;;;Kopf_Perron's Angle Trisection Scheme
;;;Kopf  published in 1919
;;;
;;;Kopf_Perron.LSP
;;;May 18,2006 by Takaya Iwamoto
;;;
(defun C:Kopf_Perron()
	(setup_Kopf_Perron)
		;;define angle
	(setvar  "OSMODE" 512)	;; nearest mode
	(setq pnt_a(getpoint pnt_org "\nDefine an angle Theta"))
	
	(make_pt "0" 1 pnt_a)  (mark_id pnt_a "A" 2 0.1)
	(make_line_1 "0" 3 pnt_a pnt_org)  
	
	(setvar "OSMODE" 0)	;;reset Snap mode to zero
		(command "_.delay" 1000)
		;;Draw an arc
	(make_arc_cbe "0" 4 pnt_org pnt_b pnt_a)
		;;draw line CA
	(make_line_1 "0" 8 pnt_c pnt_a)
		(setq line_ca (entlast))
		;;extend line CA to intersect the arc at A'
	(command "_.extend" last_arc "" pnt_a "")

	(setq pnt_t (cdr (assoc 11 (entget (entlast)))))
	
	(make_line_1 "0" 2 pnt_p pnt_t)
	(make_pt "0" 1 pnt_t)  (mark_id pnt_t "T" 1 0.1)
		;;line PT is the trisecting line
	

	(command "_.zoom" "_Extent")
	(command "_.regen")
	(reset_sysvar)
);;;C:Kopf_Perron
;;;
;;;
(defun setup_kopf_Perron()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq   sqrt_3 (sqrt 3.)
		pnt_org '(0 0) pnt_b '(1 0) pnt_c '(-1 0) 
		pnt_d '(-0.5 0) pnt_e (list -0.5 (* 0.5 sqrt_3))
		pnt_p '(-2 0)  	y_up '(0 1.5) 		
		chr_size 0.1 chr_size2 0.08 chr_size3 0.06
		len_de (distance pnt_d pnt_e) len_df (/ len_de 3.)
		pnt_f (pld pnt_d pnt_c len_df)
		len_fb (distance pnt_f pnt_b)
	)
		;;draw reference lines
	(make_line_1 "0" 8 y_up pnt_org)
	(make_line_1 "0" 8 pnt_p pnt_b)
	(make_line_1 "0" 8 pnt_d pnt_e)
		;;draw key points
	(make_pt "0" 0 pnt_org)  (mark_id pnt_org "O" 4 chr_size)
	(make_pt "0" 0 pnt_b)  (mark_id pnt_b "B" 4 chr_size)
	(make_pt "0" 0 pnt_c)  (mark_id pnt_c "C" 4 chr_size)
	(make_pt "0" 0 pnt_d)  (mark_id pnt_d "D" 4 chr_size)
	(make_pt "0" 0 pnt_e)  (mark_id pnt_e "E" 2 chr_size)
	(make_pt "0" 0 pnt_f)  (mark_id pnt_f "F" 4 chr_size)
	(make_pt "0" 0 pnt_p)  (mark_id pnt_p "P" 4 chr_size)
		;;draw a semi circle
	(make_arc_cbe "0" 8 pnt_org pnt_b pnt_c)
	(make_arc_cbe "0" 4 pnt_f pnt_b y_up)
		(setq last_arc (entlast))
	
	(command "_.zoom" "_Extent")
	(command "_.regen")
	


);;;setup_Kopf_Perron
;;;
;;;FIND_T
;;;
(defun find_t()
	(setq k len_ae 		m c
		k_sqr (* k k) m_sqr (* m m)
		num_1 (* m k_sqr)
		num_2 (* k (sqrt (+ (* 4 m_sqr) 4 (- k_sqr))))
		denom (* 2 (+ m_sqr 1) )
		y_sol (/ (+ num_1 num_2) denom)
		x_sol (+ (* m y_sol) 1. (- (* 0.5 k_sqr)))
		pnt_t (list x_sol y_sol)
	)
);;;FIND_T
;;;
;;;DISTANCE_CHECK
;;;check if length AT is the average of BC2, C2C1, C1A
;;;
(defun c:distance_check()
	(setq bc2 (distance pnt_b pnt_c2)
		c2c1 (distance pnt_c2 pnt_c1)
		c1a (distance pnt_c1 pnt_a)
		at (distance pnt_a pnt_t)
		average (/ (+ bc2 c2c1 c1a) 3.)
		t_x (car pnt_t) t_y (cadr pnt_t)
		pnt_td (list (- t_x) t_y)
		ttd (distance pnt_t pnt_td)
	)
	
);;;distance_check
;;;
;;;
(prompt "error_table loading")
;;;
(defun C:error_table()
	(setup_sysvar)
	(setq start_val 0. end_val 90. step_val  10.)
	(setq cur_val 0. nstep 1)
	(setq er_list nil)
	(while (<= (setq cur_val (+ start_val (* (- nstep 1) step_val))) end_val)
		(setq th (dtr cur_val)
			m (/ (sin th) (+ 1 (cos th)))
			f  ( / (+ 3 (sqrt 3.)) 6.)
			m_sqr (* m m) f_sqr (* f f)
			a (+ m_sqr 1)
			b (+ m_sqr f)
			c (+ m_sqr (- (* 2 f)) -1)
			c1 (sqrt (- (* b b) (* a c)))
			num (- c1 b) denom a
			x_0 (/ num denom)
			y_0 (* m (+ x_0 1))
			arg (/ y_0  (+ 2 x_0))
			
			tri_th (rtd (atan arg))
			third_th (/ cur_val 3.)
			error_deg (abs (- third_th tri_th))
			error_rad (dtr error_deg)
			error_in_minsec (angtos error_rad 1 4)
			output (list nstep cur_val third_th tri_th error_deg error_in_minsec)
			er_list (append   er_list (list (* 3600. error_deg)))
			nstep (1+ nstep)
		)
		(princ "output= ")(princ output)(terpri)
	);;;while loop end



	(reset_sysvar)
);;;error_table