Draw Bezier curves with Go

Draw Bezier curves with Go

I would like to give a detailed explanation, but for the time being the source code

Source code

package bezier

import (

type Point struct{
  X,Y float64

// n! (factorial of n)
func factorial(n int)(int){
  if n == 0{
    return 1
  return n * factorial(n-1)

func biCoe(n,i int)(float64){
  return float64(factorial(n) / (factorial(n-i) * factorial(i)))

func bernstein(n,i int,t float64)(float64){
  var N float64 = float64(n)
  var I float64 = float64(i)
  return biCoe(n,i) * math.Pow(t,I ) * math.Pow(1-t,N-I)

func BezierCurve(p []Point,t float64)(result Point){
  for i,v := range p{
    B := bernstein(len(p)-1,i,t)
    result.X += v.X*B
    result.Y += v.Y*B

//If the amount of change value is increased, a becomes a crisp curve.
func Curve(p []Point,a float64)(result []Point){
  var t float64
  for {
    result = append(result, BezierCurve(p,t) )
    t += a
    if t >= 1{

Curve ([] Point, float64) is a function that gives the control point and the amount of change in t and returns a slice of P (t, 0> = t <= 1).

The user usually draws using this function (assuming that).

Usage example

package bezier

import (

func TestBezierCurve(t *testing.T){
  //Control point
  P := []Point{Point{10,10},Point{10,590},Point{590,590}}

  //Amount of change
  const A = 0.01
  result := Curve(P,A)

  dc := gg.NewContext(600,600)

  //Drawing control points
  for _,v :=range P{

  //Draw a curve
  //Move to the starting point
  for _,v :=range result{

  // P(t)Drawing of
  for _,v :=range result{

  dc.SavePNG("out.png ")

Test execution result


The blue point is the control point and the red is the circle centered on the coordinates of P (t).

in conclusion

I'm not good at mathematics, but I came up with an implementation in a few hours (too much time) by staring at mathematical formulas. There was a great sense of accomplishment. (Impression of elementary school students)

I would like to update it little by little when I am fine.

I hope this article will be useful to someone.


I am always indebted to http://github.com/fogleman/gg.

The article by @Rahariku was very helpful. Thank you very much.


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