(prompt "\nDoubling the Cube by AutoCAD - Menaechmus_Delian.LSP")
(prompt "\nCommands:  TEST  MENAECHMUS_Delian ")
(prompt "\n           ")
;----------------------------------------------------------
;; Draw parabolas & rectangular hyperbola used for Delian Problems
;; Menaechmus has invented conics and used conics to solve Delian Problem
;;
;;;;;
;;		8/25/00 updated Nov,2003
;;;		12/15/06	copied Menaechmus.lsp
;;;TEST
(defun C:test()
	(princ "need test routine")
)
;;;Menaechmus
(defun c:menaechmus()
	(setup_menaechmus)	;Delian solution by Conics
;;draw x2 = ay curve
	(setq pnt_start (list x_start (f_x2_ay a_value x_start)))
	(setq step 0    pnt_old  pnt_start)

	(while (< (setq x_t (+ x_start (* step x_inc))) x_end)

		(setq x_t (+ x_start (* step x_inc))
			y_t (f_x2_ay a_value x_t)
			pnt_new (list x_t y_t))

		;;;; draw a line segment--later merged into one polyline
		(make_line_1 "layer2" 2  pnt_old pnt_new )

		(setq pnt_old pnt_new
			 step (+ 1 step))
	)

;;draw y2 = bx curve
	(setq pnt_start (list  (f_y2_bx b_value y_start) y_start))
	(setq step 0    pnt_old  pnt_start)

	(while (< (setq y_t (+ y_start (* step y_inc))) y_end)

		(setq y_t (+ y_start (* step y_inc))
			x_t (f_y2_bx b_value y_t)
			pnt_new (list x_t y_t))

		;;;; draw a line segment--later merged into one polyline
		(make_line_1 "layer3" 3  pnt_old pnt_new )

		(setq pnt_old pnt_new
			 step (+ 1 step))
	)
	(command "_.zoom" "_Extent")
;;draw x*y = a*b  rectangular hyperbola
	(setq x_start 0.5)	;;;limit range for rectangular hyperbola
	(setq pnt_start (list x_start (f_xy_ab a_value b_value x_start)))
	
	(setq step 0    pnt_old  pnt_start)

	(while (< (setq x_t (+ x_start (* step x_inc))) x_end)

		(setq x_t (+ x_start (* step x_inc))
			y_t (f_xy_ab a_value b_value x_t)
			pnt_new (list x_t y_t))

		;;;; draw a line segment--later merged into one polyline
		(make_line_1 "layer4"4  pnt_old pnt_new )

		(setq pnt_old pnt_new
			 step (+ 1 step))
	)
)
;;
(prompt "\nsetup_menaechmus")
;;
;;SETUP_Menaechmus
(defun setup_menaechmus()
	(setup_sysvar)
	(set_txstyle "arial")
	(setvar "PDMODE" 34)
	(setvar "PDSIZE" -2)
	(make_line_1 "0" 8 '(-3 0) '(3 0))
	(make_line_1 "0" 8 '(0 -2) '(0 4))
	(setq chr_size 0.25)
	(textdisplay "x" '(3 0) chr_size 0.)
	(textdisplay "y" '(0 4) chr_size 0.)
	(command "_.zoom" "_Extent")
	(command "_.regen")

	(setq   a_value (getreal "\nA value:(def = 1.0)"))
		(if (= a_value nil) (setq a_value 1.))
	(setq   b_value (getreal "\nB value:(def = 2.0)"))
		(if (= b_value nil) (setq b_value 2.))


	(setq	x_start (getreal "\nStart value for X: (def = -2)"))
		(if (= x_start nil) (setq x_start -2))
	(setq	x_end (getreal "\nEnd value for X: (def = 2)"))
		(if (= x_end nil) (setq x_end 2))
	(setq	x_inc (getreal "\nIncrement for X: (def = 0.01)"))
		(if (= x_inc nil) (setq x_inc 0.01))


	(setq	y_start (getreal "\nStart value for Y: (def = -3)"))
		(if (= y_start nil) (setq y_start -3))
	(setq	y_end (getreal "\nEnd value for Y: (def = 3)"))
		(if (= y_end nil) (setq y_end 3))
	(setq	y_inc (getreal "\nIncrement for Y: (def = 0.01)"))
		(if (= y_inc nil) (setq y_inc 0.01))	

);;;setup_menaechmus
;;;
;;;

		
(prompt "\nDRAW_X2_AY")
;;;DRAW_X2_AY
;;;draw x^2 = a*y  parabola
(defun c:test_draw_x2_ay( )
	(setup_x2_ay)
    (disp_x2_ay 0.2)	;;initial display
    (while (setq pnt_temp	(getpoint
		  "\nPick a point on the Y-axis. Hit return key to quit"))
    	(setq dist_y (cadr pnt_temp))
    	;(entdel line_ent)
   	 (disp_x2_ay dist_y)
    )
	
	(reset_sysvar)
);C:TEST_DRAW_X2_AY
;;;
;;;draw x^2 = a*y  parabola automatically
(defun c:auto_draw_x2_ay( )
	(setup_x2_ay)
    
;;;------------------------------------------------------------------
	(setq n_repeat 50
		y_step 0.02
		y_start 0.0
		step 1
		pnt_old '(0 0)
	)
	(disp_x2_ay y_step) ;;dummy line
	(make_jpg)
	(command "_.delay" 500)
    (repeat n_repeat
	(entdel line_ent)
    	 (setq dist_y (+ y_start (* y_step  step)))
   	 (disp_x2_ay dist_y)
	(setq step (1+ step)
		pnt_old pnt_p
	)
	(make_jpg)
	(command "_.delay" 150)
    )
	(reset_sysvar)
);C:auto_DRAW_X2_AY
;;;
;;;
(defun disp_x2_ay(y_val )
	(setq 	pnt_y (list 0 y_val)
		x_val (sqrt (* a_val y_val))
		pnt_xbase (list x_val 0)
		new_pos (list x_val y_val)
		rad_arc (* 0.5 y_val a_val)
		ctr_arc (list 0. (* 0.5 (- y_val a_val)))
		pnt_p new_pos
	)
	(command "_.pline" pnt_a "A" "CE" ctr_arc pnt_y "L" new_pos pnt_xbase "")
	
	(setq line_ent (entlast))
	;(make_pt "0" 2 new_pos)
	(make_line_1 "0" 2 pnt_old pnt_p)
)	
;;;
(prompt "\nDRAW_XY_AB")
;;;DRAW_XY_AB
;;;draw x*y = a*b  rectangular hyperbola
(defun c:test_draw_xy_ab( )
	(setup_xy_ab)
	 (disp_xy_ab 0.75)	;;initial display
    (while (setq pnt_temp	(getpoint
		  "\nPick a point on the X-axis. Hit return key to quit"))
    	(setq dist_x (car pnt_temp))
    	;(entdel line_ent)
   	 (disp_xy_ab dist_x)
    )
	
	(reset_sysvar)
);C:test_DRAW_XY_AB
;;;
;;;draw x*y = a*b  rectangular hyperbola
(defun c:auto_draw_xy_ab( )
	(setup_xy_ab)
	(setq n_repeat 40
		x_step 0.05
		x_start 0.7
		step 1
		pnt_old (list x_start (/ (* a_val b_val) x_start) )
	)
	(disp_xy_ab x_start) ;;dummy line
	(make_jpg)
	(command "_.delay" 500)
    (repeat n_repeat
	(entdel line_ent)
    	 (setq dist_x (+ x_start (* x_step  step)))
   	 (disp_xy_ab dist_x)
	(setq step (1+ step)
		pnt_old pnt_p
	)
	(make_jpg)
	(command "_.delay" 150)
    )
	
	(reset_sysvar)
);C:test_DRAW_XY_AB
;;;
;;;
(defun disp_xy_ab(x_val )
	(setq 	pnt_f (list x_val 0)
		pnt_g (list x_val (- a_val))
		pnt_h (inters pnt_g pnt_org pnt_b pnt_D nil)
		y_val (cadr pnt_h)
		pnt_p (list x_val y_val)
	)

	(command "_.pline" pnt_f pnt_g pnt_org pnt_h pnt_p "cl")
	
	(setq line_ent (entlast))
	(make_line_1 "0" 4 pnt_old pnt_p)
	
	;(make_pt "0" 2 pnt_p)
)	
;;;


(prompt "\nDRAW_Y2_BX")
;;;DRAW_Y2_BX
;;;draw y^2 = b*x  parabola
(defun c:draw_y2_bx( )
	(setup_y2_bx)
	
	(setq step 0    pnt_old  pnt_start)

	(while (< (setq y_t (+ y_start (* step y_inc))) y_end)

		(setq y_t (+ y_start (* step y_inc))
			x_t (f_y2_bx b_value y_t)
			pnt_new (list x_t y_t))

		;;;; draw a line segment--later merged into one polyline
		(make_line_1 "layer3" 3  pnt_old pnt_new )

		(setq pnt_old pnt_new
			 step (+ 1 step))
	)
	(reset_sysvar)
);C:DRAW_Y2_BX
;;;
;;;
(prompt "\nSETUP_X2_AY")
;;;
;;SETUP_X2_AY
;; setup system variables for x^2 = a*y  parabola
;;
(defun setup_x2_ay()
	(setup_sysvar)
	(set_txstyle "arial")
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq   a_val (getreal "\nA value:"))
	(if (= a_val nil) (setq a_val 1.0))
	(setq pnt_a (list 0 (- a_val))
		pnt_org '(0 0)
		x_left '(-0.20 0)
		x_right '(1.20 0)
		y_down '(0 -1.1)
		y_up '(0 1.20)
		chr_size 0.1
	)
	(make_line_1 "0" 8 x_left x_right)
	(make_line_1 "0" 8 y_down y_up)
	
	(textdisplay "x" x_right chr_size 0.)
	(textdisplay "y" y_up chr_size 0.)	
	(make_pt "0" 0 pnt_a)
	(make_pt "0" 0 pnt_org)
	(textdisplay "A" (shift_pnt pnt_a '(-0.12 0)) chr_size 0.)
	(textdisplay "O" (shift_pnt pnt_org '(-0.12 0))  chr_size 0.)
	
	(command "_.zoom" "_E")
	(command "_.regen")
	
);;SETUP_X2_AY
(prompt "\nSETUP_Y2_BX")
;;;
;;SETUP_Y2_BX
;; setup system variables for y^2 = b*x  parabola
;;
(defun setup_y2_bx()
	(setup_sysvar)
	;(set_layer)
	(set_txstyle "arial")
	(setvar "PDMODE" 34)
	(setvar "PDSIZE" -2)
	(setq   b_value (getreal "\nB value:")
		y_start (getreal "\nStart value for Y:")
		y_end (getreal "\nEnd value for Y:")
		y_inc (getreal "\nStep value for Y:")
	)
	(setq pnt_start (list  (f_y2_bx b_value y_start) y_start))
	(command "_.zoom" "_EXTENT")
	
);;SETUP_Y2_BX
(prompt "\nSETUP_XY_AB")
;;;
;;SETUP_XY_AB
;; setup system variables for x*y = a*b  rectangular hyperbola
;;
(defun setup_xy_ab( )
	(setup_sysvar)
	
	(set_txstyle "arial")
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq   a_value (getreal "\nA value:")
		b_value (getreal "\nB value:")
	)
	(if (= a_val nil) (setq a_val 1.0))
	(if (= b_val nil) (setq b_val 2.0))
	(setq pnt_a (list 0 (- a_val))
		pnt_b (list (- b_val) 0)
		pnt_org '(0 0)
		x_right '(3.0 0)
		y_up '(0 3.0)
		chr_size 0.1
		pnt_e (list 3.0 (- a_val))
		pnt_d (list (- b_val) 3.0)
		pnt_c (list (- b_val) (- a_val))
	)
	(make_line_1 "0" 8 pnt_b x_right)
	(make_line_1 "0" 8 pnt_a y_up)
	(make_line_1 "0" 8 pnt_ab pnt_ax)
	(make_line_1 "0" 8 pnt_ab pnt_by)
	(make_line_1 "0" 1 pnt_b pnt_org)
	(make_line_1 "0" 3 pnt_a pnt_org)

	
	(textdisplay "X" (shift_pnt x_right '(-0.12 0)) chr_size 0.)
	(textdisplay "Y" (shift_pnt y_up '(0.05 -0.10)) chr_size 0.)	
	(make_pt "0" 0 pnt_a)
	(make_pt "0" 0 pnt_org)
	(make_pt "0" 0 pnt_b)
	(textdisplay "A" (shift_pnt pnt_a '(-0.12 0)) chr_size 0.)
	(textdisplay "O" (shift_pnt pnt_org '(-0.12 0))  chr_size 0.)
	(textdisplay "B" (shift_pnt pnt_b '(-0.12 0)) chr_size 0.)
	(textdisplay "C" (shift_pnt pnt_c '(-0.12 0)) chr_size 0.)
	(textdisplay "D" (shift_pnt pnt_d '(0.05 -0.10))  chr_size 0.)
	(textdisplay "E" (shift_pnt pnt_e '(-0.12 0)) chr_size 0.)
	
	(command "_.zoom" "_E")
	(command "_.regen")
	
);;SETUP_XY_AB
;;;
;;--------------------------------------------------------------------------
(princ)