This formula looks quite similar to a kinematics equation I've seen: x = x0 + v0t + 1/2(a)t^2. Every term here is raised to the t though!
showyouramen
It's pretty interesting that even though we're dealing with a largely different concept than what we've done before, we still represent object in meshes with triangles. I guess it just goes to show how powerful that interpretation is.
bernardmc8
I remember from learning about kinematics in physics that this equation and many other kinematic equations, while they are good estimates of how objects behave, they are still just approximations and don't account for other factors, like in this example the trajectory of the ball doesn't account for wind resistance or rotation. I wonder how much physics we need to take into account before rendered motion looks sufficiently realistic. I would imagine it also depends on the situation.
yfz3357
@faywerliu I think the superscript t does not mean raised to the power of t, rather it means at time t. For example, vt means velocity at time t. So I think it is the same formula.
kevintli
@bernardmc8 that's an interesting point — it kind of reminds me of the tradeoffs we had to consider with global illumination (e.g. setting a max depth, or using Russian roulette at the expense of having slightly more noise), which was also an attempt to approximate reality using not-quite-exact physics principles. I'd like to see a comparison of parabolic animations with increasing levels of detail/things taken into account, similar to how we saw what a scene would look like with more and more ray bounces added. I also wonder if there's a standard way to quantify how "realistic" an animation looks, and whether that metric is used to make tradeoffs depending on the use case.
ML2000-LT
we can actually consider this as a taylor series for the term x^(t + dt), since what we get is x + x'dt + x''d2t ...., if dt is close to zero, and x' is actually vt, x'' is actually at, therefore all the terms for dt makes perfect sense if we are taken into this mathematical consideration
This formula looks quite similar to a kinematics equation I've seen: x = x0 + v0t + 1/2(a)t^2. Every term here is raised to the t though!
It's pretty interesting that even though we're dealing with a largely different concept than what we've done before, we still represent object in meshes with triangles. I guess it just goes to show how powerful that interpretation is.
I remember from learning about kinematics in physics that this equation and many other kinematic equations, while they are good estimates of how objects behave, they are still just approximations and don't account for other factors, like in this example the trajectory of the ball doesn't account for wind resistance or rotation. I wonder how much physics we need to take into account before rendered motion looks sufficiently realistic. I would imagine it also depends on the situation.
@faywerliu I think the superscript t does not mean raised to the power of t, rather it means at time t. For example, vt means velocity at time t. So I think it is the same formula.
@bernardmc8 that's an interesting point — it kind of reminds me of the tradeoffs we had to consider with global illumination (e.g. setting a max depth, or using Russian roulette at the expense of having slightly more noise), which was also an attempt to approximate reality using not-quite-exact physics principles. I'd like to see a comparison of parabolic animations with increasing levels of detail/things taken into account, similar to how we saw what a scene would look like with more and more ray bounces added. I also wonder if there's a standard way to quantify how "realistic" an animation looks, and whether that metric is used to make tradeoffs depending on the use case.
we can actually consider this as a taylor series for the term x^(t + dt), since what we get is x + x'dt + x''d2t ...., if dt is close to zero, and x' is actually vt, x'' is actually at, therefore all the terms for dt makes perfect sense if we are taken into this mathematical consideration