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|
#lang typed/racket/base
(require (for-syntax racket/base racket/syntax racket/match racket/list)
racket/list racket/match racket/unsafe/ops
"type-doc.rkt"
"math.rkt"
"marching-utils.rkt")
(provide heights->cube-polys
;heights->cube-polys:doc
)
(define-for-syntax (->datum x)
(if (syntax? x) (syntax->datum x) x))
(define-for-syntax (t=? a b)
(eq? (->datum a) (->datum b)))
;; edge vertexes
(define-syntax-rule (edge-1-2 d d1 d2) (ann (vector (solve-t d d1 d2) 0 0) (Vectorof Real)))
(define-syntax-rule (edge-2-3 d d2 d3) (ann (vector 1 (solve-t d d2 d3) 0) (Vectorof Real)))
(define-syntax-rule (edge-3-4 d d3 d4) (ann (vector (solve-t d d4 d3) 1 0) (Vectorof Real)))
(define-syntax-rule (edge-1-4 d d1 d4) (ann (vector 0 (solve-t d d1 d4) 0) (Vectorof Real)))
(define-syntax-rule (edge-5-6 d d5 d6) (ann (vector (solve-t d d5 d6) 0 1) (Vectorof Real)))
(define-syntax-rule (edge-6-7 d d6 d7) (ann (vector 1 (solve-t d d6 d7) 1) (Vectorof Real)))
(define-syntax-rule (edge-7-8 d d7 d8) (ann (vector (solve-t d d7 d8) 1 1) (Vectorof Real)))
(define-syntax-rule (edge-5-8 d d5 d8) (ann (vector 0 (solve-t d d5 d8) 1) (Vectorof Real)))
(define-syntax-rule (edge-1-5 d d1 d5) (ann (vector 0 0 (solve-t d d1 d5)) (Vectorof Real)))
(define-syntax-rule (edge-2-6 d d2 d6) (ann (vector 1 0 (solve-t d d2 d6)) (Vectorof Real)))
(define-syntax-rule (edge-3-7 d d3 d7) (ann (vector 1 1 (solve-t d d3 d7)) (Vectorof Real)))
(define-syntax-rule (edge-4-8 d d4 d8) (ann (vector 0 1 (solve-t d d4 d8)) (Vectorof Real)))
#|
Cube vertex numbers:
8--------7
/| /|
5--------6 |
| | | | d y
| 4------|-3 | /
|/ |/ |/
1--------2 +--- x
|#
(define-type Facet (Listof (Listof (Vectorof Real))))
(define-type Facet-Fun (-> Real Real Real Real Real Real Real Real Real Facet))
(: known-cube-0000-0000 Facet-Fun)
(define (known-cube-0000-0000 d d1 d2 d3 d4 d5 d6 d7 d8) empty)
(define known-cube-1111-1111 known-cube-0000-0000)
(: known-cube-1000-0000 Facet-Fun)
(define (known-cube-1000-0000 d d1 d2 d3 d4 d5 d6 d7 d8)
(list (list (edge-1-2 d d1 d2) (edge-1-5 d d1 d5) (edge-1-4 d d1 d4))))
(define known-cube-0111-1111 known-cube-1000-0000)
(: known-cube-1100-0000 Facet-Fun)
(define (known-cube-1100-0000 d d1 d2 d3 d4 d5 d6 d7 d8)
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6)
(edge-2-3 d d2 d3) (edge-1-4 d d1 d4))))
(define known-cube-0011-1111 known-cube-1100-0000)
(: known-cube-1110-0000 Facet-Fun)
(define (known-cube-1110-0000 d d1 d2 d3 d4 d5 d6 d7 d8)
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6) (edge-3-7 d d3 d7)
(edge-3-4 d d3 d4) (edge-1-4 d d1 d4))))
(define known-cube-0001-1111 known-cube-1110-0000)
(: known-cube-1111-0000 Facet-Fun)
(define (known-cube-1111-0000 d d1 d2 d3 d4 d5 d6 d7 d8)
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6)
(edge-3-7 d d3 d7) (edge-4-8 d d4 d8))))
(define known-cube-0000-1111 known-cube-1111-0000)
(: make-known-cube-1010-0000 (-> (-> Real Real Boolean) Facet-Fun))
(define ((make-known-cube-1010-0000 test?) d d1 d2 d3 d4 d5 d6 d7 d8)
(define da (/ (+ d1 d2 d3 d4) 4))
(cond
[(test? da d)
(list (list (edge-1-2 d d1 d2) (edge-2-3 d d2 d3)
(edge-3-7 d d3 d7) (edge-1-5 d d1 d5))
(list (edge-3-4 d d3 d4) (edge-1-4 d d1 d4)
(edge-1-5 d d1 d5) (edge-3-7 d d3 d7)))]
[else
(list (list (edge-1-2 d d1 d2) (edge-1-5 d d1 d5) (edge-1-4 d d1 d4))
(list (edge-2-3 d d2 d3) (edge-3-4 d d3 d4) (edge-3-7 d d3 d7)))]))
(define known-cube-1010-0000 (make-known-cube-1010-0000 >=))
(define known-cube-0101-1111 (make-known-cube-1010-0000 <))
(: known-cube-1000-0010 Facet-Fun)
(define (known-cube-1000-0010 d d1 d2 d3 d4 d5 d6 d7 d8)
(list (list (edge-1-2 d d1 d2) (edge-1-5 d d1 d5) (edge-1-4 d d1 d4))
(list (edge-6-7 d d6 d7) (edge-3-7 d d3 d7) (edge-7-8 d d7 d8))))
(define known-cube-0111-1101 known-cube-1000-0010)
(: make-known-cube-1100-0010 (-> (-> Real Real Boolean) Facet-Fun))
(define ((make-known-cube-1100-0010 test?) d d1 d2 d3 d4 d5 d6 d7 d8)
(define da (/ (+ d2 d6 d7 d3) 4))
(cond
[(test? da d)
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6)
(edge-6-7 d d6 d7) (edge-7-8 d d7 d8))
(list (edge-1-4 d d1 d4) (edge-2-3 d d2 d3)
(edge-3-7 d d3 d7) (edge-7-8 d d7 d8))
(list (edge-1-5 d d1 d5) (edge-1-4 d d1 d4) (edge-7-8 d d7 d8)))]
[else
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6)
(edge-2-3 d d2 d3) (edge-1-4 d d1 d4))
(list (edge-6-7 d d6 d7) (edge-3-7 d d3 d7) (edge-7-8 d d7 d8)))]))
(define known-cube-1100-0010 (make-known-cube-1100-0010 >=))
(define known-cube-0011-1101 (make-known-cube-1100-0010 <))
(: make-known-cube-1100-0011 (-> (-> Real Real Boolean) Facet-Fun))
(define ((make-known-cube-1100-0011 test?) d d1 d2 d3 d4 d5 d6 d7 d8)
(define da (/ (+ d1 d5 d8 d4) 4))
(define db (/ (+ d2 d6 d7 d3) 4))
(cond
[(and (test? da d) (test? db d))
(list (list (edge-1-5 d d1 d5) (edge-5-8 d d5 d8)
(edge-6-7 d d6 d7) (edge-2-6 d d2 d6))
(list (edge-1-4 d d1 d4) (edge-2-3 d d2 d3)
(edge-3-7 d d3 d7) (edge-4-8 d d4 d8)))]
[(test? da d)
(define ec (v* (v+ (v+ (v+ (edge-1-5 d d1 d5) (edge-1-4 d d1 d4))
(v+ (edge-4-8 d d4 d8) (edge-5-8 d d5 d8)))
(v+ (v+ (edge-6-7 d d6 d7) (edge-2-6 d d2 d6))
(v+ (edge-2-3 d d2 d3) (edge-3-7 d d3 d7))))
1/8))
(list (list ec (edge-5-8 d d5 d8) (edge-6-7 d d6 d7))
(list ec (edge-1-5 d d1 d5) (edge-2-6 d d2 d6))
(list ec (edge-4-8 d d4 d8) (edge-3-7 d d3 d7))
(list ec (edge-1-4 d d1 d4) (edge-2-3 d d2 d3))
(list ec (edge-1-5 d d1 d5) (edge-5-8 d d5 d8))
(list ec (edge-1-4 d d1 d4) (edge-4-8 d d4 d8))
(list ec (edge-3-7 d d3 d7) (edge-6-7 d d6 d7))
(list ec (edge-2-3 d d2 d3) (edge-2-6 d d2 d6)))]
[(test? db d)
(define ec (v* (v+ (v+ (v+ (edge-1-5 d d1 d5) (edge-1-4 d d1 d4))
(v+ (edge-4-8 d d4 d8) (edge-5-8 d d5 d8)))
(v+ (v+ (edge-6-7 d d6 d7) (edge-2-6 d d2 d6))
(v+ (edge-2-3 d d2 d3) (edge-3-7 d d3 d7))))
1/8))
(list (list ec (edge-5-8 d d5 d8) (edge-6-7 d d6 d7))
(list ec (edge-1-5 d d1 d5) (edge-2-6 d d2 d6))
(list ec (edge-4-8 d d4 d8) (edge-3-7 d d3 d7))
(list ec (edge-1-4 d d1 d4) (edge-2-3 d d2 d3))
(list ec (edge-1-5 d d1 d5) (edge-1-4 d d1 d4))
(list ec (edge-4-8 d d4 d8) (edge-5-8 d d5 d8))
(list ec (edge-3-7 d d3 d7) (edge-2-3 d d2 d3))
(list ec (edge-6-7 d d6 d7) (edge-2-6 d d2 d6)))]
[else
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6)
(edge-2-3 d d2 d3) (edge-1-4 d d1 d4))
(list (edge-5-8 d d5 d8) (edge-6-7 d d6 d7)
(edge-3-7 d d3 d7) (edge-4-8 d d4 d8)))]))
(define known-cube-1100-0011 (make-known-cube-1100-0011 >=))
(define known-cube-0011-1100 (make-known-cube-1100-0011 <))
(: make-known-cube-1010-0101 (-> (-> Real Real Boolean) Facet-Fun))
(define ((make-known-cube-1010-0101 test?) d d1 d2 d3 d4 d5 d6 d7 d8)
(define da (/ (+ d1 d2 d3 d4) 4))
(define db (/ (+ d1 d5 d8 d4) 4))
(define dc (/ (+ d3 d4 d8 d7) 4))
(define dd (/ (+ d1 d2 d6 d5) 4))
(define de (/ (+ d2 d3 d7 d6) 4))
(define df (/ (+ d5 d6 d7 d8) 4))
(append
(list (list (edge-1-5 d d1 d5) (edge-1-2 d d1 d2) (edge-1-4 d d1 d4))
(list (edge-2-3 d d2 d3) (edge-3-7 d d3 d7) (edge-3-4 d d3 d4))
(list (edge-5-6 d d5 d6) (edge-2-6 d d2 d6) (edge-6-7 d d6 d7))
(list (edge-7-8 d d7 d8) (edge-5-8 d d5 d8) (edge-4-8 d d4 d8)))
(if (test? da d)
(list (list (edge-1-2 d d1 d2) (edge-2-3 d d2 d3)
(edge-3-4 d d3 d4) (edge-1-4 d d1 d4)))
empty)
(if (test? db d)
(list (list (edge-1-5 d d1 d5) (edge-5-8 d d5 d8)
(edge-4-8 d d4 d8) (edge-1-4 d d1 d4)))
empty)
(if (test? dc d)
(list (list (edge-3-4 d d3 d4) (edge-3-7 d d3 d7)
(edge-7-8 d d7 d8) (edge-4-8 d d4 d8)))
empty)
(if (test? dd d)
(list (list (edge-1-2 d d1 d2) (edge-2-6 d d2 d6)
(edge-5-6 d d5 d6) (edge-1-5 d d1 d5)))
empty)
(if (test? de d)
(list (list (edge-2-3 d d2 d3) (edge-3-7 d d3 d7)
(edge-6-7 d d6 d7) (edge-2-6 d d2 d6)))
empty)
(if (test? df d)
(list (list (edge-5-6 d d5 d6) (edge-6-7 d d6 d7)
(edge-7-8 d d7 d8) (edge-5-8 d d5 d8)))
empty)))
(define known-cube-1010-0101 (make-known-cube-1010-0101 >=))
(define known-cube-0101-1010 (make-known-cube-1010-0101 <))
(: make-known-cube-1110-0001 (-> (-> Real Real Boolean) Facet-Fun))
(define ((make-known-cube-1110-0001 test?) d d1 d2 d3 d4 d5 d6 d7 d8)
(define da (/ (+ d1 d5 d8 d4) 4))
(define db (/ (+ d7 d8 d4 d3) 4))
(cond
[(and (test? da d) (test? db d))
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6) (edge-3-7 d d3 d7))
(list (edge-1-5 d d1 d5) (edge-3-7 d d3 d7)
(edge-7-8 d d7 d8) (edge-5-8 d d5 d8))
(list (edge-1-4 d d1 d4) (edge-3-4 d d3 d4) (edge-4-8 d d4 d8)))]
[(test? da d)
(define ec (v* (v+ (edge-1-5 d d1 d5) (edge-3-7 d d3 d7)) 1/2))
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6) (edge-3-7 d d3 d7))
(list ec (edge-3-7 d d3 d7) (edge-3-4 d d3 d4) (edge-1-4 d d1 d4))
(list ec (edge-1-5 d d1 d5) (edge-5-8 d d5 d8) (edge-7-8 d d7 d8))
(list ec (edge-1-4 d d1 d4) (edge-4-8 d d4 d8) (edge-7-8 d d7 d8)))]
[(test? db d)
(define ec (v* (v+ (edge-1-5 d d1 d5) (edge-3-7 d d3 d7)) 1/2))
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6) (edge-3-7 d d3 d7))
(list ec (edge-1-5 d d1 d5) (edge-1-4 d d1 d4) (edge-3-4 d d3 d4))
(list ec (edge-3-7 d d3 d7) (edge-7-8 d d7 d8) (edge-5-8 d d5 d8))
(list ec (edge-3-4 d d3 d4) (edge-4-8 d d4 d8) (edge-5-8 d d5 d8)))]
[else
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6) (edge-3-7 d d3 d7))
(list (edge-1-5 d d1 d5) (edge-3-7 d d3 d7)
(edge-3-4 d d3 d4) (edge-1-4 d d1 d4))
(list (edge-7-8 d d7 d8) (edge-5-8 d d5 d8) (edge-4-8 d d4 d8)))]))
(define known-cube-1110-0001 (make-known-cube-1110-0001 >=))
(define known-cube-0001-1110 (make-known-cube-1110-0001 <))
(: known-cube-1110-0100 Facet-Fun)
(define (known-cube-1110-0100 d d1 d2 d3 d4 d5 d6 d7 d8)
(list (list (edge-1-5 d d1 d5) (edge-5-6 d d5 d6) (edge-6-7 d d6 d7)
(edge-3-7 d d3 d7) (edge-3-4 d d3 d4) (edge-1-4 d d1 d4))))
(define known-cube-0001-1011 known-cube-1110-0100)
(: known-cube-1110-0010 Facet-Fun)
(define (known-cube-1110-0010 d d1 d2 d3 d4 d5 d6 d7 d8)
(list (list (edge-1-5 d d1 d5) (edge-2-6 d d2 d6) (edge-6-7 d d6 d7)
(edge-7-8 d d7 d8) (edge-3-4 d d3 d4) (edge-1-4 d d1 d4))))
(define known-cube-0001-1101 known-cube-1110-0010)
(: make-known-cube-1010-0001 (-> (-> Real Real Boolean) Facet-Fun))
(define ((make-known-cube-1010-0001 test?) d d1 d2 d3 d4 d5 d6 d7 d8)
(define da (/ (+ d1 d2 d3 d4) 4))
(define db (/ (+ d1 d5 d8 d4) 4))
(define dc (/ (+ d3 d4 d8 d7) 4))
(append
(list (list (edge-1-5 d d1 d5) (edge-1-2 d d1 d2) (edge-1-4 d d1 d4))
(list (edge-2-3 d d2 d3) (edge-3-7 d d3 d7) (edge-3-4 d d3 d4))
(list (edge-7-8 d d7 d8) (edge-5-8 d d5 d8) (edge-4-8 d d4 d8)))
(if (test? da d)
(list (list (edge-1-2 d d1 d2) (edge-2-3 d d2 d3)
(edge-3-4 d d3 d4) (edge-1-4 d d1 d4)))
empty)
(if (test? db d)
(list (list (edge-1-5 d d1 d5) (edge-5-8 d d5 d8)
(edge-4-8 d d4 d8) (edge-1-4 d d1 d4)))
empty)
(if (test? dc d)
(list (list (edge-3-4 d d3 d4) (edge-3-7 d d3 d7)
(edge-7-8 d d7 d8) (edge-4-8 d d4 d8)))
empty)))
(define known-cube-1010-0001 (make-known-cube-1010-0001 >=))
(define known-cube-0101-1110 (make-known-cube-1010-0001 <))
(define-for-syntax known-cubes
'((0 0 0 0 0 0 0 0)
(1 0 0 0 0 0 0 0)
(1 1 0 0 0 0 0 0)
(1 1 1 0 0 0 0 0)
(1 1 1 1 0 0 0 0)
(1 0 1 0 0 0 0 0)
(1 0 0 0 0 0 1 0)
(1 1 0 0 0 0 1 0)
(1 1 0 0 0 0 1 1)
(1 0 1 0 0 1 0 1)
(1 1 1 0 0 0 0 1)
(1 1 1 0 0 1 0 0)
(1 1 1 0 0 0 1 0)
(1 0 1 0 0 0 0 1)
(1 1 1 1 1 1 1 1)
(0 1 1 1 1 1 1 1)
(0 0 1 1 1 1 1 1)
(0 0 0 1 1 1 1 1)
(0 0 0 0 1 1 1 1)
(0 1 0 1 1 1 1 1)
(0 1 1 1 1 1 0 1)
(0 0 1 1 1 1 0 1)
(0 0 1 1 1 1 0 0)
(0 1 0 1 1 0 1 0)
(0 0 0 1 1 1 1 0)
(0 0 0 1 1 0 1 1)
(0 0 0 1 1 1 0 1)
(0 1 0 1 1 1 1 0)))
;; cube transformations: mirror
(: mirror-vec-d (-> (Vectorof Real) (Vectorof Real)))
(define (mirror-vec-d v)
(match-define (vector x y d) v)
(vector x y (- 1 d)))
(: mirror-cube-d (-> Facet-Fun Facet-Fun))
(define ((mirror-cube-d f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map mirror-vec-d poly))
(f d d5 d6 d7 d8 d1 d2 d3 d4)))
(: mirror-vec-y (-> (Vectorof Real) (Vectorof Real)))
(define (mirror-vec-y v)
(match-define (vector x y d) v)
(vector x (- 1 y) d))
(: mirror-cube-y (-> Facet-Fun Facet-Fun))
(define ((mirror-cube-y f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map mirror-vec-y poly))
(f d d4 d3 d2 d1 d8 d7 d6 d5)))
(: mirror-vec-x (-> (Vectorof Real) (Vectorof Real)))
(define (mirror-vec-x v)
(match-define (vector x y d) v)
(vector (- 1 x) y d))
(: mirror-cube-x (-> Facet-Fun Facet-Fun))
(define ((mirror-cube-x f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map mirror-vec-x poly))
(f d d2 d1 d4 d3 d6 d5 d8 d7)))
;; cube transformations: rotate clockwise (looking positively along axis)
(: unrotate-vec-d (-> (Vectorof Real) (Vectorof Real)))
(define (unrotate-vec-d v)
(match-define (vector x y d) v)
(vector (- 1 y) x d))
(: rotate-cube-d (-> Facet-Fun Facet-Fun))
(define ((rotate-cube-d f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map unrotate-vec-d poly))
(f d d2 d3 d4 d1 d6 d7 d8 d5)))
(: unrotate-vec-y (-> (Vectorof Real) (Vectorof Real)))
(define (unrotate-vec-y v)
(match-define (vector x y d) v)
(vector d y (- 1 x)))
(: rotate-cube-y (-> Facet-Fun Facet-Fun))
(define ((rotate-cube-y f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map unrotate-vec-y poly))
(f d d5 d1 d4 d8 d6 d2 d3 d7)))
(: unrotate-vec-x (-> (Vectorof Real) (Vectorof Real)))
(define (unrotate-vec-x v)
(match-define (vector x y d) v)
(vector x (- 1 d) y))
(: rotate-cube-x (-> Facet-Fun Facet-Fun))
(define ((rotate-cube-x f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map unrotate-vec-x poly))
(f d d4 d3 d7 d8 d1 d2 d6 d5)))
;; cube transformations: rotate counterclockwise (looking negatively along axis)
(: rotate-vec-d (-> (Vectorof Real) (Vectorof Real)))
(define (rotate-vec-d v)
(match-define (vector x y d) v)
(vector y (- 1 x) d))
(: unrotate-cube-d (-> Facet-Fun Facet-Fun))
(define ((unrotate-cube-d f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map rotate-vec-d poly))
(f d d4 d1 d2 d3 d8 d5 d6 d7)))
(: rotate-vec-y (-> (Vectorof Real) (Vectorof Real)))
(define (rotate-vec-y v)
(match-define (vector x y d) v)
(vector (- 1 d) y x))
(: unrotate-cube-y (-> Facet-Fun Facet-Fun))
(define ((unrotate-cube-y f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map rotate-vec-y poly))
(f d d2 d6 d7 d3 d1 d5 d8 d4)))
(: rotate-vec-x (-> (Vectorof Real) (Vectorof Real)))
(define (rotate-vec-x v)
(match-define (vector x y d) v)
(vector x d (- 1 y)))
(: unrotate-cube-x (-> Facet-Fun Facet-Fun))
(define ((unrotate-cube-x f) d d1 d2 d3 d4 d5 d6 d7 d8)
(map (λ ([poly : (Listof (Vectorof Real))]) (map rotate-vec-x poly))
(f d d5 d6 d2 d1 d8 d7 d3 d4)))
(define-for-syntax (cube-points-transform trans src)
(match-define (list j1 j2 j3 j4 j5 j6 j7 j8) src)
(cond [(t=? trans #'mirror-cube-d) (list j5 j6 j7 j8 j1 j2 j3 j4)]
[(t=? trans #'mirror-cube-y) (list j4 j3 j2 j1 j8 j7 j6 j5)]
[(t=? trans #'mirror-cube-x) (list j2 j1 j4 j3 j6 j5 j8 j7)]
[(t=? trans #'rotate-cube-d) (list j4 j1 j2 j3 j8 j5 j6 j7)]
[(t=? trans #'unrotate-cube-d) (list j2 j3 j4 j1 j6 j7 j8 j5)]
[(t=? trans #'rotate-cube-y) (list j2 j6 j7 j3 j1 j5 j8 j4)]
[(t=? trans #'unrotate-cube-y) (list j5 j1 j4 j8 j6 j2 j3 j7)]
[(t=? trans #'rotate-cube-x) (list j5 j6 j2 j1 j8 j7 j3 j4)]
[(t=? trans #'unrotate-cube-x) (list j4 j3 j7 j8 j1 j2 j6 j5)]))
(define-for-syntax known-transforms
(list #'mirror-cube-d
#'mirror-cube-y
#'mirror-cube-x
#'rotate-cube-d
#'rotate-cube-y
#'rotate-cube-x
#'unrotate-cube-d
#'unrotate-cube-y
#'unrotate-cube-x))
(define-for-syntax (opposite-transform? t1 t2)
(or (and (t=? t1 #'mirror-d) (t=? t2 #'mirror-d))
(and (t=? t1 #'mirror-y) (t=? t2 #'mirror-y))
(and (t=? t1 #'mirror-x) (t=? t2 #'mirror-x))
(and (t=? t1 #'rotate-d) (t=? t2 #'unrotate-d))
(and (t=? t1 #'unrotate-d) (t=? t2 #'rotate-d))
(and (t=? t1 #'rotate-y) (t=? t2 #'unrotate-y))
(and (t=? t1 #'unrotate-y) (t=? t2 #'rotate-y))
(and (t=? t1 #'rotate-x) (t=? t2 #'unrotate-x))
(and (t=? t1 #'unrotate-x) (t=? t2 #'rotate-x))))
(define-for-syntax (first-path-to-cube/src src dst depth)
(let/ec return
(let loop ([src src] [path empty] [depth depth])
;(printf "path = ~v~n" path)
(cond [(or (equal? src dst) #;(equal? (invert-cube src) dst)) path]
[(zero? depth) #f]
[else
(for ([move (in-list known-transforms)]
#:when (or (empty? path)
(not (opposite-transform? move (first path)))))
(define new-src (cube-points-transform move src))
(define new-path (cons move path))
(if (or (equal? new-src dst)
#;(equal? (invert-cube new-src) dst))
(return new-path)
(loop new-src new-path (sub1 depth))))
#f]))))
(define-for-syntax (shortest-path-to-cube dst)
(let/ec return
(for ([depth (in-list '(1 2 3))])
(for ([src (in-list known-cubes)])
(define path (first-path-to-cube/src src dst depth))
(when path (return (cons src path)))))
(list #f #f)))
(define-for-syntax (format-cube-id ctxt cube j1 j2 j3 j4 j5 j6 j7 j8)
(format-id ctxt "~a-~a~a~a~a-~a~a~a~a" cube
(->datum j1) (->datum j2)
(->datum j3) (->datum j4)
(->datum j5) (->datum j6)
(->datum j7) (->datum j8)))
(define-syntax (define-all-cube-functions stx)
(syntax-case stx ()
[(id)
#`(begin
#,@(for*/list ([j8 (in-list '(0 1))]
[j7 (in-list '(0 1))]
[j6 (in-list '(0 1))]
[j5 (in-list '(0 1))]
[j4 (in-list '(0 1))]
[j3 (in-list '(0 1))]
[j2 (in-list '(0 1))]
[j1 (in-list '(0 1))])
(define dst (list j1 j2 j3 j4 j5 j6 j7 j8))
(match-define (cons src path) (shortest-path-to-cube dst))
(cond [(or (empty? path) (first path))
(with-syntax ([define-cube-function
(format-id #'id "define-cube-function")])
#`(define-cube-function
#,dst #,src #,path))]
[else (void)])))]))
(define-syntax (define-cube-function stx)
(syntax-case stx ()
[(id (d1 d2 d3 d4 d5 d6 d7 d8)
(s1 s2 s3 s4 s5 s6 s7 s8)
path)
(with-syntax ([cube-dst (format-cube-id #'id "cube"
#'d1 #'d2 #'d3 #'d4
#'d5 #'d6 #'d7 #'d8)]
[cube-src (format-cube-id #'id "known-cube"
#'s1 #'s2 #'s3 #'s4
#'s5 #'s6 #'s7 #'s8)])
(define new-stx
(syntax-case #'path ()
[() #'(define cube-dst cube-src)]
[(t) #'(define cube-dst (t cube-src))]
[(t2 t1) #'(define cube-dst (t2 (t1 cube-src)))]
[(t3 t2 t1) #'(define cube-dst (t3 (t2 (t1 cube-src))))]))
;(printf "~a~n" (syntax->datum new-stx))
new-stx)]))
(define-syntax (make-cube-dispatch-table stx)
(syntax-case stx ()
[(id)
#`(vector
#,@(for*/list ([j8 (in-list '(0 1))]
[j7 (in-list '(0 1))]
[j6 (in-list '(0 1))]
[j5 (in-list '(0 1))]
[j4 (in-list '(0 1))]
[j3 (in-list '(0 1))]
[j2 (in-list '(0 1))]
[j1 (in-list '(0 1))])
(format-cube-id #'id "cube" j1 j2 j3 j4 j5 j6 j7 j8)))]))
(define-all-cube-functions)
(define cube-dispatch-table
(make-cube-dispatch-table))
(define-syntax-rule (add-digit j idx)
(unsafe-fx+ (unsafe-fx* idx 2) j))
(: do-heights->cube-polys Facet-Fun)
(define (do-heights->cube-polys d d1 d2 d3 d4 d5 d6 d7 d8)
(define j1 (if (d1 . < . d) 0 1))
(define j2 (if (d2 . < . d) 0 1))
(define j3 (if (d3 . < . d) 0 1))
(define j4 (if (d4 . < . d) 0 1))
(define j5 (if (d5 . < . d) 0 1))
(define j6 (if (d6 . < . d) 0 1))
(define j7 (if (d7 . < . d) 0 1))
(define j8 (if (d8 . < . d) 0 1))
(define facet-num
(add-digit
j1 (add-digit
j2 (add-digit
j3 (add-digit
j4 (add-digit
j5 (add-digit
j6 (add-digit j7 j8))))))))
(define f (vector-ref cube-dispatch-table facet-num))
(f d d1 d2 d3 d4 d5 d6 d7 d8))
(:: heights->cube-polys (-> Real Real Real Real Real Real
Real Real Real Real Real Real Real Real Real
(Listof (Listof (Vector Real Real Real)))))
(define (heights->cube-polys xa xb ya yb za zb d d1 d2 d3 d4 d5 d6 d7 d8)
(cond [(= d d1 d2 d3 d4 d5 d6 d7 d8) empty]
[else
(define polys (do-heights->cube-polys d d1 d2 d3 d4 d5 d6 d7 d8))
(for/list ([poly (in-list polys)])
(for/list : (Listof (Vector Real Real Real)) ([uvw (in-list poly)])
(match-define (vector u v w) uvw)
(vector (unsolve-t xa xb u)
(unsolve-t ya yb v)
(unsolve-t za zb w))))]))
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