Shady.ParamSurf

Parametric surfaces with automatic normals

Documentation

type HeightField s = Complex s -> s

type Surf s = Complex s -> (s, s, s)

type USurf = forall s. Floating s => Surf s

type Curve2 s = s -> Complex s

type Curve3 s = s -> (s, s, s)

type Warp1 s = s -> s

type Warp2 s = Complex s -> Complex s

type Warp3 s = (s, s, s) -> (s, s, s)

sinU :: Floating s => s -> s

Trig functions with unit period ([-1,1])

cosU :: Floating s => s -> s

hfSurf :: HeightField s -> Surf s

Turn a height field into a surface

fcurve :: Warp1 s -> Curve2 s

Like hfSurf but for curve construction

circle :: Floating s => Curve2 s

Unit circle.

semiCircle :: Floating s => Curve2 s

Half semi circle, with theta in [-pi2,pi2]

torus :: (Floating s, VectorSpace s, Scalar s ~ s) => s -> s -> Surf s

Torus, given radius of sweep circle and cross section

revolveG :: Floating s => (s -> Curve2 s) -> Surf s

revolve :: Floating s => Curve2 s -> Surf s

sphere1 :: Floating s => Surf s

profile :: Num s => Curve2 s -> Curve2 s -> Surf s

Profile product.

sphere3 :: Floating s => Surf s

sphere2 :: Floating s => Surf s

frustum :: (Floating s, VectorSpace s, Scalar s ~ s) => s -> s -> s -> Surf s

Frustum, given base & cap radii and height.

ucylinder :: (Floating s, VectorSpace s) => Surf s

Unit cylinder. Unit height and radii

xyPlane :: Num s => Surf s

XY plane as a surface

cartF :: (a -> b -> c) -> (s -> a) -> (s -> b) -> Complex s -> c

Given a combining op and two curves, make a surface. A sort of Cartesian product with combination.

sweep :: VectorSpace s => Curve3 s -> Curve3 s -> Surf s

eggcrateH :: Floating s => HeightField s

One period, unit height eggcrate

revolveH :: (Floating s, InnerSpace s, Scalar s ~ s) => Warp1 s -> HeightField s

rippleH :: (Floating s, InnerSpace s, Scalar s ~ s) => HeightField s

ripple :: Floating s => Surf s

Simple ripply pond shape

displaceV :: (InnerSpace v, s ~ Scalar v, Floating s, HasNormal v) => v -> Scalar v -> v

Apply a displacement map at a value

displace :: (InnerSpace v, Scalar v ~ s, Floating s, HasNormal v, Applicative f) => f v -> f (Scalar v) -> f v

Apply a displacement map to a function (e.g., Curve2 or Surf) or other container.

rotate :: Floating s => s -> Warp2 s

addY :: Num s => (a -> Complex s) -> a -> (s, s, s)

addZ :: Num s => (a -> Complex s) -> a -> (s, s, s)

addX :: Num s => (a -> Complex s) -> a -> (s, s, s)

addXZ :: Num s => (a -> s) -> a -> (s, s, s)

addXY :: Num s => (a -> s) -> a -> (s, s, s)

addYZ :: Num s => (a -> s) -> a -> (s, s, s)

onY :: Warp1 s -> Warp3 s

onZ :: Warp1 s -> Warp3 s

onX :: Warp1 s -> Warp3 s

onYZ :: Warp2 s -> Warp3 s

onXZ :: Warp2 s -> Warp3 s

onXY :: Warp2 s -> Warp3 s

onY' :: Warp1 s -> (a -> (s, s, s)) -> a -> (s, s, s)

onZ' :: Warp1 s -> (a -> (s, s, s)) -> a -> (s, s, s)

onX' :: Warp1 s -> (a -> (s, s, s)) -> a -> (s, s, s)

onXZ' :: Warp2 s -> (a -> (s, s, s)) -> a -> (s, s, s)

onYZ' :: Warp2 s -> (a -> (s, s, s)) -> a -> (s, s, s)

onXY' :: Warp2 s -> (a -> (s, s, s)) -> a -> (s, s, s)

type V2 a = (a, a)

type V3 a = (a, a, a)

type ER = FloatE

type ER2 = V2 ER

type ER3 = V3 ER

type TR = ER :> ER

type T = ER2 :> ER

type SurfPt = V3 T

Derivative towers of point on a surface

type SurfD = Surf T

Differentiable surface

type VN = (R3E, R3E)

Vertex and normal

toVN :: SurfPt -> VN

type SurfVN = R2E -> VN

surfVN :: SurfD -> SurfVN