A lot of people even those who have experience in programming have very wrong ideas about how programs work. Moreover the common notion among the general public is that software development only requires knowledge and experience in programming, however its actually quite the contrary. Software development can have very high level of specialization unlike many other fields including medical, for instance one experienced cardiologist can do the same another cardiologist can. How two highly experienced web developers may not be able to do what the other can. What people don’t understand is programming on its own is just a tool and nearly worthless on its own. Its like maths, whats the use of maths? No use. But apply math in physics, chem, astronomy …… then suddenly it becomes very useful. That’s how programming is too , People often specialize in different fields like maths, physics and architecture. Like for example if a developer needs to develop a CAD program , he or she would need to have a good knowledge of architecture to effectively develop a suitable product, therefore they would need to specialize in architecture too.
So here in this post I intend to instill some ideas into the minds of new developers. To do this I will explain how to simulate a basic physics concept used in cut the rope from scratch through C++ code. I will keep it as simple as possible. However one needs basic knowledge of trigonometry to follow. Please note that all the programs embedded on this post is either HTML5 or flash, however I will be discussing from C++ point of view.
This is what we are gonna make using C++, Its pretty basic right ? Yeah it is. But even this is not very easy as people might feel, Many people will be thinking oh whats the big deal, you pull it, it follows , whats so hard? Indeed you pull it, it follows but nothing on a computer ever happens on its own, Someone should take care of the physics through code.
Ok so how do I think the right way ?
The right way to think is not to think in terms of code but
in terms of logic, Imagine this as a physics situation, there are 2 balls,
separated by a distance and an elastic rope joined between them, larger the distance, faster the ball moves.
However even if the rope becomes slack, due to inertia the ball continues to
be in motion. So inertia has to be also considered. Gravity needs to be
considered to make the thing realistic. Finally the fact that we are working in
a 2D space has to be kept in mind.
On further analysis, You might feel that there is a need
for friction / resistance between the balls, or they would never
stop moving
Physics solution :
This is the solution to the problem in physics point of view
Here 'T' is the tension force in the elastic rope. 'x' is the extension
(elongation) of the rope, 'A' is the rope’s
cross sectional area, 'L' is the natural length of the rope while 'Y' is the Young's
modulus. This is the formula derived
from Hooke's law.
We need to resolve these forces into vectors since we are working in
2D space. Then we need to add the gravitational force on the vertical
component so it will be T sinθ
+ mg.
From here its easy, all one needs to do is calculate acceleration in
both components using 'F = ma', then find change in velocity using 'v = u + at', And
from velocity you can find new position of the balls. But you might have
already realized both acceleration and velocities keep on changing , that means
to correctly calculate the final velocity, you will need to use integral calculus which is beyond the scope of this post.
However this analysis is correct and can be implemented in
programming
Programming Implementation :
Remember I said we need integration to calculate the velocities
and position at a given time? But in programming we have a work around i.e Running several iterations to approximately
calculate the velocity and position . This means we split a time interval, say
1 sec into many smaller time intervals Say 0.1 s, Since 0.1s is a very small
interval, we can assume the acceleration and velocity doesn't change in that
interval . Accuracy can be increased to any desired extent by decreasing the
small time interval.
Ok now we are finally
ready to get started
Main variables
float x1=200,y1=200,x2=200,y2=200, s=100;
float vx2=0,vy2=0;
float vx2=0,vy2=0;
(x1,y1) are the initial position of the first ball , the ball which is controlled by the mouse. (x2,y2) is the position of the ball which is connected to the first ball. 'vx2' and 'vy2' are the components of velocity of the second ball in the X and Y directions respectively. 's' is the natural length of the rope.
The following bits of code has to be put in a loop that runs the iterations
1) Getting the coordinates of the mouse and setting that as the coordinates of the first ball
x1=mousex();
y1=mousey();
y1=mousey();
2) Finding distance and angle between the 2 centres.
float d1=distance(x1,y1,x2,y2);
float ang1=angle(x1,y1,x2,y2);
float ang1=angle(x1,y1,x2,y2);
Here distance() is a function which calculates distance between 2
points at an instant of time and angle() is a function which calculates angle between 2 points i.e. angle
made by the line joining the 2 points and the horizontal.
3) Checking if the rope is stretched
We calculate distance between the 2 balls to know if the rope is stretched and angle to resolve force into components
//If the rope is stretched
if(d1-s>0) { //Resolving tension into vectors
vy2+=(d1-s)*sin(ang1)*.007;
vx2+=(d1-s)*cos(ang1)*.007;
}
/* here all the constants clubbed together as 0.007 , you can change it
We are adding the force directly to velocities by assuming balls to be of unit
mass and time interval to also be unit time
*/
if(d1-s>0) { //Resolving tension into vectors
vy2+=(d1-s)*sin(ang1)*.007;
vx2+=(d1-s)*cos(ang1)*.007;
}
/* here all the constants clubbed together as 0.007 , you can change it
We are adding the force directly to velocities by assuming balls to be of unit
mass and time interval to also be unit time
*/
4) Adding gravitational force
vy2+=.23;
//Gravitational force added on y coordinate
// 0.23 is an experimentally calculated value ( you can experiment too ! )
//Gravitational force added on y coordinate
// 0.23 is an experimentally calculated value ( you can experiment too ! )
5) Moving the body and friction
We move the body as follows as we have assumed time
interval to be unit time interval
y2+=vy2;
x2+=vx2;
//Friction reduces velocity by 1%
vy2*=.99;
vx2*=.99;
x2+=vx2;
//Friction reduces velocity by 1%
vy2*=.99;
vx2*=.99;
6) Summing up
//draws 2 circles on the screen
circle(x1,y1,25);
circle(x2,y2,25);
//draws a line between them
line(x1,y1,x2,y2);
circle(x1,y1,25);
circle(x2,y2,25);
//draws a line between them
line(x1,y1,x2,y2);
And we are done !!
Several improvements can be made like having parameters such
as length, area, masses of spheres etc. Further more this concept can be
expanded on more than 2 balls
Full code :
#include<graphics.h>
#include<math.h>
//Distance is a function which calculates Distance between 2 points
float distance(int x1,int y1,int x2,int y2)
{
return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
//Angle is a function which calculates the angle between 2 points
// ( tan inverse of the Slope of the line joining the 2 points )
float angle(int x1 , int y1, int x2 , int y2)
{
float ang;
//In case the 2 points are perpendicular
if(x1-x2==0)
{
ang=-1.57;
}
else
{
ang = atan((float)(y1 - y2) / (x1 - x2));
}
//Quadtrants
if (ang < 0 && y1> y2)
{
ang += 3.14;
}
else if (ang > 0 && x1 < x2)
{
ang += 3.14;
}
return ang;
}
int main()
{
//declaration of variables
float x1=200,y1=200,x2=200,y2=200, s=100;
float vx2=0,vy2=0;
//Creating a new window
initwindow (550, 400,"Windows BGI",50,50, false,true);
while(1)
{
//Getting the coordinates of the mouse
x1=mousex();
y1=mousey();
//Finding distance and angle between 2 points
float d1=distance(x1,y1,x2,y2);
float ang1=angle(x1,y1,x2,y2);
//If the rope is stretched
if(d1-s>0)
{
//Resolving tension into vectors
vy2+=(d1-s)*sin(ang1)*.007;
vx2+=(d1-s)*cos(ang1)*.007;
}
//Gravitational force on y coordinate
vy2+=.23;
//Now moving the body
y2+=vy2;
x2+=vx2;
//Friction reduces velocity by 1%
vy2*=.99;
vx2*=.99;
//draws 2 circles on the screen
circle(x1,y1,25);
circle(x2,y2,25);
//draws a line between them
line (x1,y1,x2,y2);
//waits for 40 milliseconds
delay(40);
//something to do with memory
swapbuffers();
//clear the screen so that a new frame can be redrawn
cleardevice();
}
return 0;
}
#include<math.h>
//Distance is a function which calculates Distance between 2 points
float distance(int x1,int y1,int x2,int y2)
{
return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
//Angle is a function which calculates the angle between 2 points
// ( tan inverse of the Slope of the line joining the 2 points )
float angle(int x1 , int y1, int x2 , int y2)
{
float ang;
//In case the 2 points are perpendicular
if(x1-x2==0)
{
ang=-1.57;
}
else
{
ang = atan((float)(y1 - y2) / (x1 - x2));
}
//Quadtrants
if (ang < 0 && y1> y2)
{
ang += 3.14;
}
else if (ang > 0 && x1 < x2)
{
ang += 3.14;
}
return ang;
}
int main()
{
//declaration of variables
float x1=200,y1=200,x2=200,y2=200, s=100;
float vx2=0,vy2=0;
//Creating a new window
initwindow (550, 400,"Windows BGI",50,50, false,true);
while(1)
{
//Getting the coordinates of the mouse
x1=mousex();
y1=mousey();
//Finding distance and angle between 2 points
float d1=distance(x1,y1,x2,y2);
float ang1=angle(x1,y1,x2,y2);
//If the rope is stretched
if(d1-s>0)
{
//Resolving tension into vectors
vy2+=(d1-s)*sin(ang1)*.007;
vx2+=(d1-s)*cos(ang1)*.007;
}
//Gravitational force on y coordinate
vy2+=.23;
//Now moving the body
y2+=vy2;
x2+=vx2;
//Friction reduces velocity by 1%
vy2*=.99;
vx2*=.99;
//draws 2 circles on the screen
circle(x1,y1,25);
circle(x2,y2,25);
//draws a line between them
line (x1,y1,x2,y2);
//waits for 40 milliseconds
delay(40);
//something to do with memory
swapbuffers();
//clear the screen so that a new frame can be redrawn
cleardevice();
}
return 0;
}
