Question: This is a good "explain the slide in your own words" opportunity. I'd like you to explain to me why the case of interpenetrating triangles is no different than the case where triangles are not interpenetrating.
phoenixdown
Min() is associative and commutative, so the order in which we test the two triangles is irrelevant, because we will only propagate the global minimum distance (except exactly along the line of intersection).
dvernet
Going back to the previous slide, we see that the test is executed over every [x][y] sample value in screen space. Each triangle primitive stores its depth at every sample, so the order that the triangles are rasterized does not matter because the depth test cares about the constant depth stored at each sample point for each primitive (and we don't have to worry about transparent primitives).
kayvonf
@dvernet: Good. Since depth is evaluated at specific sample points (and not "regions" of the image), the computation of "closest" at each sample point is independent of that at any other sampler point, and independent of the order of the triangles.
Question: This is a good "explain the slide in your own words" opportunity. I'd like you to explain to me why the case of interpenetrating triangles is no different than the case where triangles are not interpenetrating.
Min() is associative and commutative, so the order in which we test the two triangles is irrelevant, because we will only propagate the global minimum distance (except exactly along the line of intersection).
Going back to the previous slide, we see that the test is executed over every [x][y] sample value in screen space. Each triangle primitive stores its depth at every sample, so the order that the triangles are rasterized does not matter because the depth test cares about the constant depth stored at each sample point for each primitive (and we don't have to worry about transparent primitives).
@dvernet: Good. Since depth is evaluated at specific sample points (and not "regions" of the image), the computation of "closest" at each sample point is independent of that at any other sampler point, and independent of the order of the triangles.