module Diagrams.ThreeD.Shapes
(
Ellipsoid(..)
, sphere
) where
import Prelude hiding (minimum)
import Data.Semigroup
import Data.AffineSpace
import Data.Monoid.Inf (minimum)
import Data.VectorSpace
import Diagrams.Core
import Diagrams.ThreeD.Types
import Diagrams.Solve
data Ellipsoid = Ellipsoid T3
type instance V Ellipsoid = R3
instance Transformable Ellipsoid where
transform t1 (Ellipsoid t2) = Ellipsoid (t1 <> t2)
instance IsPrim Ellipsoid
instance Renderable Ellipsoid NullBackend where
render _ _ = mempty
sphere :: (Backend b R3, Renderable Ellipsoid b) => Diagram b R3
sphere = mkQD (Prim $ Ellipsoid mempty)
(mkEnvelope sphereEnv)
(mkTrace sphereTrace)
mempty
(Query sphereQuery)
where sphereEnv v = 1 / magnitude v
sphereTrace p v = minimum (quadForm a b c)
where a = v <.> v
b = 2 *^ p' <.> v
c = p' <.> p' 1
p' = p .-. origin
sphereQuery v = Any $ magnitudeSq (v .-. origin) <= 1