;;;	UTILITY_CURVES.LSP
;;;collection of special curves drawing utility
;;;
;;;
;;;	1. conchoid
;;;	2. cissoid
;;;	3. conics
;;;	4. Concentric_circles	used in Archimedian Spiral
;;;	5. Multiple_rays	used in Archimedian Spiral & Quadratrix
;;;
;;;	Jan 18, 2006 by Takaya Iwamoto
;;;	Feb 4,2006	added Concentrated_circles and Multiple_rays
;;;	Nov 26,2006	modified test_conchoid
;;;
;;;TEST_CONCHOID
;;;
(defun c:test_conchoid( / pnt_a pnt_b pnt_c a_length n_div
			pnt_a_def pnt_b_def pnt_c_def a_length_def n_div_def)
	;;;set default value for inputs
	;(setup_sysvar)
	(setvar "PDMODE" 32)
	(setq pnt_a_def '(-4 0) pnt_b_def '(4 0) pnt_c_def '(0 -1)
		a_length_def 2. n_div_def 100
		y_up '(0 5) y_down '(0 -2)
		x_left '(-5 0) x_right '(5 0)
	)
	(make_line_1 "0" 8 y_up y_down)
	(make_line_1 "0" 8 x_left x_right)
	(command "_.zoom" "_Extent")
	;;;Input data
	(setq pnt_a (getpoint "\nGet point A (def '(-4 0)): ")
		pnt_b (getpoint "\nGet point B (def '(4 0)): ")
		pnt_c (getpoint "\nGet point C (def '(0 -1)): ")
		a_length (getreal "\nSpecify constant length a (def 2): ")
		n_div (getint "\nSpecify number of division between A & B (def 100): ")
	)
	;;;default section
	(if (= pnt_a nil) (setq pnt_a pnt_a_def))
	(if (= pnt_b nil) (setq pnt_b pnt_b_def))
	(if (= pnt_c nil) (setq pnt_c pnt_c_def))
	(if (= a_length nil) (setq a_length a_length_def))
	(if (= n_div nil) (setq n_div n_div_def))

	(command "_point" pnt_a)
	(command "_point" pnt_b)
	(command "_point" pnt_c)
			
	;;;draw conchoid
	(conchoid_draw pnt_a pnt_b pnt_c a_length n_div)
	;(command "_.zoom" "_Extent")
	;(command "_.regen")
);;;TEST_CONCHOID
	
;;;
;;;
;;;DRAW_CONCHOID
;;;		pnt_a, pnt_b	end coordinate of line AB (ruler)
;;;		pnt_v		Pole
;;;		a_length	constant length
;;;		ndiv		no. of division between Point A & B
;;;
(defun conchoid_draw(pnt_a pnt_b pnt_c a_length ndiv 
		     / 	inc nstep pnt_old pnt_t pnt_new 
			dist_ca dist_ct
		    )
	(setq inc (/ 1. (float n_div))
		nstep 1
		dist_ca (distance pnt_c pnt_a)
		pnt_old (pld pnt_c pnt_a (+ dist_ca a_length))
	)
	(repeat n_div
		(setq pnt_t (plt pnt_a pnt_b (* nstep inc))
			dist_ct (distance pnt_c pnt_t)
			pnt_new (pld pnt_c pnt_t (+ dist_ct a_length))
		)
		;undo

		
		;(command "_.point" pnt_new)
		(make_line_1 "0" 2 pnt_old pnt_new)
		(setq nstep (1+ nstep)
			pnt_old pnt_new
		)
	)
);;;DRAW_CONCHOID
;;;
;;;
(prompt "\nLoading TEST_CONICS")
;;;DRAW_CONICS
;;;
;;;General routine using the CONICS EQUATION
;;;	y^2 + (1-e^2)x^2 -2kx + k^2 = 0
;;;
;;;	Select a focus point	PNT_A
;;;	Select a directrix	end points  PNT_B & PNT_C
;;;	Specify eccentricity 	E_VALUE
;;;				e < = > 1.0 , Ellipse, Parabola & HYperbola
;;;	specify Y-range		Y_MIN & Y_MAX
;;;
;;;
(defun C:test_conics()
	(setup_test)
	(setq y_inc 0 x_min 0 y_min 0 y_max 0)
	(draw_conics pnt_a pnt_b pnt_c e_value x_inc y_inc
			x_min x_max y_min y_max n_pnt)
	(reset_sysvar)
);;;test_conics
;;;
;;;
(prompt "\nLoading DRAW_CONICS")
;;;DRAW_CONICS
;;;
(defun draw_conics(pnt_a pnt_b pnt_c e_value 
			x_inc y_inc 
			x_min x_max
			y_min y_max
			n_pnt
			/
			nstep pnt_t
		  )
	;if e < 1 , ellipse
	;   e = 1 . parabola
	;   e > 1 . hyperbola
	;;;try hyperbola case here
	(setq 	nstep 1
		pnt_old (conic_formula_x x_start e_value k_val)
	)
	(repeat n_pnt
		(setq 	x_t (* nstep x_inc)
			pnt_new (conic_formula_x x_t e_value k_val)
		)
				
		(command "_.point" pnt_new)
		(make_line_1 "0" 2 pnt_old pnt_new)
		(setq nstep (1+ nstep)
			pnt_old pnt_new
		)
	)


);;;DRAW_CONICS
;;;
;;;conic_formula_x
;;;conic formula to get Y^2 value form x_value given
;;;	Y^2 = e^2*x^2 - (x-k)^2
;;;
(defun conic_formula_x(x_val e_val k_val / pnt_temp)

	(setq ex (* e_val x_val)
		x_m_k (- x_val k_val)
		result (- (* ex ex) (* x_m_k x_m_k))
	)
	(setq pnt_temp (list x_val (sqrt result)))

);;;conic_formula_x
;;;
;;;
(prompt "\nLoading setup_test")		
;;;SETUP_TEST
;;;
(defun setup_test()
	(setup_sysvar)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -3)
	;;;input parameters
	(setq pnt_a (getpoint "\nSelect a focus point(def = '(3 0))")
		pnt_b (getpoint "\nSelect one end of directrix (def = '(0 -3))")
		pnt_c (getpoint "\nSelect the other end of directrix (def = '(0 3))")
		e_value (getreal "\nInput eccentricity value (def = 2.0)")
	)
	;;;default values setting if inputs for Pnt_a,pnt_b, pnt_c, e_value are nil.
	(if (= pnt_a nil) (setq pnt_a '(3 0))  )
	(if (= pnt_b nil) (setq pnt_b '(0 -3)) )
	(if (= pnt_c nil) (setq pnt_c '(0 3))  )
	(if (= e_value nil) (setq e_value 2.0) )

	;;case for hyperbola
	(setq k_val (car pnt_a) x_zero (list (car pnt_b) 0)
		p_start (plt x_zero pnt_a (/ 1. 3))
	)
	(setq x_inc (getreal "\nInput increment in X-direction (def = 1/100)") )
		(if (= x_inc nil) (setq x_inc 0.01))
	(setq x_max (getreal "\nInput maximum range for X(def = 2k)") )
		(if (= x_max nil) (setq x_max (* 2. k_val)) )

	(setq n_pnt (getint "\nHow many points ? (def = 100)") )
		(if (= n_pnt nil) (setq n_pnt 100) )

);;;SETUP_TEST
(prompt "\nloading concentric_circles")
;;;***************Concentric_Circles************************
;;;Used in drawing Archimedian Circles
;;;
(defun Concentric_Circles(  
			/  radius step pnt_org R_base R_inc N_circles)
	(setq   pnt_org (getpoint "\nCenter of circles(def = (0 0)") 
		R_base (getreal "\nRadius of the base circle (def 0.1)") 
		R_inc (getreal "\nIncrement of radius (def = 0.1)")
		N_circles (getint "\nNumber of circles incl. base circle(def = 10)")
	)
	;;;default setting so that excution will not stop
	(if (= pnt_org nil) (setq pnt_org '(0 0)) )
	(if (= R_base nil) (setq R_base 0.1) )
	(if (= R_inc nil) (setq R_inc 0.1) )
	(if (= N_circles nil) (setq N_circles 10) )

	(setq step 0)
	(repeat N_circles
		(setq radius (+ R_base (* step R_inc)))
		(make_circle_1 "layer8" 8 pnt_org radius)
		(setq step (1+ step))
	)

);;;CONCENTRIC_CIRCLES
;;;
(prompt "\nloading mutiple_rays")
;;;***************Multiple_Rays************************
;;;Used in drawing Archimedian Circles, Quadratrix
;;;
(defun Multiple_Rays(  
			/  ray_end step pnt_org Ray_len Ang_inc N_rays)
	(setq   pnt_org (getpoint "\nRays Origin(def = (0 0)") 
		Ray_len (getreal "\nLength of Ray (def 1.0)") 
		Ang_inc (getreal "\nIncrement of angle in deg(def = 9 degrees)")
		N_rays (getint "\nNumber of rays(def = 21)")
	)
	;;;default setting so that excution will not stop
	(if (= pnt_org nil) (setq pnt_org '(0 0)) )
	(if (= Ray_len nil) (setq Ray_len 1.0) )
	(if (= Ang_inc nil) (setq Ang_inc 9) )
	(if (= N_rays nil) (setq N_rays 21) )

	(setq step 0)
	(repeat N_rays
		(setq ray_end (polar pnt_org (dtr (* step Ang_inc)) Ray_len))
		(make_line_1 "layer8" 8 pnt_org ray_end)
		(setq step (1+ step))
	)

);;;Multiple_Rays
;;;