With the guy called Google, I guess. ;)
Pretty nice thing. I never realy explored this area deeply, but will check out the code for sure... Just few questions... Does verlet means something different, than e.g. inverse or forward kinematics? And if so, were the "muscles" (the lines showed when you pressed the button) just links between nodes or were they something more?
The principles behind verlet integration are fairly simple. Normally to send an object moving you have a position, and update it by a velocity every frame. In verlet integration all you have is the position of the object at the moment, and the position it was in in a previous time step.
Now you can see that from this the velocity is simply the current position minus the old position. This means pretty much whatever force you apply to the object will be accurately carried out. It is a method used in describing molecular dynamics. Jacobsen wrote a really good article about its implementation in the hitman game series.
As for the constraints between particles, this is simply a matter of moving both particles by a factor of the distance towards the required distance from each other.... If the factor is high, say 0.5 the particles will both move half way of the distance away from required and the constraint will be met.... If on the other hand the factor is lower, like 0.05, the particles will only move some of the way, depending on the distance, and follow hookes law and be elastically attracted towards each other.
This is the basis behind my muscle and constraint code, simply have 2 particles and constrain them by distance r eg. constrain(particle1, particle2, r)
The code shows this fairly clearly, I'll post it up when I'm on my computer..
Cheers
Sam
ps. gonna give the ragdoll masters idea a go :D
edit:
and heres the code....
//these are just the rendering controls, using the tickbox, turn them on and off how you want
muscles = false;
skeleton = false;
outline = true;
//this turns wave muscles on or off
wave = false;
//verlet integration 2d
//how many points you have on the stage; points should have instances ball1, ball2, ball3 etc.
point_no = 17;
//this creates an array containing x, y, oldx, and oldy posiitions for each point
points = new Array();
for(i=1;i<point_no+1;i++){
points[i] = {x:_root["ball"+i]._x, y:_root["ball"+i]._y, x2:_root["ball"+i]._x, y2:_root["ball"+i]._y};
}
//iterations is how many times calculations are repeated per frame, should be >4 for best results but depends on what kind of
//object it is
iterations = 4;
//universal gravity
gravity = 0.4
//on enter frame call each function
function onEnterFrame(){
//clear drawing after frame
_root.clear();
// carry out main functions;
verlet();
render();
constraints();
ai();
keys();
}
//the verlet function pretty much moves the points by the difference of the previous two points
verlet = function(){
//for each particle
for(i=1;i<point_no+1;i++){
//store initial point
tempx = points[i].x
tempy = points[i].y
//verlet integration
points[i].x += points[i].x - points[i].x2
points[i].y += points[i].y - points[i].y2 + gravity
//store previous point
points[i].x2 = tempx;
points[i].y2 = tempy;
}
}
//this controls where each particle is allowed to go
constraints = function(){
//for each particle carry out distance and boundary functions
for(it=0;it<iterations;it++){
distance();
boundaries();
}
}
//this function connects each particle/point with either a solid line (constrain) or a spring (muscle);
distance = function(){
//torso
muscle(1, 2, 68);
constrain(2, 3, 60);
//chest triangle
constrain(4, 7, 65);
constrain(4, 3, 95);
constrain(7, 3, 95);
//hip triangle
constrain(10, 13, 65);
constrain(10, 2, 95);
constrain(13, 2, 95);
//waist muscles;
muscle(4, 10, 100);
muscle(7, 13, 100);
//neck muscles;
muscle(4, 1, 70);
muscle(7, 1, 70);
muscle(3, 1, 128);
muscle(13, 1, 200);
muscle(10, 1, 200);
//left arm;
constrain(4, 5, 60);
constrain(5, 6, 50);
muscle(1, 5, 130);
muscle(4, 6, 110);
//right arm;
constrain(7, 8, 60);
constrain(8, 9, 50);
muscle(1, 8, 130);
muscle(7, 9, 110);
//left leg;
constrain(10, 11, 85);
constrain(11, 12, 80);
muscle(10, 12, 165);
muscle(3, 10, 40);
//right leg;
constrain(13, 14, 85);
constrain(14, 15, 80);
muscle(13, 15, 165);
muscle(3, 13, 40);
//leg width;
muscle(12, 15, 90);
muscle(11, 14, 100);
muscle(2, 15, 280);
muscle(2, 12, 280);
//feet;
constrain(12, 16, 30);
constrain(15, 17, 30);
muscle(16, 11, 100);
muscle(17, 14, 100);
muscle(17, 16, 170);
//arms up;, the wave function only occurs on clicks
if(wave == true){
muscle(9, 13, 220);
muscle(6, 10, 220);
muscle(15, 9, 350);
muscle(12, 6, 350);
}
}
//edge of the world and friction
boundaries = function(){
for(i=1;i<point_no+1;i++){
if(points[i].x > 540) (points[i].x = 540)
if(points[i].x < 0) (points[i].x = 0)
if(points[i].y > 400){
//friction depends on the normal force ie penetration depth...
depth = points[i].y-400
points[i].x -= depth*(points[i].x-points[i].x2)/10
points[i].y = 400;
}
//move the balls to the positions
_root["ball"+i]._x = points[i].x
_root["ball"+i]._y = points[i].y
}
//position head movie clip (you'll need one of these on the stage);
head._x = ball1._x
head._y = ball1._y
}
//the constrain function
constrain = function(point, target, distance){
r = distance;
dx = points[point].x-points[target].x
dy = points[point].y-points[target].y
d1 = Math.round(Math.sqrt(dx*dx + dy*dy))
d2 = 0.5*(d1-r)/d1
dx = dx*d2;
dy = dy*d2;
points[target].x += dx; points[target].y += dy;
points[point].x -= dx; points[point].y -= dy
if(skeleton==true){
_root.lineStyle(2, 0xFF0000);
_root.moveTo(points[target].x, points[target].y);
_root.lineTo(points[point].x, points[point].y);
}
}
//the muscle function;
muscle = function(point, target, distance){
r = distance;
dx = points[point].x-points[target].x
dy = points[point].y-points[target].y
d1 = Math.round(Math.sqrt(dx*dx + dy*dy))
d2 = 0.05*(d1-r)/d1
dx = dx*d2;
dy = dy*d2;
points[target].x += dx; points[target].y += dy;
points[point].x -= dx; points[point].y -= dy;
if(muscles==true){
_root.lineStyle(2, 0x0000FF);
_root.moveTo(points[target].x, points[target].y);
_root.lineTo(points[point].x, points[point].y);
}
}
//control with the keys
keys = function(){
for(i=1;i<point_no+1;i++){
if(Key.isDown(Key.RIGHT)) points[i].x += gravity*2
if(Key.isDown(Key.LEFT)) points[i].x -= gravity*2
if(Key.isDown(Key.UP)) points[i].y -= gravity*2
if(Key.isDown(Key.DOWN)) points[i].y += gravity*2
}
}
//render it
render = function(){
if(outline==true){
_root.lineStyle(10, 0x000000, 100);
_root.moveTo(ball1._x, ball1._y);
_root.lineTo((ball4._x+ball7._x)/2, (ball4._y+ball7._y)/2);
_root.moveTo(ball4._x, ball4._y);
_root.beginFill(0x000000, 100);
_root.curveTo((ball2._x+ball3._x)/2, (ball2._y+ball3._y)/2, (ball10._x+ball11._x)/2, (ball10._y+ball11._y)/2);
_root.curveTo((ball10._x+ball13._x)/2, (ball10._y+ball13._y)/2, (ball13._x+ball14._x)/2, (ball13._y+ball14._y)/2);
_root.curveTo((ball2._x+ball3._x)/2, (ball2._y+ball3._y)/2, ball7._x, ball7._y);
_root.lineTo(ball4._x, ball4._y);
_root.endFill();
_root.lineTo(ball5._x, ball5._y);
_root.lineTo(ball6._x, ball6._y);
_root.moveTo(ball7._x, ball7._y);
_root.lineTo(ball8._x, ball8._y);
_root.lineTo(ball9._x, ball9._y);
_root.moveTo((ball10._x+ball11._x)/2, (ball10._y+ball11._y)/2);
_root.lineTo(ball11._x, ball11._y);
_root.lineTo(ball12._x, ball12._y);
_root.lineTo(ball16._x, ball16._y);
_root.moveTo((ball13._x+ball14._x)/2, (ball13._y+ball14._y)/2);
_root.lineTo(ball14._x, ball14._y);
_root.lineTo(ball15._x, ball15._y);
_root.lineTo(ball17._x, ball17._y);
}
}
//control the wave function;
_root.onMouseDown = function(){
wave = true;
}
_root.onMouseUp = function(){
wave = false;
}