# Gravity Game in R

April 8, 2010
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So why should R only be used for ’serious’ stuff? No longer! I’ve written the following code in R which executes a little gravitational physics game. The goal of the game is simple. You supply a velocity and direction to a spaceship with the goal of getting the ship to the winning area without crashing into a planet.

To give you an idea of how this game works, below is a screenshot of the 3rd level. In this screenshot, the blue dot represents the starting position of the ship. The black curve is the ships path. The red circles are the planets where the number represents the mass. Finally, the green circle is the winning area. In this example, the ship made it to the winning area safe and sound!

# Gravity Game Code

Just copy and paste the code below into R and make a call to the function ` gravity() ` and enjoy! Also, you can easily add your own levels by putting your own game parameters in the ‘define level’ code blocks.

``` ## gravity game in R gravity <- function(level=1){ ## prompt user for level cat("Enter Level (1-3)n") level <- scan(n=1, quiet=T)   ## simulation constants G <- 1000 # gravitational constant n <- 10000 # simulation steps dt <- .01 # time step size limit <- 50 # window limit m <- 1 # mass of space craft   ## define level 1 if(level==1){ ## fixed mass 1 Q1m <- 1 # mass Q1x <- 0 # x location Q1y <- -20 # y location Q1r <- 5 # radius   ## fixed mass 2 Q2m <- 1 # mass Q2x <- -10 # x location Q2y <- 30 # y location Q2r <- 5 # radius   ## win zone winx <- 30 # x location winy <- 20 # y location winr <- 2 # radius   ## start startx <- -40 # x location starty <- 20 # y location }   ## define level 2 if(level==2){ ## fixed mass 1 Q1m <- 10 # mass Q1x <- -20 # x location Q1y <- 20 # y location Q1r <- 25 # radius   ## fixed mass 2 Q2m <- 1 # mass Q2x <- 20 # x location Q2y <- -30 # y location Q2r <- 5 # radius   ## win zone winx <- 30 # x location winy <- 20 # y location winr <- 2 # radius   ## start startx <- -20 # x location starty <- -40 # y location }   ## define level 3 if(level==3){ ## fixed mass 1 Q1m <- 5 # mass Q1x <- 0 # x location Q1y <- 0 # y location Q1r <- 10 # radius   ## fixed mass 2 Q2m <- 1 # mass Q2x <- 30 # x location Q2y <- -0 # y location Q2r <- 5 # radius   ## win zone winx <- 20 # x location winy <- 20 # y location winr <- 2 # radius   ## start startx <- 20 # x location starty <- -20 # y location }   ## plot game map plot(startx, starty, col="blue", main=paste("Gravity: level", level), xlim=c(-limit, limit), ylim=c(-limit, limit), xlab="X", ylab="Y") circle(Q1x, Q1y, Q1r, "red") text(Q1x, Q1y, labels=Q1m) circle(Q2x, Q2y, Q2r, "red") text(Q2x, Q2y, labels=Q2m) circle(winx, winy, winr, "green") text(winx, winy, labels="w")   ## prompt user for velocity and angle cat("Enter Velocity (0-10, but no restrictions so don't cheat)n") velocity <- scan(n=1, quiet=T) cat("Enter Angle (in degrees, remember your trigonometry)n") angle <- scan(n=1, quiet=T)   ## define location paths, velocity, and distance vectors x <- rep(0,n) # x location y <- rep(0,n) # y location v <- c(0,0) # velocity vector r1 <- c(0,0) # distance vector to mass 1 r2 <- c(0,0) # distance vector to mass 2   ## set initial values x <- startx y <- starty v <- c(velocity*cos(angle*pi/180), velocity*sin(angle*pi/180))   for(i in 2:n){ ## calculate distance to fixed masses and win zone r1 <- c(x[i-1]-Q1x, y[i-1]-Q1y) r2 <- c(x[i-1]-Q2x, y[i-1]-Q2y) rw <- c(x[i-1]-winx, y[i-1]-winy)   ## break out of loop if ship crashed if(sqrt(r1 %*% r1)<Q1r | sqrt(r2 %*% r2)<Q2r){ x[i:n] <- x[i-1] y[i:n] <- y[i-1] cat("You crashed!n") break }   ## break out of loop if reach window limit if(abs(x[i-1])>limit*2 | abs(y[i-1])>limit*2){ x[i:n] <- x[i-1] y[i:n] <- y[i-1] cat("Lost in space!n") break }   ## break out of loop if reach win zone if(sqrt(rw %*% rw)<winr){ x[i:n] <- x[i-1] y[i:n] <- y[i-1] cat("You win!n") break }   ## calculate force vectors ## force from mass 1 f1 <- (r1/sqrt(r1 %*% r1))*(-G*Q1m*m)/(r1 %*% r1)   ## force from mass 2 f2 <- (r2/sqrt(r2 %*% r2))*(-G*Q2m*m)/(r2 %*% r2)   ## combined forces f <- f1 + f2   ## update velocity v <- v + dt*f   ## update location x[i] <- x[i-1] + dt*v/m y[i] <- y[i-1] + dt*v/m }   ## plot flight path lines(x,y) }   ## utlity function to draw a circle circle <- function(x,y,r,col){ theta <- seq(0, 2*pi, .001) xv <- r*cos(theta) + x yv <- r*sin(theta) + y lines(xv,yv, col=col) } ```

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