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October 4, 2019 00:50
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Uses dark magic (math) to calculate the unit velocity vector that will create a trajectory to your goal given a speed
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function calcTrajectoryTheta(start,goal,speed,pickHighAngle) | |
local xzStart = start * Vector3.new(1,0,1) | |
local xzGoal = goal * Vector3.new(1,0,1) | |
local range = (xzGoal-xzStart).Magnitude | |
local yDiff = goal.Y - start.Y | |
local g = workspace.Gravity | |
if range == 0 then return nil end | |
if g == 0 then | |
return math.atan(yDiff/range) -- simply return angle to the goal | |
end | |
local insideSqrt = (speed*speed*speed*speed) - (g * (g*range*range + 2*yDiff*speed*speed)) | |
if insideSqrt < 0 then return nil end -- NaN will happen | |
local sqrt = math.sqrt(insideSqrt) | |
local angleOne = (speed*speed + sqrt)/(g*range) | |
local angleTwo = (speed*speed - sqrt)/(g*range) | |
angleOne = math.atan(angleOne) | |
angleTwo = math.atan(angleTwo) | |
if pickHighAngle then | |
return math.max(angleOne,angleTwo) | |
else | |
return math.min(angleOne,angleTwo) | |
end | |
end | |
function directionToReachGoal(start,goal,speed,pickHighAngle) | |
local theta = calcTrajectoryTheta(start,goal,speed,pickHighAngle) | |
if not theta then return nil end | |
local facingDirection = ((goal-start) * Vector3.new(1,0,1)).Unit | |
local facingCFrame = CFrame.new(Vector3.new(), facingDirection) | |
local angledCFrame = facingCFrame * CFrame.fromAxisAngle(Vector3.new(1,0,0), theta) | |
return angledCFrame.LookVector | |
end | |
return directionToReachGoal |
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