# FieldTrip

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## 1 Abstract

Torus pair modeled and rendered in FieldTrip

FieldTrip is a library for functional 3D graphics, intended for building static, animated, and interactive 3D geometry, efficient enough for real-time synthesis and display. Our first renderer uses OpenGL, with the usual visual limitations. Since FieldTrip is functional, it is about being rather than doing. One describes what models are, not how to render them.

Besides this wiki page, here are more ways to find out about and get involved with FieldTrip:

## 2 Basic types

The basic purpose of the core FieldTrip library is to allow a user build 3D geometry, from individual simple shapes to full 3D scenes. The principal types are as follows.

Geometry3
3D geometry. These values can be spatially transformed in space (affinely: scale, rotate, translate) and combined (union).
Surf a = (a,a) -> (a,a,a)
Parametric surfaces, i.e., mappings from 2D to 3D. Normals are constructed automatically and exactly via derivatives, thanks to the vector-space library. These normals are used for shading. For simplicity and composability, surfaces are curved, not faceted. Surface rendering tessellates adaptively, caching tessellations in an efficient, infinite data structure for reuse. The mechanism for choosing tessellation is a very primitive placeholder. FieldTrip provides some basic shapes of surfaces (spheres, torus, cubes, etc) and many functions for manipulating surfaces, colors, etc.
Geometry2
2D geometry. There's a function (
flatG
) to embed 2D into 3D.
Image o = (R,R) -> o
A primitive placeholder for functional imagery in the spirit of Pan. The intention is to use this type or something like it for texture mapping. Much design and implementation work to be done.

## 3 Example

The code for the static torus pair shown above:

```torusPair :: Geometry3
torusPair = f red (1/2) `mappend` pivot3X (f green (-1/2))
where
tor = torus 1 (2/5)
f :: Col -> R -> Geometry3
f col dx = plasmat col (move3X dx tor)```
where
pivot3X
and
move3X
are simple helper functions for 3D transformation, and
plasmat
applies a color with a plastic look (defined in `Test.hs`).

The `torus` function used here is a simple wrapper around a parametric surface defined as follows:

```-- | Torus, given radius of sweep circle and cross section
torus :: (Floating s, VectorSpace s, Scalar s ~ s) => s -> s -> Surf s
torus sr cr = revolve (const (sr,0) ^+^ cr *^ circle)```
where
revolve
and
circle
are defined in `Graphics.FieldTrip.ParamSurf`, along with other tools for shape generation. The trick to turning this polymorphic
torus
function into a
Geometry3
is to use a derivative tower (from vector-space) for the type parameter
s
.
```surfG :: Surf (Vector2 R :> R) -> Geometry3

torus :: R -> R -> Geometry3
torus sr cr = surfG (P.torus (pureD sr) (pureD cr))```

[fill in more examples]

## 4 FieldTrip meets Reactive

FieldTrip contains no support for animation, because we intend it to be used with the Reactive functional reactive programming (FRP) library (and possibly other animation frameworks). By design, FieldTrip is completely orthogonal to any formulation or implementation of FRP.

The reactive-fieldtrip project connects Reactive and FieldTrip.

The picture above comes from an animation in reactive-fieldtrip. Load `src/Test.hs`, as follows:

```    ~/Haskell\$ cd reactive-fieldtrip/src
~/Haskell/reactive-fieldtrip/src\$ ghci
GHCi, version 6.10.1: http://www.haskell.org/ghc/  :? for help
Loading package ghc-prim ... linking ... done.
Loading package integer ... linking ... done.
Loading package base ... linking ... done.
Prelude> :l Test
:l Test
[1 of 2] Compiling FRP.Reactive.FieldTrip.Adapter ( FRP/Reactive/FieldTrip/Adapter.hs, interpreted )
[2 of 2] Compiling Test             ( Test.hs, interpreted )
Ok, modules loaded: FRP.Reactive.FieldTrip.Adapter, Test.
```

Then run the example:

```    *Test> anim3 (spinningG torusPair)
Loading package OpenGL-2.2.1.1 ... linking ... done.
Loading package syb ... linking ... done.
Loading package base-3.0.3.0 ... linking ... done.
[...]
Loading package reactive-0.9.0 ... linking ... done.
Loading package FieldTrip-0.2.2 ... linking ... done.
Loading package reactive-glut-0.0.5 ... linking ... done.
```

A video of the torus demo running in GHCi.