If you have used the Love2D physics module you might be familiar with some of these questions:
What will be the future position/angle of body A?
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--- Returns the future position assuming no external forces are acting on the body
-- @x, @y Current position at the beginning of the time step
-- @lvx, lvy Current linear velocity at the beginning of the time step
-- @damping Linear damping
-- @gx, gy Gravity
-- @dt Time step
-- @return Future position at the end of the time step
function steering.futurePos(x, y, lvx, lvy, damping, gx, gy, dt)
-- integrate gravity
local fpx = lvx + gx*dt
local fpy = lvy + gy*dt
-- apply damping
local d = 1 - dt*damping
if d < 0 then
d = 0
elseif d > 1 then
d = 1
end
return fpx*d + x, fpy*d + y
end
--- Returns the future angle assuming no external forces are acting on the body
-- @x, @y Current angle at the beginning of the time step
-- @lvx, lvy Current angular velocity at the beginning of the time step
-- @damping Angular damping
-- @dt Time step
-- @return Future angle at the end of the time step
function steering.futureAng(a, av, damping, dt)
-- apply damping
local d = 1 - dt*damping
if d < 0 then
d = 0
elseif d > 1 then
d = 1
end
return av*d + a
end
What velocity should I set so that body A is not affected by damping/gravity?
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--- Compensates for the effects of gravity
-- @lvx, lvy Desired linear velocity at the end of the time step
-- @gx, gy Gravity
-- @dt Time step
-- @return Target linear velocity at the beginning of the time step
function steering.compG(lvx, lvy, gx, gy, dt)
return lvx - gx*dt, lvy - gy*dt
end
--- Compensates for the effects of linear damping
-- @lvx, lvy Desired linear velocity at the end of the time step
-- @damping Linear damping
-- @maxLV Maximum linear velocity
-- @dt Time step
-- @return Target linear velocity at the beginning of the time step
function steering.compLD(lvx, lvy, damping, maxLV, dt)
local d = 1 - dt*damping
if d <= 0 then
local lv = math.sqrt(lvx*lvx + lvy*lvy)
local nx, ny = lvx/lv, lvy/lv
return nx*maxLV, ny*maxLV
elseif d > 1 then
d = 1
end
return lvx/d, lvy/d
end
--- Compensates for the effects of angular damping
-- @av Desired angular velocity at the end of the time step
-- @damping Linear damping
-- @maxAV Maximum angular velocity
-- @dt Time step
-- @return Target angular velocity at the beginning of the time step
function steering.compAD(av, damping, maxAV, dt)
local d = 1 - dt*damping
if d <= 0 then
if av < 0 then
return -maxAV
else
return maxAV
end
elseif d > 1 then
d = 1
end
return av/d
end
How much force/torque do I need to apply so that body A can reach a given velocity?
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--- Returns the force required to reach a given linear velocity
--- force = ( change in velocity / time ) * mass
-- @ivx, @ivy Initial linear velocity at the beginning of the time step
-- @fvx, @fvy Final linear velocity at the end of the time step
-- @mass Mass
-- @dt Time step
-- @return Force
function steering.force(ivx, ivy, fvx, fvy, mass, dt)
return (fvx - ivx)/dt*mass, (fvy - ivy)/dt*mass
end
--- Returns the torque required to reach a given angular velocity
--- inertia = mass * initial velocity
--- torque = ( change in velocity / time ) * inertia
-- @iv Initial angular velocity at the beginning of the time step
-- @fv Final angular velocity at the end of the time step
-- @mass Mass
-- @dt Time step
-- @return Torque
function steering.torque(iv, fv, mass, dt)
local inertia = mass*iv
return (fv - iv)/dt*inertia
end
How long does it take to accelerate to a given velocity?
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--- Returns the time required to accelerate to a given linear velocity
--- time = change in velocity * mass / force
-- @ivx, @ivy Initial linear velocity
-- @fvx, @fvy Final linear velocity
-- @mass Mass
-- @force Maximum force
-- @return Time
function steering.atime(ivx, ivy, fvx, fvy, mass, force)
-- change in velocity
local dx, dy = fvx - ivx, fvy - ivy
local d = math.sqrt(dx*dx + dy*dy)
return d*mass/force
end
--- Returns the time required to accelerate to a given angular velocity
--- inertia = mass * initial velocity
--- time = change in velocity * inertia / torque
-- @iv Initial angular velocity
-- @fv Final angular velocity
-- @mass Mass
-- @force Maximum torque
-- @return Time
function steering.aatime(iv, fv, mass, torque)
local inertia = mass*iv
return (fv - iv)*inertia/torque
end
example use:
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-- current linear velocity
local cvx, cvy = body:GetLinearVelocity()
-- target linear velocity required to counteract the effects of gravity and linear damping:
local lvx, lvy = steering.compG(0, 0, gx, gy, interval)
lvx, lvy = steering.compLD(lvx, lvy, damping, maxLV, interval)
-- force required to reach the target linear velocity
local fx, fy = steering.force(cvx, cvy, lvx, lvy, mass, interval)
-- keep the body aloft using only forces
body:ApplyForce(fx, fy)
-- update simulation(interval)
