STL (Standard Tessellation Language) is considered to be the standard in 3D printing, having been created in 1987 by the inventor of 3D printing, Chuck Hull. Its long history makes it compatible with most 3D CAD software and 3D printing hardware and software.

It stores geometry data using tessellation, which is the process of covering a surface with triangles to create a 3D model. However, it only stores geometry data and doesn't include information such as color, texture, and material. The number of triangles used to create a model determines the level of detail, and the more triangles used, the larger the file size.

An important feature of STL is its use of tessellations to represent geometry. This involves covering a surface with a pattern of shapes. In an STL file, a 3D object's shape is represented by a multitude of triangles that make up its surface.

The more complex a surface, the more triangles are needed to accurately represent it. However, a high number of triangles results in a larger file size.

Another defining aspect of STL is that it only contains geometry information. It does not include details such as color, texture, or material, which were not a concern in the past when 3D printers could only produce single-color, single-material prints. While this may still suffice for basic prototypes, advancements in multi-color and multi-material 3D printing may lead to the eventual phasing out of the STL format as it becomes insufficient for fully functional, ready-to-use objects.

The OBJ file format was created by WaveFront Technologies and was initially used in the world of graphic design. Its function was exchanging information between different software programs. Over time, as 3D printing technology has advanced to include multi-color and multi-material capabilities, the OBJ format has also become widely used in the 3D printing industry.

The OBJ file format is widely popular, taking second place after STL, in the world of 3D printing. Unlike STL, OBJ files can store not only geometry data but also information about color, texture, and material. This information is stored in a separate MTL (Material Template) file. To print with color, the OBJ file must be accompanied by its corresponding MTL file.

One of the key benefits of the OBJ file format is the ability to choose how the geometry of your model is encoded. OBJ files support the use of various shapes, such as polygons and quadrilaterals, in addition to triangles, to create tessellations. Advanced and more precise methods, such as free-form curves and surfaces, can also be employed in OBJ files. This allows for greater accuracy in the storage of 3D models.

AMF is a more advanced file format that can store a greater level of detail and information than STL. This includes color and texture information, which is lacking in STL. In addition, AMF supports more advanced geometry encodings such as free-form curves and surfaces, and it provides a way to specify the material properties of the object being printed.

Another advantage of AMF is that it provides a more efficient method for storing data, which results in smaller file sizes. This allows for faster data transfer and easier sharing and editing of models. AMF is also designed to be flexible, allowing for updates and new features to be added in the future.
However, despite its advantages, AMF is not as widely used as STL and is supported by fewer software and hardware platforms. This means that compatibility and ease of use can be a concern for some users.

In conclusion, AMF is a modern, advanced file format for 3D printing that offers a number of benefits over STL. However, its limited compatibility and reduced popularity in the industry may make it less accessible for some users.

The 3MF consortium, consisting of prominent companies in the 3D printing industry such as Autodesk, 3D Systems, Stratasys, HP, and Microsoft, was formed to address the limitations and slow adoption of the AMF file format. The consortium developed the 3MF 3D printing file format, which is similar to AMF but has gained wider acceptance.
The widespread acceptance of the 3MF 3D printing file format is due to the industry presence and large customer base of the 3MF consortium, as well as the capabilities of the file format itself.

The 3MF file format features all the technical characteristics of AMF, such as the use of curved triangular tessellations for encoding geometry and the ability to store color, texture, material, and orientation information with high precision.
The 3MF 3D printing file format stores data in a readable XML format, making it easier for development and editing. These files are known for their low error rates and are regarded as immediately ready for printing, which is a highly valued feature in the 3D printing industry.