How to move the npc along a parabolic trajectory?

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1

Hello,
I’m trying to create a leap ability for a boss npc in my game. When the ability is activated, the npc will leap towards the target position in a curve.

The effect I’m looking for is similar to this video:

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2

You’re looking for projectile motion modelling

3

Yes, I’ve tried the methods from that post step by step before. but sadly physical (I mean directly apply velocity) way are barely works on npc,but this is exactly what i want to achieve

4

There are many parabolic orbits which reach a particular point.
I assume that there is no other power such as air resistance.

All they are in this condition:
x/v = 2u/g
(g is gravitational acceleration, v is parallel velocity, x is the distance between player and boss, u is vertical velocity)

If you set all the values as they are in this condition, player always reach to the boss.

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5

I may forgot the probability that the boss is moving.

6

I’m still having trouble understanding this. Could you explain it and show how I can use it in a script? (I’m beginner on scripting)

8

If simulating the parabolic trajectory is insufficient, you can manually interpolate the trajectory by creating a function of time that maps out its positions:

local function getPositionAtTime(timePosition: number, origin: Vector3, initialVelocity: Vector3): Vector3
    local displacement = initialVelocity * timePosition + 0.5 * GRAVITY_ACCELERATION * timePosition ^ 2
    
    return origin + displacement
end

Related kinematic equation:

image
image330×114 14.2 KB

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9

I’m not a native English speaker, so the description may be hard to understand.

· gravity can be got from Workspace.Gravity

· distance between player and the boss can be got from Player:DistanceFromCharacter(Boss.Position)

· You can add velocity by ApplyImpulse.

· Parallel Vector of ApplyImpulse should be parallel to Boss.Position - Player.Position (But z component isn’t). Then, Parallel velocity(v) can be set as
t*(Boss.Position.X - Player.Position.X, Boss.Position.Y - Player.Position.Y, 0) (t can be any number you like)

Vertical velocity(u) should be in this condition:
u = gx/2v
so Z = gx/ParallelVector.Magnitude*2
Thus, the Vector you should apply is found.

In conclusion:

local g = workspace.Gravity
local boss = workspace.Boss --your boss
local t = _ --whatever value you like

local function attack(player, boss)--[[player is who used the ability]]
 local humanoid = player.Character:FindFirstChild("Humanoid")
 if not humanoid then return end
 local root = humanoid:FindFirstChild("HumanoidRootPart")
 local x = boss.Position - player.Position
 local ParaV = Vector3.new(boss.Position.X - player.Position.X, boss.Position.Y - player.Position.Y, 0) *t
 local u =  g*x.Magnitude/2*ParaV.Magnitude
 local TheV = Vector3.new(boss.Position.X - player.Position.X, boss.Position.Y - player.Position.Y, u) --This is the Vector applied to player

 root:ApplyImpulse(TheV *t)
end
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10

I forgot to use this, so you can write as:

local x = player:DistanceFromCharacter(boss.Position)
 local ParaV = Vector3.new(boss.Position.X - player.Position.X, boss.Position.Y - player.Position.Y, 0)
 local u =  g*x/2*ParaV.Magnitude

Instead of

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11

Thanks, but the caster of leap ability is npc instead of player (player is target)

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I made a mistake. This script can be used only in the case that Z Position of player and the boss are same.
Improved idea:
h is the deference of Z Position of player and that of boss.
u +√(u^2 - 8gh)/g = x/v

If you want a script, I will reply later.

For this, Just change Player and Boss.

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