Making a list of waypoints for a bezier curve

[IWacky_Galaxy (IWacky)]

I really have no experience with Bezier curves and was wondering if someone could help me out with my fishing pole system which I’m intending to use a Bezier curve to cast the line.

I really dont know where to start and how to get a list of waypoints so that I can lerp the position smoothly across them.

[greenboo5]

Trigger warning: math.

Reparameterization: Tips and Tricks

This guide was originally written for scriptinghelpers. The original can be found here. Here’s a guide about reparameterization. It has a few nifty tricks that can be applied to all sorts of things outside the topic. Awhile back I wrote an article on the wiki discussing Bezier curves. Near the end of the article I started to talk about reparameterization (arc-length parameterization) and how it could be done without calculus. Today we are going to talk about how it can be done with calculus …

[joebersons (joeberson)]

This is one that I like to use. Its easy to get any time value along the curve you create as well. CatRom.rbxm (10.9 KB)

[BendsSpace]

Egomoose comes in clutch for this twice over, he also has some easy code to modify in his projectile motion tutorial:

local attach0 = Instance.new("Attachment", game.Workspace.Terrain);
local attach1 = Instance.new("Attachment", game.Workspace.Terrain);

local beam = Instance.new("Beam", game.Workspace.Terrain);
beam.Attachment0 = attach0;
beam.Attachment1 = attach1;

local function beamProjectile(g, v0, x0, t1)
	-- calculate the bezier points
	local c = 0.5*0.5*0.5;
	local p3 = 0.5*g*t1*t1 + v0*t1 + x0;
	local p2 = p3 - (g*t1*t1 + v0*t1)/3;
	local p1 = (c*g*t1*t1 + 0.5*v0*t1 + x0 - c*(x0+p3))/(3*c) - p2;
	
	-- the curve sizes
	local curve0 = (p1 - x0).magnitude;
	local curve1 = (p2 - p3).magnitude;
	
	-- build the world CFrames for the attachments
	local b = (x0 - p3).unit;
	local r1 = (p1 - x0).unit;
	local u1 = r1:Cross(b).unit;
	local r2 = (p2 - p3).unit;
	local u2 = r2:Cross(b).unit;
	b = u1:Cross(r1).unit;
	
	local cf1 = CFrame.new(
		x0.x, x0.y, x0.z,
		r1.x, u1.x, b.x,
		r1.y, u1.y, b.y,
		r1.z, u1.z, b.z
	)
	
	local cf2 = CFrame.new(
		p3.x, p3.y, p3.z,
		r2.x, u2.x, b.x,
		r2.y, u2.y, b.y,
		r2.z, u2.z, b.z
	)
	
	return curve0, -curve1, cf1, cf2;
end

game:GetService("RunService").RenderStepped:Connect(function(dt)
	local g = Vector3.new(0, -game.Workspace.Gravity, 0);
	local x0 = hrp.CFrame * Vector3.new(0, 2, -2)
	local v0 = (mouse.Hit.p - x0 - 0.5*g*t*t)/t;
	
	local curve0, curve1, cf1, cf2 = beamProjectile(g, v0, x0, t);
	beam.CurveSize0 = curve0;
	beam.CurveSize1 = curve1;
	-- convert world space CFrames to be relative to the attachment parent
	attach0.CFrame = attach0.Parent.CFrame:inverse() * cf1;
	attach1.CFrame = attach1.Parent.CFrame:inverse() * cf2;
end)

(See the first section of the beamProjectile section)

Modeling a projectile's motion

This guide was originally written for scriptinghelpers. The original can be found here. As a somewhat active member of the Scripting Helpers discord one of the most common questions I see is how to have a projectile travel an arc. Most people want to know how to do this for things like basketballs or cannon balls and so forth. Since this is such a popular question I thought it would be worth writing a blog post on it and talking about a few other things we can extend from our findings. Deri…