dronir / bezier.jl Goto Github PK

Hi,

I was looking to implementing Bézier curves into one my projects and came across this project, which I see is already included on Pkg.jl

I see it uses Bernstein polynomials, and therefore the number of control points is limited. Maybe using the de Casteljau formula one can improve this limitation. Also, the de Casteljau method allows to easily extend to Bézier patches (I have a preliminary version of this).

Also, it might be a good idea to add dependency to GeometryBasics.jl (from JuliaGeometry) to handle the type of control points and return points. It has the advantage that plotting a vector of points is already implemented (see example below). Hence, I would propose:

using GeometryBasics

struct BezierCurve
    control_points::Vector{Point}
end

function (curve::BezierCurve)(t::Real)
    # Bezier curve using the de Casteljau algorithm 
   
    b = copy(curve.control_points)
    while length(b) > 1
        br = copy(b) 
        b  = [(1-t)*br[i] + t*br[i+1] for i in 1:(length(br)-1)]
    end
    return b[1]
end 

A MWE of use:

using Plots

control_points = Vector{Point}(undef,4)
control_points[1] = Point(0.0,1.0)
control_points[2] = Point(0.0,0.0)
control_points[3] = Point(2.0,0.0)
control_points[4] = Point(3.0,3.0)
curve = BezierCurve(control_points)

plot(curve.control_points, color=:gray,label="")
scatter!(curve.control_points, color=:gray,label="Control points")

points = [curve(t) for t in 0.0:1e-2:1.0]
plot!(points, color=:blue,label="Bezier curve")

There is the following warning (which should be resolved)

WARNING: using Plots.BezierCurve in module Main conflicts with an existing identifier.

Indeed Plots.jl already implements plotting Bézier curves with curves