3D curves and surfaces mathematically defined

[Kalleheikki Kannisto]

[Nicolas Guionnet] ” I really don’t know how to go from my usual expression defined curves ( defined with : x(t) = … ; y(t) = … , z(t) = … ) to a set of lights … “indicating” the way”

It works the same way. You just use x(time), y(time), z(time) for the position of a single light. The position over time of each light becomes a separate path.

Kalleheikki Kannisto
Senior Graphic Designer

[Nicolas Guionnet]

Thanks Kalleheikki,

I first thought : That’s it ! … then came another question :
How can you animate the path then ? … as the time variable already defines the path … and the problem is the same in Trapcode and Stardust …

[Kalleheikki Kannisto]

You have to draw the entire shape in one frame, using particles with a life span of one frame and then draw the next stage of the shape in the next frame, etc.
Works just fine in Particular, where I’ve done it many a time. Haven’t tried in Stardust, but should work the same.

Kalleheikki Kannisto
Senior Graphic Designer

[Nicolas Guionnet]

> “You have to draw the entire shape in one frame”

Well, I don’t really get it.

I could do it with a 2D shape (drawn in a layer with some simple expressions with a loop on createPath and depending on time). But I need a 3D curve …

And everywhere I saw a 3D curve defined with a mathematical function it was this way : x(time), y(time), z(time) with time as variable … and to animate it I would need this :

x( time , lamdda ) , y( time , lamdda ) , z( time , lamdda )
… where lamda is a parameter changing the curve …

BUT … to animate the curve I need to change lamdda : labda = lamdda(time) … and I don’t think it is possible to tell Trapcode or Stardust : “draw the curve acting as if lamdda was a constant.” … and animate lamda “under the table” hidden from Trapcode or Stardust ….

I begin to think that the only way to do this is outside of AE : Blender Script and then import the OBJ … but what a pain in the … hips … to animate it and synchronize it with the audio …

[Nicolas Guionnet]

(Not being able to) Animate a 3D curve with TAO

I finally installed Trapcode trial and tried to use TAO to animate a 3d curve.

I used a light to draw my 3D-curve. In fact, it is a series of 3D Curves concatenated (tricky) … that would be used for the animation.

I just needed to find a way to tell TAO to :
Draw only a part of the curve, the one for :
lambda < time < lambda + myComp.frame.duration
(… and then animate lambda.)

It seems there is no way in TAO . I could try to implement a kind of non-robust hacky floppy tricky workaround using … size offset to reveal only the wanted part of my curve and animate it. But … no

Let’s try Stardust

[Kalleheikki Kannisto]

Can you give an example formula that you want to use? Would be easier to sort it out.

Kalleheikki Kannisto
Senior Graphic Designer

[Nicolas Guionnet]

I think I am going to try Particular, in the way you described up there. As you said, Stardust has no real documentation …

An example formula ? A nice one :

x(t) = 100.exp ( – (t-5)² . lambda ) . cos (10*t)
y(t) = 100.exp ( – (t-5)² . lambda ) . sin (10*t)
z(t) = 20t

0 < t < 10
0 < lambda < 30

[Nicolas Guionnet]

… and I forgot to say that lambda is the parameter to be animated.

[Kalleheikki Kannisto]

Not sure if I’m interpreting this right, but here’s what I got for the light position:

fps = 1/thisComp.frameDuration;
t = Math.floor(fps*time)/fps;
cur_frame = time*fps;
lambda = cur_frame%1*30;
x= 100*Math.exp(-(t-5)*(t-5)*lambda)*Math.cos(10*t);
y = 100*Math.exp(-(t-5)*(t-5)*lambda)*Math.sin(10*t);
z = 20*t;
[x,y,z]

With 30000 particles per second and a particle life of one frame, I get something that looks like this (a still from early in the animation). This shape unfurls along time.

Kalleheikki Kannisto
Senior Graphic Designer

[Nicolas Guionnet]

Great ! Great ! !

It’s such a relief for me to see it is finally possible.
You did it with particular, didn’t you ?

I went to bed yesterday, really late, deducing from my failureS that it was not possible, which is really vain, for after 3 hours of work on a piece of software like Particular, you can’t deduce much of its real possibilities.

Now, I am on my way to (try to) reproduce your success …

Thank you so much Kalleheikki …