Tessellating viruses

Home Art Create a Simple Tessellation. Certain basic shapes can be easily tessellated: squares hexagons triangles Combination shapes, complicated shapes, and animals such as the ones found on these sites are also examples to print and color: Shapes that Tessellate Lizards, M. Escher and more What exactly is a tessellation?

They can be made by positioning the same shape with one of these three operations: translation rotation reflection Translation can be thought of as sliding the shape along a plane. Inventions Tessellation Project.

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Three basic types of Reasoning. Three Types of Search Engines. The Tessellation Control Shader TCS determines how much tessellation to do it can also adjust the actual patch data, as well as feed additional patch data to later stages.

Therefore, the TCS is primarily responsible for ensuring continuity across patches. So if you have two adjacent patches that need to have different levels of tessellation, the TCS invocations for the different patches need to use their tessellation controls to ensure that the shared edge s between the patches use the same level of tessellation.

Without this protection, gaps and breaks in what are supposed to be contiguous patches can occur. The tessellation primitive generator takes the input patch and subdivides it based on values computed by the TCS or provided as defaults. The Tessellation Evaluation Shader TES takes the tessellated patch and computes the vertex values for each generated vertex. The number of vertices per patch can be defined on the application-level using:.

The maximum number of patch vertices is implementation-dependent, but will never be less than Patch primitives are always a sequence of individual patches; there is no such thing as a "patch strip" or "patch loop" or such. If you need to do something like triangle strips, you should use Indexed Rendering to get similar behavior, though it will not reduce the number of vertices in the index list.

Fortunately, the Post-Transform Cache should help mitigate the performance impact of providing more indices. The first step of tessellation is the optional invocation of a tessellation control shader TCS.

The TCS has two jobs:. The TCS can change the size of a patch, adding more vertices per-patch or providing fewer. However, a TCS cannot discard a patch directly; it can do so indirectly , nor can it write multiple patches. Therefore, for each patch provided by the application, one patch will be provided to the next tessellation stage. The TCS is optional. If no TCS is active in the current program or program pipeline, then the patch data is passed directly from the Vertex Shader invocations to the tessellation primitive generation step.

The amount of tessellation done in this case is taken from default values set into the context. These are defined by the following function:.

Primitive generation is a fixed-function stage responsible for creating a set of new primitives from the input patch.

This stage is only executed if a tessellation evaluation shader TES is active in the current program or program pipeline. Primitive generation is affected by the following factors:. Notice that the primitive generation is not affected by the user-defined outputs of the TCS or vertex shader if no TCS is active , the TCS's output patch size, or any per-patch TCS outputs besides the tessellation levels.

The primitive generation part of the tessellation stage is completely blind to the actual vertex coordinates and other patch data. The purpose of the primitive generation system is to determine how many vertices to generate, in which order to generate them, and what kind of primitives to build out of them.

The actual per-vertex data for these vertices, such as position, color, etc. Because of this dichotomy, the primitive generator operates on what could be considered an "abstract patch". It doesn't look at the patch output from the TCS; it thinks only in terms of tessellating an abstract quad, triangle, or "isoline" block. Depending on the abstract patch type, the primitive generator evaluates a different number of tessellation levels and applies different tessellation algorithms.

Each generated vertex has a normalized position i. This position has two or three components, depending on the type of the patch. The amount of tessellation that is done over the abstract patch type is defined by inner and outer tessellation levels. These, as previously stated, are provided either by the TCS or by context parameters specified via glPatchParameter. They are a 4-vector of floats defining the "outer tessellation levels" and a 2-vector of floats defining the "inner tessellation levels.

The specific interpretation depends on the abstract patch type being used, but the general idea is this. In most cases, each tessellation level defines how many segments an edge is tessellated into; so a tessellation level of 4 means that an edge will become 4 edges 2 vertices become 5. The "outer" tessellation levels define the tessellation for the outer edges of the primitive. This makes it possible for two or more patches to properly connect, while still having different tessellation levels within the patch.

The inner tessellation levels are for the number of tessellations within the abstract patch. For example, triangles only uses one inner level and 3 outer levels. The rest are ignored. The patch can be discarded if any outer tessellation level is 0 or less, but only for tessellation levels that the abstract patch actually uses. The patch can also be discarded if one of these values is a floating-point NaN. A patch that is discarded does not get tessellated, and no TES is invoked for it. It is simply swallowed by the system as though it never were.

This allows a TCS to effectively cull patches by passing 0 for a relevant outer tessellation level. The tessellation levels specified in this way are not directly used. Different Pentagons. Triangles 3. Squares 4. Hexagons 6. Curvy Shapes.