;******************************************************************************************* ;* Helicoid/Catenoid (Spring) Minimal Surface, by Paul Nylander, bugman123.com, 3/11/09 ;******************************************************************************************* ;Basic Functions (defun sinh (x) (* 0.5 (- (exp x) (exp (- x))))) (defun cosh (x) (* 0.5 (+ (exp x) (exp (- x))))) ;Converts Polygon into AutoCAD's Triangle Elements, only works for convex polygons ;(TriangulateElem '(1 2 3 4 5 6 7 8 9 10)) -> '((1 2 -3) (-1 3 -4) (-1 4 -5) (-1 5 -6) (-1 6 -7) (-1 7 -8) (-1 8 -9) (-1 9 10)) (defun TriangulateElem (elem / n i i0 i1 i2 elems) (setq n (length elem)) (if (= n 3) (list elem) (progn (setq i0 (car elem) i1 (caddr elem) elems (list (list i0 (cadr elem) (- i1))) i 3) (while (< i (1- n)) (setq i2 (nth i elem) elems (append elems (list (list (- i0) i1 (- i2)))) i1 i2 i (1+ i))) (append elems (list (list (- i0) i1 (last elem)))) ));i );d (defun mesh (nodes elems1 / elems2 nnode nelem elem) (setq elems2 (apply 'append (mapcar 'TriangulateElem elems1))); introduces AutoCAD's negative index notation (setq nnode (length nodes) nelem (length elems2)) (entmake (list '(0 . "POLYLINE") '(70 . 64) (cons 71 nnode) (cons 72 nelem))) (foreach p nodes (entmake (list '(0 . "VERTEX") (cons 10 p) '(70 . 192)))) (foreach elem elems2 (entmake (list '(0 . "VERTEX") '(10 0.0 0.0 0.0) '(70 . 128) (cons 71 (car elem)) (cons 72 (cadr elem)) (cons 73 (caddr elem)) (cons 74 (- (abs (car elem)))) )));f (entmake '((0 . "SEQEND"))) );d (defun ParametricPlot3D (f u1 u2 du v1 v2 dv / u v i j i1 i2 i3 i4 imax jmax nodes elems) (setq imax (fix (+ (/ (- u2 u1) du) 0.5)) jmax (fix (+ (/ (- v2 v1) dv) 0.5))) (setq j 0); calculate nodes (while (<= j jmax) (setq v (+ v1 (* j dv)) i 0) (while (<= i imax) (setq u (+ u1 (* i du)) nodes (append nodes (list (f u v))) i (1+ i))) (setq j (1+ j)) );w (setq i 1); assemble quad elements (while (<= i imax) (setq j 0) (while (< j jmax) (setq i1 (+ i (* j (1+ imax))) i2 (1+ i1) i3 (+ i1 (1+ imax) 1) i4 (+ i1 (1+ imax)) elems (append elems (list (list i1 i2 i3 i4))) j (1+ j) ));w (setq i (1+ i)) );w (mesh nodes elems) );d ;Helicoid/Catenoid (Spring) Minimal Surface (setq alpha 0.8175188542971654 sina (sin alpha) cosa (cos alpha) dz (* 2 pi cosa) vmax 2.25) (defun HelicoidCatenoid (u v / sinu cosu sinhv coshv x y z) (setq sinu (sin u) cosu (cos u) sinhv (sinh v) coshv (cosh v)) (setq x (+ (* sina coshv cosu) (* cosa sinhv sinu))) (setq y (- (* sina coshv sinu) (* cosa sinhv cosu))) (setq z (+ (* u cosa) (* v sina))) (list x y z) );d (ParametricPlot3D HelicoidCatenoid (* -2 pi) (* 3 pi) (/ pi 9) (- vmax) vmax (/ vmax 5)) (command "vpoint" (list -1.0 -1.0 1.0)); (command "zoom" "extents")