Rendering polygons is not as easy as it used to be, the reason being the vast amount of different rendering techniques, methods and algorithms available. Not only is choosing the right ones a problem, even worse, all that are selected need to work together. This means, one cannot select algorithms just based on their visible results on screen, but one must also have a look at the resources needed. Input and output format and values need to match when one rendering method provides the input for another. Therefore, different techniques need to be integrated, i.e. they must be made compatible. Not only by means of input/output values, but also by means of their resource usage and their general environment. All must be considered and matched. Sometimes however, the selection of one particular rendering method comes with such a heavy resource penalty (i.e. fill rate, transform rate, storage space, cpu-time, etc.) that some other, already selected and implemented methods, need to be simplified and/or revised so that the added method integrates well into the general framework. At some point, one figures, that there are some algorithms, which simply do not work together. In that case, only one may be used, the other one needs to be replaced by a more compatible method.

All those problems hint that a general approach to shading is quite valuable and helps in making the right decisions. The general approach of Star Wars: Rogue Leader on the Nintendo Gamecube is described and the decisions made based on it, are outlined. This includes sketching down most of the shading algorithms, their specific implementations, and noting some technical details; as well as various clever bits and pieces.

The second part of this features introduces the application of the principles introduced to the area of landscape shading/texturing.

Potential Algorithms

Technically many shading methods work on current generation hardware as on the Nintendo
Gamecube. These methods include (but are not limited to):

For each of those methods, one is guaranteed to find a couple of implementations on various platforms and many references in books and scientific papers. The problem is however, that all those methods are looked at on their own. One has to find a common environment to integrate them. This process is (naturally) not hassle free and leads to certain limitations.

Limitations

The problems that can arise during integrating (or just using/implementing) different shading methods fall into four different classes: algorithm compatibility, hardware limitations, performance metrics, and memory limitations.

Some shading methods are not compatible. It can be as simple as a self-shadowing pre-render pass producing eight bit z-depth values and a shadow projection method requiring eight bit alpha values. In addition, sometimes one algorithm needs geometry data being preprocessed in a very specific way to be feasible on the target, while another needs a completely different representation of the same data. Worst case here would be allocating twice the storage amount, which is not the best solution at all.

All hardware has its limits. They can be as minor as the maximum number of constant color registers in the texture environment (TEV) and as major as the fact that there is just one destination-alpha (stencil) buffer. However, if one has five shading methods, which all are using one constant color register to combine colors and the hardware supports just four, one has a problem. This can only be resolved in cutting a feature or in clever reuse of the color registers (i.e. making some colors just intensities and therefore end up with three color registers plus four intensity registers (rgba := four intensity values)). The flexible design of the Nintendo Gamecube hardware allows for many tricks like that, where one limited resource is substituted by another one with almost no additional cost. However, if you want to use two shading methods which both are based on a stencil buffer approach, you can’t introduce any tradeoff, since there is just one of it. The rendering need to be done in two passes or some alternative method needs to be used.

Each system has a specific performance metric (and it will never change). Determining which operations are relatively cheap and which are slightly expensive is a basic requirement to figure out what can be done and what will hurt in the large-scale application of a specific method. Luckily, the Nintendo Gamecube is powerful and by being so, allows for many state of the art techniques. Fill rate is not a problem and due to the eight textures that can be applied in one go (i.e. in one render pass), the requirements to the transform unit are not as elaborate as on other architectures. As another advantage, the PowerPC CPU performs well and memory access is very fast. Moreover, when it really should come down to hands-on assembly, one can find a lot of literature and examples due to the wide application of the CPU family in other areas. However, even the tightest assembly loop can’t process infinite amounts of data. If a shading method requires elaborate pre-render passes and pre-computing per frame on the CPU, the amounts of polygons is limited. Also, should complicated shading make it a requirement that there is more than one pre-render pass per object, things can quickly get slow. In that case, it can be beneficial to merge two of those passes into one, if the selected algorithms allow that (and that’s indeed possible when pre-rendering for self-shadowing and projected shadows).

Almost the same goes without much further discussion for memory storage. It is another inherently limited resource. Shading methods that require many additional texture channels and/or pre-render buffers lose against methods that don’t have such requirements.

General approach

As outlined before, a common environment can give the required structure to host the different shading methods that are about to be used at once. Of course, it’s quite difficult to plot such an environment beforehand without knowing exactly where the problems are. Therefore, this is an iterative process for the novice. The two major points, which guided Rogue Leader’s shading subsystem are consistent lighting for all geometry and a consistent illumination model.

The fact, that all geometry was lit the same in a consistent way helped tremendously to achieve the required look. By doing so, there was no room for lighting error, which may have been introduced if things where partly pre-lit and party dynamically lit. It’s always very hard to keep things, once they go different ways, consistent. In addition, one directional and one ambient light on the Nintendo Gamecube are guaranteed to be computationally for free. Therefore, that decision does not impose a performance penalty (strictly speaking, as soon as one starts to use more complex shader setups, even more hardware lights come at no performance penalty, because the graphics processor computes light values in parallel to other things).

Because of that approach, color per vertex is only used as pure paint. This means that a model may be textured completely just using intensity textures (grayscale) and color will be applied by painting vertex colors. To compute the material color, both values are multiplied together. The result is then exposed to the lighting calculations.

Local lights are all computed per vertex and are added ‘on-demand’, i.e. if an object intersects with a local light’s bounding sphere, the appropriate lights are fetched and the lighting calculations are enabled.

Equally important to the consistent lighting of all geometry is the usage of a consistent illumination model. Computations for different shaders need to be done in the same consistent manner so the results are comparable and do not depend on specific features (e.g. bump mapping, illumination maps, specularity, etc.) being enabled or not.

Specifically, the classification of lights into global (directional and ambient) and local (point and spot) lights helps with specific shadowing problems. The hardware supports this quite nicely by having two color channels (GX_COLOR0 and GX_COLOR1) that can be routed around independently in the texture environment.

Another strict distinction is helpful. Color computations are separated in material color and light color computations. The first takes place in the models own domain whereas the second one relies on the game’s light database and the shadowing techniques used. In fact, the shading subsystem uses many different methods to compute light values (c.f. Lighting Pipeline).

Figure 1: Basic illumination model.

Figure1 illustrates the basic flow of color values through the texture environment. This flow is the same for all different shaders used (i.e. diffuse shader, phong shader, lambert shader, reflective shader, etc.). Shading is a two-fold problem Technically speaking, shading polygons has to deal with two different problem domains, which are solved at different times during runtime. Those are configuration of the texture environment (shading subsystem) and light collection and selection (lighting pipeline).

Figure 2: Control flow during rendering.

Shading is a Two-Fold Problem

Technically speaking, shading polygons has to deal with two different problem domains, which are solved at different times during runtime: configuration of the texture environment (shading subsystem) and light collection and selection (lighting pipeline) The reason for that distinction and the problem that comes with it are illustrated in Figure 2. It’s quite possible that a specific shader is used for a couple of objects that are rendered sequentially (i.e. a large number of objects of the same kind). This results in the shader only once being translated into a sequence of GX commands, Nintendo’s graphics API, but the local lights for each object of course can be different. All of the objects will very likely be at different world positions and therefore be exposed to different local lights or even no local lights at all. During rendering, the lighting pipeline now has to take care that GX knows about the correct lights and needs to issue the required sequence of commands.

The reason for that distinction and the problem that comes with it are illustrated in figure 2. It’s quite possible that a specific shader is used for a couple of objects that are rendered sequentially (i.e. a large number of objects of the same kind). This results in the shader only once being translated into a sequence of GX commands, Nintendo’s graphics API, but the local lights for each object of course can be different. All of the objects will very likely be at different world positions and therefore be exposed to different local lights or even no local lights at all. During rendering, the lighting pipeline now has to take care that GX knows about the correct lights and needs to issue the required sequence of commands.

Shading subsystem

To clarify the term shader, Figure 3 shows the data structure that defines one. A shader is a data structure that describes “how to compute colors” for rendering polygons. The term building a shader refers to the process of transforming such a data structure into a stream of GX commands, which configure the hardware to produce the desired output. One should note that during the shader build many features are activated dynamically. For instance, if an object should get tinted a color multiplication is added to the final output color whatever shader was setup before. In addition, layered fog adds another stage at the end of the color computation that blends depending on the pixel’s height in world space and distance from the camera in eye space between a fog color and the original pixel color. Of course, it would be nice, if the complete shader subsystem would be dynamic like that. However, experience shows that many shaders can only be built by hand into an optimal (i.e. least cycle usage) setup.

typedef struct tShader {
char mName[16]; // shader name, as in Maya...

tShaderLimit mShaderLimit; // shading limit, i.e. type...
tShaderFlags mShaderFlags; // additional flags...

tShaderColor mColor; // material color, if used...
tShaderColor mSpecularColor; // specular color, if used...


f32 mReflectivity; // reflectivity strength...
f32 mEmbossScale; // emboss depth...
f32 mMovieFade; // movie shader weight...

tShaderDataDescriptor mDataInfo; // texture info...
} tShader;

Figure 3: A ‘tShader’ data structure describing how to render polygons.

Mostly the structure’s members describe various properties of a shader (like the material color, the specular color and cosine power for phong shaders, the reflectivity for reflective phong shaders, etc.). The most important member is the mShaderLimit , which describes what kind of shading is actually performed. The term limit illustrates at what point the color computation actually should stop. Roughly, the following shading limits were implemented:

This clearly shows, that an automatic way of generating code to generate shader setups would be very nice, since all the shaders listed above need to be maintained. However, as mentioned above, a couple of features where added in automagically already, like self-shadowing and tinting for example.

typedef struct tConfig {

// resources currently allocated...
GXTevStageID stage; // current tevstage...
GXTexCoordID coord; // current texture coordinate...
GXTexMapID map; // current texture map...

// ...

} tConfig;

void shadingConfig_ResetAllocation(tConfig *pConfig);
void shadingConfig_Allocate(tConfig *pConfig, s32 stages, s32 coords, s32 maps);
void shadingConfig_Flush(tConfig *pConfig);

Figure 4: Data structure ‘tConfig’ describing resource allocation.

Since a shader setup is built by various functions, one needs to keep track of various hardware resources. For example, texture environment stages, texture matrices, texture coordinates, texture maps and such need to be allocated in a sequential manner. Some resources require special order requirements; texture coordinates for emboss mapping always need to be generated last. Therefore, infrastructure is needed to deal with the allocation problems. The solution here is another tiny data structure tConfig (c.f. figure 4).

This structure holds information about the resources used during setup. Before any resources are used, the allocation information is reset using the shadingConfig_ResetAllocation(); call. For each tevstage, texture coordinate and etcetera used, a call to shadingConfig_Allocate(); is made, which marks the corresponding resources as being allocated. When one now calls a subroutine that inserts additional GX commands, the tConfig structure is passed along as a parameter. The called function can now have a look at the structure’s members and knows what tevstage, texture coordinate and etcetera to use next. When the shader construction is done, the function shadingConfig_Flush(); is called, which actually passes the number ofresources used to the hardware. Error checking can be preformed here as well.

Figure 5: Shading subsystem client control flow.

The shading subsystem needs to maintain a global GX state as well. This is because the shading subsystem is not the only client to GX. Other parts of the game program will issue GX commands and setup their own rendering methods in specific ways. However, since the shading subsystem has to initialize quite a bit of GX state to work properly, a protocol needs to be introduced to reduce the amount of redundant state changes (c.f. figure 5). The straightforward solution of initializing the complete GX state as needed by the shading subsystem is of course way to slow. A boolean variable keeps track if the shading subsystem has initialized GX for its usage. Every time it is about to be used, a function shading_PreRenderInit(); is called. This function checks the flag. If it’s false GX is initialized and the flag is set to true. The next time some shading needs to be done, the boolean is already true and the setup can be skipped. On the other hand, when other parts of the game program do some ‘hard coded’ GX usage, they need to reset that boolean by calling shading_GxDirty();.

Finally, the shading subsystem keeps books about various default settings for the texture environment. If subsequent shader setups share some settings that are the same, a couple of GX commands can be skipped, since it is in an already known state. If another shader is setup, the function shading_CleanupDirtyState(); cleans the marked dirty state and leaves GX in the expected way behind. Those optimizations helped quite a bit in the end to maintain a reasonable frame rate.

Lighting Pipeline

The actual purpose of the so-called lighting pipeline is to deliver light color values per shaded pixel. As mentioned before, all lights are classified into either global or local lights and the methods of computing light color values vary. The results of global lighting can be computed in three different ways: per vertex, per pixel using emboss mapping, and per pixel using bump mapping.

All three of these methods come in two variants one with self-shadowing and one without. When self-shadowing is enabled, the directional component of the global light is not added to the output color value if the pixel to be shaded falls in shadow. The ambient color is the only term that then contributes to the global lighting. The conditional add is facilitated using the two different color channels GX_COLOR0 and GX_COLOR1. The first one carries the directional component of the global light whereas the second one is assigned to all local lights and the ambient term.

Local lights are always computed per vertex using the lighting hardware and are fed into GX_COLOR1. Note that both channels are combined when self-shadowing is not enabled. There is a tiny problem when color per vertex is used for painting and two channels are used. The hardware is not able to feed one set of color per vertex data without sending the same data twice into the graphics processor. Therefore, one needs to decide if the local lights are computed unpainted (which only leads to visible artifacts, if local lights are contributing) or if color per vertex data is sent twice into both color channels, eating up vertex performance. Experience showed that not painting the local lights was quite ok, and nobody really noticed.

The control flow of the lighting pipeline is a bit tricky. The problem here is that at an object’s rendering time all local lights possibly intersecting the object’s bounding sphere, need to be known (c.f. figure 6).

Figure 6: Lighting pipeline, control flow.

This requires the creation of a local light database that holds information about all local lights influencing the visible geometry. The game program needs to add all local lights to the database before any rendering takes place. Care needs to be taken when it comes down to culling lights for visibility against the view frustum. The reason is that the distance attenuation function as used per default by GX has no precise cutoff point and therefore setting up a point light with a 50m radius does not mean that no light will contribute to any polygons starting at any distance > 50m. Light will pop on and off if the lights are collected by software culling assuming a 50m radius. A fludge factor of 2.0f proved to be quite successful here.

Once all visible lights are added, rendering can begin. First, all logical lights are transformed into an array of GXLightObj objects. This array is double (or triple) buffered to let the graphics processor always have a private copy to read from while the CPU is generating the array for the next frame. An array is constructed since each object is likely to receive it’s own set of local lights. Instead of storing many copies of GXLightObj objects in the FIFO using GXLoadLightObjImm(); we instruct the graphics processor to fetch lights indirectly from the constructed array using the faster GXLoadLightObjIdx(); function.

As rendering of an object starts, all intersecting lights are collected (up to a maximum number of eight lights) and loaded from the array. Note that one should remember which lights are loaded to avoid unnecessary loads. The light mask is computed (an eight bit value as sent to GXSetChanCtrl(); ) that describes what lights actually contribute to the lighting calculation in hardware. This mask value is the interface between the shading subsystem and the lighting pipeline. This is because GXSetChanCtrl(); not only specifies what lights are enabled but also how color per vertex is used and what kind of light calculation is performed. Therefore, parameters to this GX call are coming in from the two different subsystems at different times. By storing the light mask value as an easy accessible variable and making sure, that no bogus values are loaded in case of the first shader setup (i.e. when no lights have been collected yet), this problem can be solved.

Description of Shading Methods

In the next couple of sections, many of the shading methods used in Star Wars: Rogue Leader are briefly described. Specific aspects on how they integrate in the shading environment are discussed in detail. Additional information can be found in the Nintendo Gamecube SDK.

Figure 7: Illumination mapping.

Method 1: Illumination Maps

Illumination maps are used by the artists when they want specific areas to be self-illuminated. Good examples are lights of small windows. Illumination mapping requires an additional texture, which typically is just an intensity texture (one for four bits). Note that strictly speaking, an illumination map could be colored, however, since the white of the illumination map will be multiplied by the texture color of the color map anyways, colored illumination maps can be circumvented. After the light calculation is done, the self-illuminating term is fetched from a texture and simply added to the light color (c.f. figure 7).

Figure 8: Texture used for specular highlights.

Method 2: Specular Highlights

Specular highlights are a very important feature visually. The shiny reflection of light on surfaces gives the eye another hint about where in the scene light sources are located and adds to the overall realism. Technically speaking, specular highlights are relatively simple to implement. The light database needs to be able to determine the dominant light direction, which is, in most cases, derived from one of the directional lights (i.e. from the brightest one).

There are two different methods available to implement specular highlights. The lighting hardware can compute a specular term per vertex. This is quick to setup and the results are quite reasonable with highly tessellated geometry, but as always, computing something per pixel always gives results that are more pleasant. Therefore generating texture coordinates per vertex and looking up a specular highlight texture (c.f. figure 8) looks better.

Figure 9: Specular highlights.

The generation of texture coordinates is done in two steps (c.f. section “Texture Coordinate Generation”). First, the normal data is transformed from model into eye space using a texture matrix. Note that this step is common for all geometry and provides the basis for all other shading methods as well. This has the benefit that the interface to the geometry engine (computing skinned meshes, etc.) can be kept fairly simple and interdependencies between both subsystems are reduced. The transformed normals are now transformed again into using the “eye_normal to specular_coords” matrix using the dual transform feature of the hardware. This matrix depends on the cosine power (i.e. size) of the material being rendered and the direction of the light (also in eye space), c.f. code fraction 1 for more details. Since the specular texture is so frequently used, one should consider preloading them into the hardware texture cache permanently.

Method 3: Reflection/Environment Mapping

A mapping method that is quite similar to specular mapping is environment mapping. The surroundings of an object are reflecting from its surface. It’s not feasible with current generation hardware to implement this correctly. This is because a ray tracing approach would be required; which can’t be done in consumer hardware. Instead, a generic view of the scene is used that is rendered by an artist or generated during startup just once. However, this view (consisting of six texture maps, one in each direction) needs to be converted into a spherical environment map. This generated map is used to lookup pixels during runtime. This map needs to be regenerated as soon as the camera orientation is changing. The Nintendo Gamecube SDK contains examples on how to do so.

Figure 10: Environment mapping.

Code fraction 2 shows how to setup the second pass matrix in this case. In addition, some care needs to be taken on how the computed environment color is used and how it interacts with the computed light color for the same pixel (i.e. fragment). A linear interpolation between those two values solves the problem and gives control over how reflective a material is.Note that highly reflective surfaces will get almost no contribution from the computed light color (which is correct, since the surface reflects the incoming light), but since color per vertex painting is done via multiplication in the lighting hardware, the painted colors will be removed. This is an example of bad shader integration, but since the solution to the problem (passing color per vertex values unmodified and multiplying in the texture environment) is a significant performance hit it also introduces other problems. The trade off seems quite reasonable.

Method 4: Emboss mapping

Are more subtle but nevertheless important method is bump mapping where a height field mapped onto a surface describes its elevation per pixel without adding geometric data. On the Nintendo Gamecube two different methods are straightforward to implement. Emboss mapping computes light values per pixel. It is not possible to compute “bumped” specular highlights and reflection with this method. “Real” per pixel bump mapping using the indirect texture unit is capable of doing so (c.f. method 5).

The hardware has direct support for emboss mapping. The height field is looked up twice, first with the original set of texture coordinates as generated by the texturing artist. Afterwards with a slightly different set of texture coordinates as generated by the lighting hardware, which shifts the original texture coordinates depending of the direction of the light. Note that the amount of shifting (and therefore the resulting depth impression) comes from the scale of the normal matrix as loaded with GXLoadNrmMtxImm(); . This means that the matrices need to be scaled to the desired values. This does not affect lighting calculation since the normals are renormalized for light computations anyways, but it does mean that one mesh (i.e. set of polygons rendered with one set of matrices) can have only one depth value for emboss mapping and imposes a interdependency between the shading and geometry subsystems. The resulting height values are subtracted and multiplied by the computed light color (c.f. figure 11).

Figure 11: Emboss mapping.

Emboss mapping does not support the computation of specular highlights. However, one can just ignore the emboss map and add non-bumpy specular highlights. Nevertheless, by doing so, the dark edges of the bumpy surface will be removed (due to the adding) and the effect falls apart to some extent (not to mention that the specular highlights by itself ignore the height field completely).

Finally, emboss mapping (as bump mapping) needs binormals to describe the orientation of
the height field on the surface. Since they need to be transformed the same way the normals
are transformed this can add a bit overhead.

Method 5: Bump Mapping

Visually better results can be achieved using “real” bump mapping as supported with the indirect texture unit. Using this method the hardware computes a normal per pixel and uses that to lookup different textures including a diffuse light map (containing all directional and ambient lights), an environment map (as described in method 3) and even a specular map. Thereby all those shading effects are computed correctly in a bumped way. However, since the global lights are now fetched from a texture instead of being computed by the lighting hardware, the texture needs to be generated dynamically as soon as the camera orientation and/or the lights change (again, one can find an example on how this is done in the demo section of the Nintendo Gamecube SDK).

In addition, the height field needs to be pre-processed into a “delta U/delta V texture” (which is an intensity/alpha texture with four bit per component) and therefore needs (without further measures) twice as much memory for texture storage than the emboss mapping method described in method 4.

Figure 12: Bump mapping.

The delta-texture is fed into the indirect unit where it is combined with the surface normals, describing the orientation of the bump map. In the last stage of this three-cycle setup, the diffuse light map is looked up and the result is the bumped light color for the global lights. Note that the local lights are still computed per vertex (because they have a location and the normal used as input data does not give this information) and are added later in the texture environment.

Figure 13: Actions in the texture environment and
the indirect texturing unit during bump mapping.

Since the computation of the perturbed normal is so elaborate, doing more than one lookup with the computation result amortizes the effort slightly. Specular highlights and environment reflections can be looked up in subsequent stages. The lookup of the bumped specularity is a bit tricky, since the coordinates are kept in the indirect unit and passed from stage to stage. However, they are already denormalized and this is what makes it tricky (c.f. code fraction 3). The processes in the texture environment and the indirect texture unit are described in figure 13.

Method 7: Self Shadowing

Per-object self-shadowing can be realized quite nicely on the Nintendo Gamecube. The benefit of doing self-shadowing on a per object basis is that one does not need to be concerned so much with precision. Almost all reasonably sized (e.g. in diameter) objects can be represented nicely in an eight-bit Z texture as needed by the algorithm. To figure out if a pixel falls within shadow or not the object is pre-rendered from the viewpoint of the main directional light. “Viewpoint” means, the point that is reached when going backwards in the light direction from the center point of the model in question (note that a directional light by itself does not have a point of origin). This pre-render step is done using an orthogonal projection and the top/down, left/right and near/far planes have to be set in a way that the texture area used for pre-rendering is used to its maximum extend (i.e. deriving this planes from the bounding sphere). After the pre-rendering is complete, the Z buffer is grabbed.

Later, when the object is rendered into the view, each rendered pixels coordinates are projected into texture coordinates of the grabbed Z texture. Using a ramp texture, the distance of each pixel to the imaginary light point is measured and the resulting two values are compared. Depending on the outcome of this test, the rendered fragment either falls into shadow or not. Local lights are passed through a second color channel and added conditionally to the global colors (c.f. figure 14). Yet again, the Nintendo Gamecube SDK contains examples that describe the technical details.

Figure 14: Self shadowing.

Method 8: Projected Shadows

A similar technique is projecting shadows. In this case, the shadow is not cast on the object in question itself but onto receiver geometry. Once again, the object is pre-rendered from the imaginary point of light using an orthogonal projection (same as in method 7). However, now one does not grab Z values but the outline of the object in the color buffer. This outline is rendered in a second pass on the receiver geometry (using the receiver geometry itself and compute texture coordinates from its vertices). Strictly speaking, with the texturing capabilities there is no need to render the receiver geometry in a second pass, however, allowing multiple shadows to be cast on one piece of receiving geometry would add much to the complexity of the algorithm. Nevertheless, if the number of shadows is fixed, one should render them in a single go to save on transform time (c.f. figure 15 for more details).

This approach results in a big requirement for the geometry subsystem. It needs to be able to return chunks of geometry. Of course, one just needs to re-render those polygons that are affected by the shadow outline. Fast methods of constructing these chunks are an important requirement.

During the second render pass, one has two options to shade the fragments: darkening the pixels that fall in shadow, or re-rendering the pixels as described by the receivers material properties omitting global directional light.

It is worth noting that the pre-render passes for the projected shadows can be easily combined with the pre-rendering passes required for self-shadowing. This is because both render the object from the same virtual point of light. Instead of rendering one depth map and another outline just the depth map is rendered and grabbed. Nothing changes for the self-shadowing technique. However, the during rendering the projected shadows onto the receiver geometry the actual Z values are fetched and compared against 0xff, which represents the far clipping plane during the pre-render pass for self-shadowing. If the fetched depth is < 0xff the receiver geometry falls into shadow otherwise it is exposed to light.

Figure 15: Projected shadows.

Method 9: Projected Reflections

Projected Reflections are very similar to projected shadows (c.f. figure 16). A receiving piece of geometry is re-rendered here as well. In this case, the object is pre-rendered from an imaginary viewpoint, which the object would be looked at if the camera would be mirrored at the reflective plane. In this case, however, it is important that a perspective projection is used to project the geometry onto the receiving geometry.

If the reflective geometry is intersecting the mirroring plane (as it could be the case with water being the reflective element in a scene), pixels falling underneath that plane must be carefully cut-off. Outputting an alpha of zero for those pixels (using the same techniques as described in method 10, layered fog) and configuring GX to skip alpha = 0 pixels does the job.

Figure 16: Projected reflections.

Method 10: Layered Fog

To compute layered fog (e.g. fog, which changes its intensity not only based on the distance to the camera but also on the height in world space) one needs to compute/lookup an intensity value, which describes how much a pixel is fogged. To do so, a texture coordinate generation is setup that transforms vertices back from eye into world space using the dual transform feature. It’s nice that one can actually use exactly the same matrix (e.g. GX_PNMTX0) to do the first part of the texture coordinate transformation. The second matrix multiply maps the Y component onto a ramp texture. Scaling and transformation have to be carefully adjusted to map the wanted gradient of world Y coordinates onto the U [0, …, 1] range. In the same manner eye Z is mapped into V [0, …, 1], c.f. figure 17 and code fraction 4 for more details.

Figure 17: Layered Fog.

Note that one could use a color texture instead of an intensity texture to get results that are even more advanced.

There is a drawback generating layered fog like this. It only works right as long as the camera is reasonably outside the fog volume. As soon as it dives deeply into it and looks up, the un-fogged polygons higher up are still visible. However, that can be compensated with figuring out how much the camera is in fog (height wise) and then fog everything, i.e. dynamically adjusting the fog ceiling.

Method 11: Custom Dithering

For some surfaces banding is a problem. Especially sky textures with their subtle color gradients suffer when the frame buffer is configured using a destination alpha buffer that is required by so many rendering methods (only six bits are stored per component to allow for an additional six bit alpha channel). The built in hardware dither helps already, however, the results could be better. Adding a repetitive pattern to the outputted pixels fools the human eye into not recognizing the banding as much as before. The pattern just needs to be a “four x four” pixel texture that contains biased positive and negative offsets that are added to the outputted pixels. Additional control can be given, when the dither pattern is multiplied by a factor before adding and therefore adjustment of the dither strength is possible. The only problem here is that the dither pattern must be screen-space aligned. Each vertex must be transformed into screen space aligned texture coordinates. A trick similar to the one used in method 10 (layered fog) helps here (c.f. figure 18). The incoming vertices are transformed into eye space using the regular model to eye matrix and using the dual transform feature the dither pattern is aligned onto the screen.

Figure 18: Custom dithering.

Pre-Rendering

Many of the sketched shading methods require pre-rendering objects. This suggests that pre-rendering has to become an integral component of the game program and measures need to be taken to ensure proper resource usage for both processing time and texture storage. The first thing is that pre-render passes should be combined when possible (c.f. method 7 and method 8). This is quite an obvious gain both in time and in storage.

In addition, storage should be organized in pools that provide a fixed number of slots to be rendered into. Before pre-rendering starts, all objects that require it have to be gathered, sorted by distance from the camera and then get slots assigned (the first couple of slots can even have a slightly bigger texture size). If the pool runs out of slots, pre-rendering stops and some object will loose their respective properties (like self shadowing).

The last and most important thing is that shading and geometric information have to be strictly separated. It must be possible to render an object fully lit, with all texturing features, etc. and to the same extent it must be easy to render just raw, fully lit polygons of the same geometry. This is because many pre-render passes just need the outline or depth values. Sending more data into the graphics processor, like texture coordinates or colors will just slow the process down. It also must be possible to render objects from different viewpoints. Unfortunately, this is only possible with the construction of different sets of matrices that all need to be computed by the CPU. Storage organization of these matrices is important. In addition, one does not need to forget that rendering the same geometry with the same set of matrices does not mean that those matrices need to be recomputed.

Figure 19: Texture coordinate generation.

Texture Coordinate Generation

A couple of shading methods are using the fragments orientation (i.e. normal data) as a basis and it is a common step to transform the model space normals into eye space first. Therefore, it is a good idea to split all texture coordinate generations into two passes. The first pass is shared between all methods and the math needs to be revised to operate on the proper eye space normals (c.f. figure 19).

Indirect texturing

A unique and very interesting feature of the Nintendo Gamecube is the indirect texture unit. It is capable of modifying/generating texture coordinates per pixel and therefore allows for a wide variation of effects. Rippled decals, heat effects and shockwaves are common uses. When it is used together with grabbing the frame buffer, the results are impressive. Figure 20 illustrates the control flow when rendering shockwaves. The problem here is that texture coordinates for the shockwave geometry needs to be computed. One more time, the dual transform feature of the texturing hardware helps. The model coordinates are transformed into eye space and then projected onto the screen using the same matrix as loaded with GXSetProjection(); . The output is rendered back into the frame buffer. The point of grabbing the frame buffer must be determined carefully since it can not be truly the very last thing since this would affect all overlays and score displays as well.

Figure 20: Indirect texturing example.

Merging different shading algorithms does not come without any effort, however, the balanced architecture of the Nintendo Gamecube supports a wide variety of methods that combined together make the visual difference.

To summarize: Care must be taken while combining algorithms, shader should be constructed out of components or parts, and separation of global and local lights helps a great deal. Consistent lighting during runtime is a big step forward. Make all geometry lit dynamically during runtime and use color per vertex just for painting, not pre-lighting. Per pixel methods usually give better results, however, they are more expensive. Geometry and shading should be strictly separated.

Landscape Shading

The landscape in Rogue Leader is height-map based, and uniformly divided into smaller render-units called meta-tiles (c.f. figure 21). One meta-tile covers 128x128 meters, and all triangles belonging to a meta-tile must use the same shader. This restriction is enforced to simplify and improve the triangle stripping of the landscape (on the Nintendo GameCube™, as most other modern graphics pipelines, efficient triangle stripping is important to obtain high performance). When deciding the size of the meta-tiles, local lighting also has to be considered. Since the Nintendo Gamecube has a limited number of hardware lights (eight), large meta-tiles imply “fewer lights per area”. In addition, the larger the meta-tiles, the greater the chance to draw too much geometry with lighting enabled when it’s not necessary (which is not good – enabling hardware lights certainly do not come for free).

Figure 21: Landscape split up in metatiles and their LOD values.

When the landscape engine was programmed, the geometry part was implemented before the landscape shaders (c.f. figure 22). This meant that during the working phase for the landscape geometry, it was hard to see how high polygon-count was needed to make the results look sufficiently detailed and complex. As the shaders started to get in place, it became clear that the complexity of the geometry could be reduced without sacrificing the complexity in visual appearance (in the final game, a typical landscape view uses about 14k triangles). This experience shows the importance of a balance between the complexity in geometry, and the shaders applied to that geometry.

Figure 22: Geometry vs. shading.

Landscape Texturing

A texture layer is defined to be an affinely transformed repeated texture image. This implies that one texture image can give rise to several texture layers. Texture layers are applied to the landscape by vertically projecting them onto the surface; which is ok since the surface is a height-map, so any vertical line only intersects the surface once. Besides being easy to implement on both the tools and engine side, this approach is also memory efficient, since the texture coordinates do not need to be stored/loaded, but are derived directly from the position of the vertices (c.f. figure 23).

Figure 23: Texture coordinate generation.

The actual texturing of the landscape is done by blending/mixing several texture layers together across the surface. This multi-texturing approach eliminates the need for transition textures, and gives a varied look from a relatively few high-detail texture images. Since the scaling of a texture layer can be non-uniform, this approach can also help to combat the texture stretching which is common in height-map based landscapes in areas with steep slopes. According to the gradient of the height-map surface, one can apply texture layers that are scaled down in roughly that direction.

The work of specifying how the texture layers should be blended together was done in the in-house level design program called L3DEdit. This tool has features for managing texture layers, as well as blending them together. More technically, for each texture layer, L3DEdit maintains a corresponding gray-scale image which says how much of that texture layer should be present. These gray-scale images are called mix-maps, and the sum of all corresponding pixels from all mix-maps should always be one (or 255, if you like). L3DEdit can preview the blended landscape on the texture artist’s workstation, and allows for interactive changes to the mix-maps.

Figure 24: Mixing three texture layers.

For performance and memory reasons, on the Nintendo GameCube™ a meta-tile is not allowed to use more than three different texture layers blended together. In the data conversion each meta-tile that has non-trivial blending, is assigned a 32x32 pixels texture image that contains the mix-map information for that meta-tile. For meta-tiles that blend two or three texture layers, we store this information in four bits (I4) and eight bits (IA4) mix-map textures, accordingly. Duplicate mix-map texture tiles are ignored to preserve memory. To avoid seams between adjacent meta-tiles due to bi-linear texture filtering, only 31x31 unique pixels are used for each meta-tile – the last pixel rows are copied from the next, adjacent meta-tiles. To implement the texture layer blending on the Nintendo GameCube™, the texture environment is then set up to compute

mIT0 + (1-mI)T1

for blending two texture layers, and

mIT0 + mAT1 + (1-mI-mA)T2

for blending three texture layers (c.f. figure 24 for the most complicated case).

Landscape Self-Shadowing

The self-shadowing of the height-map surface is pre-computed as a shadow table in the data conversion. It turned out that doing ground-sun line segment intersections with the landscape in real-time was too expensive; even when the results were sparsely updated and cached. The shadow table stores the ground-sun intersection result for 256 different sun positions for each height-map vertex (in the game in-between values are interpolated). On a meta-tile basis, series of 256 intersection results is efficiently encoded for in a state-change array, and the number of state-changes is stored using a simple form of static Huffman encoding. The size of the shadow table is of course very dependent on how the sun is moving. In most levels, the shadow table is small (150-300k), but in some level where the sun is raising the table is >800k. In the game engine, meta-tile shadow information is decoded when it’s needed, and cached together with other vertex data. To get softer shadows a nine point/tap filter is applied to the shadow values (c.f. figure 25).

Figure 25: Landscape self shadowing.

This filter smoothes the shadow values, and can be efficiently implemented using only four additions and two shifts (by reusing previously computed columns for adjacent vertices). These shadow values are then sent to the texture environment as a color per vertex. The polygon interpolated shadow value is then multiplied with the global light color.

Together with the texture layers, additional effect maps are used to further enhance the detail/depth impression: emboss style bump-mapping, far-distance detail map, and a cloud map. The emboss style bump mapping is only used for up-close meta-tiles. A color per vertex value describes how to fade the map in/out over distance (these values are the level of detail morphing values from the height-map geometry computation). The far-distance detail map is used to break up repeated texturing far away, and it’s faded out close to the camera. This fade is done similar to how the emboss map is fading. The cloud map is used to give the impression of clouds casting moving shadows on the ground. It’s also just a vertically projected map, but this time with an animated translation.

Landscape Shader Optimizations

At first the height-map tiles were drawn in front to back order, but since this resulted in a lot of shader changes, it turned out that it was far more efficient to first sort the meta-tiles in shader order (and within one set of meta-tiles using the same shader, sort front to back).

A trick that is worth mentioning is how to avoid sending the same bi-normals and tangents for emboss mapping repeatedly to the transform unit (XF) of the graphics processor. It turns out that if these vectors are not present in the vertex format, XF will provide the previously transformed bi-normal and tangent, which reside in internal registers. Thus, if a dummy triangle is drawn with the bi-normal and tangent immediately before the landscape is drawn, then there is no need to send the same vectors over again for the rest of the height-map triangles. This means that only one vertex format is needed for the entire landscape, and it saves memory, transfer bandwidth and most importantly transform performance.

The landscape in Rogue Leader uses a multi-texturing approach that is implemented with a specialized set of shaders for blending/mixing texture layers. For efficient processing, the landscape if divided into manageable render-units. This is also important for utilizing the local lighting hardware support. To obtain high performance, it’s important to achieve efficient triangle stripping, and minimize the number of shader changes.

Code Listing 1: Generating texture coordinates for specular highlights.

void shadingMath_ComputeSpecularPostMtx(mt32 *pOut, v32 *ldir_viewspace, f32 size)

{
f32 scale, dotp, r, tweak;
v32 vaxis, vhalf;
q32 q;

// convert input...
assert(size >= 0.0f && size <= 1.0f);

size = mathClampMinMax(size, 0.0f, 1.0f);
tweak = (PHONG_MAX - PHONG_MIN)*size + PHONG_MIN;

// check for singular point...
dotp = -ldir_viewspace->z;

if (dotp <= -1.0f)
{
mathMatSetScale(pOut, 0.0f);
return;
}

// The obtained half-angle vector directs an opposite side...
if (dotp >= 1.0f)
{
// Looking exactly with the light...
mathMatInit(pOut);
}
else
{
vhalf.x = -ldir_viewspace->x;
vhalf.y = -ldir_viewspace->y;
vhalf.z = -ldir_viewspace->z + 1.0f;

mathVecNormalize(&vhalf);

r = facos(-vhalf.z);
vaxis.x = -vhalf.y;
vaxis.y = vhalf.x;
vaxis.z = 0.0f;

mathQuatMakeRad(&q, &vaxis, r);
mathQuatToMatrix(pOut, &q);
};

scale = 2.0f * tweak + 1.5f;
mathMatAddScale(pOut, scale);

pOut->m[RD_U][RD_T] =
pOut->m[RD_V][RD_T] = 0.5f;

// setup w to be always one...
pOut->m[RD_W][RD_X] =
pOut->m[RD_W][RD_Y] =
pOut->m[RD_W][RD_Z] = 0.0f;
pOut->m[RD_W][RD_T] = 1.0f;
}

Code Listing 2: Generating texture coordinates for environment lookups.

void shadingMath_ComputeSphereLookupPostMtx(mt32 *pOut, f32 nrm_scale, bool bBinormal)

Code Listing 3: Correcting texture coordinates for bumped specular lookups.

Code Listing 4: Computing intensity values for layered fog lookup textures.

static u8 _fogFunction(tLayeredFog *pFog, f32 x, f32 y)

{
f32 v;
assert(pFog);
assert(x >= 0.0f && x < pFog->rampWidth);
assert(y >= 0.0f && y < pFog->rampHeight);
assert(pFog->inFogFactor >= 0.0f && pFog->inFogFactor <= 1.0f);
x /= pFog->rampWidth - 1.0f;
y /= pFog->rampHeight - 1.0f;
// height...
v = x * x;
v = v * (1.0f - pFog->inFogFactor) + pFog->inFogFactor;
// distance...
v *= y * y;
v *= 255.0f;
return ((u8)mathClampMax(v, pFog->currentSettings.maxIntensity));
}

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