#| turtle.scm Copyright 2018 Kavalogic, Inc. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: (1) Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. (2) Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. (3) The name of the author may not be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |# (use-modules (inspekt3d viewer) (libfive shapes) (libfive kernel) (libfive vec) (libfive transforms) (libfive csg)) (define +P+ 1.6180339889) (define (half-space-pts point1 point2 point3) "half-space-pts point1 point2 point3 (specify points in CW order for RH outward facing normal)" (let* ((V1 (- point1 point2)) (V2 (- point3 point2)) (X (cross V1 V2)) (l (norm X)) (N (/ X l)) (pos (/ (+ point1 point2 point3) 3))) (half-space N pos))) (define* (icosohedron #:optional (P +P+)) (let* ((-P (- P)) (2P (* 2 P)) (-2P (- 2P)) (-1-2P (- -1 2P)) (1+2P (+ 1 2P)) (2+P (+ 2 P)) (-2-P (- -2 P)) (3P (* 3 P)) (-3P (- 3P)) (vertices (list->vector ;; TODO: use permutations to generate these (list #[ -P 2 -1-2P ] #[ -1 -3P 0 ] #[ 2+P -2P 1 ] #[ 0 1 3P ] #[ -1 -2-P 2P ] #[ -3P 0 1 ] #[ 1 -2-P 2P ] #[ -2P 1 -2-P ] #[ 1 2+P -2P ] #[ 2 1+2P -P ] #[ -2-P -2P 1 ] #[ -2-P 2P -1 ] #[ -1 -2-P -2P ] #[ -P -2 -1-2P ] #[ -1-2P -P 2 ] #[ 1+2P P 2 ] #[ -1 3P 0 ] #[ 1+2P P -2 ] #[ -2 1+2P P ] #[ -1-2P -P -2 ] #[ 3P 0 1 ] #[ P -2 1+2P ] #[ 1+2P -P -2 ] #[ 0 -1 -3P ] #[ 0 -1 3P ] #[ 1 2+P 2P ] #[ -1-2P P -2 ] #[ -2 1+2P -P ] #[ 1 -3P 0 ] #[ 1+2P -P 2 ] #[ -2P -1 -2-P ] #[ 2P 1 2+P ] #[ P 2 1+2P ] #[ 2+P 2P -1 ] #[ -2-P -2P -1 ] #[ P -2 -1-2P ] #[ 2 -1-2P P ] #[ 3P 0 -1 ] #[ -2P 1 2+P ] #[ -1-2P P 2 ] #[ -P -2 1+2P ] #[ 2+P -2P -1 ] #[ -1 2+P 2P ] #[ -P 2 1+2P ] #[ 1 3P 0 ] #[ -2P -1 2+P ] #[ P 2 -1-2P ] #[ 1 -2-P -2P ] #[ 2P 1 -2-P ] #[ 2P -1 2+P ] #[ -1 2+P -2P ] #[ 2 1+2P P ] #[ 2+P 2P 1 ] #[ -2 -1-2P -P ] #[ 0 1 -3P ] #[ -3P 0 -1 ] #[ 2P -1 -2-P ] #[ 2 -1-2P -P ] #[ -2 -1-2P P ] #[ -2-P 2P 1 ]))) (pentagons '(#(12 47 35 23 13) ; flipped #(18 59 11 27 16) #(19 30 7 26 55) #(6 4 40 24 21) ; flipped #(42 25 32 3 43) ; flipped #(44 9 33 52 51) #(8 50 0 54 46) ; flipped #(56 22 37 17 48) ; flipped #(49 31 15 20 29) #(5 39 38 45 14) #(34 10 58 1 53) ; flipped #(57 28 36 2 41))) (hexagons '(#(10 14 45 40 4 58) #(11 26 7 0 50 27) #(42 43 38 39 59 18) ; flipped #(2 36 6 21 49 29) #(20 37 22 41 2 29) #(25 51 52 15 31 32) #(26 11 59 39 5 55) #(57 47 12 53 1 28) ; flipped #(28 1 58 4 6 36) #(49 21 24 3 32 31) ; flipped #(53 12 13 30 19 34) ; flipped #(20 15 52 33 17 37) ; flipped #(41 22 56 35 47 57) #(16 27 50 8 9 44) ; flipped #(45 38 43 3 24 40) #(48 46 54 23 35 56) #(14 10 34 19 55 5) ; flipped #(51 25 42 18 16 44) #(30 13 23 54 0 7) ; flipped #(9 8 46 48 17 33)))) ;; intersect all half-spaces from a triangle of each of the pentagons ;; and hexagons (apply intersection (append (map (lambda (pentagon) (half-space-pts (vector-ref vertices (vector-ref pentagon 0)) (vector-ref vertices (vector-ref pentagon 1)) (vector-ref vertices (vector-ref pentagon 2)))) pentagons) (map (lambda (hexagon) (half-space-pts (vector-ref vertices (vector-ref hexagon 0)) (vector-ref vertices (vector-ref hexagon 1)) (vector-ref vertices (vector-ref hexagon 2)))) hexagons))))) (define (my-rounded-cube len r) ;; cube in #[-len/2 -len/2 0] to #[len/2 len/2 len] ;; with all edges and corners rounded at radius r (let* ((offset (/ len 2)) (base (extrude-z (rounded-rectangle #[(- offset) (- offset)] #[offset offset] r) 0 len)) (faceted (intersection base (move (rotate-x base (/ pi 2)) #[0 offset offset]) (move (rotate-y base (/ pi 2)) #[offset 0 offset]))) (sph (difference (sphere r) (box #[(- r) 0 (- r)] #[r r r]) (box #[(- r) (- r) 0] #[r r r]) (box #[0 (- r) (- r)] #[r r r]))) (corner (difference (box #[(- r) (- r) (- r)] #[ 0 0 0]) sph)) (half-corners (union (move corner #[(- r offset) (- r offset) r]) (move (rotate-y corner (/ pi 2)) #[(- offset r) (- r offset) r]) (move (rotate-x corner (/ pi 2)) #[(- r offset) (- offset r) r]) (move (rotate-y (rotate-x corner (/ pi 2)) (/ pi 2)) #[(- offset r) (- offset r) r]))) (corners (union half-corners (move (rotate-x half-corners pi) #[0 0 len])))) (difference faceted corners))) (define (make-turtle-shape) (let* ((bball-radius (sqrt (+ (* 9 (* +P+ +P+)) 1))) (base-sphere (sphere (* bball-radius 0.925))) ;; bottom (bottom (scale-xyz base-sphere #[1 0.225 1])) ;; head (head-cutout-sphere (scale-xyz (move (sphere 2) #[(+ bball-radius 0) 1.5 0]) #[1 .5 1])) ;; shell (shell-sphere (sphere bball-radius)) (bball (icosohedron)) (shell (morph bball shell-sphere .3)) (half-shell (difference shell (half-space #[0 1 0]))) (base-shell-unscaled (union half-shell bottom)) (base-shell (scale-xyz base-shell-unscaled #[1.25 1 1])) (shell-cutout (scale-xyz (sphere bball-radius) #[1 0.15 1.1])) ;; body (body (intersection (move (scale-xyz base-sphere #[1.1 0.5 1]) #[0 0.5 0]) base-shell)) ;; shell assembly (turtle-shell (difference base-shell ;; head area (move shell-cutout #[(+ bball-radius 0.75) 0.4 0]) head-cutout-sphere ;; tail area (move shell-cutout #[(- (+ bball-radius 0.75)) 0.4 0]))) ;; head/neck (neck (cylinder-z 0.8 3.0 #[0 0.1 0])) (eye (sphere 0.35)) ;;(mouth (ang-wedge (/ pi 50) 2 2)) (head (union (move (scale-xyz (my-rounded-cube 2.2 0.8) #[1 1 1.1]) #[0 0.4 -1.3]) (move eye #[0.77 0.6 -0.7]) (move eye #[-0.77 0.6 -0.7]))) (head/neck (scale-xyz (move (rotate-z (rotate-y (union neck head) (/ pi 2)) (/ pi 12)) #[6.75 1.05 0]) #[1 1 0.95])) (leg (rotate-z (scale-xyz (sphere 1.0) #[2.2 0.4 0.7]) (/ pi 9))) (legs (union (move (rotate-y leg (/ pi 5)) #[-3.5 0.5 -3.3]) (move (rotate-y leg (- (/ pi 5))) #[-3.5 0.5 3.3]) (move (rotate-y leg (* pi (/ 4 5))) #[3.5 0.5 -3.3]) (move (rotate-y leg (- (* pi (/ 4 5)))) #[3.5 0.5 3.3]))) (tail (move (scale-xyz (sphere 1.0) #[2.0 0.3 0.35]) #[-5 0.5 0])) ;; turtle assembly (turtle (union turtle-shell body head/neck legs tail))) turtle)) (make-viewer) (set-shape (make-turtle-shape) '((-20 . 20) (-20 . 20) (-20 . 20)) 10)