;;;Conics_by_line.lsp	by Takaya Iwamoto
;;;changed name from test_818 to conics_by_line.lsp
;Collection of curves created by envelope, lines & circles
;;;updated on June 18,2007	by T.Iwamoto
;
;;;---------------ellipse case ----------------
;envelope trial version _1  ellipse case; pedals on a circle
(defun c:ellipse_model()
	(setup_env_1)
	
	(setq pnt_temp (getpoint "\nPick a point on the circle."))
	(if (= pnt_temp nil) (setq pnt_temp '(-0.2588  0.9659)))	;;1.<105.
	(setq temp_angle (angle pnt_org pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
	(make_pt "0" 0 pnt_p)
	(mark_id pnt_p "P" 3 chr_size)
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_r (polar pnt_org (+ pi temp_angle) ref_rad)
			pnt_t (plt pnt_f1 pnt_p 2.0)
			pnt_u (inters pnt_t pnt_f2 pnt_p pnt_s nil)
		)
	(make_pt "0" 0 pnt_q)
	(mark_id pnt_q "Q" 3 chr_size)
	(make_pt "0" 0 pnt_r)
	(mark_id pnt_r "R" 4 chr_size)
	(make_pt "0" 0 pnt_s)
	(mark_id pnt_s "S" 1 chr_size)
	(make_pt "0" 0 pnt_t)
	(mark_id pnt_t "T" 1 chr_size)
	(make_pt "0" 0 pnt_u)
	(mark_id pnt_u "U" 1 chr_size)
	
		(make_line_1 "0" 2  pnt_p pnt_s )
		(make_line_1 "0" 2  pnt_q pnt_r )
		(make_line_1 "0" 8  pnt_q pnt_p )
		(make_line_1 "0" 8  pnt_p pnt_r )
		(make_line_1 "0" 8  pnt_r pnt_s )

		(make_line_1 "0" 8  pnt_p pnt_t )
		(make_line_1 "0" 0  pnt_t pnt_u )
		(make_line_1 "0" 0  pnt_f1 pnt_u )
		(make_line_1 "0" 0  pnt_f2 pnt_u )
	(command "_.zoom" "_E")
	
;;draw the resulting ellipse a = a_major b = b_minor
	(command "_.color" 3)
	(command "_.ellipse" pnt_a pnt_b pnt_c)
	(command "_.regen")
	(command "_.color" "BYLAYER")
;;mark right angles, tick-mark same length lines
	(line_tick_mark pnt_f1 pnt_p 1 1)
	(line_tick_mark pnt_p pnt_t 1 1)
	(line_tick_mark pnt_f1 pnt_u 2 2)
	(line_tick_mark pnt_u pnt_t 2 2)
	(mark_right_angle pnt_q pnt_p pnt_s 3 0)
	(mark_right_angle pnt_s pnt_p pnt_t 3 0)
	(if (= (Yes_or_No "Continue ?") "_Y") 
	(progn
		(make_circle_1 "0" 8 pnt_f2 (* 2. ref_rad))
			(setq big_circle (entlast))
		(command "_.zoom" "_E")
		(make_line_1 "0" 8 pnt_p pnt_s)
			(setq base_line1 (entlast))
		(make_line_1 "0" 8 pnt_s pnt_p)
			(setq base_line2 (entlast))
		(command "_.extend" big_circle "" base_line1 "")
		(command "_.extend" big_circle "" base_line2 "")
;;Identify point V & W
		(setq pnt_v (cdr (assoc 10 (entget base_line1)))
			pnt_w (cdr (assoc 10 (entget base_line2)))
		)
		(make_pt "0" 0 pnt_v)
		(mark_id pnt_v "V" 2 chr_size)
		(make_pt "0" 0 pnt_w)
		(mark_id pnt_w "W" 2 chr_size)
		;(command "_.erase" base_line1 base_line2 "")

	)
	);;;end if
	(command "_.zoom" "_E")
	(command "_.regen")
	(reset_sysvar)
);
;;;
;;;
(defun setup_env_1()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq ref_rad 1.0  c 0.75
		pnt_f1 (list (- c) 0) pnt_f2 (list c 0)
		pnt_org '(0 0)	chr_size 0.125 
		a_major ref_rad
		b_minor (sqrt (- (* a_major a_major) (* c c)))
		pnt_a (list (- ref_rad) 0)
		pnt_b (list ref_rad 0)
		pnt_c (list 0 b_minor)
	)
	(make_pt "0" 0 pnt_f1)
	(make_pt "0" 0 pnt_f2)

	(mark_id pnt_org "O" 1 chr_size)
	(mark_id pnt_f1 "F1" 4 chr_size)
	(mark_id pnt_f2 "F2" 4 chr_size)
	(mark_id '(1.1 0 ) "x" 1 chr_size)
	(mark_id '(0 1.1 ) "y" 1 chr_size)
	(make_circle_1 "0" 8 pnt_org ref_rad)
	(make_line_1 "0" 8  '(0 -1.1) '(0 1.1) )
	(make_line_1 "0" 8  '(-1.1 0) '(1.1 0) )
	(command "_.zoom" "_EXTENT" )
	(command "_.regen")
)
;;;
;;;
(defun c:ellipse_manual()
	(setup_env_1)
	(alert "\nPick a point along the circle\nHit ESC key to end.")
	(while (setq pnt_temp (cadr (grread )))
		(setq temp_angle (angle pnt_org pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_r (polar pnt_org (+ pi temp_angle) ref_rad)
		)
		(make_line_1 "0" 2  pnt_p  pnt_s )
		(make_line_1 "0" 2  pnt_q  pnt_r )
	);;end of while loop
	(reset_sysvar)
);
(defun c:ellipse_auto()
	(setup_env_1)
	(setq ndiv 40
		count 1
		start_angle 0.
		del_theta (/ pi ndiv)
	)
	(alert "\nStart ?")
	(make_jpg)
	(make_jpg)
	(repeat (1+ ndiv)
		(setq temp_angle (+ start_angle (* count del_theta))
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_r (polar pnt_org (+ pi temp_angle) ref_rad)
		)
		(make_line_1 "0" 2  pnt_p  pnt_s )
		(make_line_1 "0" 2  pnt_q pnt_r )
		(setq count (1+ count))
		(make_jpg)
		(command "_.delay" 250)
	);;end of repeat loop

	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
);
;;;
;;;
(defun c:ellipse_by_triangle()
	(setup_env_1)
	(setq blk_scale 0.30)
	(command "_.zoom" "_E")
	(command "_.regen")
	(make_jpg)
	(make_jpg)
	(alert "\nPick a point along the circle\nHit ESC key to end.")
	(while (setq pnt_temp (getpoint "\nPick a point"))
		(if (/= trig_block nil) (entdel trig_block))
		(setq temp_angle (angle pnt_org pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			angle_ins (rtd (+ pi angle_b))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_r (polar pnt_org (+ pi temp_angle) ref_rad)
		)
		(my_block_insert2 "triangle_45_45_hatch" pnt_p blk_scale  angle_ins)
			(setq trig_block (entlast))
		(make_line_1 "0" 2  pnt_p  pnt_s )
			(command "_.draworder" (entlast) "" "_F")
		(make_jpg)
		
		(command "_.delay" 500)
		
	);;end of while loop
	(make_pt "0" 0 pnt_p)
	(mark_id pnt_p "P" 2 chr_size)
	(make_pt "0" 0 pnt_s)
	(mark_id pnt_s "S" 2 chr_size)
	(make_pt "0" 0 pnt_q)
	(mark_id pnt_q "Q" 3 chr_size)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
);
;;;
;;;
;ellipse by pedals on a circle
(defun c:ellipse_manual_2()
	(setup_env_1)
	(setq block_scale 0.4)
	(alert "\nPlace cursor near -x- mark.\nAfter hit return key\n,move cursor along the circle
	\ncounter clockwise.\nHit ESC key to end.")
	(while (setq pnt_temp (cadr (grread T)))
		(setq temp_angle (angle pnt_org pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_r (polar pnt_org (+ pi temp_angle) ref_rad)
		)
		(make_line_1 "0" 2 pnt_p  pnt_s )
		(make_line_1 "0" 2 pnt_q  pnt_r )
	);;end of while loop
)
;;;
;;;ellipse_by_folding		ellipse by folding a circular paper
;;;
(defun c:ellipse_by_folding()
	(setup_env_1)
	(setq half_pi (* 0.5 pi))
	(make_circle_1 "0" 8 pnt_f2 (* 2. ref_rad))
		(setq big_circle (entlast))
	(command "_.zoom" "_E")
	(make_jpg)
	(make_jpg)
	
	(while (setq pnt_tmp (getpoint "\nPick a point on the circle."))
	
	(setq tmp_angle (angle pnt_f2 pnt_tmp)
		pnt_t (polar pnt_f2 tmp_angle (* 2. ref_rad))
		pnt_p (mid_point pnt_f1 pnt_t)
	)
	
	(make_pt "0" 0 pnt_t)
	(setq   angle_f1_p_o (angle_3p pnt_p pnt_f1 pnt_org)
		angle_b (angle pnt_f1 pnt_p)
		angle_g (- angle_b angle_f1_p_o )
		pnt_s (polar pnt_org angle_g   ref_rad)
	)
		(make_line_1 "0" 2 pnt_p pnt_s)
			(setq base_line1 (entlast))
			(setq pick_line1 (plt pnt_p pnt_s 0.01))
			(setq pick_line2 (plt pnt_p pnt_s 0.99))
		(command "_.extend" big_circle "" pick_line1 "")
		(command "_.extend" big_circle "" pick_line2 "")
;;Identify point V & W
		(setq pnt_v (cdr (assoc 10 (entget (entlast))))
			pnt_w (cdr (assoc 11 (entget (entlast))))
		)
;;form an arc and rotate this around the chord pnt_v - pnt_w 180 deg & back
		(command "_.pline" pnt_w "_A" "_CE" pnt_f2 pnt_v "_L" "cl")
 		(setq arc_line (entlast))
		(command "bhatch" "_Sel" (entlast) "" "Prop" "ansi31"  "1." "0." "")
			(setq arc_hatch (entlast))
			(setq ss (ssadd))
			(ssadd arc_line ss)(ssadd arc_hatch ss)
		;(command "_.rotate3d"  ss "" "2" pnt_v pnt_w 180.)
		(slow_rotate3d_origami ss pnt_v pnt_w 180.)
		(entdel arc_hatch)(entdel arc_line)
	(command "_.delay" 250)
	);;;end of while loop
;;draw the resulting ellipse a = a_major b = b_minor
	(command "_.color" 3)
	(command "_.ellipse" pnt_a pnt_b pnt_c)
	(command "_.regen")
	(command "_.color" "BYLAYER")		
	(command "_.zoom" "_E")
	(command "_.regen")
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
);
;;;
;;;----------------------hyperbola -----------------------
;hyperbola #basic geometry
;;;
(defun c:hyperbola_model()
	(setup_env_3)

	(setq pnt_temp (getpoint "\nPick a point on the circle."))
		(if (= pnt_temp nil) (setq pnt_temp '(0.583855 0.811858)) )
		(setq temp_angle (angle pnt_org pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		(make_pt "0" 0 pnt_p)
		(mark_id pnt_p "P" 1 chr_size)
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_end2 (polar pnt_org (+ pi temp_angle) ref_rad)
			pnt_a (pld pnt_end2 pnt_q (* 2.75 ref_rad))
			pnt_b (pld pnt_p pnt_s (* 2.75 ref_rad))
			pnt_t (plt pnt_f1 pnt_p 2.0)
			pnt_u (inters pnt_t pnt_f2 pnt_p pnt_s nil)

		)
		(make_circle_1 "0" 8 pnt_f2 (* 2. ref_rad))
	
		(command "_.zoom" "_E")
		(make_pt "0" 0 pnt_q)
		(mark_id pnt_q "Q" 2 chr_size)
		(make_pt "0" 0 pnt_s)
		(mark_id pnt_s "S" 1 chr_size)
		(make_pt "0" 0 pnt_a)
		(mark_id pnt_a "A" 1 chr_size)
		(make_pt "0" 0 pnt_b)
		(mark_id pnt_b "B" 1 chr_size)
		(make_pt "0" 0 pnt_t)
		(mark_id pnt_t "T" 1 chr_size)
		(make_pt "0" 0 pnt_u)
		(mark_id pnt_u "U" 1 chr_size)


		(make_line_1 "0" 8  pnt_p pnt_t)
		(make_line_1 "0" 8  pnt_t pnt_u)
		(make_line_1 "0" 8  pnt_f1 pnt_u)
		(make_line_1 "0" 8  pnt_f1 pnt_p)
		(make_line_1 "0" 8  pnt_p pnt_s)
		
		(make_line_1 "0" 2  pnt_s pnt_b )
		(make_line_1 "0" 3  pnt_q  pnt_a )
;;mark right angles, tick-mark same length lines
	(line_tick_mark pnt_f1 pnt_p 1 1)
	(line_tick_mark pnt_p pnt_t 1 1)
	(line_tick_mark pnt_f1 pnt_u 2 2)
	(line_tick_mark pnt_u pnt_t 2 2)
	(mark_right_angle pnt_f1 pnt_p pnt_u 3 0)
	(mark_right_angle pnt_t pnt_p pnt_u 3 0)
	(reset_sysvar)
	
);;;hyperbola_model
;;;
;;;
(defun setup_env_3()
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq ref_rad 1.0)
	(setq pnt_f1 '(-1.5 0) pnt_f2 '(1.5 0) pnt_org '(0 0)
		a 1.0 c 1.5 half_pi (* 0.5 pi) two_pi (* 2. pi)
		chr_size 0.20
		y_up '(0 1.5) y_down '(0 -1.1)
		x_right '(2.2 0) x_left '(-1.7 0)
	)
	(make_pt "0" 0 pnt_f1)
	(make_pt "0" 0 pnt_f2)
	(make_pt "0" 0 pnt_org)
	(mark_id pnt_org "O" 1 chr_size)
	(mark_id  pnt_f1  "F1" 2 chr_size)

	(mark_id pnt_f2 "F2" 2 chr_size)
	(mark_id x_right "x" 2 chr_size)
	(mark_id y_up    "y" 3 chr_size)

	(make_circle_1 "0" 8 pnt_org ref_rad)

	(make_line_1 "0" 8 x_left x_right )
	(make_line_1 "0" 8 y_up y_down )
	(command "_.zoom" "_E" )
	(command "_.regen")
)
;;;
(defun c:hyperbola_manual()
	(setup_env_3)
	(mark_id (shift_pnt pnt_f1 '(-0.2 0)) "(-c,0)" 4 chr_size)

	(mark_id (shift_pnt pnt_f2 '(-0.2 0)) "(c,0)" 4 chr_size)
	(setq dist1 (distance pnt_f1 pnt_org)
		dist2 (- dist1 ref_rad)
		dist3 (+ dist1 ref_rad)
		dist4 (sqrt (* dist2 dist3))
		theta (atan (/ dist4 ref_rad))
		alpha (- half_pi theta)
		pnt_tang1 (polar pnt_f1 alpha dist4)
		pnt_tang2 (polar pnt_f1 (- two_pi alpha) dist4)
		pnt_asym1 (plt pnt_org pnt_tang1 4.)
		pnt_asym3 (plt pnt_org pnt_tang1 -4.)
		pnt_asym2 (plt pnt_org pnt_tang2 -4.)
		pnt_asym4 (plt pnt_org pnt_tang2 4.)
	)
	(mark_id pnt_tang1 "K" 2 chr_size)
	(mark_id pnt_tang2 "L" 2 chr_size)
	

	(make_line_1 "0" 8  pnt_asym1 pnt_asym3)
	(make_line_1 "0" 8  pnt_asym2 pnt_asym4)
	(command "_.delay" 500)
	(alert "\nPlace cursor  near point K.\nAfter hitting return,move cursor clockwise.
	\nfrom point K clockwise to point L\n	Hit ESC or R-click to stop.")
	(while (setq pnt_temp (cadr (grread )))
		(setq temp_angle (angle pnt_org pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_end2 (polar pnt_org (+ pi temp_angle) ref_rad)
			pnt_a (pld pnt_end2 pnt_q (* 4.0 ref_rad))
			pnt_b (pld pnt_p pnt_s (* 4.0 ref_rad))
		)
		
		(make_line_1 "0" 2  pnt_s pnt_b )
		(make_line_1 "0" 3  pnt_q  pnt_a )
	)
)
;;;
;;;
;;;
(defun c:hyperbola_by_triangle()
	(setup_env_3)
	(setq blk_scale 0.50)
	(mark_id (shift_pnt pnt_f1 '(-0.2 0)) "(-c,0)" 4 chr_size)

	(mark_id (shift_pnt pnt_f2 '(-0.2 0)) "(c,0)" 4 chr_size)
	(setq dist1 (distance pnt_f1 pnt_org)
		dist2 (- dist1 ref_rad)
		dist3 (+ dist1 ref_rad)
		dist4 (sqrt (* dist2 dist3))
		theta (atan (/ dist4 ref_rad))
		alpha (- half_pi theta)
		pnt_tang1 (polar pnt_f1 alpha dist4)
		pnt_tang2 (polar pnt_f1 (- two_pi alpha) dist4)
		pnt_asym1 (plt pnt_org pnt_tang1 4.)
		pnt_asym3 (plt pnt_org pnt_tang1 -4.)
		pnt_asym2 (plt pnt_org pnt_tang2 -4.)
		pnt_asym4 (plt pnt_org pnt_tang2 4.)
	)
	(mark_id pnt_tang1 "K" 2 chr_size)
	(mark_id pnt_tang2 "L" 2 chr_size)
	

	(make_line_1 "0" 8  pnt_asym1 pnt_asym3)
	(make_line_1 "0" 8  pnt_asym2 pnt_asym4)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
	(alert "\nPlace cursor  near point K.\nAfter hitting return,move cursor clockwise.
	\nfrom point K clockwise to point L\n	Hit ESC or R-click to stop.")
	(while (setq pnt_temp (getpoint "\nPick a point"))
		(if (/= trig_block nil) (entdel trig_block))
		(setq temp_angle (angle pnt_org pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			angle_ins (rtd (- angle_b pi))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_end2 (polar pnt_org (+ pi temp_angle) ref_rad)
			pnt_a (pld pnt_end2 pnt_q (* 4.0 ref_rad))
			pnt_b (pld pnt_p pnt_s (* 4.0 ref_rad))
		)
		(if (< temp_y 0.) (setq angle_ins (- angle_ins 90.)) )
		(my_block_insert2 "triangle_45_45_hatch" pnt_p blk_scale  angle_ins)
			(setq trig_block (entlast))
		(make_line_1 "0" 2  pnt_s pnt_b )
		(make_jpg)
		;(make_line_1 "0" 3  pnt_q  pnt_a )
	)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
)
;hyperbola #2
(defun c:hyperbola_manual_2()
	(setup_env_3)
	(setq dist1 (distance pnt_f1 pnt_org)
		dist2 (- dist1 ref_rad)
		dist3 (+ dist1 ref_rad)
		dist4 (sqrt (* dist2 dist3))
		theta (atan (/ dist4 ref_rad))
		alpha (- half_pi theta)
		pnt_tang1 (polar pnt_f1 alpha dist4)
		pnt_tang2 (polar pnt_f1 (- two_pi alpha) dist4)
		pnt_asym1 (plt pnt_org pnt_tang1 4.)
		pnt_asym3 (plt pnt_org pnt_tang1 -4.)
		pnt_asym2 (plt pnt_org pnt_tang2 -4.)
		pnt_asym4 (plt pnt_org pnt_tang2 4.)
	)
	(mark_id pnt_tang1 "K" 2 chr_size)
	(mark_id pnt_tang2 "L" 2 chr_size)
	

	(make_line_1 "0" 8  pnt_asym1 pnt_asym3)
	(make_line_1 "0" 8  pnt_asym2 pnt_asym4)
	(command "_.delay" 500)
	(alert "\nPlace cursor  near point K.\nAfter hitting return,move cursor clockwise.
	\nfrom point K clockwise to point L\n	Hit ESC to stop.")
	(while (setq pnt_temp (cadr (grread T)))
		(setq temp_angle (angle pnt_org pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_end2 (polar pnt_org (+ pi temp_angle) ref_rad)
			pnt_a (pld pnt_end2 pnt_q (* 4.0 ref_rad))
			pnt_b (pld pnt_p pnt_s (* 4.0 ref_rad))
		)
		
		(make_line_1 "0" 2  pnt_s pnt_b)
		(make_line_1 "0" 3  pnt_q pnt_a)
	)
)


;hyperbola_auto
(defun c:hyperbola_auto()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	
	(setq ref_rad 2.0 half_pi (* 0.5 pi) two_pi (* 2.0 pi)
		ref_length (* 3.0 ref_rad) chr_size 0.20 
		pnt_f1 '(-2.5 0) pnt_f2 '(2.5 0) pnt_org '(0 0)
	)
		
	(make_pt "0" 0  pnt_f1)
	(make_pt "0" 0  pnt_f2)
	(make_pt "0" 0  pnt_org)

	(mark_id  pnt_f1  "F1" 2 chr_size)
	(mark_id pnt_f2 "F2" 2 chr_size)
	(mark_id pnt_org "O" 1 chr_size)
	(mark_id '(3 0) "x" 2 chr_size)
	(mark_id '(0 3) "y" 1 chr_size)

	(command "_circle" '(0 0) ref_rad)
	(command "_.line" '(0 -3) '(0 3) "")
	(command "_.line" '(-3 0) '(3 0) "")
	(command "_.zoom" "_EXTENT" )
	(command "_.regen")
	(setq dist1 (distance pnt_f1 pnt_org)
		dist2 (- dist1 ref_rad)
		dist3 (+ dist1 ref_rad)
		dist4 (sqrt (* dist2 dist3))
		theta (atan (/ dist4 ref_rad))
		alpha (- half_pi theta)
		pnt_tang1 (polar pnt_f1 alpha dist4)
		pnt_tang2 (polar pnt_f1 (- two_pi alpha) dist4)
		pnt_asym1 (plt pnt_org pnt_tang1 4.)
		pnt_asym3 (plt pnt_org pnt_tang1 -4.)
		pnt_asym2 (plt pnt_org pnt_tang2 -4.)
		pnt_asym4 (plt pnt_org pnt_tang2 4.)
		
	)
	(mark_id pnt_tang1 "K" 2 chr_size)
	(mark_id pnt_tang2 "L" 2 chr_size)
	
	;draw two asymptote lines
	(make_line_1 "0" 8  pnt_asym1 pnt_asym3)
	(make_line_1 "0" 8  pnt_asym2 pnt_asym4)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 500)
	(alert "\nStart ?")
	(setq theta_start (angle pnt_org pnt_tang1)
		theta_range (* 1.9999 theta_start)
		ndiv 60
		del_theta (- (/ theta_range ndiv))
		step 0
	)
	(repeat  (1+ ndiv)
		(setq temp_angle (+ theta_start (* del_theta step))
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			pnt_p (list temp_x temp_y)
		)
		
		(setq   angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			pnt_q (polar pnt_org (+ pi angle_g)    ref_rad)
			pnt_end2 (polar pnt_org (+ pi temp_angle) ref_rad)
			pnt_a (pld pnt_end2 pnt_q (* 3.0 ref_rad))
			pnt_b (pld pnt_p pnt_s (* 3.0 ref_rad))
		)
		
		(make_line_1 "0" 2  pnt_s pnt_b)
		(make_line_1 "0" 3  pnt_q pnt_a)
		;(princ "step theta")(princ step)(princ "::")(princ temp_angle)(terpri)
		(make_jpg)
		(command "_.delay" 250)

		(setq step (1+ step))
	);;;end of repeat loop
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
);;;
;;;
;hyperbola by foling a circular paper
;;;
(defun c:hyperbola_by_folding()
	(setup_env_3)
	(setq pu (list ref_rad (* 2. ref_rad))
		pd (list ref_rad (- (* 2. ref_rad)))
	)
	(make_line_1 "0" 9 pu pd)
	(make_circle_1 "0" 8 pnt_f2 (* 2. ref_rad))
		(setq big_circle (entlast))
	(command "_.zoom" "_E")
	(make_jpg)
	(make_jpg)
	(while (setq pnt_tmp (getpoint "\nPick a point on the big circle."))
		(setq tmp_angle (angle pnt_f2 pnt_tmp)
			pnt_t (polar pnt_f2 tmp_angle (* 2. ref_rad))
			pnt_p (mid_point pnt_f1 pnt_t)
		)
		(make_pt "0" 0 pnt_t)
		;(mark_id pnt_p "P" 1 chr_size)
		(setq   temp_angle (angle pnt_org pnt_p)
			angle_b (angle pnt_f1 pnt_p)
			angle_a (- temp_angle angle_b)
			angle_g (- temp_angle (* 2.0 angle_a))
			pnt_s (polar pnt_org angle_g           ref_rad)
			;pnt_b (plt pnt_p pnt_s 2.5)
		)
		(make_line_1 "0" 8  pnt_p pnt_s)
			(setq base_line1 (entlast))
			(setq pick_line1 (plt pnt_p pnt_s 0.001))
			(setq pick_line2 (plt pnt_p pnt_s 0.999))
		(command "_.extend" big_circle "" pick_line1 "")
		(command "_.extend" big_circle "" pick_line2 "")
;;Identify point V & W
		(setq pnt_v (cdr (assoc 10 (entget (entlast))))
			pnt_w (cdr (assoc 11 (entget (entlast))))
		)
;;form an arc and rotate this around the chord pnt_v - pnt_w 180 deg & back
		(if (> (cadr pnt_p) 0.)
		  (command "_.pline" pnt_w "_A" "_CE" pnt_f2 pnt_v "_L" "cl")
		  (command "_.pline" pnt_v "_A" "_CE" pnt_f2 pnt_w "_L" "cl")
		);;;end if
 		(setq arc_line (entlast))
		(command "bhatch" "_Sel" (entlast) "" "Prop" "ansi31"  "1." "0." "")
			(setq arc_hatch (entlast))
			(setq ss (ssadd))
			(ssadd arc_line ss)(ssadd arc_hatch ss)
		;(command "_.rotate3d"  ss "" "2" pnt_v pnt_w 180.)
		(slow_rotate3d_origami ss pnt_v pnt_w 180.)
		(entdel arc_hatch)(entdel arc_line)
	(make_jpg)
	(make_jpg)
	(command "_.delay" 250)	
	);;;end of while loop
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
	
);;;hyperbola_by_folding
;;;
----------------parabola case -------------------
;parabola #1
(defun c:parabola_model()
	(setup_parabola)
	(setq pnt_temp (getpoint "\nPick a point on y_axis."))
	(if (= pnt_temp nil) (setq pnt_temp '(0 1.)))
	
		(setq 	temp_y (cadr pnt_temp)
			pnt_b (list 0.0 temp_y)
			ref_angle (angle pnt_f pnt_b)
			ref_length  (* 1.25 (distance pnt_f pnt_b))
		)
		(if (> temp_y 0.0)
		(setq pnt_a (polar pnt_b (- ref_angle half_pi) ref_length))
		(setq pnt_a (polar pnt_b (+ ref_angle half_pi) ref_length))
		)
		(mark_id pnt_a "A" 1 chr_size)
		(mark_id pnt_b "B" 4 chr_size)	
		
		(mark_id dir_up "D1" 1 chr_size)
		(mark_id dir_down "D2" 1 chr_size)
		(mark_id pnt_h "H" 1 chr_size)
		(mark_id pnt_h "(-c, 0)" 4 chr_size)
		(mark_id pnt_f "(c, 0)" 4 chr_size)
		(make_line_1 "0" 8 pnt_f pnt_b)
		(make_line_1 "0" 2 pnt_b pnt_a)
	(line_tick_mark pnt_h pnt_org 1 0)
	(line_tick_mark pnt_org pnt_f 1 0)
	(mark_right_angle pnt_a pnt_b pnt_f 3 0)
	(mark_right_angle pnt_a pnt_b pnt_c 3 0)
;;extend FB to C
	
	(setq pnt_c (plt pnt_f pnt_b 2.0)
		pnt_e (list 2.0 (cadr pnt_c))
		pnt_g (inters pnt_a pnt_b pnt_c pnt_e nil)
	)
	(mark_id pnt_c "C" 1 chr_size)
	(mark_id pnt_g "G (x,y)" 1 chr_size)
	(make_line_1 "0" 8 pnt_b pnt_c)
	(make_line_1 "0" 0 pnt_c pnt_g)
	(make_line_1 "0" 0 pnt_g pnt_f)	
;;line tick marks
	(line_tick_mark pnt_c pnt_b 1 1)
	(line_tick_mark pnt_b pnt_f 1 1)
	(line_tick_mark pnt_c pnt_g 2 2)
	(line_tick_mark pnt_g pnt_f 2 2)

	(reset_sysvar)
)
;;;
;;;
;parabola #2
(defun c:parabola_by_triangle()
	(setup_parabola)
	(setq blk_scale 0.65)
	(command "_.zoom" "_E")
	(command "_.regen")
	(make_jpg)
	(make_jpg)
	(alert "\nPick a point on y_axis.\nHit return key to end")	
	(while (setq pnt_temp (getpoint "\nPick a point"))
		(if (/= trig_block nil) (entdel trig_block))
		(setq 	temp_y (cadr pnt_temp)
			pnt_b (list 0.0 temp_y)
			ref_angle (angle pnt_f pnt_b)
			ref_length (* 1.25 (distance pnt_f pnt_b))
			angle_ins (rtd (- ref_angle pi ))
		)
		(if (> angle_ins 0.) (setq angle_ins (- (- 90. angle_ins))) )
		(if (> temp_y 0.0)
		(setq pnt_a (polar pnt_b (- ref_angle half_pi) ref_length))
		(setq pnt_a (polar pnt_b (+ ref_angle half_pi) ref_length))
		)
		(my_block_insert2 "triangle_45_45_hatch" pnt_b blk_scale  angle_ins)
			(setq trig_block (entlast))			
		;(make_line_1 "0" 8 pnt_f pnt_b)
		(make_line_1 "0" 2 pnt_b pnt_a)
		(make_jpg)
	);;;end of while loop
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
)
;;;;
;;;
;;;
;parabola #2
(defun c:parabola_manual_1()
	(setup_parabola)
	(alert "\nPick a point on y_axis.\nHit ESC key to end")	
	(while (setq pnt_temp (cadr (grread )))
		(setq 	temp_y (cadr pnt_temp)
			pnt_b (list 0.0 temp_y)
			ref_angle (angle pnt_f pnt_b)
			ref_length (* 1.25 (distance pnt_f pnt_b))
		)
		(if (> temp_y 0.0)
		(setq pnt_a (polar pnt_b (- ref_angle half_pi) ref_length))
		(setq pnt_a (polar pnt_b (+ ref_angle half_pi) ref_length))
		)
					
		(make_line_1 "0" 8 pnt_f pnt_b)
		(make_line_1 "0" 2 pnt_b pnt_a)
	)
)
;parabola #3
(defun c:parabola_manual_2()
	(setup_parabola)
	(alert "\nPlace your cursor up along the y_axis\nand after hitting return key
\n move cursor slowly downward. Hit ESC key to end.")	
	(while (setq pnt_temp (cadr (grread T)))
		(setq 	temp_y (cadr pnt_temp)
			pnt_b (list 0.0 temp_y)
			ref_angle (angle pnt_f pnt_b)
			ref_length (* 1.25 (distance pnt_f pnt_b))
		)
		(if (> temp_y 0.0)
		(setq pnt_a (polar pnt_b (- ref_angle half_pi) ref_length))
		(setq pnt_a (polar pnt_b (+ ref_angle half_pi) ref_length))
		)
					
		(make_line_1 "0" 8 pnt_f pnt_b)
		(make_line_1 "0" 2 pnt_b pnt_a)
	)
)
;parabola #4
(defun c:parabola_manual_3()
	(setup_parabola)
	(alert "\nPlace your cursor up along the y_axis\nand after hitting return key
\n move cursor slowly downward. Hit ESC key to end.")	
	(while (setq pnt_temp (cadr (grread T)))
		(setq 	temp_y (cadr pnt_temp)
			pnt_b (list 0.0 temp_y)
			ref_angle (angle pnt_f pnt_b)
			ref_length (* 1.25 (distance pnt_f pnt_b))
		)
		(if (> temp_y 0.0)
		(setq pnt_a (polar pnt_b (- ref_angle half_pi) ref_length))
		(setq pnt_a (polar pnt_b (+ ref_angle half_pi) ref_length))
		)
					
		;(make_line_1 "0" 8 pnt_f pnt_b)
		(make_line_1 "0" 2 pnt_b pnt_a)
	)
)
;parabola #5
(defun c:parabola_auto()
	(setup_parabola)
	(setq y_start 2.
		y_end -2.
		ndiv 20
		del_y (/ (- y_end y_start) ndiv)
		step 0
	)
	(make_jpg)
	(make_jpg)
	(alert "\nDraw automatically.")

	(repeat (1+ ndiv) 	
	 (setq pnt_temp (list 0 (+ y_start (* del_y step))) )
		(setq 	temp_y (cadr pnt_temp)
			pnt_b (list 0.0 temp_y)
			ref_angle (angle pnt_f pnt_b)
			ref_length (* 1.25 (distance pnt_f pnt_b))
		)
		(if (> temp_y 0.0)
		(setq pnt_a (polar pnt_b (- ref_angle half_pi) ref_length))
		(setq pnt_a (polar pnt_b (+ ref_angle half_pi) ref_length))
		)
					
		(make_line_1 "0" 2  pnt_b pnt_a )
		(setq step (1+ step))
		(make_jpg)
		(make_jpg)
		(command "_.delay" 250)
	);;end of repeat loop
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
)
;;;
(defun setup_parabola()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	(setq  half_pi (* 0.5 pi) two_pi (* 2.0 pi)
	 	pnt_f '(2.0 0) pnt_org '(0 0)
		y_up '(0 4) y_down '(0 -4)
		x_left '(-2 0) x_right '(4 0)
		chr_size 0.3
		dir_up '(-2 4)
		dir_down '(-2 -4)
		pnt_h '(-2 0)
	)
	(make_pt "0" 0 pnt_f)
	(mark_id pnt_f "F" 2 chr_size)	
	(mark_id y_up "y" 1 chr_size)
	(mark_id x_right "x" 1 chr_size)
	(mark_id pnt_org "O" 1 chr_size)

	(make_line_1 "0" 8 y_up y_down)
	(make_line_1 "0" 8 x_left x_right)
	(make_line_1 "0" 8 dir_up dir_down)

	(command "_.zoom" "_EXTENT" )
)
;;;
---------------hypo-cycloid case -------------------------
;;;
;astroid created by an envelop
(defun c:envelop_8()
	(setvar "PDMODE" 32)
	(setq  line_length 4.0
		x_left '(-4.5 0) x_right '(4.5 0)
		y_up '(0 4.5) y_down '(0 -4.5)
		l_sqrd (* line_length line_length)
	)
		
	(command "_.line" x_left x_right "")
	(command "_.line" y_down y_up "")
	(command "_.zoom" "_EXTENT" )
		
	(while (setq pnt_temp (cadr (grread T)))
		(setq 	temp_y (cadr pnt_temp)
			pnt_ref (list 0.0 temp_y)
		)
		(if (<= (abs temp_y ) line_length)
			(setq temp_x (sqrt (- l_sqrd (* temp_y temp_y))))
			(setq temp_x 0.0)	;dummy for out of range case
		)
		(setq r_new_x (list temp_x 0.)	l_new_x (list (- temp_x) 0.))
		(if (<= (abs temp_y ) line_length)
			(command "_.line" l_new_x pnt_ref r_new_x "")
		)			
		
	)
)

;envelop by a circle along parabola
(defun c:env_c1()
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -1)
	(setq  pnt_origin '(0 0)
		x_left '(-45 0) x_right '(45 0)
		y_up '(0 45) y_down '(0 -45)
	)
		
	(command "_.line" x_left x_right "")
	(command "_.line" y_down y_up "")
	(command "_.zoom" "_EXTENT" )
		
	(while (setq pnt_temp (cadr (grread T)))
		(setq 	temp_y (cadr pnt_temp)
			temp_x (* 0.125 (* temp_y temp_y))
			pnt_ref (list temp_x temp_y)
			temp_radius (distance pnt_ref pnt_origin)
		)
		(command "_.point" pnt_ref)
		(command "_circle" pnt_ref temp_radius)			
		
	)
)

;envelop by a circle along hyperbola
(defun c:env_c2()
	(setvar "PDMODE" 32)
	(setq  pnt_origin '(0 0)
		x_left '(-5 0) x_right '(5 0)
		y_up '(0 5) y_down '(0 -5)
	)
		
	(command "_.line" x_left x_right "")
	(command "_.line" y_down y_up "")
	(command "_.zoom" "_EXTENT" )
	(while (setq pnt_temp (cadr (grread T)))
		(setq 	temp_y (cadr pnt_temp)	temp_x (sqrt (+ 1.0 (* temp_y temp_y)))
			pnt_ref1 (list temp_x temp_y)	pnt_ref2 (list (- temp_x) temp_y)
			temp_radius (distance pnt_ref1 pnt_origin)
		)
		(command "_.point" pnt_ref1)
		(command "_.point" pnt_ref2)
		(command "_circle" pnt_ref1 temp_radius)
		(command "_circle" pnt_ref2 temp_radius)			
	)
)

;envelop by a circle along an ellipse
(defun c:env_c3()
	(setvar "PDMODE" 32)
	(setq  pnt_origin '(0 0)
		x_left '(-4.5 0) x_right '(4.5 0)
		y_up '(0 4.5) y_down '(0 -4.5)
	)
	(command "_.point" '(0 2))
	(command "_.point" '(0 -2))
	
	(command "_.line" x_left x_right "")
	(command "_.line" y_down y_up "")
	(command "_.zoom" "_EXTENT" )
		
	(while (setq pnt_temp (cadr (grread )))
		(setq 	temp_y (cadr pnt_temp)
			temp_x (sqrt (- 9.0 (* 2.15 (* temp_y temp_y))))
			pnt_ref1 (list temp_x temp_y)
			pnt_ref2 (list (- temp_x) temp_y)
			temp_radius (distance pnt_ref1 pnt_origin)
		)
		(command "_.point" pnt_ref1)
		(command "_.point" pnt_ref2)
		(command "_circle" pnt_ref1 temp_radius)
		(command "_circle" pnt_ref2 temp_radius)			
		
	)
)
;envelop of circles on a circle with a selcted ref_point
(defun c:env_c4()
	(setvar "PDMODE" 32)
	(setq ref_rad 2.0)
	(setq pnt_s '(-1.5 0) pnt_center '(0 0))
	(command "_.point" pnt_s)
	(command "_circle" '(0 0) ref_rad)
	(command "_.line" '(0 -3) '(0 3) "")
	(command "_.line" '(-3 0) '(3 0) "")
	(command "_.zoom" "_EXTENT" )

	(while (setq pnt_temp (cadr (grread T)))
		(setq temp_angle (angle pnt_center pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			cir_loc (list temp_x temp_y)
			temp_rad (distance cir_loc pnt_s)
		)
						
		(command "_circle"  cir_loc  temp_rad)
	)
)

;special cas eof env_c4 -- cardioid ref_point is on the circle.
(defun c:env_c5()
	(setvar "PDMODE" 32)
	(setq ref_rad 2.0)
	(setq pnt_s '(-2.0 0) pnt_center '(0 0))
	(command "_.point" pnt_s)
	(command "_circle" '(0 0) ref_rad)
	(command "_.line" '(0 -3) '(0 3) "")
	(command "_.line" '(-3 0) '(3 0) "")
	(command "_.zoom" "_EXTENT" )

	(while (setq pnt_temp (cadr (grread T)))
		(setq temp_angle (angle pnt_center pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			cir_loc (list temp_x temp_y)
			temp_rad (distance cir_loc pnt_s)
		)
						
		(command "_circle"  cir_loc  temp_rad)
	)
)

;special case eof env_c3 -- ref_point is outside of the circle.
(defun c:env_c6()
	(setvar "PDMODE" 32)
	(setq ref_rad 2.0)
	(setq pnt_s '(-3.0 0) pnt_center '(0 0))
	(command "_.point" pnt_s)
	(command "_circle" '(0 0) ref_rad)
	(command "_.line" '(0 -3) '(0 3) "")
	(command "_.line" '(-3 0) '(3 0) "")
	(command "_.zoom" "_EXTENT" )

	(while (setq pnt_temp (cadr (grread T)))
		(setq temp_angle (angle pnt_center pnt_temp)
			temp_x (* (cos temp_angle) ref_rad)
			temp_y (* (sin temp_angle) ref_rad)
			cir_loc (list temp_x temp_y)
			temp_rad (distance cir_loc pnt_s)
		)
						
		(command "_circle"  cir_loc  temp_rad)
	)
)
;the last example of Cindy & Rollett
(defun c:envelop_9()
	(setvar "PDMODE" 32)
	(setq  	x_left '(-3 0) x_right '(3 0)
		y_up '(0 3) y_down '(0 -3)
	)
		
	(command "_.line" x_left x_right "")
	(command "_.line" y_down y_up "")
	(command "_circle" '(0 0) 2.0)
	(command "_.zoom" "_EXTENT" )
		
	(while (setq pnt_temp (cadr (grread T)))
		(setq 	temp_x (car pnt_temp)
			temp_arg (- 4.0 (* temp_x temp_x))
		)
		(if (>= temp_arg 0.0) (setq temp_y (sqrt temp_arg))
					(setq temp_y 0.0)
		)
		(setq pnt_ref (list temp_x 0.0))
		(if (>= temp_arg 0.0)
			(command "_circle" pnt_ref temp_y)
		)
	)
)
;cardioid & limacon trial version 8/13/98
(defun c:cardioid()
	(setq pnt_o '(0 0)  length 1.0)
	(command "_.line" '(-5 0) '(5 0) "")
	(command "_.line" '(0 -5) '(0 5) "")
	(command "_circle" '(0 1.) "1.0")
	(command "_.zoom" "e" )
	(while (setq pnt_temp (cadr (grread T)))
		(setq theta (angle pnt_o pnt_temp)
			a (tan theta) two_a (* 2.0 a)
			denom (+ 1.0 (* a a))
		)
		(setq int_x (/ two_a denom)
			int_y (* a int_x)
			pnt_int (list int_x int_y)
		)
		(setq far_end (polar pnt_int theta length)
			near_end (polar pnt_int (+ theta pi) length)
		)
 
		(command "_.line" near_end pnt_int far_end "")
	)
)
;utility function for tangent
(defun tan( theta / sine cosine tangent)
	(setq sine (sin theta)
		cosine (cos theta)
		tangent (/ sine cosine)
	)
)

;cissoid trial version 8/13/98
(defun c:cissoid()
	(setq pnt_o '(0 2)  length 1.0)
	(command "_.line" '(-4 0) '(4 0) "")
	(command "_.line" '(0 -1) '(0 4) "")
	(command "_circle" '(0 1.) "1.0")
	(command "_.zoom" "e" )
	(while (setq pnt_temp (cadr (grread T)))
		(setq coord_x (car pnt_temp) 
			pnt_base (list coord_x 0.)
		)
		(setq theta (angle pnt_base pnt_o )
			a (tan theta) two_a (* 2.0 a)
			denom (+ 1.0 (* a a))
		)
		(setq int_x (- (/ two_a denom))
			int_y (+ 2.0 (* a int_x))
			pnt_int (list int_x int_y)
		)
		(setq 
			ref_dist (distance pnt_int pnt_base)
			near_end (polar pnt_o (+ theta pi) ref_dist)
		)
		(command "_.line"  near_end  pnt_base "")
	)
)
	

(defun c:cissoid2()
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" 0.005)
	(setq pnt_o '(0 2)  length 1.0)
	(command "_.line" '(-4 0) '(4 0) "")
	(command "_.line" '(0 -1) '(0 4) "")
	(command "_circle" '(0 1.) "1.0")
	(command "_.zoom" "e" )
	(while (setq pnt_temp (cadr (grread T)))
		(setq coord_x (car pnt_temp) 
			pnt_base (list coord_x 0.)
		)
		(setq theta (angle pnt_base pnt_o )
			a (tan theta) two_a (* 2.0 a)
			denom (+ 1.0 (* a a))
		)
		(setq int_x (- (/ two_a denom))
			int_y (+ 2.0 (* a int_x))
			pnt_int (list int_x int_y)
		)
		(setq 
			ref_dist (distance pnt_int pnt_base)
			near_end (polar pnt_o (+ theta pi) ref_dist)
		)
		(command "_.point"  near_end  )
	)
)
;test #2  draw a line from (0 0) following the cursor location
(defun radial_2()
	(setq pnt_0 '(0 0))
	(while (setq pnt_1 (cadr (grread T)))
		(command "_.line" pnt_0 pnt_1 "")
	)
)

;test #3  ESC key interrupt test
(defun test_3()
	(setq pnt_0 '(0 0))
	(while (setq gd  (grread T))
		(setq temp (car gd))
		(prin1 temp)
	)
)
;;;
;;;************************************************************************
;;; Function: NORMAL_BISECTOR_END
;;;
;;; compute two end points of a normal bisector
;;;
(defun NORMAL_bisector_end(
	pnt_1
	pnt_2
	/
	ang_12 line_length left_ang right_ang
	half_pi
	)

	(setq half_pi (/ pi 2.0))
	(setq  pnt_0 (plt pnt_1 pnt_2 0.5)
		ang_12 (angle pnt_1 pnt_2)
		line_length (distance pnt_1 pnt_2)
		left_ang (+ ang_12 half_pi)
		right_ang (- ang_12 half_pi)
		pnt_left (polar pnt_0 left_ang line_length)
		pnt_right (polar pnt_0 right_ang line_length)
	)
);NORMAL_BISECTOR_END
;;;
;;;************************************************************************
;;; Function: PLT
;;;
;;; get a point off the line segment defined by two end points and angle.
;;;	
; utility routine 
;; get a point along the line segment defined by two end points 
;;
;; pnt_a pnt_b      end points
;; loc_from_a       ratio of distance from a to length AB
;; output           point data (x,y)
(defun PLT
	(pnt_a 
	pnt_b 
	loc_from_a  
	/ 
	xa xb ya yb dist_ab dx dy xm ym
	)

	(setq xa (car pnt_a) ya (cadr pnt_a)
		xb (car pnt_b) yb (cadr pnt_b)
		dx (- xb xa) dy (- yb ya)
		xm (+ xa (* loc_from_a dx))
		ym (+ ya (* loc_from_a dy))
	)
	(list xm ym )
);PLT
;
;parabola #BASIC
(defun c:parabola_1()
	(setvar "PDMODE" 32)
	(setq  pnt_f '(1 0) x_left '(-1 0) x_right '(10 0)
		y_low '(-1 -10) y_up '(-1 10)
	)
		
	(command "_.point" pnt_f)
	(command "_.line" x_left x_right "")
	(command "_.line" y_low  y_up    "")
	(command "_.zoom" "_EXTENT" )
	(alert "\npick a point near x = -1 line")	
	(while (setq pnt_temp (cadr (grread )))
		(setq 	temp_y (cadr pnt_temp)
			pnt_ref (list -1 temp_y)
			pnt_ref_right (list 10 temp_y)
		)
		(normal_bisector_end pnt_ref pnt_f)
		(setq para_pnt (inters pnt_left pnt_right pnt_ref pnt_ref_right nil))
		(command "_.point" para_pnt)					
	);end of while loop

);;PARABOLA_1
;;;
;;;
;;;Tick mark at the midpoint of a line to show two line length
;;;are the same. options:1,2 & 3 tick marks
;;;line_tick_mark
;;;
(defun line_tick_mark(pnt_1 pnt_2 option color_id
			/ pnt_mid t_list pnt_a pnt_b
				pnt_ae pnt_be)
	(setq pnt_mid (plt pnt_1 pnt_2 0.5))
	(make_line_1 "0" 8 pnt_1 pnt_2)
		
	(command "_.rotate" (entlast) "" pnt_mid 90.)
	(setq t_list (entget (entlast))
		pnt_a (cdr (assoc 10 t_list))
		pnt_b (cdr (assoc 11 t_list))
		pnt_ae (plt pnt_a pnt_b 0.45)
		pnt_be (plt pnt_a pnt_b 0.55)
	)
	(entdel (entlast))
;;option :1
	(if (= option 1) (make_line_1 "0" color_id pnt_ae pnt_be))
;;option :2
	(if (= option 2)
		(progn
			(make_line_1 "0" color_id pnt_ae pnt_be)
			(command "_.copy" (entlast) "" pnt_mid pnt_mid)
			(command "_.rotate" (entlast) "" pnt_mid 45.)
		)
	);;;end if
;;option :3
	(if (= option 3)
		(progn
			(make_line_1 "0" color_id pnt_ae pnt_be)
			(command "_.copy" (entlast) "" pnt_mid pnt_mid)
			(command "_.rotate" (entlast) "" pnt_mid 45.)
			(command "_.copy" (entlast) "" pnt_mid pnt_mid)
			(command "_.rotate" (entlast) "" pnt_mid 90.)
		)
	);;;end if
)
;;; 
;;;Mark_right_angle
;;;
;;;
;;;mark_right_angle
;;;
(defun mark_right_angle(pnt_a pnt_o pnt_b col_id side_len  / pnt_c pnt_d pnt_e pnt_m)
	(if (= side_len 0) (setq side_len (* 0.1 (distance pnt_a pnt_o))) )
	(setq pnt_c (pld pnt_o pnt_a side_len)
		pnt_e (pld pnt_o pnt_b side_len)
		pnt_m (plt pnt_c pnt_e 0.5)
		pnt_d (plt pnt_o pnt_m 2.0)
	)
	(make_line_1 "0" col_id pnt_c pnt_d)
	(make_line_1 "0" col_id pnt_d pnt_e)
)
;;;
;;;
;;;
;;;slow_rotate3d_origami	rotate3d slow display origami version
;;;
(defun slow_rotate3d_origami(3d_ent ax_1 ax_2 rot_angle )
	(setq n_repeat 12
		n_repeat_return  8
		del_th (/ (float rot_angle) n_repeat)
		min_del_th (- (/ (float rot_angle) n_repeat_return) ) 
	)
	(repeat n_repeat
		(command "_.rotate3d" 3d_ent "" "2" ax_1 ax_2 del_th)
		(setq temp (entlast))
		(make_jpg)
		(command "_.delay" 100)
	)
	(command "_.delay" 1000)
	(repeat n_repeat_return
		(command "_.rotate3d" temp "" "2" ax_1 ax_2 min_del_th)
		(setq temp (entlast))
		(make_jpg)
		(command "_.delay" 50)
	)
);;;
;;;