I learned at school that the z-axis is up. It is the same in modeling software like Blender. However in many games the y-axis is up.
What is the reason?
Answer
I think the direction of the coordinate axes are holdovers from different domains where the crucial plane was different, and X/Y were aligned with that crucial plane. In some applications the ground plane was the most important, thus X/Y were the ground and Z ended up perpendicular to that. For games however the crucial plane is usually the screen (especially of course back when they were 2D and just starting to transition to 3D) thus X/Y were the screen and then when games went 3D Z ended up perpendicular to that.
You can see that kind of distinction between the two biggest 3D art tools: 3ds max and Maya. The Z axis is up in 3ds max because that grew out of architectural tools, while the Y axis is up in Maya because that grew out of movie-making tools.
The important thing to realize when comparing any specific tool to what you learned in school is that it's all arbitrary. It really doesn't matter which way the axes are pointed as long as you keep everything consistent and translate correctly between different coordinate systems.
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