Diagrams - Tangent and normal

Illustrating the tangent and normal vectors to a point on a curve.

Author: Pontus Granström

> import Diagrams.Backend.SVG.CmdLine

> import Diagrams.Prelude

Some arbitrary points, with a cubic curve passing through them.

> pts = map p2 [(0,0), (1,1), (2,1), (3,0), (3.5,0)]
> 
> spline :: Located (Trail V2 Double)
> spline = cubicSpline False pts

Computing tangent and normal vectors at a particular point on the curve.

> param = 0.45 -- parameter on the curve where the tangent and normal are drawn
> pt = atParam spline param
> tangentVector = tangentAtParam spline param
> normalVector = normalAtParam spline param

We can draw the tangent and normal vectors with lines of twice their length, with a square in between them to denote the right angle.

> symmetricLine v = fromOffsets [2 *^ v] # center
> tangentLine = symmetricLine tangentVector
> normalLine = symmetricLine normalVector
> 
> rightAngleSquare = square 0.1 # alignBL # rotate (signedAngleBetween tangentVector unitX)

Putting it all together, with some labels.

> example :: Diagram B
> example = frame 0.5 $
>   strokeLocTrail spline
>   <> mconcat
>      [ tangentLine
>      , baselineText "tangent" # translate tangentVector
>      , normalLine
>      , topLeftText "normal" # translate normalVector
>      , rightAngleSquare
>      ] # moveTo pt # fontSize large

> main = mainWith (example :: Diagram B)