![]() ![]() Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the Moroccan architecture and decorative geometric tiling of the Alhambra palace. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions.Ī real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. A tiling that lacks a repeating pattern is called "non-periodic". The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.Ī periodic tiling has a repeating pattern. Patch.vertex * barycentricCoordinates.x + patch.vertex * barycentricCoordinates.An example of non‑periodicity due to another orientation of one tile out of an infinite number of identical tiles.Ī tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. The X, Y, and Z coordinates determine the weights of the first, second, and third control points. To find the position of this vertex, we have to interpolate across the original triangle domain, using the barycentric coordinates. įloat3 barycentricCoordinates : SV_DomainLocation Inside the function, we have to generate the final vertex data. OutputPatch patch, float3 barycentricCoordinates : SV_DomainLocation They have the SV_DomainLocation semantic. To make this possible, the domain function is invoked once per vertex and is provided the barycentric coordinates for it. It's up to the domain shader to use those coordinates to derive the final vertices. Instead, it comes up with barycentric coordinates for those vertices. While the tessellation stage determines how the patch should be subdivided, it doesn't generated any new vertices. TessellationFactors factors, OutputPatch patch ![]() The domain program is fed the tessellation factors that were used, as well as the original patch, which is of type OutputPatch in this case. We signal this again via the UNITY_domain attribute. Shader "Custom/Tessellation" īoth the hull and domain shader act on the same domain, which is a triangle. Duplicate that shader, rename it to Tessellation Shader and adjust its menu name. To clearly see that triangles get subdivided, we'll make use of the Flat Wireframe Shader. Let's put the code that we'll need in its own file, MyTessellation.cginc, with its own include guard. The first step is to create a shader that has tessellation enabled. We're going to need a hull program and domain program. But it's not as simple as adding just one other program to our shader. This stage sits in between the vertex and the fragment shader stages. We cannot control that, but there's also a tessellation stage that we are allowed to configure. It does this for various reasons, for example when part of a triangle ends up clipped. The GPU is capable of splitting up triangles fed to it for rendering. This makes it possible to add more details to geometry, though in this tutorial we'll focus on the tessellation process itself. ![]() In our case, we're going to subdivide triangles so we end up with smaller triangles that cover the same space. Tessellation is the art of cutting things into smaller parts. If you don't have enough triangles, make some more. This tutorial is made with Unity 2017.1.0. It uses the Flat and Wireframe Shading tutorial as a basis. This tutorial covers how to add support for tessellation to a custom shader. ![]()
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