A forgotten Historical benefit, of Marching Tetrahedra?

One of the facts which the WiKiPedia mentions, is, that for 20 years, there was a patent on the “Marching Cubes” algorithm, which basically forced some software developers – especially Linux and other, open-source developers – to use “Marching Tetrahedra” as an alternative. But I think that this article has one flaw:

Its assumptions are too modern.

What this article states is that, like Marching Cubes, individual tetrahedra can be fed to the GPU as “Triangle Strips”. The problem with this is the fact, that triangle strips are only recognized by the GPU, if DirectX 10(+), or OpenGL 3(+) is available, which means, that ‘a real Geometry Shader’ needs to be running.

Coders were working with Iso-surfaces, during the DirectX 9.0c / OpenGL 2 days, when there were no real Geometry Shaders. And then, one of the limitations that existed in the hardware was, that even if the Fragment Shader received vertices grouped as triangles, usually, Vertex Shaders would only get to probe one vertex at a time. So, what early coders actually did was, to implement a kind of poor man’s geometry shader, within the Fragment Shader. This was possible because one of the pixel formats which the FS could output, also corresponded to one of the vertex formats, which a VS could read as input.

Hence, a Fragment Shader running in this fashion would render its output – under the pretense that it would form an image – into the Vertex Buffer of another rendering pipeline. This was therefore appropriately named “Render-To-Vertex-Buffer”, or, ‘R2VB‘. And today, graphics cards exist, which no longer permit R2VB, but which permit OpenGL 4 and/or real Geometry Shaders, the latter of which, in turn, can group their Output Topologies into Triangle Strips.

This poses the question, ‘Because any one shader invocation can only see its own data, how could this result in a Marching Tetrahedra implementation?’ And I don’t fully know the answer.

Today, I can no longer imagine in a satisfyingly complete way, how the programmers in the old days solved such problems. Like many other people today, I need to imagine that the GPU does offer a Geometry Shader – a GS – explicitly, in order to implement a GS.


 

In a slightly different way, Marching Tetrahedra will continue to be important in the near future, because coders needed to implement the algorithm on the CPU, not the GPU, because they had Iso-Surfaces to render, but no patent-rights to the Marching Cubes algorithm, and, because programmers are not usually asked to rewrite all their predecessors’ code. Hence, code exists, which does all this purely on the CPU, and for which the man-hours don’t exist, to convert it all to Marching Cubes code.

(Update 5/09/2020, 17h30… )

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A bit of my personal history, experimenting in 3D game design.

I was wide-eyed and curious. And much before the year 2000, I only owned Windows-based computers, purchased most of my software for money, and also purchased a license of 3D Game Studio, some version of which is still being sold today. The version that I purchased well before 2000 was using the ‘A4′ game engine, where all the 3DGS versions have a game engine specified by the latter ‘A’ and a number.

That version of 3DGS was based on DirectX 7 because Microsoft owns and uses DirectX, and DirectX 7 still had as one of its capabilities to switch back into software-mode, even though it was perhaps one of the earliest APIs that offered hardware-rendering, provided that is, that the host machine had a graphics card capable of hardware-rendering.

I created a simplistic game using that engine, which had no real title, but which I simply referred to as my ‘Defeat The Guard Game’. And in so doing I learned a lot.

The API which is referred to as OpenGL, offers what DirectX versions offer. But because Microsoft has the primary say in how the graphics hardware is to be designed, OpenGL versions are frequently just catching up to what the latest DirectX versions have to offer. There is a loose correspondence in version numbers.

Shortly after the year 2000, I upgraded to a 3D Game Studio version with their ‘A6′ game engine. This was a game engine based on DirectX 9.0c, which was also standard with Windows XP, which no longer offered any possibility of software rendering, but which gave the customers of this software product their first opportunity to program shaders. And because I was playing with the ‘A6′ game engine for a long time, in addition owning a PC that ran Windows XP for a long time, the capabilities of DirectX 9.0c became etched in my mind. However, as fate would have it, I never actually created anything significant with this game engine version – only snippets of code designed to test various capabilities.

Continue reading A bit of my personal history, experimenting in 3D game design.