;;;Archytas's 3D solid solution to Delian Problem
;;;This is the first and only 3D approach
;;;File name	:  Archytas_Delian.lsp
;;;
;;;
;;;Jan 15,2006		Takaya Iwamoto
;;;modification records
;;;	jan 16,2006	clean up
;;;	jan 17,2006	two commands Archytas_Delian & Archytas_Delian_Model
;;;			Full cone is needed for smooth UNION execution.
;;;	jan 18,2006	Finishing touch to Archytas_Delian command
;;;
;;;Prototype   Archytas_Delian_0
;;;
(defun c:Archytas_Delian_0()
	;draw base circle and generator line for Cone
	(setup_archytas)

	;create a cylinder with color yellow(2)
	(alert "\nCreate a cylinder")
	(setvar "CECOLOR" "2")
	(command "_.cylinder" cylinder_center cylinder_rad cylinder_length)
		(setq cylinder_1 (entlast))
	;Create a torus with zero inner radius
	(alert "\nCreate a torus with zero inner radius")
	(setvar "CECOLOR" "4")
	(command "_.torus" torus_center torus_rad tube_rad)
		(setq torus_1 (entlast))
	;Create a right cone first on X-Y plane and rotate it 90 degrees
	;about the line connecting  points C & D so that the center line
	;will coincide with X-axis (line AC)
	(alert "\nCreate a cylinder whose generator line is AD")
	(setvar "CECOLOR" "6")	'magenta color
	(command "_.cone" pnt_c cone_base_rad cone_height)
	(setq cone_1 (entlast))
	(alert "\nRotate this cone about line CD by 90 degrees")
	(command "_.rotate3d" cone_1 "" "2" pnt_d pnt_c 90.)
	;shade this shademode Gouroud shading
	(command "_.shade" )
	;Take union of 3 solids
	




	(reset_sysvar)
)
;;;
;;;
;;;Archytas_Delian
;;;Solve the Delian problem by taking intersections of 3 solids
;;;	Torus, Cylinder & Cone
;;;
;;;
(defun c:Archytas_Delian()
	;draw base circle and generator line for Cone
	(setup_archytas)

;;;create a cylinder with color yellow(2)
	(alert "\nCreate a semi circle with diameter AC 
		\nand create extrusion in Z-direction")
	
	(setvar "CECOLOR" "2")
	(command "_.pline" pnt_az pnt_cz "_A" "_CE" pnt_oz pnt_az "")
	(setq semi_circle_1 (entlast))
	(command "_.extrude" semi_circle_1 "" cylinder_height  extrusion_angle)
		(setq cylinder_1 (entlast))
;;;Create a torus with zero inner radius
	(alert "\nCreate a quadrant of torus with zero inner radius
		\nby rotating a semi circle around Z-axis")

	(setvar "CECOLOR" "4")
	(command "_.pline" pnt_a pnt_c "_A" "_CE" pnt_o pnt_a "")
	(setq semi_circle_2 (entlast))
	(command "_.rotate3d" semi_circle_2 "" "2" pnt_a pnt_c 90.)
		(setq torus_base (entlast))
	(command "_.revolve" torus_base ""  "_O" zaxis_line 90.)
		(setq torus_1 (entlast))
;;;Create a right cone first on X-Y plane and rotate it 90 degrees
	;about the line connecting  points C & D so that the center line
	;will coincide with X-axis (line AC)
	(alert "\nCreate a cylinder whose generator line is AD")
	(setvar "CECOLOR" "6")	:magenta color
	(command "_.pline" pnt_a pnt_d pnt_c "cl")
		(setq cone_base (entlast))
	
	(command "_.revolve" cone_base "" "X" 360.)
	;(command "_.revolve" cone_base "" "X" 100.)
	(setq cone_1 (entlast))
	(setvar "CECOLOR" "1")	;color red
	;(alert "\nRotate this cone about line CD by 90 degrees")
	;(command "_.rotate3d" cone_1 "" "2" pnt_d pnt_c 360.)
	;shade this shademode Gouroud shading
	;(command "_.shade" )
	;Take union of 3 solids
	(alert "\nTake union of these 3 solids")
	(command "_.union" cylinder_1 torus_1 cone_1 "")
	;;;;result display
	;;;point of intersection is (set LUPREC=8)
	;;;X=0.79370053  Y=0.97848890  Z=0.96562987
	(setq 	pnt_p (list 0.79370053  0.97848890  0.96562987)
		pnt_m (list 0.79370053 0.97848890 0)
		pnt_n (inters pnt_a pnt_m pnt_b pnt_e)
		pnt_c_dash (pld pnt_a pnt_m 2.0)
		pnt_d_dash (list (car pnt_c_dash) (cadr pnt_c_dash) sqrt_3)
		dist_en (distance pnt_e pnt_n)
		dist_nb (distance pnt_n pnt_b)
		height_qn (sqrt (* dist_en dist_nb))
		pnt_q (list (car pnt_n) (cadr pnt_n) height_qn)
		pnt_ac_m (plt pnt_a pnt_c_dash 0.5)
		pnt_eb_m (plt pnt_e pnt_b 0.5)
	)
	;;;display grid symbol 
	(setvar "CECOLOR" "0")
	(command "_.point"  pnt_p )
	(command "_.point"  pnt_m )  
	(command "_.point"  pnt_b ) 
	(command "_.point"  pnt_a ) 
	(command "_.point"  pnt_q ) 
	(command "_.point"  pnt_n ) 
	(command "_.point"  pnt_c ) 
	(command "_.point"  pnt_e ) 
	(command "_.point"  pnt_c_dash ) 
	;draw two semi-circles and rotate them 90. degrees vertical to x-y plane
	(alert "\nDraw two semi-circles and rotate them 90 degrees")
	
	(command "_.arc" pnt_a "C" pnt_ac_m "A" 180.)
	(setq arc_1 (entlast))
	(command "_.rotate3d" arc_1 "" "2" pnt_c_dash pnt_a 90.)

	(command "_.arc" pnt_e "C" pnt_eb_m "A" 180.)
	(setq arc_2 (entlast))
	(command "_.rotate3d" arc_2 "" "2" pnt_b pnt_e 90.)

	;draw lines
	(setvar "CECOLOR" "8")
	(make_line_1 "0" 8 pnt_e pnt_b)
	(make_line_1 "0" 8 pnt_a pnt_c_dash)
	(make_line_1 "0" 8 pnt_q pnt_n)
	(make_line_1 "0" 8 pnt_p pnt_m)
	(make_line_1 "0" 8 pnt_a pnt_p)
	;;;display grid ID
	(setvar "CECOLOR" "0")
	(setq tx_height 0.20 tx_angle 35.)
	(textdisplay "A" '(-0.3153 -0.2512 0.0000) tx_height tx_angle)
	(textdisplay "B" '(0.5035   0.9521 0.0000) tx_height tx_angle)
	(textdisplay "C" '(2.2671  -0.1447 0.0000) tx_height tx_angle)
	(textdisplay "C'" '(1.3664  1.6613 0.0000) tx_height tx_angle)
	(textdisplay "D" '(1.6772   3.3245 0.0000) tx_height tx_angle)
	(textdisplay "E" '(0.8218  -1.0746 0.0000) tx_height tx_angle)
	(textdisplay "M" '(1.0811   0.8171 0.0000) tx_height tx_angle)
	(textdisplay "N" '(0.7051   0.4042 0.0000) tx_height tx_angle)
	(textdisplay "P" '(0.3457   1.5785 0.0000) tx_height tx_angle)
	(textdisplay "Q" '(0.0812   1.2347 0.0000) tx_height tx_angle)


	(reset_sysvar)
)
;;;
;;;
;;;Archytas_Delian_Model
;;;Show the Model used by Archytas in SOlving Delian Problem
;;;	Torus, Cylinder & Cone
;;;
;;;
(defun c:Archytas_Delian_Model()
	;draw base circle and generator line for Cone
	(setup_archytas)
	(setvar "ISOLINES" 500)
	;(command "_.vpoint"  '(-0.53425870 3.12255144 9.48554285))
	;create a cylinder with color yellow(2)
	(alert "\nCreate a semi circle with diameter AC 
		\nand create extrusion in Z-direction")
	
	(setvar "CECOLOR" "2")
	(command "_.pline" pnt_az pnt_cz "_A" "_CE" pnt_oz pnt_az "")
	(setq semi_circle_1 (entlast))
	(command "_.extrude" semi_circle_1 "" cylinder_height  extrusion_angle)
		(setq cylinder_1 (entlast))
	;Create a torus with zero inner radius
	(alert "\nCreate a quadrant of torus with zero inner radius
		\nby rotating a semi circle around Z-axis")

	(setvar "CECOLOR" "4")
	(command "_.pline" pnt_a pnt_c "_A" "_CE" pnt_o pnt_a "")
	(setq semi_circle_2 (entlast))
	(command "_.rotate3d" semi_circle_2 "" "2" pnt_a pnt_c 90.)
		(setq torus_base (entlast))
	(command "_.revolve" torus_base ""  "_O" zaxis_line 90.)
	;	(setq torus_1 (entlast))
	;Create a right cone first on X-Y plane and rotate it 90 degrees
	;about the line connecting  points C & D so that the center line
	;will coincide with X-axis (line AC)
	(alert "\nCreate a cylinder whose generator line is AD")
	(setvar "CECOLOR" "6")	'magenta color
	(command "_.pline" pnt_a pnt_d pnt_c "cl")
		(setq cone_base (entlast))
	
	(command "_.revolve" cone_base "" "X" 80.)
	(setq cone_1 (entlast))
	;(alert "\nRotate this cone about line CD by 90 degrees")
	;(command "_.rotate3d" cone_1 "" "2" pnt_d pnt_c 360.)
	;shade this shademode Gouroud shading
	;(command "_.shade" )
	;Take union of 3 solids
	




	(reset_sysvar)
)
;;;
;;;
(prompt "\nLoading setup_archytas")
;;;
(defun setup_archytas()
	(setup_sysvar)
	(setvar "FACETRES" 10)	;highest resolution
	(setvar "LUPREC" 8)	;highest precision 
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
	(setq 	sqrt_3 (sqrt 3.) 2_sqrt_3 (* 2. sqrt_3)
		cylinder_rad 1.0 torus_rad 1.0 tube_rad 1.0
		torus_center '(0 0 0) extrusion_angle 0.
		cylinder_height 2. cylinder_center '(1 0 0.01) 
		cone_base_rad 2_sqrt_3 cone_height 2.0
		pnt_a '(0 0 0) pnt_c '(2 0 0)
		
		pnt_b (list 0.5 (* 0.5 sqrt_3) 0) 
		pnt_d (list 2 2_sqrt_3 0)
		pnt_e (list 0.5 (* -0.5 sqrt_3) 0)
		pnt_o (list 1 0 0)
		pnt_zaxis '(0 0 1.5)
		pnt_dd (list 2 (- 2_sqrt_3) 0)
 	;;;these 3 points are used to create
	;;;a cylinder which does not have osculation problem
	;;;when UNION is taken with the torus.		
		pnt_az '(0 0 0.01) 
		pnt_cz '(2 0 0.01)	
		pnt_oz '(1 0 0.01)
	)
	(make_circle_1 "0" 8 pnt_o 1.0)	;base circle
	(make_line_1 "0" 8 pnt_a pnt_c)
	(make_line_1 "0" 0 pnt_a pnt_b)
	(make_line_1 "0" 8 pnt_b pnt_d)
	(make_line_1 "0" 8 pnt_c pnt_d)
	(make_line_1 "0" 0 pnt_a pnt_zaxis)
		(setq zaxis_line (entlast))
	;;;setup viewing angle
	(command "_.vpoint"  '(3.73135425 -3.92621277 4.49939932))
	(command "_.zoom" "_Extent")
	(command "_.regen")

);;;SETUP_ARCHYTAS

;;;
(prompt "\nLoading setup_archytas_base")
;;;
(defun setup_archytas_base()
	(setup_sysvar)
	(setvar "FACETRES" 10)	;highest resolution
	(setvar "LUPREC" 8)	;highest precision 
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -2)
	(setvar "ISOLINES" 24)
	(setq 	sqrt_3 (sqrt 3.) 2_sqrt_3 (* 2. sqrt_3)
		cylinder_rad 1.0 torus_rad 1.0 tube_rad 1.0
		torus_center '(0 0 0) extrusion_angle 0.
		cylinder_height 2. cylinder_center '(1 0 0.01) 
		cone_base_rad 2_sqrt_3 cone_height 2.0
		chr_size 0.25
		pnt_a '(0 0 0) pnt_c '(2 0 0)
		
		pnt_b (list 0.5 (* 0.5 sqrt_3) 0) 
		pnt_d (list 2 2_sqrt_3 0)
		pnt_e (list 0.5 (* -0.5 sqrt_3) 0)
		pnt_o (list 1 0 0)
		pnt_xaxis '(2.5 0 0)
		pnt_zaxis '(0 0 1.5)
		pnt_yaxis '(0 1.5 0)
		pnt_dd (list 2 (- 2_sqrt_3) 0)
 	;;;these 3 points are used to create
	;;;a cylinder which does not have osculation problem
	;;;when UNION is taken with the torus.		
		pnt_az '(0 0 0.01) 
		pnt_cz '(2 0 0.01)	
		pnt_oz '(1 0 0.01)
		pnt_ar '(8 0 0)
		pnt_ll '(7 -1 0)
		pnt_ur '(11 5 0)
	)
	(make_circle_1 "0" 8 pnt_o 1.0)	;base circle
	(make_line_1 "0" 0 pnt_a pnt_c)
	(make_line_1 "0" 0 pnt_a pnt_b)
	(make_line_1 "0" 8 pnt_b pnt_d)
	(make_line_1 "0" 8 pnt_c pnt_d)
	(make_line_1 "0" 8 pnt_c pnt_xaxis)
	(make_line_1 "0" 8 pnt_a pnt_yaxis)

	(make_line_1 "0" 8 pnt_a pnt_zaxis)
	
		(setq zaxis_line (entlast))
;;display node ID
	(textdisplay "A" (shift_pnt pnt_a '(-0.25 0) ) chr_size 0.)
	(textdisplay "B" (shift_pnt pnt_b '(-0.25 0) ) chr_size 0.)
	(textdisplay "C" pnt_c  chr_size 0.)
	(textdisplay "D" (shift_pnt pnt_d '(0 -0.25) ) chr_size 0.)
	(textdisplay "x" pnt_xaxis chr_size 0.)
	(textdisplay "y" pnt_yaxis chr_size 0.)
	;(textdisplay "z" '(-1.59377980  1.42524177  0.0) chr_size 0.)
	(textdisplay "z" '(0 0 2) chr_size 0.)
	;;;setup viewing angle
	(command "_.vpoint"  '(3.73135425 -3.92621277 4.49939932))

	(command "_.zoom" "_Extent")
	(command "_.regen")

);;;SETUP_ARCHYTAS_BASE
;;;
;;;------------------------draw components-----------------------------
;;;DRAW_Torus
;;;
(defun c:draw_torus( )
	(setup_archytas_base)
;;Create a torus with zero inner radius
	(alert "\nCreate a quadrant of torus with zero inner radius
		\nby rotating a semi circle around Z-axis")

	(setvar "CECOLOR" "4")
	(command "_.pline" pnt_a pnt_c "_A" "_CE" pnt_o pnt_a "")
	(setq semi_circle_2 (entlast))
;;rotate the semi circle 90 degrees, making it vertical to plane ABC
	(command "_.rotate3d" semi_circle_2 "" "2" pnt_a pnt_c 90.)
		(setq torus_base (entlast))
;;revolve this semi-circle 90 degrees around z-axiz into surface
	(command "_.revolve" torus_base ""  "_O" zaxis_line 90.)
		(setq torus_1 (entlast))
;;
;(command "_.vpoint"  '(3.73135425 -3.92621277 4.49939932))
	(reset_sysvar)

)
;;;
;;;
;;;DRAW_cylinder
;;;
(defun c:draw_cylinder( )
	(setup_archytas_base)
	(command "_.delay" 500)
;;create a cylinder with color yellow(2)
	(alert "\nCreate a semi circle with diameter AC 
		\nand create extrusion in Z-direction")
	
	(setvar "CECOLOR" "2")
	(command "_.pline" pnt_az pnt_cz "_A" "_CE" pnt_oz pnt_az "")
	(setq semi_circle_1 (entlast))
	(command "_.extrude" semi_circle_1 "" cylinder_height  extrusion_angle)
		(setq cylinder_1 (entlast))
	;(command "_.delay" 2000)
	;(alert "\nthen shade this")
	;(command "_.shademode" "G")
	(reset_sysvar)

)
;;;
;;;
;;;DRAW_cone
;;;
(defun c:draw_cone( )
	(setup_archytas_base)
;;;Create a right cone first on X-Y plane and rotate it 90 degrees
;;;about the line connecting  points C & D so that the center line
;;;will coincide with X-axis (line AC)
	(alert "\nCreate a cylinder whose generator line is AD")
	(setvar "CECOLOR" "6")	
;;:magenta color
	(command "_.pline" pnt_a pnt_d pnt_c "cl")
		(setq cone_base (entlast))
	
	(command "_.revolve" cone_base "" "X" 100.)
	(setq cone_1 (entlast))
	(reset_sysvar)

)
;;;
;;;
;;;------------------------draw components in two viewports-----------------------------
;;;Torus_2views
;;;
(defun c:torus_2views( )
	(setup_archytas_base)
;;Create a torus with zero inner radius
	(alert "\nCreate a quadrant of torus with zero inner radius
		\nby rotating a semi circle around Z-axis")

	(setvar "CECOLOR" "4")
	(command "_.pline" pnt_a pnt_c "_A" "_CE" pnt_o pnt_a "")
	(setq semi_circle_2 (entlast))
;;rotate the semi circle 90 degrees, making it vertical to plane ABC
	(command "_.rotate3d" semi_circle_2 "" "2" pnt_a pnt_c 90.)
		(setq torus_base (entlast))
;;revolve this semi-circle 90 degrees around z-axiz into surface
	(command "_.revolve" torus_base ""  "_O" zaxis_line 90.)
		(setq torus_1 (entlast))
;;;define selection set cylinder_zero
	(setq torus_zero (ssget "X"))

	(alert "\nSplit viewports into two.")
;;;open 2 viewports
	(command "_.vports" "2" "v")
	(alert "\nZoom using Object option")
	
	(setvar "CVPORT" 2)
	(command "_.zoom" "O" torus_zero "")
	(setvar "CVPORT" 3)
	(command "_.zoom" "O" torus_zero "")
	(command "_.shademode" "G")
	(reset_sysvar)

)
;;;
;;;
;;;cylinder_2views
;;;
(defun c:cylinder_2views( )
	(setup_archytas_base)
	(command "_.delay" 1000)
;;create a cylinder with color yellow(2)
	(alert "\nCreate a semi circle with diameter AC 
		\nand create extrusion in Z-direction")
	
	(setvar "CECOLOR" "2")
	(command "_.pline" pnt_az pnt_cz "_A" "_CE" pnt_oz pnt_az "")
	(setq semi_circle_1 (entlast))
	(command "_.extrude" semi_circle_1 "" cylinder_height  extrusion_angle)
		(setq cylinder_1 (entlast))
	;;;define selection set cylinder_zero
	(setq cylinder_zero (ssget "X"))

	(alert "\nSplit viewports into two.")
;;;open 2 viewports
	(command "_.vports" "2" "v")
	(alert "\nZoom using Object option")
	
	(setvar "CVPORT" 2)
	(command "_.zoom" "O" cylinder_zero "")
	(setvar "CVPORT" 3)
	(command "_.zoom" "O" cylinder_zero "")
	(command "_.shademode" "G")
	(reset_sysvar)

)
;;;
;;;
;;;cone_2views
;;;
(defun c:cone_2views( )
	(setup_archytas_base)
;;;Create a right cone first on X-Y plane and rotate it 90 degrees
;;;about the line connecting  points C & D so that the center line
;;;will coincide with X-axis (line AC)
	(alert "\nCreate a cylinder whose generator line is AD")
	(setvar "CECOLOR" "6")	
;;:magenta color
	(command "_.pline" pnt_a pnt_d pnt_c "cl")
		(setq cone_base (entlast))
	
	(command "_.revolve" cone_base "" "X" 100.)
	(setq cone_1 (entlast))
;;;define selection set cone_zero
	(setq cone_zero (ssget "X"))

	(alert "\nSplit viewports into two.")
;;;open 2 viewports
	(command "_.vports" "2" "v")
	(alert "\nZoom using Object option")
	
	(setvar "CVPORT" 2)
	(command "_.zoom" "O" cone_zero "")
	(setvar "CVPORT" 3)
	(command "_.zoom" "O" cone_zero "")
	(command "_.shademode" "G")
	(reset_sysvar)

)
;;;
;;;shade the vport #3 by Gouraud shading
;;;
;;;
(defun vp_shade(vp_target / old_cv)
	(setq old_cv (getvar "CVPORT"))
	(setvar "CVPORT" vp_target)
	(command "_.shademode" "G")
	(setvar "CVPORT" old_cv)

)
;;;;
;;;;