Computer Science Canada :: View topic - Question : Finding the closest intersection point for two moving objects

type player :
record
x, y : real
v : real
a : real
end record

var p, e : player

function setAngle (x, y : real) : real
if x = 0 and y = 0 then
result 0
elsif x = 0 and y > 0 then
result 90
elsif x = 0 and y < 0 then
result 270
elsif y = 0 and x > 0 then
result 0
elsif y = 0 and x < 0 then
result 180
elsif x > 0 and y > 0 then
result arctand (y / x)
elsif x < 0 and y > 0 then
result 180 + arctand (y / x)
elsif x > 0 and y < 0 then
result 360 + arctand (y / x)
elsif x < 0 and y < 0 then
result 180 + arctand (y / x)
else
result 0
end if
end setAngle

for j : 1 .. 5
p.x := Rand.Int(50,maxx-50)
p.y := Rand.Int(50,maxy-50)
p.v := 1
p.a := Rand.Int(0,360)

e.x := Rand.Int(50,maxx-50)
e.y := Rand.Int(50,maxy-50)
e.v := 1.5
var beta := setAngle (e.x - p.x, e.y - p.y) - p.a
e.a := setAngle (p.x - e.x, p.y - e.y) + arcsind (sind (beta) * p.v / e.v)

for i : 1 .. 200
Draw.FillOval (round (p.x), round (p.y), 1, 1, 7)
Draw.FillOval (round (e.x), round (e.y), 1, 1, 12)
p.x += (cosd (p.a) * p.v)
p.y += (sind (p.a) * p.v)

e.x += (cosd (e.a) * e.v)
e.y += (sind (e.a) * e.v)
delay (10)
end for
end for

Author:	TerranceN [ Tue May 25, 2010 8:16 pm ]
Post subject:	Question : Finding the closest intersection point for two moving objects
Since this is not language specific I figured I would put this here. Explanation of Question For my geometry wars clone, I am trying to create an enemy that can cut the player off instead of just following the player. Here is a diagram of the problem: P is the position of the player Vp is the velocity of the player Ω is the angle the player is moving in standard position (this is why I drew the horizontal lines) E is the position of the enemy Ve is the velocity of the enemy Θ is the angle the enemy is moving in standard position I is where the interception will occur t is the time it takes for the enemy to intercept the player Things I know: P Vp Ω E Ve Things I don't know: Θ I t My question is how would I go about finding any of the unknowns (once I know one it is easy to plug that in to the equations I know (see below)). What I Have Tried I started off with some equations that I know are true (note that I split 2d points into their x and y components): The next thing I did is try to remove an unknown by isolating t in two different equations (I'm only showing one cause the other is the same rearranging but it is y instead of x and sine instead of cosine): then I set the two equations equal to each other: Then I tried to solve for Θ using this equation solver, but it told me that it is not solvable. I then tried the same precess, but isolating Θ in two different equations and trying to solve for t: But once again this is unsolvable. I don't know what to do from here, and this problem has stumped my MSIP teacher (who is a math teacher), any help will be rewarded with bits and a solution (or something that directly leads me to one) will be rewarded with karma.

Author:	TerranceN [ Wed May 26, 2010 6:18 am ]
Post subject:	RE:Question : Finding the closest intersection point for two moving objects
Thanks! I will try this solution today, but from what I have read in your post and seen in your example it is exactly what I was looking for. +1 Karma +100 Bits