In this second a part of our deeper take a look at 3D recreation rendering, we’ll be focusing what occurs to the 3D world after the entire vertex processing has completed. We’ll must mud off our math textbooks once more, grapple with the geometry of frustums, and ponder the puzzle of views. We’ll additionally take a fast dive into the physics of ray tracing, lighting and supplies — glorious!

The fundamental matter of this text is about an vital stage in rendering, the place a 3 dimensional world of factors, strains, and triangles turns into a two dimensional grid of coloured blocks. This may be very a lot one thing that simply ‘occurs’, because the processes concerned within the 3D-to-2D change happen unseen, not like with our earlier article the place we might instantly see the consequences of vertex shaders and tessellation. If you are not prepared for all of this, don’t be concerned — you will get began with our 3D Game Rendering 101. But when you’re set, learn on our for our subsequent take a look at the world of 3D graphics.

Getting prepared for two dimensions

The overwhelming majority of you’ll be taking a look at this web site on a completely flat monitor or smartphone display screen; even in the event you’re cool and down with the children, and have a flowery curved monitor, the pictures it is displaying encompass a flat grid of coloured pixels. And but, whenever you’re enjoying the newest Call of Mario: Deathduty Battleyard, the pictures seem like Three dimensional. Objects transfer out and in of the atmosphere, changing into bigger or smaller, as they transfer to and from the digital camera.

Using Bethesda’s Fallout Four from 2014 for instance, we are able to simply see how the vertices have been processed to create the sense of depth and distance, particularly if run it in wireframe mode (above).

If you decide any 3D recreation of at present, or the previous 2 many years, virtually each single one among them will carry out the identical sequence of occasions to transform the 3D world of the vertices into the 2D array of pixels. The title for the method that does the change usually will get referred to as rasterization however that is simply one of many many steps in the entire shebang.

We’ll want to interrupt down the a few of varied levels and look at the methods and math employed, and for reference, we’ll use the sequence as utilized by Direct3D, to research what is going on on. The picture beneath units out what will get finished to every vertex on this planet:

We noticed what was finished on this planet house stage in our Part 1 article: right here the vertices are reworked and coloured in, utilizing quite a few matrix calculations. We’ll skip over the following part as a result of all that occurs for digital camera house is that the reworked vertices are adjusted after they have been moved, to make the digital camera the reference level.

The subsequent steps are too vital to skip, although, as a result of they’re completely crucial to creating the change from 3D to 2D — finished proper, and our brains will take a look at a flat display screen however ‘see’ a scene that has depth and scale — finished flawed, and issues will look very odd!

It’s all a matter of perspective

The first step on this sequence entails defining the sphere of view, as seen by the digital camera. This is completed by first setting the angles for the horizontal and vertical subject of views — the primary one can usually be modified in video games, as people have higher side-to-side peripheral imaginative and prescient in comparison with up-and-down.

We can get a way of this from this picture that exhibits the sphere of human imaginative and prescient:

The two subject of view angles (fov, for brief) outline the form of a frustum – a 3D square-based pyramid, that emanates from the digital camera. The first angle is for the vertical fov, the second being the horizontal one; we’ll use the symbols α and β to indicate them. Now we do not fairly see the world on this means, but it surely’s computationally a lot simpler to work out a frustum, relatively than attempting to generate a sensible view quantity.

Two different settings must be outlined as properly — the place of the close to (or entrance) and much (again) clipping planes. The former slices off the highest of the pyramid however basically determines how near the place of the digital camera that something will get drawn; the latter does the identical however defines how distant from the digital camera that any primitives are going to be rendered.

The measurement and place of the close to clipping airplane is vital, as this turns into what known as the viewport. This is basically what you see on the monitor, i.e. the rendered body, and in most graphics APIs, the viewport is ‘drawn’ from its prime left-hand nook. In the picture beneath, the purpose (a1, b2) could be the origin of the airplane, and the width and the peak of the airplane are measured from right here.

The facet ratio of the viewport isn’t solely essential to how the rendered world will seem, it additionally has to match the facet ratio of the monitor. For a few years, this was at all times 4:3 (or 1.3333… as a decimal worth). Today although, many people recreation with ratios equivalent to 16:9 or 21:9, aka widescreen and extremely widescreen.

The coordinates of every vertex within the digital camera house must be reworked in order that all of them match onto the close to clipping airplane, as proven beneath:

The transformation is completed by use of one other matrix — this specific one known as the perspective projection matrix. In our instance beneath, we’re utilizing the sphere of view angles and the positions of the clipping planes to do the transformation; we might use the size of the viewport as a substitute although.

The vertex place vector is multiplied by this matrix, giving a brand new set of reworked coordinates.

Et voila! Now we have now all our vertices written in such a means that the unique world now seems as a compelled 3D perspective, so primitives close to to the entrance clipping airplane seem greater than these nearer the far airplane.

Although the scale of the viewport and the sphere of view angles are linked, they are often processed individually — in different phrases, you might have the frustum set to provide you a close to clipping airplane that is totally different in measurement and facet ratio to the viewport. For this to occur, a further step is required within the chain, the place the vertices within the close to clipping airplane must be reworked once more, to account for the distinction.

However, this will result in distortion within the considered perspective. Using Bethesda’s 2011 recreation Skyrim, we are able to see how adjusting the horizontal subject of view angle β, whereas retaining the identical viewport facet ratio, has a major impact on the scene:

In this primary picture, we have set β = 75° and the scene seems completely regular. Now let’s strive it with β = 120°:

Two variations are instantly apparent — initially, we are able to now see far more to the edges of our ‘imaginative and prescient’ and secondly, objects now appear a lot additional away (the bushes particularly). However, the visible impact of the water floor does not look proper now, and it’s because the method wasn’t designed for this subject of view.

Now let’s assume our character has eyes like an alien and set β = 180°!

This subject of view does give us an virtually panoramic scene however at a price to a severe quantity of distortion to the objects rendered on the edges of the view. Again, it’s because the sport designers did not plan and create the sport’s property and visible results for this view angle (the default worth is round 70°).

It may look as if the digital camera has moved within the above pictures, but it surely hasn’t — all that has occurred is that the form of the frustum was altered, which in flip reshaped the size of the close to clipping airplane. In every picture, the viewport facet ratio has remained the identical, so a scaling matrix was utilized to the vertices to make the whole lot match once more.

So, are you in or out?

Once the whole lot has been accurately reworked within the projection stage, we then transfer on to what’s referred to as clip house. Although that is finished after projection, it is simpler to visualise what is going on on if we do it earlier than:

In our above diagram, we are able to see that the rubber ducky, one of many bats, and a few of the bushes can have triangles contained in the frustum; nonetheless, the opposite bat, the furthest tree, and the panda are all outdoors the frustum. Although the vertices that make up these objects have already been processed, they don’t seem to be going to be seen within the viewport. That means they get clipped.

In frustum clipping, any primitives outdoors the frustum are eliminated totally and people who lie on any of the boundaries are reshaped into new primitives. Clipping is not actually a lot of a efficiency increase, as all of the non-visible vertices have been run by means of vertex shaders, and many others. up up to now. The clipping stage itself may also be skipped, if required, however this is not supported by all APIs (for instance, commonplace OpenGL will not allow you to skip it, whereas it’s attainable to take action, by use of an API extension).

It’s price noting that the place of the far clipping airplane is not essentially the identical as draw distance in video games, because the latter is managed by the sport engine itself. Something else that the engine will do is frustum culling — that is the place code is run to find out if an object goes to be inside the frustum and/or have an effect on something that’s going to be seen; if the reply is no, then that object is not despatched for rendering. This is not the identical as frustrum clipping, as though primitives outdoors the frustrum are dropped, they’ve nonetheless been run by means of the vertex processing stage. With culling, they don’t seem to be processed in any respect, saving various efficiency.

Now that we have finished all our transformation and clipping, it could appear that the vertices are lastly prepared for the following stage in the entire rendering sequence. Except, they don’t seem to be. This is as a result of the entire math that is carried out within the vertex processing and world-to-clip house operations needs to be finished with a homogenous coordinate system (i.e. every vertex has Four elements, relatively than 3). However, the viewport is totally 2D, and so the API expects the vertex data to only have values for x, y (the depth worth z is retained although).

To do away with the 4th part, a perspective division is completed the place every part is split by the w worth. This adjustment locks the vary of values x and y can take to [-1,1] and z to the vary of [0,1] — these are referred to as normalized gadget coordinates (NDCs for brief).

If you need extra details about what we have simply coated, and also you’re completely satisfied to dive into much more math, then have a learn of Song Ho Ahn’s glorious tutorial on the topic. Now let’s flip these vertices into pixels!

Master that raster

As with the transformations, we’ll keep on with taking a look at how Direct3D units the principles and processes for making the viewport right into a grid of pixels. This grid is sort of a spreadsheet, with rows and columns, the place every cell accommodates a number of information values (equivalent to shade, depth values, texture coordinates, and many others). Typically, this grid known as a raster and the method of producing it is named rasterization. In our 3D rendering 101 article, we took a really simplified view of the process:

The above picture gives the look that the primitives are simply chopped up into small blocks, however there’s much more to it that that. The very first step is to determine whether or not or not a primitive really faces the digital camera — in a picture earlier on this article, the one exhibiting the frustrum, the primitives making up the again of the gray rabbit, for instance, would not be seen. So though they might be current within the viewport, there is not any must render them.

We can get a tough sense of what this appears like with the next diagram. The dice has gone by means of the varied transforms to place the 3D mannequin into 2D display screen house and from the digital camera’s view, a number of of the dice’s faces aren’t seen. If we assume that not one of the surfaces are clear, then a number of of those primitives may be ignored.

In Direct3D, this may be achieved by telling the system what the render state goes to be, and this instruction will inform it to take away (aka cull) entrance going through or again going through sides for every primitive (or to not cull in any respect — for instance, wireframe mode). But how does it know what’s entrance or again going through? When we regarded on the math in vertex processing, we noticed that triangles (or extra a case of the vertices) have regular vectors which inform the system which means its going through. With that data, a easy verify may be finished, and if the primitive fails the verify, then it is dropped from the rendering chain.

Next, it is time to begin making use of the pixel grid. Again, that is surprisingly complicated, as a result of the system has to work out if a pixel matches inside a primitive — both fully, partially, or in no way. To do that, a course of referred to as protection testing is completed. The picture beneath exhibits how triangles are rasterized in Direct3D 11:

The rule is sort of easy: a pixel is deemed to be inside a triangle if the pixel middle passes what Microsoft name the ‘prime left’ rule. The ‘prime’ half is a horizontal line verify; the pixel middle have to be on this line. The ‘left’ half is for non-horizontal strains, and the pixel middle should fall to the left of such a line. There are further guidelines for non-primitives, i.e. easy strains and factors, and the principles achieve additional circumstances if multisampling is employed.

If we glance rigorously on the picture from Microsoft’s documentation, we are able to see that the shapes created by the pixels do not look very very similar to the unique primitives. This is as a result of the pixels are too massive to create a sensible triangle — the raster accommodates inadequate information concerning the unique objects, resulting in a problem referred to as aliasing.

Let’s use UL Benchmark’s 3DMark03 to see aliasing in motion:

In the primary picture, the raster was set to a really low 720 by 480 pixels in measurement. Aliasing may be clear seen on the handrail and the shadow forged the gun held by the highest soldier. Compare this to what you get with a raster that has 24 occasions extra pixels:

Here we are able to see that the aliasing on the handrail and shadow has fully gone. A much bigger raster would appear to be the best way to go each time however the dimensions of the grid needs to be supported by the monitor that the body will displayed on and provided that these pixels need to be processed, after the rasterization course of, there may be going to be an apparent efficiency penalty.

This is the place multisampling will help and that is the way it capabilities in Direct3D:

Rather than simply checking if a pixel middle meets the rasterization guidelines, a number of places (referred to as sub-pixel samples or subsamples) inside every pixel are examined as a substitute, and if any of these are okay, then that entire pixel varieties a part of the form. This may appear to have no profit and presumably even make the aliasing worse, however when multisampling is used, the details about which subsamples are coated by the primitive, and the outcomes of the pixel processing, are saved in a buffer in reminiscence.

This buffer is then used to mix the subsample and pixel information in such a means that the sides of the primitive are much less blocky. We’ll take a look at the entire aliasing scenario once more in a later article, however for now, that is what multisampling can do when used on a raster with too few pixels:

We can see that the quantity of aliasing on the sides of the varied shapes has been tremendously decreased. A much bigger raster is unquestionably higher, however the efficiency hit can favor using multisampling as a substitute.

Something else that may get finished within the rasterization course of is occlusion testing. This needs to be finished as a result of the viewport might be filled with primitives that might be overlapping (occluded) — for instance, within the above picture, the entrance going through triangles that make up the solider within the foreground overlap the identical triangles within the different soldier. As properly as checking if a primitive covers a pixel, the relative depths may be in contrast, too, and if one is behind the opposite, then it could possibly be skipped from the remainder of rendering course of.

However, if the close to primitive is clear, then the additional one would nonetheless be seen, regardless that it has failed the occlusion verify. This is why practically all 3D engines do occlusion checks earlier than sending something to the GPU and as a substitute creates one thing referred to as a z-buffer as a part of the rendering course of. This is the place the body is created as regular however as a substitute of storing the ultimate pixel colours in reminiscence, the GPU shops simply the depth values. This can then be utilized in shaders to verify visibility with extra management and precision over facets involving object overlapping.

In the above picture, the darker the colour of the pixel, the nearer that object is to the digital camera. The body will get rendered as soon as, to make the z buffer, then is rendered once more however this time when the pixels get processed, a shader is run to verify them in opposition to the values within the z buffer. If it is not seen, then that pixel shade is not put into the ultimate body buffer.

For now, the primary last step is to do vertex attribute interpolation — in our preliminary simplified diagram, the primitive was an entire triangle, however remember that the viewport is simply stuffed with the corners of the shapes, not the form itself. So the system has to work out what the colour, depth, and texture of the primitive is like in between the vertices, and that is referred to as interpolation. As you’d think about that is one other calculation, and never a simple one both.

Despite the truth that the rasterized display screen is 2D, the buildings inside it are representing a compelled 3D perspective. If the strains have been really 2 dimensional, then we might use a easy linear equation to work out the varied colours, and many others as we go from one vertex to a different. But due to the 3D facet to the scene, the interpolation must account for the attitude — have a learn of Simon Yeung’s excellent weblog on the topic to get extra data on the method.

So there we go — that is how a 3D world of vertices turns into a 2D grid of coloured blocks. We’re not fairly finished, although.

It’s all again to entrance (besides when it isn’t)

Before we end off our take a look at rasterization, we have to say one thing concerning the order of the rendering sequence. We’re not speaking about the place, for instance, tessellation comes within the sequence; as a substitute, we’re referring to the order that the primitives get processed. Objects are often processed within the order that they seem within the index buffer (the block of reminiscence that tells the system how the vertices are grouped collectively) and this will have a major influence on how clear objects and results are dealt with.

The purpose for that is right down to the truth that the primitives are dealt with separately and in the event you render those within the entrance first, any of these behind them will not be seen (that is the place occlusion culling actually comes into play) and might get dropped from the method (serving to the efficiency) — that is typically referred to as ‘front-to-back’ rendering and requires the index buffer to be ordered on this means.

However, if a few of these primitives proper in entrance of the digital camera are clear, then front-to-back rendering would consequence within the objects behind the clear one to missed out. One answer is to render the whole lot back-to-front as a substitute, with clear primitives and results being finished final.

So all fashionable video games do back-to-front rendering, sure? Not if it may be helped — remember that rendering each single primitive goes to have a a lot bigger efficiency value in comparison with rendering simply these that may be seen. There are different methods of dealing with clear objects, however typically talking, there is not any one fits-all answer and each scenario must be dealt with uniquely.

This basically summarises the professionals and cons to rasterization — on fashionable {hardware}, it is actually quick and efficient, but it surely’s nonetheless an approximation of what we see. In the actual world, each object will take up, replicate and possibly refract mild, and all of this has an impact on the considered scene. By splitting the world into primitives after which solely rendering a few of them, we get a quick however tough consequence.

If solely there was one other means…

There is one other means: Ray tracing

Almost 5 many years in the past, a pc scientist named Arthur Appel labored out a system for rendering pictures on a pc, whereby a single ray of sunshine was forged in a straight line from the digital camera, till it hit an object. From there, the properties of the fabric (its shade, reflectiveness, and many others) would then modify the depth of the sunshine ray. Each pixel within the rendered picture would have one ray forged and an algorithm could be carried out, going by means of a sequence of math to work out the colour of the pixel. Appel’s course of turned often called ray casting.

About 10 years later, one other scientist referred to as John Whitted developed a mathematical algorithm that did the identical as Appel’s strategy, however when the ray hit an object, it could then generate further rays, which might hearth off in varied instructions relying the thing’s materials. Because this technique would generate new rays for every object interplay, the algorithm was recursive in nature and so was computationally much more troublesome; nonetheless, it had a major benefit over Appel’s technique because it might correctly account for reflections, refraction, and shadowing. The title for this process was ray tracing (strictly talking, it is backwards ray tracing, as we comply with the ray from the digital camera and never from the objects) and it has been the holy grail for laptop graphics and films ever since.

The title for this process was ray tracing (strictly talking, it is backwards ray tracing, as we comply with the ray from the digital camera and never from the objects) and it has been the holy grail for laptop graphics and films ever since.

In the above picture, we are able to get a way of Whitted’s algorithm works. One ray is forged from the digital camera, for every pixel within the body, and travels till it reaches a floor. This specific floor is translucent, so mild will replicate off and refract by means of it. Secondary rays are generated for each instances, and these journey off till they work together with a floor. There are further secondary, to account for the colour of the sunshine sources and the shadows they make, are additionally generated.

The recursive a part of the method is that secondary rays may be generated each time a newly forged ray intersects with a floor. This might simply get uncontrolled, so the variety of secondary rays generated is at all times restricted. Once a ray path is full, its shade at every terminal level is calculated, primarily based on the fabric properties of that floor. This worth is then handed down the ray to the previous one, adjusting the colour for that floor, and so forth, till we attain the efficient start line of the first ray: the pixel within the body.

This may be massively complicated and even easy situations can generate a barrage of calculations to run by means of. There are, thankfully, some issues may be finished to assist — one could be to make use of {hardware} that’s particularly design to speed up these specific math operations, identical to there may be for doing the matrix math in vertex processing (extra on this in a second). Another crucial one is to attempt to velocity up the method that is finished to work out what object a ray hits and the place precisely on the thing’s floor that the intersect happens at — if the thing is comprised of numerous triangles, this may be surprisingly laborious to do:

Rather than check each single triangle, in each single object, a listing of bounding volumes (BV) is generated earlier than ray tracing — these are nothing greater than cuboids that surrounds the thing in query, with successively smaller ones generated for the varied buildings inside the object.

For instance, the primary BV could be for the entire rabbit. The subsequent couple would cowl its head, legs, torso, tail, and many others; every one among these would then be one other assortment of volumes for the smaller buildings within the head, and many others, with the ultimate stage of volumes containing a small variety of triangles to check. All of those volumes are then organized in an ordered record (referred to as a BV hierarchy or BVH for brief) such that the system checks a comparatively small variety of BVs every time:

Although using a BVH does not technically velocity up the precise ray tracing, the technology of the hierarchy and the following search algorithm wanted, is mostly a lot quicker than having to verify to see if one ray intersects with one out of thousands and thousands of triangles in a 3D world.

Today, packages equivalent to Blender and POV-ray make the most of ray tracing with further algorithms (equivalent to photon tracing and radiosity) to generate extremely life like pictures:

The apparent query to ask is that if ray tracing is so good, why do not we use it all over the place? The solutions lies in two areas: initially, even easy ray tracing generates thousands and thousands of rays that need to be calculated again and again. The system begins with only one ray per display screen pixel, so at a decision of simply 800 x 600, that generates 480,000 main rays after which every one generates a number of secondary rays. This is critically laborious work for even at present’s desktop PCs. The second problem is that fundamental ray tracing is not really very life like and that a complete host of additional, very complicated equations must be included to get it proper.

Even with fashionable PC {hardware}, the quantity of labor required is past the scope to do that in real-time for a present 3D recreation. In our 3D rendering 101 article, we noticed in a ray tracing benchmark that it took tens of seconds to provide a single low decision picture.

So how was the unique Wolfenstein 3D doing ray casting, means again in 1992, and why do the likes of Battlefield V and Metro Exodus, each launched in 2019, provide ray tracing capabilities? Are they doing rasterization or ray tracing? The reply is: a little bit of each.

The hybrid strategy for now and the longer term

In March 2018, Microsoft introduced a brand new API extension for Direct3D 12, referred to as DXR (DirectX Raytracing). This was a brand new graphics pipeline, one to enhance the usual rasterization and compute pipelines. The further performance was offered by means of the introduction of the shaders, information buildings, and so forth, however did not require any particular {hardware} help — aside from that already required for Direct3D 12.

At the identical Game Developers Conference, the place Microsoft talked about DXR, Electronic Arts talked about their Pica Pica Project — a 3D engine experiment that utilized DXR. They confirmed that ray tracing can be utilized, however not for the complete rendering body. Instead, conventional rasterization and compute shader methods could be used for the majority of the work, with DXR employed for particular areas — which means the variety of rays generated is way smaller than it could be for a complete scene.

This hybrid strategy had been used previously, albeit to a lesser extent. For instance, Wolfenstein 3D used ray casting to work out how the rendered body would seem, though it was finished with one ray per column of pixels, relatively than per pixel. This nonetheless may appear to be very spectacular, till you notice that the sport initially ran at a decision of 640 x 480, so not more than 640 rays have been ever working on the identical time.

The graphics card of early 2018 — the likes of AMD’s Radeon RX 580 or Nvidia’s GeForce 1080 Ti — actually met the {hardware} necessities for DXR however even with their compute capabilities, there was some misgivings that they might be highly effective sufficient to really make the most of DXR in any significant means.

This considerably modified in August 2018, when Nvidia launched their latest GPU structure, code-named Turing. The crucial function of this chip was the introduction of so-called RT Cores: devoted logic models for accelerating ray-triangle intersection and bounding quantity hierarchy (BVH) traversal calculations. These two processes are time consuming routines for understanding the place a light-weight interacts with the triangles that make up varied objects inside a scene. Given that RT Cores have been distinctive to the Turing processor, entry to them might solely be finished through Nvidia’s proprietary API.

The first recreation to help this function was EA’s Battlefield V and once we examined using DXR, we have been impressed by the development to water, glass, and metallic reflections within the recreation, however relatively much less so with the following efficiency hit:

To be honest, later patches improved issues considerably however there was (and nonetheless is) a giant drop within the velocity at which frames have been being rendered. By 2019, another video games have been showing that supported this API, performing ray tracing for particular components inside a body. We examined Metro Exodus and Shadow of the Tomb Raider, and located an analogous story — the place it was used closely, DXR would notably have an effect on the body charge.

Around about the identical time, UL Benchmarks introduced a DXR function check for 3DMark:

However, our examination of the DXR-enabled video games and the 3DMark function check proved one factor is definite about ray tracing: in 2019, it is nonetheless critically laborious work for the graphics processor, even for the $1,000+ fashions. So does that imply that we haven’t any actual various to rasterization?

Cutting-edge options in client 3D graphics know-how are sometimes very costly and the preliminary help of recent API capabilities may be relatively patchy or sluggish (as we discovered once we examined Max Payne Three throughout a variety of Direct3D variations circa 2012) — the latter is often because of recreation builders attempting embrace as most of the enhanced options as attainable, typically with restricted expertise of them.

But the place vertex and pixel shaders, tesselation, HDR rendering, and display screen house ambient occlusion have been as soon as all extremely demanding, appropriate for top-end GPUs solely, their use is now commonplace in video games and supported by a variety of graphics playing cards. The identical might be true of ray tracing and given time, it is going to simply turn out to be one other element setting that turns into enabled by default for many customers.

Some closing ideas

And so we come to the top of our second deep dive, the place we have taken a deeper look into the world of 3D graphics. We’ve checked out how the vertices of fashions and worlds are shifted out of three dimensions and reworked right into a flat, 2D image. We noticed how subject of view settings need to be accounted for and what impact they produce. The course of of creating these vertices into pixels was explored, and we completed with a short take a look at another course of to rasterization.

As earlier than, we could not presumably have coated the whole lot and have glossed over a number of particulars right here and there — in spite of everything, this is not a textbook! But we hope you have gained a bit extra data alongside the best way and have a brand new discovered admiration for the programmers and engineers who’ve really mastered the mathematics and science required to make all of this occur in your favourite 3D titles.

We’ll be very happy to reply any questions you might have, so be happy to ship them our means within the feedback part. Until the following one.

Masthead credit score: Monochrome printing raster summary by Aleksei Derin

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