Tracé d'arc de cercle par l'algorithme de Bresenham
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Tracé d'arc de cercle par l'algorithme de Bresenham
- Code:
rem ============================================================================
rem Tracé d arc de cercle par l algorithme de Bresenham
rem ============================================================================
Init()
Demo()
end
rem ============================================================================
SUB Init()
dim xc,yc,where_x,where_y,p
width 0,800 : height 0, 600
top 0,(screen_y - height(0))/2 : left 0,(screen_x - width(0))/2
color 0,0,0,255 : 2d_pen_color 255,0,0 : font_color 0,255,255,255 : font_bold 0
xc = width(0)/2 : yc = height(0)/2 : p = 3000
END_SUB
rem ============================================================================
SUB Demo()
Les_8_Octants() : pause p : cls
Demo_1() : pause p : cls
Demo_2() : pause p : cls
Demo_3() : pause p : cls
Demo_4() : pause p : cls
Demo_5() : pause p : cls
Demo_6() : pause p : cls
Demo_7() : pause p : cls
Alphabet() : pause p : cls
Bonhommes() : pause p : cls
Texte(50,50,20)
Bonhomme(100,400,10) : Bonhomme(250,400,8) : Bonhomme(350,400,5)
Bonhomme(400,400,3) : Bonhomme(430,400,2) : Bonhomme(450,400,1)
caption 0,"terminé"
END_SUB
rem ============================================================================
' Tracer un arc de cercle : un huitième de cercle
' x_centre,y_centre : coordonnées du centre du cercle
' rayon : rayon du cercle
' octant : numéro de l'octant de 1 à 8 dans le sens trigonométrique
' octant = 1 : angle compris entre 0 et pi/4 rad soit entre 0° et 45°
' octant = 2 : angle compris entre pi/4 et pi/2 rad soit entre 45° et 90°
' octant = 3 : angle compris entre pi/2 et 3*pi/4 rad soit entre 90° et 135°
' octant = 4 : angle compris entre 3*pi/4 et pi rad soit entre 135° et 180°
' octant = 5 : angle compris entre pi et 5*pi/4 rad soit entre 180° et 225°
' octant = 6 : angle compris entre 5*pi/4 et 3*pi/2 rad soit entre 225° et 270°
' octant = 7 : angle compris entre 3*pi/2 et 7*pi/4 rad soit entre 270° et 315°
' octant = 8 : angle compris entre 7*pi/4 et 2*pi rad soit entre 315° et 360°
SUB Tracer_Octant(x_centre,y_centre,rayon,octant)
dim_local x, y, m, xp, yp
x = 0 : y = rayon : m = 5 - 4*rayon
while x <= y
select octant
case 1 : xp = x_centre + y : yp = y_centre - x
case 2 : xp = x_centre + x : yp = y_centre - y
case 3 : xp = x_centre - x : yp = y_centre - y
case 4 : xp = x_centre - y : yp = y_centre - x
case 5 : xp = x_centre - y : yp = y_centre + x
case 6 : xp = x_centre - x : yp = y_centre + y
case 7 : xp = x_centre + x : yp = y_centre + y
case 8 : xp = x_centre + y : yp = y_centre + x
end_select
2d_point xp,yp
if m > 0 then y = y - 1 : m = m - 8 * y
x = x + 1 : m = m + 8 * x + 4
end_while
where_x = xp : where_y = yp
END_SUB
rem ============================================================================
SUB Les_8_Octants()
dim_local i,j
print_locate xc-100,50 : print "Les 8 octants d'un cercle"
Cercle(xc,yc,100) : j = 9
for i = 0 to 2*pi step pi/4 : 2d_line xc,yc,xc+100*cos(i),yc+100*sin(i) : next i
for i = pi/8 to 2*pi step pi/4
j = j-1 : print_locate xc+120*cos(i),yc+120*sin(i) : print j
next i
END_SUB
rem ============================================================================
SUB Demo_1()
dim_local i,j
for j = 1 to height(0) step 150
for i = 1 to width(0) step 100 : carreau(50+i,50+j,50,1,255,255,0) : next i
next j
END_SUB
rem ----------------------------------------------------------------------------
SUB Demo_2()
Carreau(xc,yc,yc-100,1,255,0,0)
Carreau(100,100,100,1,255,255,0)
Carreau(500,100,50,1,255,255,0)
Carreau(200,300,20,1,255,255,0)
END_SUB
rem ----------------------------------------------------------------------------
SUB Demo_3()
dim_local i,j
for i = 10 to 150 step 4 : Carreau(xc,yc,i,1,255,255,0) : next i
Cercle(xc,yc-150,25) : cercle(xc,yc+150,25) : ' tracer cercle par 8 octants
2d_circle xc-200,yc,50 : 2d_circle xc+200,yc,50 : ' tracer cercle par 2d_circle
END_SUB
rem ----------------------------------------------------------------------------
SUB Demo_4()
dim_local r
r = 30
Carreau(4*r,yc,3*r,1,255,255,0)
Trefle(10*r,yc,r,1,255,255,0)
Coeur(15*r,yc,r,1,255,255,0)
Pique(20*r,yc,r,1,255,255,0)
END_SUB
rem ----------------------------------------------------------------------------
SUB Demo_5()
dim_local x,y,r
r = 25
for x = 100 to 2*xc-4*r step 4*r
for y = 2*r to 2*yc step 4*r+10 : Frise_1(x,y,r,1,255,0,0) : next y
next x
for x = 100 to 2*xc-8*r step 4*r
for y = 2*r to 2*yc step 4*r+10 : 2d_flood x+2*r,y,255,255,0 : next y
next x
END_SUB
rem ============================================================================
SUB Demo_6()
dim_local x,y,r
r = 20
for x = 0 to 2*xc step 2*r
for y = 0 to 2*yc step 2*r : Frise_2(x,y,r) : next y
next x
END_SUB
rem ============================================================================
SUB Demo_7()
dim_local x,y,r,r1
r = 30
for x = r to 2*xc step 2*r
r1 = 1-r1
for y = r to 2*yc step 2*r : Balle(x,y,r+r1) : next y
next x
pause p : cls
for r = 20 to yc/2 step 5 : cls : Balle(xc,yc,r) : pause 500 : next r
END_SUB
rem ============================================================================
' Tracé d'un cercle par octant
' Pour obtenir un cercle complet, on trace les 8 octants
SUB Cercle(x,y,r)
dim_local i
for i = 1 to 8 : Tracer_Octant(x,y,r,i) : next i
END_SUB
rem ============================================================================
' Tracé d'un carreau par combinaison d'octants
' Chaque branche est constituée par 2 octants (soit un quart de cercle)
' x,y : coordonnées du centre du carreau
' r : rayon
' p : si p > 0 , le carreau est rempli de la couleur cr,cg,cb
SUB Carreau(x,y,r,p,cr,cg,cb)
dim_local i
for i = 7 to 8 : Tracer_Octant(x-r,y-r,r,i) : next i
for i = 5 to 6 : Tracer_Octant(x+r,y-r,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x-r,y+r,r,i) : next i
for i = 3 to 4 : Tracer_Octant(x+r,y+r,r,i) : next i
if p > 0 then 2d_flood x,y,cr,cg,cb
END_SUB
rem ============================================================================
SUB Trefle(x,y,r,p,cr,cg,cb)
dim_local i,r1,x1,y1 : r1 = sqr(2)
for i = 1 to 5 : Tracer_Octant(x,y-r1*r,r,i) : next i
for i = 2 to 7 : Tracer_Octant(x-r1*r,y,r,i) : next i
for i = 1 to 3 : Tracer_Octant(x+r1*r,y,r,i) : next i
for i = 6 to 8 : Tracer_Octant(x+r1*r,y,r,i) : next i
Tracer_Octant(x,y-r1*r,r,8)
Tracer_Octant(x-r1*r,y+r1*r,r,1)
Tracer_Octant(x+r1*r,y+r1*r,r,4)
Tracer_Octant(x-r1*r,y+r1*r,r,8) : x1 = where_x : y1 = where_y
Tracer_Octant(x+r1*r,y+r1*r,r,5) : 2d_line where_x,where_y,x1,y1
if p > 0 then 2d_flood x,y,cr,cg,cb
END_SUB
rem ============================================================================
SUB Coeur(x,y,r,p,cr,cg,cb)
dim_local i
for i = 1 to 6 : Tracer_Octant(x-r,y,r,i) : next i
for i = 1 to 4 : Tracer_Octant(x+r,y,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x+r,y,r,i) : next i
for i = 3 to 4 : Tracer_Octant(x+r,y+2*r,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x-r,y+2*r,r,i) : next i
if p > 0 then 2d_flood x,y+2,cr,cg,cb
END_SUB
rem ============================================================================
SUB Pique(x,y,r,p,cr,cg,cb)
dim_local i
for i = 3 to 6 : Tracer_Octant(x-r,y,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x+r,y,r,i) : next i
for i = 7 to 8
Tracer_Octant(x+r,y,r,i) : Tracer_Octant(x-r,y+r,r,i)
Tracer_Octant(x-r,y-2*r,r,i)
next i
for i = 5 to 6
Tracer_Octant(x+r,y-2*r,r,i) : Tracer_Octant(x+r,y+r,r,i)
next i
2d_line x-r,y+r,x+r,y+r : 2d_line x-r,y+2*r,x+r,y+2*r
if p > 0 then 2d_flood x,y,cr,cg,cb: 2d_flood x,y+2*r-2,cr,cg,cb
END_SUB
rem ============================================================================
SUB Frise_1(x,y,r,p,cr,cg,cb)
dim_local i
2d_pen_color 0,0,254
for i = 1 to 4 : Tracer_Octant(x,y,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x,y,r,i) : next i
for i = 3 to 8 : Tracer_Octant(x,y+2*r,r,i) : next i
for i = 1 to 6 : Tracer_Octant(x+2*r,y,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x+2*r,y+2*r,r,i) : next i
for i = 5 to 8 : Tracer_Octant(x+2*r,y+2*r,r,i) : next i
if p > 0 then 2d_flood x,y+2*r,cr,cg,cb
END_SUB
rem ============================================================================
SUB Frise_2(x,y,r)
dim_local i
2d_pen_color 255,0,0
for i = 3 to 4 : Tracer_Octant(x,y,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x+r,y,r,i) : next i
2d_line x,y-r,x+r,y-r
for i = 5 to 6 : Tracer_Octant(x,y+r,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x+r,y+r,r,i) : next i
2d_line x,y+2*r,x+r,y+2*r : 2d_line x-r,y,x-r,y+r : 2d_line x+2*r,y,x+2*r,y+r
END_SUB
rem ============================================================================
SUB Balle(x,y,r)
dim_local i,r1
r1 = int(r/2)
for i = 1 to 8 : Tracer_Octant(x,y,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x,y-r1,r1,i) : next i
for i = 7 to 8 : Tracer_Octant(x,y-r1,r1,i) : next i
for i = 3 to 6 : Tracer_Octant(x,y+r1,r1,i) : next i
for i = 1 to 4 : Tracer_Octant(x-r1,y,r1,i) : next i
for i = 5 to 8 : Tracer_Octant(x+r1,y,r1,i) : next i
if odd(r) = 1
2d_flood x,y-r1,255,255,000 : 2d_flood x,y+r1,255,255,000
2d_flood x-r1,y,255,000,000 : 2d_flood x+r1,y,255,000,000
else
2d_flood x,y-r1,255,000,000 : 2d_flood x,y+r1,255,000,000
2d_flood x-r1,y,255,255,000 : 2d_flood x+r1,y,255,255,000
end_if
END_SUB
rem ============================================================================
SUB Alphabet()
A(050,100,20) : B(100,100,20) : C(150,100,20) : D(200,100,20) : E(250,100,20)
F(300,100,20) : G(350,100,20) : H(400,100,20) : I(450,100,20) : J(500,100,20)
K(550,100,20) : L(600,100,20) : M(650,100,20) : N(050,200,20) : O(100,200,20)
P(150,200,20) : Q(200,200,20) : R(250,200,20) : S(300,200,20) : T(350,200,20)
U(400,200,20) : V(450,200,20) : W(500,200,20) : X(550,200,20) : Y(600,200,20)
Z(650,200,20)
END_SUB
rem ============================================================================
SUB A(x,y,r)
dim_local i
for i = 1 to 4 : Tracer_Octant(x+r,y+r,r,i) : next i
2d_line x,y+r,x,y+4*r : 2d_line x+2*r,y+r,x+2*r,y+4*r : 2d_line x,y+2*r,x+2*r,y+2*r
END_SUB
rem ============================================================================
SUB B(x,y,r)
dim_local i
2d_poly_from x+r,y : 2d_poly_to x,y : 2d_poly_to x,y+4*r
2d_poly_to x+r,y+4*r : 2d_line x,y+2*r,x+r,y+2*r
for i = 1 to 2 : Tracer_Octant(x+r,y+r,r,i) : Tracer_Octant(x+r,y+3*r,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x+r,y+r,r,i) : Tracer_Octant(x+r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB C(x,y,r)
dim_local i
for i = 1 to 4 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 5 to 8 : Tracer_Octant(x+r,y+3*r,r,i) : next i
2d_line x,y+r,x,y+3*r
END_SUB
rem ============================================================================
SUB D(x,y,r)
dim_local i
2d_poly_from x+r,y : 2d_poly_to x,y : 2d_poly_to x,y+4*r :2d_poly_to x+r,y+4*r
for i = 1 to 2 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x+r,y+3*r,r,i) : next i
2d_line x+2*r,y+r,x+2*r,y+3*r
END_SUB
rem ============================================================================
SUB E(x,y,r)
dim_local i
2d_poly_from x+2*r,y : 2d_poly_to x,y : 2d_poly_to x,y+4*r
2d_poly_to x+2*r,y+4*r : 2d_line x,y+2*r,x+r,y+2*r
END_SUB
rem ============================================================================
SUB F(x,y,r)
dim_local i
2d_poly_from x+2*r,y : 2d_poly_to x,y : 2d_poly_to x,y+4*r
2d_line x,y+2*r,x+r,y+2*r
END_SUB
rem ============================================================================
SUB G(x,y,r)
dim_local i
for i = 1 to 4 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 5 to 8 : Tracer_Octant(x+r,y+3*r,r,i) : next i
2d_line x,y+r,x,y+3*r : 2d_line x+r,y+2*r,x+2*r,y+2*r : 2d_poly_to x+2*r,y+3*r
END_SUB
rem ============================================================================
SUB H(x,y,r)
2d_line x,y,x,y+4*r : 2d_line x+2*r,y,x+2*r,y+4*r : 2d_line x,y+2*r,x+2*r,y+2*r
END_SUB
rem ============================================================================
SUB I(x,y,r)
2d_line x,y,x+2*r,y : 2d_line x,y+4*r,x+2*r,y+4*r: 2d_line x+r,y,x+r,y+4*r
END_SUB
rem ============================================================================
SUB J(x,y,r)
dim_local i
2d_line x,y,x+2*r,y :2d_poly_to x+2*r,y+3*r
for i= 5 to 8 : Tracer_Octant(x+r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB K(x,y,r)
dim_local i
2d_line x,y,x,y+4*r
for i = 3 to 4 : Tracer_Octant(x+2*r,y+r,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x,y+r,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x,y+3*r,r,i) : next i
for i = 5 to 6 : Tracer_Octant(x+2*r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB L(x,y,r)
2d_poly_from x,y : 2d_poly_to x,y+4*r : 2d_poly_to x+2*r,y+4*r
END_SUB
rem ============================================================================
SUB M(x,y,r)
dim_local i
for i = 5 to 8 : Tracer_Octant(x+r,y,r,i) : next i
2d_line x,y,x,y+4*r : 2d_line x+2*r,y,x+2*r,y+4*r
END_SUB
rem ============================================================================
SUB N(x,y,r)
dim_local i
2d_line x,y,x,y+4*r : 2d_line x+2*r,y,x+2*r,y+4*r
for i = 1 to 2 : Tracer_Octant(x,y+r,r,i) : next i
for i = 5 to 6 : Tracer_Octant(x+2*r,y+r,r,i) : next i
END_SUB
rem ============================================================================
SUB O(x,y,r)
dim_local i
for i = 1 to 4 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 5 to 8 : Tracer_Octant(x+r,y+3*r,r,i) : next i
2d_line x,y+r,x,y+3*r : 2d_line x+2*r,y+r,x+2*r,y+3*r
END_SUB
rem ============================================================================
SUB P(x,y,r)
dim_local i
for i = 1 to 2 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x+r,y+r,r,i) : next i
2d_poly_from x+r,y : 2d_poly_to x,y
2d_poly_to x,y+4*r : 2d_line x,y+2*r,x+r,y+2*r
END_SUB
rem ============================================================================
SUB Q(x,y,r)
dim_local i
for i = 1 to 4 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 5 to 8 : Tracer_Octant(x+r,y+3*r,r,i) : next i
2d_line x,y+r,x,y+3*r : 2d_line x+2*r,y+r,x+2*r,y+3*r
for i = 5 to 6 : Tracer_Octant(x+2*r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB R(x,y,r)
dim_local i
2d_poly_from x+r,y : 2d_poly_to x,y : 2d_poly_to x,y+4*r : 2d_line x,y+2*r,x+r,y+2*r
for i = 1 to 2 : Tracer_Octant(x+r,y+r,r,i) : Tracer_Octant(x+r,y+3*r,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x+r,y+r,r,i) : next i
2d_line x+2*r,y+3*r,x+2*r,y+4*r
END_SUB
rem ============================================================================
SUB S(x,y,r)
dim_local i
for i = 1 to 6 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x+r,y+3*r,r,i) : next i
for i = 5 to 8 : Tracer_Octant(x+r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB T(x,y,r)
2d_line x,y,x+2*r,y : 2d_line x+r,y,x+r,y+4*r
END_SUB
rem ============================================================================
SUB U(x,y,r)
dim_local i
for i = 5 to 8 : Tracer_Octant(x+r,y+3*r,r,i) : next i
2d_line x,y,x,y+3*r : 2d_line x+2*r,y,x+2*r,y+3*r
END_SUB
rem ============================================================================
SUB V(x,y,r)
dim_local i
2d_line x,y,x,y+3*r : 2d_line x+2*r,y,x+2*r,y+3*r
for i = 1 to 2 : Tracer_Octant(x,y+4*r,r,i) : next i
for i = 3 to 4 : Tracer_Octant(x+2*r,y+4*r,r,i) : next i
END_SUB
rem ============================================================================
SUB W(x,y,r)
dim_local i
2d_line x,y,x,y+4*r : 2d_line x+2*r,y,x+2*r,y+4*r
for i = 7 to 8 : Tracer_Octant(x,y+3*r,r,i) : next i
for i = 5 to 6 : Tracer_Octant(x+2*r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB X(x,y,r)
dim_local i
2d_line x,y,x,y+r : 2d_line x+2*r,y,x+2*r,y+r
2d_line x,y+3*r,x,y+4*r : 2d_line x+2*r,y+3*r,x+2*r,y+4*r
for i = 5 to 8 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 1 to 4 : Tracer_Octant(x+r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB Y(x,y,r)
dim_local i
2d_line x,y,x,y+r : 2d_line x+2*r,y,x+2*r,y+3*r
for i = 5 to 8 : Tracer_Octant(x+r,y+r,r,i) : Tracer_Octant(x+r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB Z(x,y,r)
dim_local i
2d_line x,y,x+2*r,y : 2d_poly_to x+2*r,y+r
2d_line x,y+3*r,x,y+4*r : 2d_poly_to x+2*r,y+4*r
for i = 7 to 8 : Tracer_Octant(x+r,y+r,r,i) : next i
for i = 3 to 4 : Tracer_Octant(x+r,y+3*r,r,i) : next i
END_SUB
rem ============================================================================
SUB Bonhommes()
Bonhomme(100,50,30) : Bonhomme(300,50,20) : Bonhomme(450,50,15)
Bonhomme(550,50,10) : Bonhomme(620,50,05) : Bonhomme(660,50,02)
Bonhomme(680,50,01)
END_SUB
rem ============================================================================
SUB Bonhomme(x,y,r)
dim_local i
for i = 1 to 4 : Tracer_Octant(x,y,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x-2*r,y,r,i) : next i
for i = 5 to 6 : Tracer_Octant(x+2*r,y,r,i) : next i
2d_line x-2*r,y+r,x+2*r,y+r
2d_line x-r,y+r,x-r,y+2*r : 2d_line x+r,y+r,x+r,y+2*r
for i = 5 to 8 : Tracer_Octant(x,y+2*r,r,i) : next i
2d_line x-2*r,y+3*r,x+2*r,y+3*r
for i = 3 to 4 : Tracer_Octant(x-2*r,y+4*r,r,i) : next i
for i = 1 to 2 : Tracer_Octant(x+2*r,y+4*r,r,i) : next i
2d_line x-3*r,y+4*r,x-3*r,y+10*r : 2d_poly_to x-2*r,y+10*r
2d_line x+3*r,y+4*r,x+3*r,y+10*r : 2d_poly_to x+2*r,y+10*r
for i = 5 to 6 : Tracer_Octant(x-2*r,y+10*r,r,i) : next i
for i = 7 to 8 : Tracer_Octant(x+2*r,y+10*r,r,i) : next i
2d_line x-2*r,y+6*r,x-2*r,y+15*r : 2d_line x+2*r,y+6*r,x+2*r,y+15*r
2d_line x-2*r,y+9*r,x+2*r,y+9*r
2d_line x,y+9*r,x,y+15*r
2d_line x-2*r,y+15*r,x+2*r,y+15*r
for i = 5 to 8 : Tracer_Octant(x-r,y+15*r,r,i) : Tracer_Octant(x+r,y+15*r,r,i) : next i
END_SUB
rem ============================================================================
SUB Texte(x,y,r)
dim_local s,x1, y1 ,y2
s = 3*r : y1 = y + 4*r+10 : y2 = y+10*r : x1 = x+6*r
P(x,y,r) : A(x+s,y,r) : N(x+2*s,y,r) : O(x+3*s,y,r) : R(x+4*s,y,r)
A(x+5*s,y,r) : M(x+6*s,y,r) : I(x+7*s,y,r) : C(x+8*s,y,r)
E(x1,y1,r) : C(x1+s,y1,r) : R(x1+2*s,y1,r) : I(x1+3*s,y1,r) : T(x1+4*s,y1,r)
P(x,y2,r) : A(x+s,y2,r) : R(x+2*s,y2,r)
O(x+4*s,y2,r) : C(x+5*s,y2,r) : T(x+6*s,y2,r) : A(x+7*s,y2,r)
N(x+8*s,y2,r) : T(x+9*s,y2,r) : S(x+10*s,y2,r)
END_SUB
rem ==========================================================================
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