I believe you can only do that if you draw the curve by segments waiting a few milliseconds each time you draw a segment of the curve. Since I'm not familiar with the function cuve(), here's an example usins lines (making a curve using lines):

Hey thanks for the reply! Well, can i fix the Origin and destination points somehow?
I have this image in the background. I want arcs from one point on the image to another.. Like proper full arcs with animation( image is also being rendered in 'draw()', making it difficult

You're welcome ;)

Ah, yes, (thank you for the prompt reply). Since i am not able to get another solution and i have to complete within an hour!  
So, yeah, if i can do some animation on top of the image. What you reckon? I thought i ll use PVectors(probably no use here, but i wrote the code anyway). i was looking at this as well- http://processing.org/learning/topics/movingoncurves.html   NOTE: when i click one location/area on the image, simultaneous paths come out of it and go to different points in the image  My draw looks something like this -

can you post your entire code?

Can you give me the full code for see exactly what you're trying to do?

Absolutely.

You want to draw a curve between the two points on the map right?

Yes!!! but the curves should come out at the same time when i click it..

here you see my test with a 3D function myCurve that takes two Vectors as start and end point of the flight.
For test purposes the points are shown blue (by func myPointPVector).
The control points (for the form of the curve) are calculated roughly as (start and end point of the flight:) y+1200. They are painted in red (but outside of the screen of course).

you have to for loop and bring all flights to this func. You need screen coors of course yo you have to map all origins and destinations to screen points before giving it to my func.


see
http://www.processing.org/reference/curve_.html

for moving points:
http://www.processing.org/reference/curvePoint_.html
(with another for loop) Is this 3D?? I dunno.

unfortunately I have to go now.

Good luck.

Greetings, Chrisir   

1. 
   
2. void setup()
3. {
4.   size( 800, 800, P3D );
5. } // setup
6. void draw()
7. {
8.   // myCurveTest() ;
9.   PVector firstpoint = new PVector (120, 320, -30);
10.   PVector secondpoint = new PVector (320, 220, -30);
11.   myCurve (firstpoint, secondpoint ) ;
12.   firstpoint = new PVector (420, 220, 30);
13.   secondpoint = new PVector (620, 120, -30);
14.   myCurve (firstpoint, secondpoint ) ;
15. }
16. void myCurve (
17. PVector firstpoint,
18. PVector secondpoint) {
19.   //x1   float: coordinates for the beginning control point
20.   //y1   float: coordinates for the beginning control point
21.     //x2   float: coordinates for the first point
22.   //y2   float: coordinates for the first point
23.     //x3   float: coordinates for the second point
24.   //y3   float: coordinates for the second point
25.     //x4   float: coordinates for the ending control point
26.   //y4   float: coordinates for the ending control point
27.     //z1   float: coordinates for the beginning control point
28.   //z2   float: coordinates for the first point
29.   //z3   float: coordinates for the second point
30.   //z4   float: coordinates for the ending control point
31.     PVector beginningcontrolpoint = new PVector (120, firstpoint.y+1200, -30);
32.   PVector endingcontrolpoint = new PVector (720, secondpoint.y+1200, -30);
33.   myPointPVector(beginningcontrolpoint, color(255, 0, 0));
34.   myPointPVector(firstpoint, color(0, 0, 255)); 
35.   myPointPVector(secondpoint, color(0, 0, 255)); 
36.   myPointPVector(endingcontrolpoint, color(255, 0, 0));
37.   stroke (255);
38.   noFill();
39.   curve(
40.   beginningcontrolpoint.x, beginningcontrolpoint.y, beginningcontrolpoint.z,
41.   firstpoint.x, firstpoint.y, firstpoint.z,
42.   secondpoint.x, secondpoint.y, secondpoint.z,
43.   endingcontrolpoint.x, endingcontrolpoint.y, endingcontrolpoint.z);
44. }
45. void myCurveTest () {
46.   //x1   float: coordinates for the beginning control point
47.   //y1   float: coordinates for the beginning control point
48.     //x2   float: coordinates for the first point
49.   //y2   float: coordinates for the first point
50.     //x3   float: coordinates for the second point
51.   //y3   float: coordinates for the second point
52.     //x4   float: coordinates for the ending control point
53.   //y4   float: coordinates for the ending control point
54.     //z1   float: coordinates for the beginning control point
55.   //z2   float: coordinates for the first point
56.   //z3   float: coordinates for the second point
57.   //z4   float: coordinates for the ending control point
58.     PVector beginningcontrolpoint = new PVector (120, 620, -30);
59.   PVector firstpoint = new PVector (120, 320, -30);
60.   PVector secondpoint = new PVector (320, 220, -30);
61.   PVector endingcontrolpoint = new PVector (720, 720, -30);
62.   myPointPVector(beginningcontrolpoint, color(255, 0, 0));
63.   myPointPVector(firstpoint, color(0, 0, 255)); 
64.   myPointPVector(secondpoint, color(0, 0, 255)); 
65.   myPointPVector(endingcontrolpoint, color(255, 0, 0));
66.   stroke (255);
67.   noFill();
68.   curve(
69.   beginningcontrolpoint.x, beginningcontrolpoint.y, beginningcontrolpoint.z,
70.   firstpoint.x, firstpoint.y, firstpoint.z,
71.   secondpoint.x, secondpoint.y, secondpoint.z,
72.   endingcontrolpoint.x, endingcontrolpoint.y, endingcontrolpoint.z);
73. }
74. void myPointPVector (PVector test, color col1) {
75.   MyBox(test.x, test.y, test.z,
76.   test.x+3, test.y, test.z,
77.   9,
78.   col1);
79. }
80. void MyBox(float x1, float y1, float z1, float x2, float y2, float z2, float weight, color strokeColour)
81. // was called drawLine; programmed by James Carruthers
82. // see http://processing.org/discourse/yabb2/YaBB.pl?num=1262458611/0#9
83. {
84.   PVector p1 = new PVector(x1, y1, z1);
85.   PVector p2 = new PVector(x2, y2, z2);
86.   PVector v1 = new PVector(x2-x1, y2-y1, z2-z1);
87.   float rho = sqrt(pow(v1.x, 2)+pow(v1.y, 2)+pow(v1.z, 2));
88.   float phi = acos(v1.z/rho);
89.   float the = atan2(v1.y, v1.x);
90.   v1.mult(0.5);
91.   pushMatrix();
92.   translate(x1, y1, z1);
93.   translate(v1.x, v1.y, v1.z);
94.   rotateZ(the);
95.   rotateY(phi);
96.   noStroke();
97.   fill(strokeColour);
98.   box(weight, weight, p1.dist(p2)*1.2);
99.   popMatrix();
100. }

I found an easier way:

Thank you so much guys! I mean really appreciate you guys taking out the time to help people out.
@Chrisir: WOW.  the program executes fine. Have you tried running the code? Is it my graphics card or something. There is this half arc already in the middle when i run it. Anything i am missing? (oh the link you provided on line 82 is broken)

I tried that program and it worked fine.

Hey sorry about that! Removed them from draw, so now it appears for 2-3 seconds, then disappears..  

Have you tried the updated code? Now I believe you can easily include it in your project.

Hey, yes, i think* it is working :D
The curvePoint seems to be confusing. Tried looking up as well.. 

So, one last question- i want to draw the arc/curve from point Delhi(428, 218) to Mumbai (169, 310);

Somethings wrong- here's my draw() function-
This gives a line already present, and a curve which disappears after about 3 seconds/completing its path
(sorry for bothering again)

As you may have noticed there are only two different curve points, one for value  X and one for value Y.

Everything works fine to me now:

Thanks alot! That was great help! :D

ijeoma, thanks for the reply. Unfortunately, i have to put the project online. Hence, i can't use any libraries. 
Probably, using javascript libs will help!