Hey, so I’ve been dabbling with the art of Bezier curves for a while now and one of the biggest problems that I was facing, is to make them linear or uniform speed.
There is numerous articles that shows how and different algorithms however I couldn’t wrap my head around any one of them so today I have made a module that can take any parametric functions with argument t and process it into a table of linear points or calculate it’s length, etc…
But before I launch it to the public and make a video about, I need your feedback about it!
So here is my implementation, I made it myself, so I want to know your thoughts and feedback about it.
Example:
Here is a simple example for the ‘Bake’ and ‘Length’ functions:
local CurveFunction = require(script.CurveFunction)
local TAU = 2*math.pi
local SQRT_2 = math.sqrt(2)
local cos, sin = math.cos, math.sin
local vector2 = Vector2.new
local abs = math.abs
-- Radius of the circle
local R = 1
-- Polygon sides count
local N = 4
-- Circle's parametric function
local function circle(t)
local angle = t * TAU
return R * vector2( cos(angle), sin(angle) )
end
-- Create a table with N+1 points using the parametric function circle
local data = CurveFunction.Bake(circle, N+1)
local length = CurveFunction.Length(data)
-- The perimeter of the polygon with N sides
-- that is inscribed inside the circle with the radius R
print("Perimeter:", length)
-- Formula for square's perimeter inscribed inside a circle with radius r
local function squarePerimeterInCircle(r)
return 4 * SQRT_2 * r
end
-- There is an error (underestimation) of 9.6812937222523e-08
-- between the real formula and the calculated one in this case
print("Error margin:", squarePerimeterInCircle(R)-length)
-- Function to create a part in the specified position
local function part(pos)
local p = Instance.new("Part")
p.Anchored = true
p.CFrame = CFrame.lookAt(pos, Vector3.zero, Vector3.new(0, 1, 0))
p.BrickColor = BrickColor.Black()
p.Size = Vector3.one*0.1
p.Parent = workspace
end
-- Draw the points generated using parts
for _, point in ipairs(data) do
part(Vector3.new(point.X, point.Y, 0))
end
You can also use bezier curves here, because it’s a parametric function
You can use the BakeLinear function to control the speed of the curve because bezier curves aren’t uniform like circle parametric function.
In fact, I made this module for any parametric function, with bezier curves in mind
