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>> Sketching parabolic arcs. So in animation, there's a lot of cases where we find parabolic
arcs, one of the obvious situations is when we have something flying through the air,
the path of action is parabolic arc, we talked about that in a previous tutorial. Now, another
instance where we find a parabolic arc is when we have an object that is falling or
rising and falling, then the motion curve in the graph editor is also a parabolic arc.
And in fact, if we have something that's flying through the air and we see the path of action,
say this ball flying through the air that has a path of action that's a parabolic arc.
And then the motions curves in the graph editor, the motion curve for the horizontal position
would be a straight line, but the motion curve for the vertical position is again, a parabolic
arc. Now the parabolic arc of the path of action is not necessarily the same curvature
as a parabolic arc in the motion curve. So they are both parabolic arcs, but they may
have different curvatures just like you can have a line that has a slope that's either
steep or shallow, you can have parabolic arcs that either curve a lot or curve more gently,
so. Now let's see how to sketch a parabolic arc. Now when you decide to make a parabolic
arc, the first thing is you want to decide where the arc is going to start and where
the arc is going to end. Next you decide where the top of the arc will be, so this is the
height of the arc and now I've just drawn a box around these two and the start and ends
points and then the height. Well, I want to locate the apex, and the apex is supposed
to be half way between the start and end points, now I can either just roughly estimate this
middle position or I could be more careful and draw these diagonals and I know that the
diagonals intersect at the center of the rectangle and so then I just draw a vertical from this
intersection and then I know that that's half way between the start and end points, and
that's my apex. The next thing and almost the final thing is I need to put some points
on either side of the apex. So let's look at the points that's on the side of the apex
where the arc is coming down, so we have the apex and then the end point, we want the point
that is in between those two to be half way horizontally and a quarter of the way down.
So this quarter of the way down, this is the fourth down at half time rule that's discussed
in another tutorial, but even if you're not familiar with that just remember that from
the apex to the bottom that point should be a quarter of the way down when it's half way
in between from horizontally, it should be a quarter of the way down vertically. Of course
it's the same for the point on the other side of the apex between the start and the apex.
Well, now we're basically done because all we have to do is sketch a smooth curve that
connects those points, you want to make sure it's flat at the top, and there's your parabolic
arc. And youou can compare with examples of things flying through the air like this stream
of water. You can even check the shadows also of parabolic arc. Now this technique is even
simpler when you want to sketch a parabolic arc in the graph editor for example for this
ball that's falling down, this first key frame is at the top, the last key frame is at the
bottom, the key frame that's half way in time between those two is here and this is easy
to find because the graph editor has a grid and so this is pretty easy to either estimate
or just count out. Now we want at this frame, we want the ball to be a forth of the way
down. Again using the grid, it's pretty easy to see that this is half way down and then
between the apex and half way down is a fourth of the way down. So this is where we put that
key frame and with that we already basically have a nice parabolic arc. If we want to do
a ball bounce then we just duplicate this arc on each side, and that's the ball bounce.
Now parabolic arcs in perspective are a little bit more complicated but it's the same procedure,
you have the starting point and ending point and you pick the maximum height that you want
for the arc, now locating the middle is a little bit more complicated because we're
working perspective so here we use the diagonals to locate the center and then draw a vertical
from there and then that's the position of the apex. Use fourth down at half time, again
to locate okay this is a fourth of the way down, we can even use diagonals to help us
locate that, and that's the point from the start, half way between the start and the
apex's position there, and then on the other side, it's the same thing. So that's basically
the same procedure we had before, only remembering that lines that are parallel here in perspective
should be converging to a vanishing point. And then that we just finish and we sketch
the arc, this is not a great arc since PowerPoint doesn't have the best drawing tools in the
world, but anyway it's roughly a parabolic arc. And if we have a half arc, it's exactly
the same procedure, so just locate the fourth down at half time point, and once you have
that then sketch in the arc. Now being able to sketch arcs has a lot of useful applications.
One thing is for example we want to make sure that if we have path of action that's a parabolic
arc that the apex is located in the center of the arc. So we can use some of these principles
that we saw to locate the center, and then here I'm finding that this arc is roughly
centered. Here's another example from a simple pencil test. So we see the character runs
up, jumps and lands. So we can check here's where the frame where the character jumps,
this is the apex located here and then the character lands, and then using a little perspective,
we can look to see, well, between the starting and landing where is the position of the center,
and this red bar is the location for the center and so the apex should be located a little
bit back from where the character actually had the apex. So in this pencil test, it looks
like the arc of that jump is a little bit skewed forward, so the character reached the
apex closer to the foreground than is correct. Although it's pretty close though, it's probably
close enough. So in summary, to sketch a parabolic arc you pick the starting and ending points,
and you pick the height that you want the apex. Then the position of the apex is between
those two ends point. To find the points on either side of the apex, you use the fourth
down at half time rule, and then sketching arcs in perspective, you just have to remember
that vertical lines are drawn as verticals, however horizontal lines have to converge
to a vanishing point. Then there's a lot of useful things you can do once you can sketch
these arcs, for example checking the position of apex of a jump. Probably the best thing
is to go back and pause on some of those slides, and try sketching some of those arcs for yourself.
After you practice with a couple of them and get the hang of it, it will be second nature,
kind of like drawing ellipses after you learn to draw ellipses, it just takes a little practice
to get them right. Anyway we'll talk about other types of path of action in upcoming
tutorials. So we'll see you then.