Processing 1.0 - Processing Discourse - Sample Bezier Curve X, Y Coordinates?

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Sample Bezier Curve X, Y Coordinates? (Read 1648 times)

danielt

Sample Bezier Curve X, Y Coordinates?
Sep 3^rd, 2009, 8:32pm

Hello,

I'm trying to design a generic animation curve editor. Before I write my own bezier curve function, I'm wondering if this may have already been done before?

I am aware of the bezier() and bezierPoint() functions in processing. But what I am hoping to do it to be able to input an x (time) coordinate of the curve I wish to sample. And have the function return the y value of the curve for that point in time.

Does anyone have any pointers in this area? I'm fairly new to processing. Is there a way I can take a peak at the underliying code to the bezier function?

Thanks in Advance,

Dan.

PhiLho YaBB Moderator Offline Posts: 4190 Near Paris (France)	Re: Sample Bezier Curve X, Y Coordinates? Reply #1 - Sep 4^th, 2009, 1:39am danielt wrote on Sep 3^rd, 2009, 8:32pm: Is there a way I can take a peak at the underliying code to the bezier function PGraphics.java

danielt

Re: Sample Bezier Curve X, Y Coordinates?
Reply #2 - Sep 5^th, 2009, 12:00am

Thanks for the link. A bit advanced for me at the moment to try to de-syfer at this low level I think.

Here's an example:
Code:


float i;

void setup(){
size(100,100);
}

void draw(){
background(100);
noFill();
bezier(0, 100, 90, 90, 10, 10, 100, 0);
fill(255);
int steps = 100;
  i = mouseX;
  float t = i / float(steps);
  float x = bezierPoint(0, 90, 10, 100, t);
  float y = bezierPoint(100, 90, 10, 0, t);
  ellipse(x, y, 5, 5);
}

if you scrub mouse in x you can see that the ellipse doesn't stay locked in x with mouseX. This is because the ellipse x,y is derived based on the length of the curve and not the distance traveled in mouseX. I was hoping for a secret formular for this

I looked at a few bezier curve examples on the net and they all seem to derive the point on the curve by halving linear interpolation between control and anchor points http://www.cubic.org/docs/bezier.htm

Is there another way to plot a bezier curve than this? I imagine there's a common approach because ever animation package has this ability. Just wondering if anyone knows what this approach is?

Thanks again,

Dan.

koogy

Re: Sample Bezier Curve X, Y Coordinates?
Reply #3 - Sep 5^th, 2009, 5:02am

ok, this is from memory so could be wrong.

you have control points p0-p3and from these it draws a curve using

p(t) =
1 * p0 * t^0 * (1-t)^3 +
3 * p1 * t^1 * (1-t)^2 +
3 * p2 * t^2 * (1-t)^1 +
1 * p3 * t^3 * (1-t)^0

(see wikipedia page. n^0 is 1 and n^1 = n which simplifies things but... )

where t (time) goes from 0 to 1 (that's what the t in bezierPoint() is doing)

for the value of y that matches the given x you're going to have to find t in the above equation so that p(t).x = your x. which doesn't strike me as trivial.

and yes using t = .5 doesn't mean that you're halfway along the curve. but it might be a start. use a binary chop or newton-raphson (i seem to recall someone has done this)

ah, jo wood brings the maths and philho brings the code:
http://processing.org/discourse/yabb2/num_1219808869.html

there's also this
http://processing.org/discourse/yabb2/num_1240800499.html
which sounds like what you might be trying to do - someone's attempt at a timeline.

danielt YaBB Newbies Offline Posts: 36 South Australia	Re: Sample Bezier Curve X, Y Coordinates? Reply #4 - Sep 6^th, 2009, 2:27am Thanks koogy, I will check out the formula when I get some time. But in the mean time those links you posted were very interesting. Especially the Timeline program. Sounds almost exactly what I was looking for! Cheers.

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