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Julian Harris
Julian Harris

Sample Cube |BEST|

Optionally, consider installing Excel to browse your multidimensional data as you proceed through the tutorial. Installing Excel enables the Analyze in Excel feature that starts Excel using a PivotTable field list that is connected to the cube you are building. Using Excel to browse data is recommended because you can quickly build a pivot report that lets you interact with the data.

sample cube

The sample projects use data source impersonation settings that specify the security context under which data is imported or processed. By default, the impersonation settings specify the Analysis Services service account for accessing the data. To use this default setting, you must ensure that the service account under which Analysis Services runs has data reader permissions on the AdventureWorksDW database.

Unzip the sample projects: right-click on the file and select Extract All. After extracting the files, you should have folders Lesson 1, 2, 3, 5, 6, 7, 8, 9, 10 Complete and Lesson 4 Start.

If Analysis Services and the Database Engine are installed as the default instance (MSSQLServer) and all software is running on the same computer, you can click Deploy Solution on the Build menu to build and deploy the sample project to the local Analysis Services instance. During deployment, data is processed (or imported) from the AdventureWorksDW database on the local Database Engine instance. A new Analysis Services database is created on the Analysis Services instance that contains the data retrieved from the Database Engine.

A sampling of our laser ready sheets of hardwood. Each cube contains a mix of quarter and eighth inch thick pieces that are 4 x 4 inches big. Each code contains a random assortment of thicknesses and species that were milled at Makers Workshop. Each 44 cube contains between 14 and 30 pieces depending on thickness. Each cube will contain a minimum of three different species, often times more than three.

Till, Y. (2006), Sampling Algorithms, Springer.Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. Computational Statistics, 21/1:53--62. Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, Journes de Mthodologie Statistique, Paris.Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. Biometrika, 91:893--912.Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. Journal of Statistical Planning and Inference, 128/2:411--425.

We've been using 2D textures for a while now, but there are more texture types we haven't explored yet and in this chapter we'll discuss a texture type that is a combination of multiple textures mapped into one: a cube map.

A cubemap is a texture that contains 6 individual 2D textures that each form one side of a cube: a textured cube. You may be wondering what the point is of such a cube? Why bother combining 6 individual textures into a single entity instead of just using 6 individual textures? Well, cube maps have the useful property that they can be indexed/sampled using a direction vector. Imagine we have a 1x1x1 unit cube with the origin of a direction vector residing at its center. Sampling a texture value from the cube map with an orange direction vector looks a bit like this:

If we imagine we have a cube shape that we attach such a cubemap to, this direction vector would be similar to the (interpolated) local vertex position of the cube. This way we can sample the cubemap using the cube's actual position vectors as long as the cube is centered on the origin. We thus consider all vertex positions of the cube to be its texture coordinates when sampling a cubemap. The result is a texture coordinate that accesses the proper individual face texture of the cubemap.

A cubemap is a texture like any other texture, so to create one we generate a texture and bind it to the proper texture target before we do any further texture operations. This time binding it to GL_TEXTURE_CUBE_MAP:

Because a cubemap contains 6 textures, one for each face, we have to call glTexImage2D six times with their parameters set similarly to the previous chapters. This time however, we have to set the texture target parameter to match a specific face of the cubemap, telling OpenGL which side of the cubemap we're creating a texture for. This means we have to call glTexImage2D once for each face of the cubemap.

Here we have a vector called textures_faces that contain the locations of all the textures required for the cubemap in the order as given in the table. This generates a texture for each face of the currently bound cubemap.

Don't be scared by the GL_TEXTURE_WRAP_R, this simply sets the wrapping method for the texture's R coordinate which corresponds to the texture's 3rd dimension (like z for positions). We set the wrapping method to GL_CLAMP_TO_EDGE since texture coordinates that are exactly between two faces may not hit an exact face (due to some hardware limitations) so by using GL_CLAMP_TO_EDGE OpenGL always returns their edge values whenever we sample between faces.

Within the fragment shader we also have to use a different sampler of the type samplerCube that we sample from using the texture function, but this time using a vec3 direction vector instead of a vec2. An example of fragment shader using a cubemap looks like this:

That is still great and all, but why bother? Well, it just so happens that there are quite a few interesting techniques that are a lot easier to implement with a cubemap. One of those techniques is creating a skybox.

A skybox is a (large) cube that encompasses the entire scene and contains 6 images of a surrounding environment, giving the player the illusion that the environment he's in is actually much larger than it actually is. Some examples of skyboxes used in videogames are images of mountains, of clouds, or of a starry night sky. An example of a skybox, using starry night sky images, can be seen in the following screenshot of the third elder scrolls game:

You probably guessed by now that skyboxes like this suit cubemaps perfectly: we have a cube that has 6 faces and needs to be textured per face. In the previous image they used several images of a night sky to give the illusion the player is in some large universe while he's actually inside a tiny little box.

If you would fold those 6 sides into a cube you'd get the completely textured cube that simulates a large landscape. Some resources provide the skybox in a format like that in which case you'd have to manually extract the 6 face images, but in most cases they're provided as 6 single texture images.

Since a skybox is by itself just a cubemap, loading a skybox isn't too different from what we've seen at the start of this chapter. To load the skybox we're going to use the following function that accepts a vector of 6 texture locations:

A cubemap used to texture a 3D cube can be sampled using the local positions of the cube as its texture coordinates. When a cube is centered on the origin (0,0,0) each of its position vectors is also a direction vector from the origin. This direction vector is exactly what we need to get the corresponding texture value at that specific cube's position. For this reason we only need to supply position vectors and don't need texture coordinates.

The interesting part of this vertex shader is that we set the incoming local position vector as the outcoming texture coordinate for (interpolated) use in the fragment shader. The fragment shader then takes these as input to sample a samplerCube:

The fragment shader is relatively straightforward. We take the vertex attribute's interpolated position vector as the texture's direction vector and use it to sample the texture values from the cubemap.

Rendering the skybox is easy now that we have a cubemap texture, we simply bind the cubemap texture and the skybox sampler is automatically filled with the skybox cubemap. To draw the skybox we're going to draw it as the first object in the scene and disable depth writing. This way the skybox will always be drawn at the background of all the other objects since the unit cube is most likely smaller than the rest of the scene.

If you run this you will get into difficulties though. We want the skybox to be centered around the player so that no matter how far the player moves, the skybox won't get any closer, giving the impression the surrounding environment is extremely large. The current view matrix however transforms all the skybox's positions by rotating, scaling and translating them, so if the player moves, the cubemap moves as well! We want to remove the translation part of the view matrix so only rotation will affect the skybox's position vectors.

So to give us a slight performance boost we're going to render the skybox last. This way, the depth buffer is completely filled with all the scene's depth values so we only have to render the skybox's fragments wherever the early depth test passes, greatly reducing the number of fragment shader calls. The problem is that the skybox will most likely render on top of all other objects since it's only a 1x1x1 cube, succeeding most depth tests. Simply rendering it without depth testing is not a solution since the skybox will then still overwrite all the other objects in the scene as it's rendered last. We need to trick the depth buffer into believing that the skybox has the maximum depth value of 1.0 so that it fails the depth test wherever there's a different object in front of it.

We now have the entire surrounding environment mapped in a single texture object and we could use that information for more than just a skybox. Using a cubemap with an environment, we could give objects reflective or refractive properties. Techniques that use an environment cubemap like this are called environment mapping techniques and the two most popular ones are reflection and refraction. 041b061a72


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