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+-- Copyright (c) 2000 Galois Connections, Inc.
+-- All rights reserved. This software is distributed as
+-- free software under the license in the file "LICENSE",
+-- which is included in the distribution.
+
+module Construct
+ ( Surface (..)
+ , Face (..)
+ , CSG (..)
+ , Texture
+ , Transform
+ , union, intersect, difference
+ , plane, sphere, cube, cylinder, cone
+ , transform
+ , translate, translateX, translateY, translateZ
+ , scale, scaleX, scaleY, scaleZ, uscale
+ , rotateX, rotateY, rotateZ
+ , eye, translateEye
+ , rotateEyeX, rotateEyeY, rotateEyeZ
+ ) where
+
+import Geometry
+
+-- In each case, we model the surface by a point and a pair of tangent vectors.
+-- This gives us enough information to determine the surface
+-- normal at that point, which is all that is required by the current
+-- illumination model. We can't just save the surface normal because
+-- that isn't preserved by transformations.
+
+data Surface
+ = Planar Point Vector Vector
+ | Spherical Point Vector Vector
+ | Cylindrical Point Vector Vector
+ | Conic Point Vector Vector
+ deriving Show
+
+data Face
+ = PlaneFace
+ | SphereFace
+ | CubeFront
+ | CubeBack
+ | CubeLeft
+ | CubeRight
+ | CubeTop
+ | CubeBottom
+ | CylinderSide
+ | CylinderTop
+ | CylinderBottom
+ | ConeSide
+ | ConeBase
+ deriving Show
+
+data CSG a
+ = Plane a
+ | Sphere a
+ | Cylinder a
+ | Cube a
+ | Cone a
+ | Transform Matrix Matrix (CSG a)
+ | Union (CSG a) (CSG a)
+ | Intersect (CSG a) (CSG a)
+ | Difference (CSG a) (CSG a)
+ | Box Box (CSG a)
+ deriving (Show)
+
+-- the data returned for determining surface texture
+-- the Face tells which face of a primitive this is
+-- the Point is the point of intersection in object coordinates
+-- the a is application-specific texture information
+type Texture a = (Face, Point, a)
+
+union, intersect, difference :: CSG a -> CSG a -> CSG a
+
+union p@(Box b1 _) q@(Box b2 _) = Box (mergeBox b1 b2) (Union p q)
+union p q = Union p q
+
+-- rather pessimistic
+intersect p@(Box b1 _) q@(Box b2 _) = Box (mergeBox b1 b2) (Intersect p q)
+intersect p q = Intersect p q
+
+difference (Box b1 p) q = Box b1 (Difference p q)
+-- no need to box again inside
+-- difference p@(Box b1 _) q = Box b1 (Difference p q)
+difference p q = Difference p q
+
+mkBox b p = Box b p
+
+plane, sphere, cube, cylinder, cone :: a -> CSG a
+
+plane = Plane
+sphere s =
+ mkBox (B (-1 - epsilon) (1 + epsilon)
+ (-1 - epsilon) (1 + epsilon)
+ (-1 - epsilon) (1 + epsilon)) (Sphere s)
+cone s =
+ mkBox (B (-1 - epsilon) (1 + epsilon)
+ ( - epsilon) (1 + epsilon)
+ (-1 - epsilon) (1 + epsilon)) (Cone s)
+cube s =
+ mkBox (B (- epsilon) (1 + epsilon)
+ (- epsilon) (1 + epsilon)
+ (- epsilon) (1 + epsilon)) (Cube s)
+cylinder s =
+ mkBox (B (-1 - epsilon) (1 + epsilon)
+ ( - epsilon) (1 + epsilon)
+ (-1 - epsilon) (1 + epsilon)) (Cylinder s)
+
+----------------------------
+-- Object transformations
+----------------------------
+
+type Transform = (Matrix, Matrix)
+
+transform :: Transform -> CSG a -> CSG a
+
+transform (m, m') (Transform mp mp' p) = Transform (multMM m mp) (multMM mp' m') p
+transform mm' (Union p q) = Union (transform mm' p) (transform mm' q)
+transform mm' (Intersect p q) = Intersect (transform mm' p) (transform mm' q)
+transform mm' (Difference p q) = Difference (transform mm' p) (transform mm' q)
+transform mm'@(m,_) (Box box p) = Box (transformBox m box) (transform mm' p)
+transform (m, m') prim = Transform m m' prim
+
+translate :: Coords -> CSG a -> CSG a
+translateX, translateY, translateZ :: Double -> CSG a -> CSG a
+
+translate xyz = transform $ transM xyz
+translateX x = translate (x, 0, 0)
+translateY y = translate (0, y, 0)
+translateZ z = translate (0, 0, z)
+
+scale :: Coords -> CSG a -> CSG a
+scaleX, scaleY, scaleZ, uscale :: Double -> CSG a -> CSG a
+
+scale xyz = transform $ scaleM xyz
+scaleX x = scale (x, 1, 1)
+scaleY y = scale (1, y, 1)
+scaleZ z = scale (1, 1, z)
+uscale u = scale (u,u,u)
+
+rotateX, rotateY, rotateZ :: Radian -> CSG a -> CSG a
+
+rotateX a = transform $ rotxM a
+rotateY a = transform $ rotyM a
+rotateZ a = transform $ rotzM a
+
+unit = matrix
+ ( ( 1.0, 0.0, 0.0, 0.0 ),
+ ( 0.0, 1.0, 0.0, 0.0 ),
+ ( 0.0, 0.0, 1.0, 0.0 ),
+ ( 0.0, 0.0, 0.0, 1.0 ) )
+
+transM (x, y, z)
+ = ( matrix
+ ( ( 1, 0, 0, x ),
+ ( 0, 1, 0, y ),
+ ( 0, 0, 1, z ),
+ ( 0, 0, 0, 1 ) ),
+ matrix
+ ( ( 1, 0, 0, -x ),
+ ( 0, 1, 0, -y ),
+ ( 0, 0, 1, -z ),
+ ( 0, 0, 0, 1 ) ) )
+
+scaleM (x, y, z)
+ = ( matrix
+ ( ( x', 0, 0, 0 ),
+ ( 0, y', 0, 0 ),
+ ( 0, 0, z', 0 ),
+ ( 0, 0, 0, 1 ) ),
+ matrix
+ ( ( 1/x', 0, 0, 0 ),
+ ( 0, 1/y', 0, 0 ),
+ ( 0, 0, 1/z', 0 ),
+ ( 0, 0, 0, 1 ) ) )
+ where x' = nonZero x
+ y' = nonZero y
+ z' = nonZero z
+
+rotxM t
+ = ( matrix
+ ( ( 1, 0, 0, 0 ),
+ ( 0, cos t, -sin t, 0 ),
+ ( 0, sin t, cos t, 0 ),
+ ( 0, 0, 0, 1 ) ),
+ matrix
+ ( ( 1, 0, 0, 0 ),
+ ( 0, cos t, sin t, 0 ),
+ ( 0, -sin t, cos t, 0 ),
+ ( 0, 0, 0, 1 ) ) )
+
+rotyM t
+ = ( matrix
+ ( ( cos t, 0, sin t, 0 ),
+ ( 0, 1, 0, 0 ),
+ ( -sin t, 0, cos t, 0 ),
+ ( 0, 0, 0, 1 ) ),
+ matrix
+ ( ( cos t, 0, -sin t, 0 ),
+ ( 0, 1, 0, 0 ),
+ ( sin t, 0, cos t, 0 ),
+ ( 0, 0, 0, 1 ) ) )
+
+rotzM t
+ = ( matrix
+ ( ( cos t, -sin t, 0, 0 ),
+ ( sin t, cos t, 0, 0 ),
+ ( 0, 0, 1, 0 ),
+ ( 0, 0, 0, 1 ) ),
+ matrix
+ ( ( cos t, sin t, 0, 0 ),
+ ( -sin t, cos t, 0, 0 ),
+ ( 0, 0, 1, 0 ),
+ ( 0, 0, 0, 1 ) ) )
+
+-------------------
+-- Eye transformations
+
+-- These are used to specify placement of the eye.
+-- `eye' starts out at (0, 0, -1).
+-- These are implemented as inverse transforms of the model.
+-------------------
+
+eye :: Transform
+translateEye :: Coords -> Transform -> Transform
+rotateEyeX, rotateEyeY, rotateEyeZ :: Radian -> Transform -> Transform
+
+eye = (unit, unit)
+translateEye xyz (eye1, eye2)
+ = (multMM m1 eye1, multMM eye2 m2)
+ where (m1, m2) = transM xyz
+rotateEyeX t (eye1, eye2)
+ = (multMM m1 eye1, multMM eye2 m2)
+ where (m1, m2) = rotxM t
+rotateEyeY t (eye1, eye2)
+ = (multMM m1 eye1, multMM eye2 m2)
+ where (m1, m2) = rotyM t
+rotateEyeZ t (eye1, eye2)
+ = (multMM m1 eye1, multMM eye2 m2)
+ where (m1, m2) = rotzM t
+
+-------------------
+-- Bounding boxes
+-------------------
+
+mergeBox (B x11 x12 y11 y12 z11 z12) (B x21 x22 y21 y22 z21 z22) =
+ B (x11 `min` x21) (x12 `max` x22)
+ (y11 `min` y21) (y12 `max` y22)
+ (z11 `min` z21) (z12 `max` z22)
+
+transformBox t (B x1 x2 y1 y2 z1 z2)
+ = (B (foldr1 min (map xCoord pts'))
+ (foldr1 max (map xCoord pts'))
+ (foldr1 min (map yCoord pts'))
+ (foldr1 max (map yCoord pts'))
+ (foldr1 min (map zCoord pts'))
+ (foldr1 max (map zCoord pts')))
+ where pts' = map (multMP t) pts
+ pts = [point x1 y1 z1,
+ point x1 y1 z2,
+ point x1 y2 z1,
+ point x1 y2 z2,
+ point x2 y1 z1,
+ point x2 y1 z2,
+ point x2 y2 z1,
+ point x2 y2 z2]
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