Curve that touches three points: Difference between revisions
Added Go
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::# Do not use functions of a library, implement the curve() function yourself
::# coordinates:(x,y) starting point (10,10) medium point (100,200) final point (200,10)
=={{header|Go}}==
{{libheader|Go Graphics}}
<br>
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>
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