Curve that touches three points

Curve that touches three points is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Draw a curve that touches 3 points (1 starting point, 2 medium, 3 final point)

1.  Do not use functions of a library, implement the curve() function yourself
2.  coordinates:(x,y) starting point (10,10) medium point (100,200) final point (200,10)

Go

Library: Go Graphics

There are, of course, an infinity of curves which can be fitted to 3 points. The most obvious solution is to fit a quadratic curve (using Lagrange interpolation) and so that's what we do here.

As we're not allowed to use library functions to draw the curve, we instead divide the x-axis of the curve between successive points into equal segments and then join the resulting points with straight lines.

The resulting 'curve' is then saved to a .png file where it can be viewed with a utility such as EOG. <lang go>package main

import "github.com/fogleman/gg"

var p = [3]gg.Point{{10, 10}, {100, 200}, {200, 10}}

func lagrange(x float64) float64 {

   return (x-p[1].X)*(x-p[2].X)/(p[0].X-p[1].X)/(p[0].X-p[2].X)*p[0].Y +
       (x-p[0].X)*(x-p[2].X)/(p[1].X-p[0].X)/(p[1].X-p[2].X)*p[1].Y +
       (x-p[0].X)*(x-p[1].X)/(p[2].X-p[0].X)/(p[2].X-p[1].X)*p[2].Y

}

func getPoints(n int) []gg.Point {

   pts := make([]gg.Point, 2*n+1)
   dx := (p[1].X - p[0].X) / float64(n)
   for i := 0; i < n; i++ {
       x := p[0].X + dx*float64(i)
       pts[i] = gg.Point{x, lagrange(x)}
   }
   dx = (p[2].X - p[1].X) / float64(n)
   for i := n; i < 2*n+1; i++ {
       x := p[1].X + dx*float64(i-n)
       pts[i] = gg.Point{x, lagrange(x)}
   }
   return pts

}

func main() {

   const n = 50 // more than enough for this
   dc := gg.NewContext(210, 210)
   dc.SetRGB(1, 1, 1) // White background
   dc.Clear()
   for _, pt := range getPoints(n) {
       dc.LineTo(pt.X, pt.Y)
   }
   dc.SetRGB(0, 0, 0) // Black curve
   dc.SetLineWidth(1)
   dc.Stroke()
   dc.SavePNG("quadratic_curve.png")

}</lang>