates [eq]#(s,t,r,q,a)# and (if present) the [eq]#D~ref~# coordinate are transformed as follows: [latexmath] +++++++++++++++++++ \begin{aligned} s & = \frac{s}{q}, & \text{for 1D, 2D, or 3D image} \\ \\ t & = \frac{t}{q}, & \text{for 2D or 3D image} \\ \\ r & = \frac{r}{q}, & \text{for 3D image} \\ \\ D_{\textit{ref}} & = \frac{D_{\textit{ref}}}{q}, & \text{if provided} \end{aligned} +++++++++++++++++++ === Derivative Image Operations Derivatives are used for LOD selection. These derivatives are either implicit (in an code:ImplicitLod image instruction in a fragment shader) or explicit (provided explicitly by shader to the image instruction in any shader). For implicit derivatives image instructions, the derivatives of texel coordinates are calculated in the same manner as derivative operations above. That is: [latexmath] +++++++++++++++++++ \begin{aligned} \partial{s}/\partial{x} & = dPdx(s), & \partial{s}/\partial{y} & = dPdy(s), & \text{for 1D, 2D, Cube, or 3D image} \\ \partial{t}/\partial{x} & = dPdx(t), & \partial{t}/\partial{y} & = dPdy(t), & \text{for 2D, Cube, or 3D image} \\ \partial{u}/\partial{x} & = dPdx(u), & \partial{u}/\partial{y} & = dPdy(u), & \text{for Cube or 3D image} \end{aligned} +++++++++++++++++++ Partial derivatives not defined above for certain image dimensionalities are set to zero. For explicit LOD image instructions, if the optional: SPIR-V operand [eq]#Grad# is provided, then the operand values are used for the derivatives. The number of components present in each derivative for a given image dimensionality matches the number of partial derivatives computed above. If the optional: SPIR-V operand [eq]#Lod# is provided, then derivatives are set to zero, the cube map derivative transformation is skipped, and the scale factor operation is skipped. Instead, the floating point scalar coordinate is directly assigned to [eq]#{lambda}~base~# as described in <>. === Cube Map Face Selection and Transformations For cube map image instructions, the [eq]#(s,t,r)# coordinates are treated as a direction vector [eq]#(r~x~,r~y~,r~z~)#. The direction vector is used to select a cube map face. The direction vector is transformed to a per-face texel coordinate system [eq]#(s~face~,t~face~)#, The direction vector is also used to transform the derivatives to per-face derivatives. === Cube Map Face Selection The direction vector selects one of the cube map's faces based on the largest magnitude coordinate direction (the major axis direction). Since two or more coordinates can: have identical magnitude, the implementation must: have rules to disambiguate this situation. The rules should: have as the first rule that [eq]#r~z~# wins over [eq]#r~y~# and [eq]#r~x~#, and the second rule that [eq]#r~y~# wins over [eq]#r~x~#. An implementation may: choose other rules, but the rules must: be deterministic and depend only on [eq]#(r~x~,r~y~,r~z~)#. The layer number (corresponding to a cube map face), the coordinate selections for [eq]#s~c~#, [eq]#t~c~#, [eq]#r~c~#, and the selection of derivatives, are determined by the major axis direction as specified in the following two tables. .Cube map face and coordinate selection [width="75%",frame="all",options="header"] |==== | Major Axis Direction | Layer Number | Cube Map Face | [eq]#s~c~# | [eq]#t~c~# | [eq]#r~c~# | [eq]#+r~x~# | [eq]#0# | Positive X | [eq]#-r~z~# | [eq]#-r~y~# | [eq]#r~x~# | [eq]#-r~x~# | [eq]#1# | Negative X | [eq]#+r~z~# | [eq]#-r~y~# | [eq]#r~x~# | [eq]#+r~y~# | [eq]#2# | Positive Y | [eq]#+r~x~# | [eq]#+r~z~# | [eq]#r~y~# | [eq]#-r~y~# | [eq]#3# | Negative Y | [eq]#+r~x~# | [eq]#-r~z~# | [eq]#r~y~# | [eq]#+r~z~# | [eq]#4# | Positive Z | [eq]#+r~x~# | [eq]#-r~y~# | [eq]#r~z~# | [eq]#-r~z~# | [eq]#5# | Negative Z | [eq]#-r~x~# | [eq]#-r~y~# | [eq]#r~z~# |==== .Cube map derivative selection [width="75%",frame="all",options="header"] |==== | Major Axis Direction | [eq]#{partial}s~c~ / {partial}x# | [eq]#{partial}s~c~ / {partial}y# | [eq]#{partial}t~c~ / {partial}x# | [eq]#{partial}t~c~ / {partial}y# | [eq]#{partial}r~c~ / {partial}x# | [eq]#{partial}r~c~ / {partial}y# | [eq]#+r~x~# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-r~x~# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#-{partial}r~x~ / {partial}x# | [eq]#-{partial}r~x~ / {partial}y# | [eq]#+r~y~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#+{partial}r~y~ / {partial}x# | [eq]#+{partial}r~y~ / {partial}y# | [eq]#-r~y~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+r~z~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#-r~z~# | [eq]#-{partial}r~x~ / {partial}x# | [eq]#-{partial}r~x~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# |==== === Cube Map Coordinate Transformation [latexmath] ++++++++++++++++++++++++ \begin{aligned} s_{\textit{face}} & = \frac{1}{2} \times \frac{s_c}{|r_c|} + \frac{1}{2} \\ t_{\textit{face}} & = \frac{1}{2} \times \frac{t_c}{|r_c|} + \frac{1}{2} \\ \end{aligned} ++++++++++++++++++++++++ === Cube Map Derivative Transformation [latexmath] ++++++++++++++++++++++++ \begin{aligned} \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{\partial}{\partial{x}} \left ( \frac{1}{2} \times \frac{s_{c}}{|r_{c}|} + \frac{1}{2}\right ) \\ \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \frac{\partial}{\partial{x}} \left ( \frac{s_{c}}{|r_{c}|} \right ) \\ \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{s_c}/\partial{x} -s_c \times {\partial{r_{c}}}/{\partial{x}}} {\left ( r_{c} \right )^2} \right ) \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \frac{\partial{s_{\textit{face}}}}{\partial{y}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{s_c}/\partial{y} -s_c \times {\partial{r_{c}}}/{\partial{y}}} {\left ( r_{c} \right )^2} \right )\\ \frac{\partial{t_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{t_c}/\partial{x} -t_c \times {\partial{r_{c}}}/{\partial{x}}} {\left ( r_{c} \right )^2} \right ) \\ \frac{\partial{t_{\textit{face}}}}{\partial{y}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{t_c}/\partial{y} -t_c \times {\partial{r_{c}}}/{\partial{y}}} {\left ( r_{c} \right )^2} \right ) \end{aligned} ++++++++++++++++++++++++ ifdef::editing-notes[] [NOTE] .editing-note ================== (Bill) Note that we never revisited ARB_texture_cubemap after we introduced dependent texture fetches (ARB_fragment_program and ARB_fragment_shader). The derivatives of [eq]#s~face~# and [eq]#t~face~# are only valid for non-dependent texture fetches (pre OpenGL 2.0). ================== endif::editing-notes[] === Scale Factor Operation, Level-of-Detail Operation and Image Level(s) Selection LOD selection can: be either explicit (provided explicitly by the image instruction) or implicit (determined from a scale factor calculated from the derivatives). The implicit LOD selected can: be queried using the SPIR-V instruction code:OpImageQueryLod, which gives access to the [eq]#{lambda}#' and [eq]#d~l~# values, defined below. [[textures-scale-factor]] ==== Scale Factor Operation The magnitude of the derivatives are calculated by: :: [eq]#m~ux~ = {vert}{partial}s/{partial}x{vert} {times} w~base~# :: [eq]#m~vx~ = {vert}{partial}t/{partial}x{vert} {times} h~base~# :: [eq]#m~wx~ = {vert}{partial}r/{partial}x{vert} {times} d~base~# :: [eq]#m~uy~ = {vert}{partial}s/{partial}y{vert} {times} w~base~# :: [eq]#m~vy~ = {vert}{partial}t/{partial}y{vert} {times} h~base~# :: [eq]#m~wy~ = {vert}{partial}r/{partial}y{vert} {times} d~base~# where: :: [eq]#{partial}t/{partial}x = {partial}t/{partial}y = 0# (for 1D images) :: [eq]#{partial}r/{partial}x = {partial}r/{partial}y = 0# (for 1D, 2D or Cube images) and :: [eq]#w~base~ = image.w# :: [eq]#h~base~ = image.h# :: [eq]#d~base~ = image.d# (for the pname:baseMipLevel, from the image descriptor). A point sampled in screen space has an elliptical footprint in texture space. The minimum and maximum scale factors [eq]#({rho}~min~, {rho}~max~)# should: be the minor and major axes of this ellipse. The _scale factors_ [eq]#{rho}~x~# and [eq]#{rho}~y~#, calculated from the magnitude of the derivatives in x and y, are used to compute the minimum and maximum scale factors. [eq]#{rho}~x~# and [eq]#{rho}~y~# may: be approximated with functions [eq]#f~x~# and [eq]#f~y~#, subject to the following constraints: [latexmath] ++++++++++++++++++++++++ \begin{aligned} & f_x \text{\ is\ continuous\ and\ monotonically\ increasing\ in\ each\ of\ } m_{ux}, m_{vx}, \text{\ and\ } m_{wx} \\ & f_y \text{\ is\ continuous\ and\ monotonically\ increasing\ in\ each\ of\ } m_{uy}, m_{vy}, \text{\ and\ } m_{wy} \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \max(|m_{ux}|, |m_{vx}|, |m_{wx}|) \leq f_{x} \leq \sqrt{2} (|m_{ux}| + |m_{vx}| + |m_{wx}|) \\ \max(|m_{uy}|, |m_{vy}|, |m_{wy}|) \leq f_{y} \leq \sqrt{2} (|m_{uy}| + |m_{vy}| + |m_{wy}|) \end{aligned} ++++++++++++++++++++++++ ifdef::editing-notes[] [NOTE] .editing-note ================== (Bill) For reviewers only - anticipating questions. We only support implicit derivatives for normalized texel coordinates. So we are documenting the derivatives in s,t,r (normalized texel coordinates) rather than u,v,w (unnormalized texel coordinates) as in OpenGL and OpenGL ES specifications. (I know, u,v,w is the way it has been documented since OpenGL V1.0.) Also there is no reason to have conditional application of [eq]#w~base~, h~base~, d~base~# for rectangle textures either, since they do not support implicit derivatives. ================== endif::editing-notes[] The minimum and maximum scale factors [eq]#({rho}~min~,{rho}~max~)# are determined by: :: [eq]#{rho}~max~ = max({rho}~x~, {rho}~y~)# :: [eq]#{rho}~min~ = min({rho}~x~, {rho}~y~)# The sampling rate is determined by: [latexmath] ++++++++++++++++++++++++ \begin{aligned} N & = \min \left (\left \lceil \rho_{max}/\rho_{min} \right \rceil ,max_{Aniso} \right ) \end{aligned} ++++++++++++++++++++++++ where: :: [eq]#sampler.max~Aniso~ = pname:maxAnisotropy# (from sampler descriptor) :: [eq]#limits.max~Aniso~ = pname:maxSamplerAnisotropy# (from physical device limits) :: [eq]#max~Aniso~ = min(sampler.max~Aniso~, limits.max~Aniso~)# If [eq]#{rho}~max~ = {rho}~min~ = 0#, then all the partial derivatives are zero, the fragment's footprint in texel space is a point, and [eq]#N# should: be treated as 1. If [eq]#{rho}~max~ {neq} 0# and [eq]#{rho}~min~ = 0# then all partial derivatives along one axis are zero, the fragment's footprint in texel space is a line segment, and [eq]#N# should: be treated as [eq]#max~Aniso~#. However, anytime the footprint is small in texel space the implementation may: use a smaller value of [eq]#N#, even when [eq]#{rho}~min~# is zero or close to zero. An implementation may: round [eq]#N# up to the nearest supported sampling rate. If [eq]#N = 1#, sampling is isotropic. If [eq]#N > 1#, sampling is anisotropic. [[textures-level-of-detail-operation]] ==== Level-of-Detail Operation The LOD parameter [eq]#{lambda}# is computed as follows: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \lambda_{base}(x,y) & = \begin{cases} shaderOp.Lod & \text{(from optional: SPIR-V operand)} \\ \log_2 \left ( \frac{\rho_{max}}{N} \right ) & \text{otherwise} \end{cases} \\ \lambda'(x,y) & = \lambda_{base} + \mathbin{clamp}(sampler.bias + shaderOp.bias,-maxSamplerLodBias,maxSamplerLodBias) \\ \lambda & = \begin{cases} lod_{max}, & \lambda' > lod_{max} \\ \lambda', & lod_{min} \leq \lambda' \leq lod_{max} \\ lod_{min}, & \lambda' < lod_{min} \\ \textit{undefined}, & lod_{min} > lod_{max} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} sampler.bias & = mipLodBias & \text{(from sampler descriptor)} \\ shaderOp.bias & = \begin{cases} Bias & \text{(from optional: SPIR-V operand)} \\ 0 & \text{otherwise} \end{cases} \\ sampler.lod_{min} & = minLod & \text{(from sampler descriptor)} \\ shaderOp.lod_{min} & = \begin{cases} MinLod & \text{(from optional: SPIR-V operand)} \\ 0 & \text{otherwise} \end{cases} \\ \\ lod_{min} & = \max(sampler.lod_{min}, shaderOp.lod_{min}) \\ lod_{max} & = maxLod & \text{(from sampler descriptor)} \end{aligned} ++++++++++++++++++++++++ and [eq]#maxSamplerLodBias# is the value of the slink:VkPhysicalDeviceLimits feature <>. [[textures-image-level-selection]] ==== Image Level(s) Selection The image level(s) [eq]#d#, [eq]#d~hi~#, and [eq]#d~lo~# which texels are read from are determined by an image-level parameter [eq]#d~l~#, which is computed based on the LOD parameter, as follows: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d_{l} = \begin{cases} nearest(d'), & \text{mipmapMode is VK_SAMPLER_MIPMAP_MODE_NEAREST} \\ d', & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d' = level_{base} + \text{clamp}(\lambda, 0, q) \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} nearest(d') & = \begin{cases} \left \lceil d' + 0.5\right \rceil - 1, & \text{preferred} \\ \left \lfloor d' + 0.5\right \rfloor, & \text{alternative} \end{cases} \end{aligned} ++++++++++++++++++++++++ and :: [eq]#level~base~ = pname:baseMipLevel# :: [eq]#q = pname:levelCount - 1# pname:baseMipLevel and pname:levelCount are taken from the pname:subresourceRange of the image view. If the sampler's pname:mipmapMode is ename:VK_SAMPLER_MIPMAP_MODE_NEAREST, then the level selected is [eq]#d = d~l~#. If the sampler's pname:mipmapMode is ename:VK_SAMPLER_MIPMAP_MODE_LINEAR, two neighboring levels are selected: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d_{hi} & = \lfloor d_{l} \rfloor \\ d_{lo} & = min( d_{hi} + 1, q ) \\ \delta & = d_{l} - d_{hi} \end{aligned} ++++++++++++++++++++++++ [eq]#{delta}# is the fractional value used for <> between levels. [[textures-normalized-to-unnormalized]] === (s,t,r,q,a) to (u,v,w,a) Transformation The normalized texel coordinates are scaled by the image level dimensions and the array layer is selected. This transformation is performed once for each level ([eq]#d# or [eq]#d~hi~# and [eq]#d~lo~#) used in <>. [latexmath] ++++++++++++++++++++++++ \begin{aligned} u(x,y) & = s(x,y) \times width_{level} \\ v(x,y) & = \begin{cases} 0 & \text{for 1D images} \\ t(x,y) \times height_{level} & \text{otherwise} \end{cases} \\ w(x,y) & = \begin{cases} 0 & \text{for 2D or Cube images} \\ r(x,y) \times depth_{level} & \text{otherwise} \end{cases} \\ \\ a(x,y) & = \begin{cases} a(x,y) & \text{for array images} \\ 0 & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ Operations then proceed to Unnormalized Texel Coordinate Operations. == Unnormalized Texel Coordinate Operations [[textures-unnormalized-to-integer]] === (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 [eq]#l# is computed as: :: [eq]#l = clamp(RNE(a), 0, pname:layerCount - 1) {plus} pname:baseArrayLayer# where pname:layerCount is the number of layers in the image subresource range of the image view, pname:baseArrayLayer is the first layer from the subresource range, and where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \mathbin{RNE}(a) & = \begin{cases} \mathbin{roundTiesToEven}(a) & \text{preferred, from IEEE Std 754-2008 Floating-Point Arithmetic} \\ \left \lfloor a + 0.5 \right \rfloor & \text{alternative} \end{cases} \end{aligned} ++++++++++++++++++++++++ The sample index n is assigned the value zero. Nearest filtering (ename:VK_FILTER_NEAREST) computes the integer texel coordinates that the unnormalized coordinates lie within: [latexmath] ++++++++++++++++++++++++ \begin{aligned} i &= \lfloor u \rfloor \\ j &= \lfloor v \rfloor \\ k &= \lfloor w \rfloor \end{aligned} ++++++++++++++++++++++++ Linear filtering (ename:VK_FILTER_LINEAR) computes a set of neighboring coordinates which bound the unnormalized coordinates. The integer texel coordinates are combinations of [eq]#i~0~# or [eq]#i~1~#, [eq]#j~0~# or [eq]#j~1~#, [eq]#k~0~# or [eq]#k~1~#, as well as weights [eq]#{alpha}, {beta}#, and [eq]#{gamma}#. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_0 &= \lfloor u - 0.5 \rfloor \\ i_1 &= i_0 + 1 \\ j_0 &= \lfloor v - 0.5 \rfloor \\ j_1 &= j_0 + 1 \\ k_0 &= \lfloor w - 0.5 \rfloor \\ k_1 &= k_0 + 1 \\ \alpha &= \left(u - 0.5\right) - i_0 \\ \beta &= \left(v - 0.5\right) - j_0 \\ \gamma &= \left(w - 0.5\right) - k_0 \end{aligned} ++++++++++++++++++++++++ ifdef::VK_IMG_filter_cubic[] include::VK_IMG_filter_cubic/filter_cubic_texel_selection.txt[] endif::VK_IMG_filter_cubic[] If the image instruction includes a [eq]#ConstOffset# operand, the constant offsets [eq]#({DeltaUpper}~i~, {DeltaUpper}~j~, {DeltaUpper}~k~)# are added to [eq]#(i,j,k)# components of the integer texel coordinates. [[textures-sample-operations]] == Image Sample Operations [[textures-wrapping-operation]] === Wrapping Operation code:Cube images ignore the wrap modes specified in the sampler. Instead, if ename:VK_FILTER_NEAREST is used within a mip level then ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE is used, and if ename:VK_FILTER_LINEAR is used within a mip level then sampling at the edges is performed as described earlier in the <> section. The first integer texel coordinate i is transformed based on the pname:addressModeU parameter of the sampler. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i &= \begin{cases} i \bmod size & \text{for repeat} \\ (size - 1) - \mathbin{mirror} ((i \bmod (2 \times size)) - size) & \text{for mirrored repeat} \\ \mathbin{clamp}(i,0,size-1) & \text{for clamp to edge} \\ \mathbin{clamp}(i,-1,size) & \text{for clamp to border} \\ \mathbin{clamp}(\mathbin{mirror}(i),0,size-1) & \text{for mirror clamp to edge} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} & \mathbin{mirror}(n) = \begin{cases} n & \text{for}\ n \geq 0 \\ -(1+n) & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ [eq]#j# (for 2D and Cube image) and [eq]#k# (for 3D image) are similarly transformed based on the pname:addressModeV and pname:addressModeW parameters of the sampler, respectively. [[textures-gather]] === Texel Gathering SPIR-V instructions with code:Gather in the name return a vector derived from a 2{times}2 rectangular region of texels in the base level of the image view. The rules for the ename:VK_FILTER_LINEAR minification filter are applied to identify the four selected texels. Each texel is then converted to an RGBA value according to <> and then <>. A four-component vector is then assembled by taking the component indicated by the code:Component value in the instruction from the swizzled color value of the four texels: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[R] &= \tau_{i0j1}[level_{base}][comp] \\ \tau[G] &= \tau_{i1j1}[level_{base}][comp] \\ \tau[B] &= \tau_{i1j0}[level_{base}][comp] \\ \tau[A] &= \tau_{i0j0}[level_{base}][comp] \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[level_{base}][comp] &= \begin{cases} \tau[level_{base}][R], & \text{for}\ comp = 0 \\ \tau[level_{base}][G], & \text{for}\ comp = 1 \\ \tau[level_{base}][B], & \text{for}\ comp = 2 \\ \tau[level_{base}][A], & \text{for}\ comp = 3 \end{cases}\\ comp & \,\text{from SPIR-V operand Component} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_KHR_sampler_ycbcr_conversion[] code:OpImage*Gather must: not be used on a sampled image with <> enabled. endif::VK_KHR_sampler_ycbcr_conversion[] [[textures-texel-filtering]] === Texel Filtering If [eq]#{lambda}# is less than or equal to zero, the texture is said to be _magnified_, and the filter mode within a mip level is selected by the pname:magFilter in the sampler. If [eq]#{lambda}# is greater than zero, the texture is said to be _minified_, and the filter mode within a mip level is selected by the pname:minFilter in the sampler. Within a mip level, ename:VK_FILTER_NEAREST filtering selects a single value using the [eq]#(i, j, k)# texel coordinates, with all texels taken from layer l. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[level] &= \begin{cases} \tau_{ijk}[level], & \text{for 3D image} \\ \tau_{ij}[level], & \text{for 2D or Cube image} \\ \tau_{i}[level], & \text{for 1D image} \end{cases} \end{aligned} ++++++++++++++++++++++++ Within a mip level, ename:VK_FILTER_LINEAR filtering combines 8 (for 3D), 4 (for 2D or Cube), or 2 (for 1D) texel values, using the weights computed earlier: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{3D}[level] & = reduce((1-\alpha)(1-\beta)(1-\gamma),\tau_{i0j0k0}[level], \\ & \, (\alpha)(1-\beta)(1-\gamma),\tau_{i1j0k0}[level], \\ & \, (1-\alpha)(\beta)(1-\gamma),\tau_{i0j1k0}[level], \\ & \, (\alpha)(\beta)(1-\gamma),\tau_{i1j1k0}[level], \\ & \, (1-\alpha)(1-\beta)(\gamma),\tau_{i0j0k1}[level], \\ & \, (\alpha)(1-\beta)(\gamma),\tau_{i1j0k1}[level], \\ & \, (1-\alpha)(\beta)(\gamma),\tau_{i0j1k1}[level], \\ & \, (\alpha)(\beta)(\gamma),\tau_{i1j1k1}[level]) \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{2D}[level] & = reduce((1-\alpha)(1-\beta),\tau_{i0j0}[level], \\ & \, (\alpha)(1-\beta),\tau_{i1j0}[level], \\ & \, (1-\alpha)(\beta),\tau_{i0j1}[level], \\ & \, (\alpha)(\beta),\tau_{i1j1}[level]) \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{1D}[level] & = reduce((1-\alpha),\tau_{i0}[level], \\ & \, (\alpha),\tau_{i1}[level]) \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[level] &= \begin{cases} \tau_{3D}[level], & \text{for 3D image} \\ \tau_{2D}[level], & \text{for 2D or Cube image} \\ \tau_{1D}[level], & \text{for 1D image} \end{cases} \end{aligned} ++++++++++++++++++++++++ The function [eq]#reduce()# is defined to operate on pairs of weights and texel values as follows. When using linear or anisotropic filtering, the values of multiple texels are combined using a weighted average to produce a filtered texture value. ifdef::VK_EXT_sampler_filter_minmax[] However, a filtered texture value can: also be produced by computing per-component minimum and maximum values over the set of texels that would normally be averaged. The slink:VkSamplerReductionModeCreateInfoEXT::pname:reductionMode controls the process by which multiple texels are combined to produce a filtered texture value. When set to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE_EXT, a weighted average is computed. If the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN_EXT or ename:VK_SAMPLER_REDUCTION_MODE_MAX_EXT, reduce() computes a component-wise minimum or maximum, respectively, of the components of the set of provided texels with non-zero weights. endif::VK_EXT_sampler_filter_minmax[] ifdef::VK_IMG_filter_cubic[] include::VK_IMG_filter_cubic/filter_cubic_texel_filtering.txt[] endif::VK_IMG_filter_cubic[] Finally, mipmap filtering either selects a value from one mip level or computes a weighted average between neighboring mip levels: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau &= \begin{cases} \tau[d], & \text{for mip mode BASE or NEAREST} \\ reduce((1-\delta),\tau[d_{hi}],\delta,\tau[d_{lo}]), & \text{for mip mode LINEAR} \end{cases} \end{aligned} ++++++++++++++++++++++++ [[textures-texel-anisotropic-filtering]] === Texel Anisotropic Filtering Anisotropic filtering is enabled by the pname:anisotropyEnable in the sampler. When enabled, the image filtering scheme accounts for a degree of anisotropy. The particular scheme for anisotropic texture filtering is implementation dependent. Implementations should: consider the pname:magFilter, pname:minFilter and pname:mipmapMode of the sampler to control the specifics of the anisotropic filtering scheme used. In addition, implementations should: consider pname:minLod and pname:maxLod of the sampler. The following describes one particular approach to implementing anisotropic filtering for the 2D Image case, implementations may: choose other methods: Given a pname:magFilter, pname:minFilter of ename:VK_FILTER_LINEAR and a pname:mipmapMode of ename:VK_SAMPLER_MIPMAP_MODE_NEAREST: Instead of a single isotropic sample, N isotropic samples are be sampled within the image footprint of the image level [eq]#d# to approximate an anisotropic filter. The sum [eq]#{tau}~2Daniso~# is defined using the single isotropic [eq]#{tau}~2D~(u,v)# at level [eq]#d#. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{2Daniso} & = \frac{1}{N}\sum_{i=1}^{N} {\tau_{2D}\left ( u \left ( x - \frac{1}{2} + \frac{i}{N+1} , y \right ), \left ( v \left (x-\frac{1}{2}+\frac{i}{N+1} \right ), y \right ) \right )}, & \text{when}\ \rho_{x} > \rho_{y} \\ \tau_{2Daniso} &= \frac{1}{N}\sum_{i=1}^{N} {\tau_{2D}\left ( u \left ( x, y - \frac{1}{2} + \frac{i}{N+1} \right ), \left ( v \left (x,y-\frac{1}{2}+\frac{i}{N+1} \right ) \right ) \right )}, & \text{when}\ \rho_{y} \geq \rho_{x} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_EXT_sampler_filter_minmax[] When slink:VkSamplerReductionModeCreateInfoEXT::pname:reductionMode is set to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE_EXT, the above summation is used. If the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN_EXT or ename:VK_SAMPLER_REDUCTION_MODE_MAX_EXT, then the value is instead computed as [eq]#\tau_{2Daniso} = reduce(\tau_1, ..., \tau_N)#, combining all texel values with non-zero weights. endif::VK_EXT_sampler_filter_minmax[] [[textures-instructions]] == Image Operation Steps Each step described in this chapter is performed by a subset of the image instructions: * Texel Input Validation Operations, Format Conversion, Texel Replacement, Conversion to RGBA, and Component Swizzle: Performed by all instructions except code:OpImageWrite. * Depth Comparison: Performed by code:OpImage*code:Dref instructions. * All Texel output operations: Performed by code:OpImageWrite. * Projection: Performed by all code:OpImage*code:Proj instructions. * Derivative Image Operations, Cube Map Operations, Scale Factor Operation, Level-of-Detail Operation and Image Level(s) Selection, and Texel Anisotropic Filtering: Performed by all code:OpImageSample* and code:OpImageSparseSample* instructions. * (s,t,r,q,a) to (u,v,w,a) Transformation, Wrapping, and (u,v,w,a) to (i,j,k,l,n) Transformation And Array Layer Selection: Performed by all code:OpImageSample, code:OpImageSparseSample, and code:OpImage*code:Gather instructions. * Texel Gathering: Performed by code:OpImage*code:Gather instructions. * Texel Filtering: Performed by all code:OpImageSample* and code:OpImageSparseSample* instructions. * Sparse Residency: Performed by all code:OpImageSparse* instructions.