A-M baby
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19005 changed files with 197040 additions and 7 deletions
41
Task/Animate-a-pendulum/Factor/animate-a-pendulum.factor
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41
Task/Animate-a-pendulum/Factor/animate-a-pendulum.factor
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USING: accessors alarms arrays calendar colors.constants kernel
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locals math math.constants math.functions math.rectangles
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math.vectors opengl sequences system ui ui.gadgets ui.render ;
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IN: pendulum
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CONSTANT: g 9.81
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CONSTANT: l 20
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CONSTANT: theta0 0.5
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: current-time ( -- time ) nano-count -9 10^ * ;
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: T0 ( -- T0 ) 2 pi l g / sqrt * * ;
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: omega0 ( -- omega0 ) 2 pi * T0 / ;
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: theta ( -- theta ) current-time omega0 * cos theta0 * ;
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: relative-xy ( theta l -- xy )
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[ [ sin ] [ cos ] bi ]
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[ [ * ] curry ] bi* bi@ 2array ;
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: theta-to-xy ( origin theta l -- xy ) relative-xy v+ ;
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TUPLE: pendulum-gadget < gadget alarm ;
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: O ( gadget -- origin ) rect-bounds [ drop ] [ first 2 / ] bi* 0 2array ;
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: window-l ( gadget -- l ) rect-bounds [ drop ] [ second ] bi* ;
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: gadget-xy ( gadget -- xy ) [ O ] [ drop theta ] [ window-l ] tri theta-to-xy ;
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M: pendulum-gadget draw-gadget*
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COLOR: black gl-color
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[ O ] [ gadget-xy ] bi gl-line ;
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M:: pendulum-gadget graft* ( gadget -- )
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[ gadget relayout-1 ]
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20 milliseconds every gadget (>>alarm) ;
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M: pendulum-gadget ungraft* alarm>> cancel-alarm ;
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: <pendulum-gadget> ( -- gadget )
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pendulum-gadget new
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{ 500 500 } >>pref-dim ;
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: pendulum-main ( -- )
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[ <pendulum-gadget> "pendulum" open-window ] with-ui ;
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MAIN: pendulum-main
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33
Task/Animate-a-pendulum/HicEst/animate-a-pendulum-1.hicest
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Task/Animate-a-pendulum/HicEst/animate-a-pendulum-1.hicest
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REAL :: msec=10, Lrod=1, dBob=0.03, g=9.81, Theta(2), dTheta(2)
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BobMargins = ALIAS(ls, rs, ts, bs) ! box margins to draw the bob
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Theta = (1, 0) ! initial angle and velocity
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start_t = TIME()
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DO i = 1, 1E100 ! "forever"
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end_t = TIME() ! to integrate in real-time sections:
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DIFFEQ(Callback="pendulum", T=end_t, Y=Theta, DY=dTheta, T0=start_t)
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xBob = (SIN(Theta(1)) + 1) / 2
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yBob = COS(Theta(1)) - dBob
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! create or clear window and draw pendulum bob at (xBob, yBob):
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WINDOW(WIN=wh, LeftSpace=0, RightSpace=0, TopSpace=0, BottomSpace=0, Up=999)
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BobMargins = (xBob-dBob, 1-xBob-dBob, yBob-dBob, 1-yBob-dBob)
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WINDOW(WIN=wh, LeftSpace=ls, RightSpace=rs, TopSpace=ts, BottomSpace=bs)
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WRITE(WIN=wh, DeCoRation='EL=4, BC=4') ! flooded red ellipse as bob
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! draw the rod hanging from the center of the window:
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WINDOW(WIN=wh, LeftSpace=0.5, TopSpace=0, RightSpace=rs+dBob)
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WRITE(WIN=wh, DeCoRation='LI=0 0; 1 1, FC=4.02') ! red pendulum rod
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SYSTEM(WAIT=msec)
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start_t = end_t
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ENDDO
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END
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SUBROUTINE pendulum ! Theta" = - (g/Lrod) * SIN(Theta)
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dTheta(1) = Theta(2) ! Theta' = Theta(2) substitution
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dTheta(2) = -g/Lrod*SIN(Theta(1)) ! Theta" = Theta(2)' = -g/Lrod*SIN(Theta(1))
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END
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93
Task/Animate-a-pendulum/HicEst/animate-a-pendulum-2.hicest
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Task/Animate-a-pendulum/HicEst/animate-a-pendulum-2.hicest
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import gui
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$include "guih.icn"
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# some constants to define the display and pendulum
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$define HEIGHT 400
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$define WIDTH 500
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$define STRING_LENGTH 200
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$define HOME_X 250
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$define HOME_Y 21
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$define SIZE 30
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$define START_ANGLE 80
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class WindowApp : Dialog ()
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# draw the pendulum on given context_window, at position (x,y)
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method draw_pendulum (x, y)
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# reference to current screen area to draw on
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cw := Clone(self.cwin)
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# clear screen
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WAttrib (cw, "bg=grey")
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EraseRectangle (cw, 0, 0, WIDTH, HEIGHT)
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# draw the display
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WAttrib (cw, "fg=dark gray")
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DrawLine (cw, 10, 20, WIDTH-20, 20)
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WAttrib (cw, "fg=black")
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DrawLine (cw, HOME_X, HOME_Y, x, y)
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FillCircle (cw, x, y, SIZE+2)
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WAttrib (cw, "fg=yellow")
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FillCircle (cw, x, y, SIZE)
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# free reference to screen area
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Uncouple (cw)
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end
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# find the average of given two arguments
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method avg (a, b)
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return (a + b) / 2
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end
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# this method gets called by the ticker
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# it computes the next position of the pendulum and
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# requests a redraw
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method tick ()
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static x, y
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static theta := START_ANGLE
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static d_theta := 0
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# update x,y of pendulum
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scaling := 3000.0 / (STRING_LENGTH * STRING_LENGTH)
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# -- first estimate
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first_dd_theta := -(sin (dtor (theta)) * scaling)
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mid_d_theta := d_theta + first_dd_theta
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mid_theta := theta + avg (d_theta, mid_d_theta)
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# -- second estimate
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mid_dd_theta := - (sin (dtor (mid_theta)) * scaling)
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mid_d_theta_2 := d_theta + avg (first_dd_theta, mid_dd_theta)
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mid_theta_2 := theta + avg (d_theta, mid_d_theta_2)
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# -- again first
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mid_dd_theta_2 := -(sin (dtor (mid_theta_2)) * scaling)
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last_d_theta := mid_d_theta_2 + mid_dd_theta_2
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last_theta := mid_theta_2 + avg (mid_d_theta_2, last_d_theta)
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# -- again second
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last_dd_theta := - (sin (dtor (last_theta)) * scaling)
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last_d_theta_2 := mid_d_theta_2 + avg (mid_dd_theta_2, last_dd_theta)
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last_theta_2 := mid_theta_2 + avg (mid_d_theta_2, last_d_theta_2)
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# -- update stored angles
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d_theta := last_d_theta_2
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theta := last_theta_2
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# -- update x, y
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pendulum_angle := dtor (theta)
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x := HOME_X + STRING_LENGTH * sin (pendulum_angle)
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y := HOME_Y + STRING_LENGTH * cos (pendulum_angle)
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# draw pendulum
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draw_pendulum (x, y)
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end
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# set up the window
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method component_setup ()
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# some cosmetic settings for the window
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attrib("size="||WIDTH||","||HEIGHT, "bg=light gray", "label=Pendulum")
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# make sure we respond to window close event
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connect (self, "dispose", CLOSE_BUTTON_EVENT)
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# start the ticker, to update the display periodically
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self.set_ticker (20)
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end
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end
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procedure main ()
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w := WindowApp ()
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w.show_modal ()
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end
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44
Task/Animate-a-pendulum/J/animate-a-pendulum.j
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Task/Animate-a-pendulum/J/animate-a-pendulum.j
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require 'gl2 trig'
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coinsert 'jgl2'
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DT =: %30 NB. seconds
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ANGLE=: 0.25p1 NB. radians
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L =: 1 NB. metres
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G =: 9.80665 NB. ms_2
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VEL =: 0 NB. ms_1
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PEND=: noun define
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pc pend;pn "Pendulum";
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xywh 0 0 320 200;cc isi isigraph rightmove bottommove;
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pas 0 0;pcenter;
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rem form end;
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)
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pend_run =: verb def ' wd PEND,'';pshow;timer '',":DT * 1000 '
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pend_close =: verb def ' wd ''timer 0; pclose'' '
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pend_isi_paint=: verb def ' drawPendulum ANGLE '
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sys_timer_z_=: verb define
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recalcAngle ''
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wd 'psel pend; setinvalid isi'
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)
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recalcAngle=: verb define
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accel=. - (G % L) * sin ANGLE
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VEL =: VEL + accel * DT
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ANGLE=: ANGLE + VEL * DT
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)
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drawPendulum=: verb define
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width=. {. glqwh''
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ps=. (-: width) , 40
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pe=. ps + 280 <.@* (cos , sin) 0.5p1 + y NB. adjust orientation
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glrgb 91 91 91
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glbrush''
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gllines ps , pe
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glellipse (,~ ps - -:) 40 15
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glellipse (,~ pe - -:) 20 20
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glrect 0 0 ,width, 40
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)
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pend_run'' NB. run animation
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nomainwin
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WindowWidth = 400
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WindowHeight = 300
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open "Pendulum" for graphics_nsb_nf as #main
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#main "down;fill white; flush"
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#main "color black"
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#main "trapclose [quit.main]"
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Angle = asn(1)
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DeltaT = 0.1
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PendLength = 150
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FixX = int(WindowWidth / 2)
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FixY = 40
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timer 30, [swing]
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wait
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[swing]
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#main "cls"
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#main "discard"
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PlumbobX = FixX + int(sin(Angle) * PendLength)
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PlumbobY = FixY + int(cos(Angle) * PendLength)
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AngAccel = -9.81 / PendLength * sin(Angle)
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AngVelocity = AngVelocity + AngAccel * DeltaT
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Angle = Angle + AngVelocity * DeltaT
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#main "backcolor black"
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#main "place ";FixX;" ";FixY
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#main "circlefilled 3"
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#main "line ";FixX;" ";FixY;" ";PlumbobX;" ";PlumbobY
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#main "backcolor red"
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#main "circlefilled 10"
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wait
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[quit.main]
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close #main
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end
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29
Task/Animate-a-pendulum/Logo/animate-a-pendulum.logo
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Task/Animate-a-pendulum/Logo/animate-a-pendulum.logo
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make "angle 45
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make "L 1
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make "bob 10
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to draw.pendulum
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clearscreen
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seth :angle+180 ; down on screen is 180
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forward :L*100-:bob
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penup
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forward :bob
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pendown
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arc 360 :bob
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end
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make "G 9.80665
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make "dt 1/30
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make "acc 0
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make "vel 0
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to step.pendulum
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make "acc -:G / :L * sin :angle
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make "vel :vel + :acc * :dt
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make "angle :angle + :vel * :dt
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wait :dt*60
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draw.pendulum
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end
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hideturtle
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until [key?] [step.pendulum]
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freq = 8; length = freq^(-1/2);
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Animate[Graphics[
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List[{Line[{{0, 0}, length {Sin[T], -Cos[T]}} /. {T -> (Pi/6) Cos[2 Pi freq t]}], PointSize[Large],
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Point[{length {Sin[T], -Cos[T]}} /. {T -> (Pi/6) Cos[2 Pi freq t]}]}],
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PlotRange -> {{-0.3, 0.3}, {-0.5, 0}}], {t, 0, 1}, AnimationRate -> 0.07]
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