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Gravity/Momentum
Tutorial #1
When I say gravity, I don't mean the kind that makes all objects fall to the
ground, but actually it refers to all objects attracted to each other. You
can use the particle engine for this effect, but
we'll start a little simpler.
The easiest way to achieve
attraction between objects is by using only 1 particle with an elastic attraction
to the center of the screen:
float x = 0;
float y = 5;
float xp = 5;
float yp = 0;
float slowdown = 250;
int DrawGLScene(GLvoid) // Here's Where We Do All The Drawing
{
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glLoadIdentity();
glTranslatef(0,0,-15);
xp += (0-x)/slowdown; //set xp according to distance from
0(elastic)
yp += (0-y)/slowdown; //set yp according to distance from
0(elastic)
x += xp/slowdown; // move x according to xp
y += yp/slowdown; // move y according to yp
glBegin(GL_POINTS);
glColor4f(1,1,1,1); // Set color to white
glVertex3f(x,y,0); // Draw pixel
glEnd();
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As you
may have noticed, elastic attraction is not what we want to achieve
here. There are ways to transform the algorithm into gravitational attraction. The
simplest way I have found that uses true-to-life physics is the following:
double Reciprocal(double n)
{
double close = .1f;
if (n < close && n >= 0) // prevent devision of 0
{
return 1/close;
}
else if (n > -close && n < 0) // prevent devision of 0
{
return 1/-close;
}
return 1/n;
}
int DrawGLScene(GLvoid) // Here's Where We Do All The Drawing
{
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glLoadIdentity();
glTranslatef(0,0,-15);
Hypot = hypot(x,y);
if (x < 0)
angle = -acos(-y/-Hypot);
else
angle = acos(y/Hypot);
dist = Reciprocal(Hypot)/20;
xp -= sin(angle)*(dist); //set xp according to distance from 0(center of screen)
yp -= cos(angle)*(dist); //set yp according to distance from 0(center of screen)
x += xp/slowdown; // move x according to xp
y += yp/slowdown; // move y according to yp
glBegin(GL_POINTS);
glColor4f(1,1,1,1);
glVertex3f(x,y,0); // Draw pixel
glColor4f(1,0,0,dist*50);
glVertex3f(sin(angle),cos(angle),0); // Draw pixel
glColor4f(0,1,0,1);
glVertex3f(0,0,0); // Draw pixel
glEnd();
return TRUE; // Keep Going
} |
I'd
like to explain a few things here. First, the line dist = Reciprocal(Hypot)/20;
is very important. It is fundamental to allow a gravitational force
instead of an elastic force. Also, the angle variable is used to
control the angle of force(much more advanced than the previous example).
Lastly, the xp and yp variables are now being controlled by the angle
and the dist. The
algorithm is pretty complicated so instead of blabbing on and on like a math
teacher, I'll give you an example program at this point:
download here
The green dot is the
center of the screen, the white dot is the moving particle, and the red dot is
direction of force. Basically, the particle has a stronger attraction when an object is
close(gravity) rather than a stronger attraction when the object is
far(elasticity).
Wow! We have
something cool now! But I'm sure you want something better right? Of
course you do.=) A great way to use the gravity technique is with a large
system of particles. Try the next tutorial to see what I mean.
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This page was last updated
04/19/07
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