;;;	pursuit_apollonius.lsp
;;;		Takaya Iwamoto   Oct 17,2004
;;;		modified  June 01,2005		added pursuit_test command
;;;Reference: Excursions in Geometry,    C.Stanley Ogilvy   Dover 1969
;;;Test for Pursuit curve
;;;Suppose a ship leaves point B and steams in a fixed direction at a constant speed.
;;; A second ship,leaving point A at the same time,can go k times as fast as the first ship.
;;; Assuming a plane ocean,what course should the first ship steer in order to intercept
;;; the slow ship as quickly as possible ?
;;;The solution;
;;; find points C & D on the line connecting A & B such that AC = k * CB & AD = k * BD
;;; This means that points C & D divide AB harmonically,i.e  AC/CB = AD/BD
;;; Then draw a circle with CD as a diameter. The point of intercept is on this circle.
;;;
;;; Letting the mid-point between A & B is O.
;;; The OC = r*(k-1)/(k+1)	OD = r* (k+1)/(k-1)
;;; The diameter of the Apollonius circle  is  r * 4k/(k^2 -1)
;;; The distance of the center of the circle from point "O" is r*(k^2 + 1)/(k^2 - 1)
;;;
;;;The Geeek mathematician Apollonius discovered that a circle may be defined in a way quite 
;;;different from the usual "all points equidistant from a fixed point."
;;;Apolloinius's defintion states that if a point moves in such a way that its distance from
;;;one fixed point is always a constant multiple of its distance from another fixed point,
;;;then its path is a circle.
;;;	
;;;
;;;There are two demo scripts
;;;	test_circle	up to 7 pairs of circles drawn to show the intersections are on
;;;			the Apolllonius circle
;;;	Pursuit_test	Harmonic division, explained by Ship chasing
;;;
;;;
(defun c:test_circle()
	(setup_sysvar)
	(setup_pursuit_int)
	(ap_circles)
	(reset_sysvar)
);;;TEST_CIRCLE
;;;
(defun ap_circles()
	(setq col_id 0)
	(while (< col_id 7)
		(setq col_id (1+ col_id))
	(command "_color" (itoa col_id))
	(command "_circle" pnt_b PAUSE)
	(setq rad2 (* k (getvar "CIRCLERAD")))
	(command "_.circle" pnt_a rad2)
	)
	(command "_COLOR" "BYLAYER")
)
;;;	
;;;
(defun c:Pursuit_ap()
	(setup_sysvar)
	(setup_pursuit_ap)
	(pursuit_apollo_1)
	(reset_sysvar)
);;;PURSUIT_AP
;;;
;;;Main routine for red boat chasing blue boat--PURSUIT_TEST
;;;
(defun c:Pursuit_test()
	(setup_sysvar)
	(setup_pursuit_step1)
;;case (a)
	;;;Define point C as internal
	(step1)
	(pursuit_apollo_1A)
		(make_pt "0" 0 pnt_c1)
		(mark_id pnt_c1 "C" 4 0.25)
	(alert "\nPoint C divides\nLine segment AB INTERNALLY to\nthe ratio  K : 1\n\nAC : BC = K : 1")
		(entdel red_bt) (entdel blue_bt)
;;case (b)	
	;;;Define Point D as external
	(step2)
	(pursuit_apollo_1B)
		(make_pt "0" 0 pnt_c2)
		(mark_id pnt_c2 "D" 4 0.25)
	(alert "\nPoint D divides\nLine segment AB EXTERNALLY to\nthe ratio  K : 1\n\nAD : BD = K : 1")
		(entdel red_bt) (entdel blue_bt)
	(alert "\nDraw a circle with a dimeter CD")
	;;;General cases	target point on the circle
		(make_circle_1 "0" 8 cir_cen ap_rad)
		(setq ap_circle (entlast))
		(command "_.delay" 500)
;;case (c)
	(while (= (Yes_or_No "Want to try a general case ? ") "_Y")
		(general_ap)
			(command "_.delay" 1000)
			(entdel red_bt) (entdel blue_bt)
	)	;;;end of while loop
	;;;drawing aid for a proof
	(proof_ap)
	(reset_sysvar)
);;;PURSUIT_TEST
;;;
;;;
(defun c:Pursuit_test_1()
	(setup_sysvar)
	(setup_pursuit_step1)
;;case (a)
	;;;Define point C as internal
	(step1)
	(pursuit_apollo_1A)
		(make_pt "0" 0 pnt_c1)
		(mark_id pnt_c1 "C" 4 0.25)
	(alert "\nPoint C divides\nLine segment AB INTERNALLY to\nthe ratio  K : 1\n\nAC : BC = K : 1")
		;(entdel red_bt); (entdel blue_bt)
	(reset_sysvar)
);;;pursuit_test_1
;;;
(defun c:Pursuit_test_2()
	(setup_sysvar)
	(setup_pursuit_step1)
;;case (b)	
	;;;Define Point D as external
	(step2)
	(pursuit_apollo_1B)
		(make_pt "0" 0 pnt_c2)
		(mark_id pnt_c2 "D" 4 0.25)
	(alert "\nPoint D divides\nLine segment AB EXTERNALLY to\nthe ratio  K : 1\n\nAD : BD = K : 1")
		;(entdel red_bt) ;(entdel blue_bt)
	(reset_sysvar)
);;;pursuit_test_2
;;;
;;;
(defun c:Pursuit_test_3()
	(setup_sysvar)
	(setup_pursuit_step1)
	(alert "\nDraw a circle with a dimeter CD")
	;;;General cases	target point on the circle
		(make_circle_1 "0" 8 cir_cen ap_rad)
		(setq ap_circle (entlast))
		(command "_.delay" 500)
;;case (c)
	(while (= (Yes_or_No "Want to try a general case ? ") "_Y")
		(general_ap)
			(command "_.delay" 500)
			;(entdel red_bt) ;(entdel blue_bt)
	)	;;;end of while loop
	;;;drawing aid for a proof
	;(proof_ap)
	(reset_sysvar)
);;;PURSUIT_TEST_3
;;;
;;;PROOF_AP	Proof for harmonic division
(defun proof_ap()
	(make_line_1 "0" 8 pnt_c1 pnt_es)
	(make_line_1 "0" 8 pnt_es pnt_c2)
	(setq len_ap (distance pnt_1 pnt_es)
		len_bp (distance pnt_2 pnt_es)
		pnt_g (pld pnt_es pnt_1 len_bp)
		pnt_e (pld pnt_es pnt_1 (- len_bp))
		pnt_h (inters pnt_c1 pnt_es pnt_2 pnt_g nil)
		pnt_f (inters pnt_c2 pnt_es pnt_2 pnt_e nil)
	)
	(make_line_1 "0" 8 pnt_g pnt_2)
	(make_line_1 "0" 8 pnt_2 pnt_e)
	(make_line_1 "0" 8 pnt_es pnt_e)
	
	(mark_id pnt_e "E" 1 0.25)
	(mark_id pnt_f "F" 1 0.25)
	(mark_id pnt_g "G" 2 0.25)
	(mark_id pnt_h "H" 1 0.25)
	(setq mark_size 0.2)
	(mark_angle pnt_2 pnt_es pnt_f 0.3 "f" mark_size 4)
	(mark_angle pnt_f pnt_es pnt_e 0.4 "f" mark_size 1)
	(mark_angle pnt_g pnt_es pnt_h 0.6 "q" mark_size 3)
	(mark_angle pnt_h pnt_es pnt_2 0.7 "q" mark_size 3)
);;;PROOF_AP

;;;GENERAL_AP	any point on the Apollonius circle selected 
;;;
(defun general_ap()
	(alert "\nSelect a point on this circle\nto specify escape direction.")
		;;;Set OSNAP to the NEAREST to pick a point on the circle
	(command "_.line" pnt_2 (setq pnt_es (getpoint pnt_2 "\nSpecify Escape direction")) "")
	(mark_id pnt_es "P" 2 0.25)
	(terpri)
	(command "_.delay" 500)
	(step3)
	(pursuit_apollo_1C)
);;;GENERAL_AP
;;;
(defun setup_pursuit_ap()
	(setq pnt_xl '(-2 0) pnt_xr '(5 0)  pnt_o '(0 0)
		pnt_yu '(0 3) pnt_yl '(0 -3)
	)
	
	(make_line_1 "0" 8 pnt_xl pnt_xr)
	(make_line_1 "0" 8 pnt_yl pnt_yu)
	(command "_.zoom" "_EXTENT")
	(command "_.regen")
	(setvar "OSMODE" 512)
	(setvar "PDMODE" 32)
	(command "_.point" (setq pnt_1 (getpoint "\nGet Point A:")))
	(command "_.point" (setq pnt_2 (getpoint "\nGet Point B:")))
	(command "_.line" pnt_2 (setq pnt_3 (getpoint pnt_2 "\nSpecify Escape direction")) "")
		(setq escape_line (entlast))
	
	
	(setq k (getreal "\nRelative speed of the Pursuiter(>1.0)(def=2.0) = "))
	(if (= k nil) (setq k 2.0))	
	(setq 
		pnt_a pnt_1
		pnt_b pnt_2
		pnt_c pnt_3
		ksq (* k k) ksqp1 (+ ksq 1) ksqm1 (- ksq 1)
		len_oc (/ (* 0.5 (distance pnt_a pnt_b) (- k 1)) (+ k 1))
		ap_rad (/ (* (distance pnt_a pnt_b) k) ksqm1)
		cir_cen (shift_pnt (mid_point pnt_a pnt_b) (list (+ ap_rad len_oc) 0))
		rel_speed k
	)
	(make_circle_1 "0" 8 cir_cen ap_rad)
		(setq ap_circle (entlast))
	(command "_.trim" (entlast) "" pnt_c "")
	(setq pnt_c (cdr (assoc 11 (entget escape_line))) )	;;redefine pnt_c on a circle

	(setq rate (getreal "\nSpecify speed as a distance  % of length AB:(def= 0.1 %)  "))
	(if (= rate nil) (setq rate 0.1))
	(setq 	delta (* (distance pnt_b pnt_c) (/ rate 100.))
		n_repeat (fix (/ 100 rate))
		speed (getint "\nSpecify speed (1-100) 1:veryfast 100:very slow(def = 50)")
	)
	(if (= speed nil) (setq speed 50))
		
	(make_line_1 "0" 8 pnt_a pnt_c)
	;set arrow at the starting points
	(setq theta_a (+ 180. (rtd (angle pnt_a pnt_c)))
		theta_b (+ 180.  (rtd  (angle pnt_b pnt_c)))
	)
	(command "_.insert" "red_boat" pnt_a 0.5 0.5 theta_a )
	(princ "after insert")(terpri)
		(setq red_bt (entlast))
	(command "_.insert" "blue_boat" pnt_b 0.5 0.5 theta_b )
		(setq blue_bt (entlast))
);;;SETUP
;;;
;;;
(defun setup_pursuit_step1()
	(setq pnt_xl '(-2 0) pnt_xr '(5 0)  pnt_o '(0 0)
		lower_left '(-2.4 -2.1) upper_right '(4.5 2.6)
	)
	
	(make_line_1 "0" 8 pnt_xl pnt_xr)
	
	;(make_line_1 "0" 8 pnt_yl pnt_yu)
	(command "_.zoom" "_Window" lower_left upper_right)
	(command "_.regen")
	(setvar "OSMODE" 512)
	(setvar "PDMODE" 32)
	;(command "_.point" (setq pnt_1 (getpoint "\nGet Point A:")))
	;(command "_.point" (setq pnt_2 (getpoint "\nGet Point B:")))
	(setq pnt_1 pnt_xl  pnt_2 '(1.0 0) 
		pnt_c1 '(0 0) pnt_c2 '(4 0)	;;;C1 & C2 are harmonic division points
	)
	(make_pt "0" 0 pnt_1)
	(make_pt "0" 0 pnt_2)
	(mark_id pnt_1 "A" 4 0.25)
	(mark_id pnt_2 "B" 4 0.25)
	(setq k (getreal "\nRelative speed of the Pursuiter(>1.0)(def=2.0) = "))
	(if (= k nil) (setq k 2.0))	
	(setq 
		pnt_a pnt_1
		pnt_b pnt_2
		ksq (* k k) ksqp1 (+ ksq 1) ksqm1 (- ksq 1)
		len_oc (/ (* 0.5 (distance pnt_a pnt_b) (- k 1)) (+ k 1))
		ap_rad (/ (* (distance pnt_a pnt_b) k) ksqm1)
		cir_cen (shift_pnt (mid_point pnt_a pnt_b) (list (+ ap_rad len_oc) 0))
		rel_speed k
	)
	;(make_circle_1 "0" 8 cir_cen ap_rad)
	;	(setq ap_circle (entlast))
	
	(setq rate 1. n_repeat (fix (/ 100 rate)) speed 50 )
);;;SETUP
;;;
;;;STEP1
;;;
(defun step1()
	(setq 	pnt_c pnt_c1
		delta (* (distance pnt_b pnt_c) (/ rate 100.)	)
	)		
	;set arrow at the starting points
	
	(command "_.insert" "red_boat" pnt_a 0.5 0.5 180. )
	;(princ "after insert")(terpri)
		(setq red_bt (entlast))
	(command "_.insert" "blue_boat" pnt_b 0.5 0.5 0. )
		(setq blue_bt (entlast))

);;;STEP1
;;;
;;;STEP2
;;;
(defun step2()
	(setq 	pnt_c pnt_c2
		pnt_a pnt_1
		pnt_b pnt_2
		delta (* (distance pnt_b pnt_c) (/ rate 100.)	)
	)		
	;set arrow at the starting points
	
	
	(command "_.insert" "blue_boat" pnt_b 0.5 0.5 180. )
		(setq blue_bt (entlast))
	(command "_.insert" "red_boat" pnt_a 0.5 0.5 180. )
		(setq red_bt (entlast))
);;;STEP2
;;;STEP3
;;;
(defun step3()
	(setq 	pnt_c pnt_es
		pnt_a pnt_1
		pnt_b pnt_2
		delta (* (distance pnt_b pnt_c) (/ rate 100.)	)
	)		
	;set arrow at the starting points
	(setq theta_a (+ 180. (rtd (angle pnt_a pnt_c)))
		theta_b (+ 180.  (rtd  (angle pnt_b pnt_c)))
	)
	
	(command "_.insert" "red_boat" pnt_a 0.5 0.5 theta_a )
		(setq red_bt (entlast))
	(command "_.insert" "blue_boat" pnt_b 0.5 0.5 theta_b )
		(setq blue_bt (entlast))

);;;STEP3
;;;
;;;PURSUIT for a straight line case
;;;	The case of dog and rabbit running at the independetn pre-destined target points
;;;	initial points		pnt_rs for rabbit, pnt_ds for dog
;;;	target points		pnt_rt for rabbit, pnt_dt for dog
;;;	rel_speed		dog's speed/ rabbit's speed
;;;	The following code must be updated in the future (June 3,2005)
;;;PURSUIT_APOLLO_1
;;;
(defun pursuit_apollo_1()
	;(setup_sysvar)
	(if (= (Yes_or_No "Start ?") "_Y")
		 
	(repeat n_repeat
	   	(setq pnt_bc (pld pnt_b pnt_c delta)
			pnt_ac (pld pnt_a pnt_c (* rel_speed delta))
		)
		(slow_line speed "0" 1 pnt_a pnt_ac)
		(slow_line speed "0" 5 pnt_b pnt_bc)
			
		(command "_.move" blue_bt "" pnt_b pnt_bc )
		(command "_.move" red_bt "" pnt_a pnt_ac)

		(setq pnt_a pnt_ac 	pnt_b pnt_bc )
	)	;;;end of repeat loop
	)	;;;end of if loop
);;;PURSUIT_apollo_1
;;;
;;;PURSUIT_APOLLO_1A
;;;
(defun pursuit_apollo_1A()
	(setq nstep 0)
		
	(make_jpg)	;;apollo_1a  jpg file
			 
	(if (= (Yes_or_No "Start ?") "_Y")
	
	(repeat n_repeat
	   	(setq pnt_bc (pld pnt_b pnt_c delta)
			pnt_ac (pld pnt_a pnt_c (* rel_speed delta))
		)
		(slow_line speed "0" 1 pnt_a pnt_ac)
		(slow_line speed "0" 5 pnt_b pnt_bc)
			
		(command "_.move" blue_bt "" pnt_b pnt_bc )
		(command "_.move" red_bt "" pnt_a pnt_ac)
		(setq pnt_a pnt_ac 	pnt_b pnt_bc nstep (1+ nstep))
		(if (= (rem nstep 10) 0) (make_jpg))
		
	)	;;;end of repeat loop
	)	;;;end of if loop
);;;PURSUIT_apollo_1A
;;;
;;;PURSUIT_APOLLO_1B
;;;
(defun pursuit_apollo_1B()
	(setq nstep 0)
	(make_jpg) ;;apollo_1b  jpg file
	(if (= (Yes_or_No "Start ?") "_Y")
	
	(repeat n_repeat
	   	(setq pnt_bc (pld pnt_b pnt_c delta)
			pnt_ac (pld pnt_a pnt_c (* rel_speed delta))
		)
		(slow_line speed "0" 1 pnt_a pnt_ac)
		(slow_line speed "0" 5 pnt_b pnt_bc)
			
		(command "_.move" blue_bt "" pnt_b pnt_bc )
		(command "_.move" red_bt "" pnt_a pnt_ac)

		(setq pnt_a pnt_ac 	pnt_b pnt_bc nstep (1+ nstep))
		(if (= (rem nstep 10) 0) (make_jpg) )
		
	)	;;;end of repeat loop
	)	;;;end of if loop
);;;PURSUIT_apollo_1B
;;;
;;;
;;;PURSUIT_APOLLO_1C
;;;
(defun pursuit_apollo_1C()
	(setq nstep 0)
	(make_jpg)	;apollo_1c jpg file
	(if (= (Yes_or_No "Start ?") "_Y")
	
	(repeat n_repeat
	   	(setq pnt_bc (pld pnt_b pnt_c delta)
			pnt_ac (pld pnt_a pnt_c (* rel_speed delta))
		)
		(slow_line speed "0" 1 pnt_a pnt_ac)
		(slow_line speed "0" 5 pnt_b pnt_bc)
			
		(command "_.move" blue_bt "" pnt_b pnt_bc )
		(command "_.move" red_bt "" pnt_a pnt_ac)

		(setq pnt_a pnt_ac 	pnt_b pnt_bc nstep (1+ nstep))
		(if (= (rem nstep 10) 0) (make_jpg) )
		
	)	;;;end of repeat loop
	)	;;;end of if loop
);;;PURSUIT_apollo_1C
;;;
;;;
(defun setup_pursuit_int()
	(setq pnt_xl '(-2 0) pnt_xr '(5 0)  pnt_o '(0 0)
		pnt_yu '(0 3) pnt_yl '(0 -3)
	)
	
	(make_line_1 "0" 8 pnt_xl pnt_xr)
	(make_line_1 "0" 8 pnt_yl pnt_yu)
	(command "_.zoom" "_EXTENT")
	(command "_.regen")
	(setvar "OSMODE" 512)
	(setvar "PDMODE" 32)
	(command "_.point" (setq pnt_1 (getpoint "\nGet Point A:")))
	(command "_.point" (setq pnt_2 (getpoint "\nGet Point B:")))
	;(command "_.line" pnt_2 (setq pnt_3 (getpoint pnt_2 "\nSpecify Escape direction")) "")
	
	(setq k (getreal "\nRatio of distance from A & B(>1.0) = "))
		
	(setq 
		pnt_a pnt_1
		pnt_b pnt_2
		pnt_c pnt_3
		d_ref 1.e10
		ksq (* k k) ksqp1 (+ ksq 1) ksqm1 (- ksq 1)
		len_oc (/ (* 0.5 (distance pnt_a pnt_b) (- k 1)) (+ k 1))
		ap_rad (/ (* (distance pnt_a pnt_b) k) ksqm1)
		cir_cen (shift_pnt (mid_point pnt_a pnt_b) (list (+ ap_rad len_oc) 0))

	)
	
	(setq d_ab (distance pnt_a pnt_b))
	
	;set arrow at the starting points
	(command "_.insert" "red_arrow" pnt_a 0.5 0.5 -90.)
	(princ "after insert")(terpri)
		(setq red_arw (entlast))
	(mark_id pnt_a "A" 2 0.25)
	(command "_.insert" "blue_arrow" pnt_b 0.5 0.5 -90. )
		(setq blue_arw (entlast))
	(mark_id pnt_b "B" 2 0.25)
	(setvar "OSMODE" 32)
	(alert "draw 5 pairs of circles")
);;;
;;;PURSUIT for a straight line case
;;;