Is this distance functions or distance field as commonly used as what we mainly studied (polygon mesh)? What are its applications?
keenan
Distance functions that are based on closed-form expressions (like $x^2 + y^2 + z^2 - r^2$) are very uncommon, because it is hard to describe interesting geometry this way. The example above is perhaps an exception, but it takes a huge amount of work to design scenes this way, and the rendering performance is still rather poor compared to an optimized mesh-based renderer.
However, the advantage is that there are potentially fewer "geometric aliasing" artifacts. For instance, if you zoom in on a mesh of a sphere, eventually you will see a blocky polygonal boundary. Not true with the implicit description above. Also, it is easier to draw fractal surfaces with infinite detail if you're willing to ray trace implicit surfaces. (But again, controlling this fractal detail is very difficult, and performance is typically not great.)
Is this distance functions or distance field as commonly used as what we mainly studied (polygon mesh)? What are its applications?
Distance functions that are based on closed-form expressions (like $x^2 + y^2 + z^2 - r^2$) are very uncommon, because it is hard to describe interesting geometry this way. The example above is perhaps an exception, but it takes a huge amount of work to design scenes this way, and the rendering performance is still rather poor compared to an optimized mesh-based renderer.
However, the advantage is that there are potentially fewer "geometric aliasing" artifacts. For instance, if you zoom in on a mesh of a sphere, eventually you will see a blocky polygonal boundary. Not true with the implicit description above. Also, it is easier to draw fractal surfaces with infinite detail if you're willing to ray trace implicit surfaces. (But again, controlling this fractal detail is very difficult, and performance is typically not great.)