![]() Tessellation allows you to refine your geometry on the fly, without requiring you to allocate additional memory to hold the resulting vertices. Instancing is best used when the repetition of meshes won’t be noticeable, as when rendering debris, foliage, or crowds. Normal mapping does not refine the silhouette edge the mesh, so the effect is not always convincing, but it is a great way to reduce the number of vertices in a mesh.Īnother technique that allows you to get more mileage out of less geometry is instancing, which draws the same mesh multiple times without duplicating the vertex data in memory. One possible approach is to decimate (reduce) the geometry of the mesh while producing a texture map whose texels store fine-grained surface normals. There are many techniques that can be used to reduce the memory footprint of geometry. If you’ve used Metal to render 3D meshes composed of triangles, you may have encountered a situation where the mesh you wanted to draw was too large to fit into memory. The tessellated triangles then pass through the remainder of the graphics pipeline (vertex shader, rasterizer, etc.) on their way to the framebuffer. The number of triangles generated by a patch is controlled by configuring a fixed-function stage of the pipeline called the tessellator. A patch is a triangular or quadrilateral domain that can be subdivided by the GPU to produce triangles. Conversely, when tessellating, our draw calls are denominated in patches. With ordinary draw calls, we render primitives such as triangles, lines, or points. Tessellation is a form of geometry amplification: programmatically turning geometry into more geometry. Polyhedrons subdivided with Metal tessellation A Brief Introduction to Tessellation It consists of a Mac app written in Swift that shows how to dynamically subdivide a cube and icosahedron, optionally smoothing the resulting shapes into approximate spheres. The source code for this article is available here. ![]() This article discusses the fundamentals of tessellation and how to do it in Metal future articles will showcase specific use cases. Tessellation is a powerful technique for generating geometry dynamically with many use cases from CAD/CAM to game development and beyond. Here are a variety of basic geometric shapes that can tessellate from this same pattern, including a hexagon, triangle, square, trapezoid, parallelogram, pentagon (irregular), rhombus (diamond), and rectangle:Ĭopyright © 2014 Chris McMullen, author of the Improve Your Math Fluency series of math workbooksĬlick to view my Goodreads author page.In this article we will take a look at how to do tessellation on the GPU with Metal. The same pattern can make a tessellation with stars and hexagons: The lattice structure below can be shaded in several different ways to create simple geometric patterns that tessellate:įor example, here is a tessellation composed of hexagons: Some of the more extreme examples of this can be seen in M.C. ![]() Even arrangements of curved objects can tessellate. There are many other shapes that tessellate, such as stars combined with other shapes. (Quadrilaterals are polygons with four sides.) Although regular pentagons don’t tessellate, some irregular polygons can (such as the pentagon made by placing an isosceles triangles on a square, as children often do to draw a simple picture of a house). (A regular polygon is one with equal sides and angles.) All quadrilaterals can form tessellations. Tessellations can also be made from irregular polygons. For example, it won’t work with pentagons. Not any regular polygon will work, however. ![]() Simple tessellations can be made by creating a two-dimensional lattice out of regular geometric shapes, like equilateral triangles, squares, and hexagons. A tessellation is a repeated two-dimensional geometric pattern, with tiles arranged together without any space or overlap. ![]()
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