;;;Approximate Construction of pi
;;;
;;;Pi_construction.lsp
;;;
;;;	Takaya Iwamoto		Feb 9, 2007
;;;
;;;	Kochansky(1685)
;;;	Gelder(1849)
;;;	Hobson(1913)
;;;Ref. Petr Beckmann	"a History of Pi"
;;;
;;;Kochansky
(defun C:Kochansky()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq   sqrt_3 (sqrt 3.)
		pnt_org '(0 0)
		pnt_a '(0 -1)
		pnt_b '(0 1)
		pnt_d '(3. -1)
		pnt_c (list (/ sqrt_3 3.) 1.)
	)
;;make_pt
	(make_pt "0" 1 pnt_org)
	(make_pt "0" 0 pnt_a)
 	(make_pt "0" 0 pnt_b)
	(make_pt "0" 0 pnt_c)
	(make_pt "0" 0 pnt_d)
	
;;mark_id
	(mark_id pnt_org "O" 3 0.15)
	(mark_id pnt_a "A" 3 0.15)
	(mark_id pnt_b "B" 3 0.15)
	(mark_id pnt_c "C" 2 0.15)
	(mark_id pnt_d "D" 4 0.15)
	(command "_.dimaligned" pnt_a pnt_d "_T" "" '(1.5 -1.2))
	(command "_.dimlinear" pnt_a pnt_b '(0.8 0))
	(mark_angle pnt_b pnt_org pnt_c 0.5 "p/6" 0.10 2)
;;make_line_1
	(make_line_1 "0" 8 pnt_a pnt_b)
	(make_line_1 "0" 8 pnt_b pnt_c)
	(make_line_1 "0" 8 pnt_a pnt_d)
	(make_line_1 "0" 8 pnt_org pnt_c)
	
	(command "_.arc" "_C" pnt_org pnt_a pnt_b)
		(setq half_circle (entlast))
	;(command "_.dimradius" half_circle ""  '(2.3 0))

	(make_line_1 "0" 2 pnt_c pnt_d)
	(command "_.dimaligned" pnt_c pnt_d "_T" "" '(2.3 0))
	(command "_.zoom" "_E")
	(command "_.regen")
	(reset_sysvar)
)
;;;
;;;Gelder
(defun C:Gelder()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq 	pnt_a '(-1 0)
		pnt_b '(1 0)
		pnt_c '(0 0)
		pnt_d '(0 1)
		pnt_e '(0 0.875)
		pnt_f (pld pnt_a pnt_e 0.5)
		pnt_g (list (car pnt_f) 0.)
		ratio (/ 0.5 (distance pnt_a pnt_e))
		pnt_h (plt pnt_a pnt_g ratio)
	)
;;make_pt
	(make_pt "0" 1 pnt_c)
	(make_pt "0" 0 pnt_a)
 	(make_pt "0" 0 pnt_b)
	(make_pt "0" 0 pnt_d)
	(make_pt "0" 0 pnt_e)
	
;;mark_id
	(mark_id pnt_c "C" 4 0.10)
	(mark_id pnt_a "A" 3 0.10)
	(mark_id pnt_b "B" 1 0.10)
	(mark_id pnt_d "D" 2 0.10)
	(mark_id pnt_e "E" 4 0.10)
;;make_line_1
	(make_line_1 "0" 8 pnt_a pnt_b)
	(make_line_1 "0" 8 pnt_c pnt_d)
;;semi_circle
	(command "_.arc" "_C" pnt_c pnt_b pnt_a)
;;pnt_F
	(make_line_1 "0" 8 pnt_a pnt_e)
	(make_pt "0" 0 pnt_f)
	(mark_id pnt_f "F" 2 0.10)
;;pnt_G
	(make_pt "0" 0 pnt_g)
	(mark_id pnt_g "G" 4 0.10)
	(make_line_1 "0" 8 pnt_f pnt_g)
;;line GE
	(make_line_1 "0" 8 pnt_g pnt_e)
;;pnt_H
	(make_line_1 "0" 8 pnt_f pnt_h)
	(make_pt "0" 0 pnt_h)
	(mark_id pnt_h "H" 4 0.10)
;;line_AH
	(make_line_1 "0" 2 pnt_a pnt_h)
;;
	(command "_.dimlinear" pnt_a pnt_h '(-0.5 -0.5))
	(command "_.zoom" "_E")
	(command "_.regen")
	(reset_sysvar)
);;
;;;
;;;Hobson
(defun C:Hobson()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq pnt_org '(0 0)
		pnt_a '(-1 0)
		pnt_b '(1 0)
		pnt_d '(-0.6 0)
		pnt_e '(0.5 0)
		pnt_f '(1.5 0)
		pnt_g (list 0. (sqrt 0.3))
		pnt_h (list 0. (- (sqrt 1.5)) )
		root_pi (distance pnt_g pnt_h)
		pnt_i (list root_pi (- (sqrt 1.5)))
		pnt_j (list root_pi (sqrt 0.3))
		y_up '(0 1)
		y_down '(0 -1.5)
		rad_1 (* 0.5 (distance pnt_d pnt_e))
		rad_2 (* 0.5 (distance pnt_a pnt_f))
		pnt_c1 '(-0.05 0)
		pnt_c2 '(0.25 0)
	)
;;make_pt
	(make_pt "0" 1 pnt_org)
	(make_pt "0" 0 pnt_a)
 	(make_pt "0" 0 pnt_b)
	(make_pt "0" 0 pnt_d)
	(make_pt "0" 0 pnt_e)
	(make_pt "0" 0 pnt_f)
;;mark_id
	(mark_id pnt_org "O" 4 0.1)
	(mark_id pnt_b "B" 4 0.1)
	(mark_id pnt_a "A" 3 0.1)
	(mark_id pnt_e "E" 4 0.1)
	(mark_id pnt_d "D" 4 0.1)
	(mark_id pnt_f "F" 1 0.1)

	(make_line_1 "0" 8 pnt_a pnt_f)
	(make_line_1 "0" 8 y_up y_down)
	
	(command "_.arc" "_C" pnt_c1 pnt_e pnt_d)
		;(setq in_circle (entlast))
	
	(command "_.arc" "_C" pnt_c2 pnt_a pnt_f)
		;(setq out_circle (entlast))
	
;;;trim operation
	(make_pt "0" 0 pnt_g)
	(make_pt "0" 0 pnt_h)
	(make_pt "0" 0 pnt_i)
	(make_pt "0" 0 pnt_j)
	(mark_id pnt_g "G" 1 0.1)
	(mark_id pnt_h "H" 4 0.1)
	(mark_id pnt_i "I" 4 0.1)
	(mark_id pnt_j "J" 2 0.1)

	;(command "_.trim" in_circle "" y_up "")
	;(command "_.trim" out_circle "" y_down "")
	(make_circle_1 "0" 2 pnt_org 1.0)
;;;polygon
	(command "_.polygon" 4 "_E" pnt_g pnt_h)
	(command "_.zoom" "_E")
	(command "_.regen")
	(reset_sysvar)
)
;;;