! this still needs a head on the velocity vector
! circle center cursor text in magenta??
! color code equations to show sum of line and circle


!! File: CycloidCurves
!! August 25, 2003 Hubert Hohn

PUBLIC PCFlag,Mac5Flag,M68KFlag,UnixFlag,xmax,ymax
PUBLIC toolLft,toolRgt,toolBas,toolTop,toolhdr,toolHgt,toolWid  ! tool boundaries
PUBLIC winLft,winRgt,winBas,winTop,winHgt,winWid      ! window
PUBLIC workLft,workRgt,workBas,workTop,workMidx  ! work area
PUBLIC backclr,black,drkgry,drkmid,midgry,litmid,litgry,white
PUBLIC red,yellow,green,cyan,blue,magenta,pink,colorscheme
PUBLIC planeclr,gridclr,rimclr,axisclr,axislabelclr,titleclr,rightsclr
PUBLIC numberlineclr,slotdrkclr,slotlgtclr,slideclr
PUBLIC largefonts, title$, SLUmode

LET toolHgt= 560
LET toolWid= 780
LET window$= "The d'Arbeloff Interactive Math Project"
LET colorscheme= 0

LET title$ = "Cycloid Curves"

SUB ThisProgram
    CALL TrochoidCurves
    CLEAR
END SUB


!! ---------------------------------------------------------
!! ------ Start TB4 Mac Header and Subs ------

!LET M68KFlag = 1
!LIBRARY "MacTools*", "HHLib.trc"
!ASK PIXELS winWid,winHgt
!LET winLft= 0
!LET winTop= 0
!LET winRgt= winWid-1
!LET winBas= winHgt-1
!SET WINDOW 0,winRgt,winBas,0
!CALL Palette
!CLEAR
!
!CALL ToolPanel
!CALL ThisProgram
!
!END
!EXTERNAL
!
!MODULE Mac4Parts
!    SUB SetTextFont(font,size,style$)
!        CALL MacTextFont(font)
!        CALL MacTextSize(size)
!        CALL MacTextFace(style$)
!    END SUB
!
!    SUB StringWidth(sw$,sl)
!        DECLARE DEF MacStringWidth
!        LET sl= MacStringWidth(sw$)
!    END SUB
!
!    SUB SetLineWeight(wgt)
!        CALL MacPenSize(wgt,wgt)
!    END SUB
!
!    SUB BoxDisk(Lft,Rgt,Bas,Top)
!        CALL MacPaintOval(Lft,Rgt,Bas,Top)
!    END SUB
!END MODULE

!! --- End TB4 Mac Header and Subs ---
!!---------------------------------------------------------
!!--- Start TB5 Cross-Platform header and subs ---

LIBRARY "c:\TB Gold\TBLibs\TrueCtrl.trc"     ! windows
LIBRARY "c:\TB Gold\TBLibs\HHLib.trc"

!LIBRARY ":TBLibs:TrueCtrl.trc"                   ! macintosh
!LIBRARY "HHLib.trc"
!
PUBLIC WinID
DECLARE PUBLIC OBJM_SET,OBJM_SYSINFO
LET winHgt= toolHgt
LET winWid= toolWid
DIM values(1)

CALL TC_Init

CALL Object(OBJM_SYSINFO,WinID,"MACHINE",system$,values())
IF system$="MAC" then
   LET Mac5Flag= 1
ELSE IF system$="WIN32" then
   LET PCFlag  = 1
END IF

CALL TC_SetUnitsToPixels                         ! 5.1 and up needs this
CALL TC_GetScreenSize(scrnLft,scrnRgt,scrnBas,scrnTop)
LET winLft= int((scrnRgt-scrnLft-winWid)/2)
LET winRgt= winLft+winWid-1
LET winTop= int((scrnBas-scrnTop-winHgt)/2) + 10
LET winBas= winTop+winHgt-1

CALL TC_Win_Create (WinID,"TITLE",winLft,winRgt,winBas,winTop)
LET values(1)= 2
CALL Object(OBJM_SET, WinID, "TYPE", "", values())

IF PCFlag=1 then                                 ! kill dithering
   LET  values(1)= 1
   CALL Object(OBJM_SET, WinID, "SOLID MIX", "", values())
END IF

LET  values(1)= 0
CALL TC_SetRect(WinID,winLft,winRgt,winBas,winTop)
CALL TC_Win_SetTitle(WinID,window$)
CALL TC_Show(WinID)

SET MODE "COLORSTANDARD"

ASK PIXELS winWid,winHgt                         ! must follow set mode
LET winLft= 0
LET winTop= 0
LET winRgt= winWid-1
LET winBas= winHgt-1
SET WINDOW 0,winRgt,winBas,0

CALL Palette

IF PCFlag=1 then
   LET  values(1)= 0                             ! now force solid colors
   CALL Object(OBJM_SET, WinID, "SOLID MIX", "", values())
   CALL TC_Win_RealizePalette(WinID)             ! some PCs need this

   CALL TC_Win_SetFont(WinID,"arial",9,"plain")
   CALL StringWidth("0",sw)
   IF sw>7 then LET largefonts=1 else LET largefonts=0
END IF

CALL TC_Win_Switch(WinID)

CALL ToolPanel
CALL ThisProgram

CALL SetTextFont(1,12,"bold")                    ! now shut down and clean up
LET quit$= "click the mouse or press a key to close..."
CALL PlotTextCJ(workmidx,(workbas+worktop)/2,quit$,yellow)
CALL TC_CleanUp

END
EXTERNAL

MODULE TB5Parts
    SUB StringWidth(sw$,sl)
        DECLARE PUBLIC WinID
        LET sl= StrWidth(WinID,sw$)
    END SUB

    SUB SetLineWeight(wgt)
        DECLARE PUBLIC OBJM_SET
        DECLARE PUBLIC WinID
        DIM values(1)
        LET values(1)= wgt
        CALL Object(OBJM_SET,WinID, "WIDTH", "", values())
    END SUB

    SUB SetTextFont(font,size,style$)
        DECLARE PUBLIC WinID,Mac5Flag,PCFlag,largefonts
        IF Mac5Flag=1 then
           SELECT CASE font
           CASE 4
                LET font$= "Courier"
           CASE 16
                LET font$= "Times"
           CASE else
                LET font$= "Geneva"
           END SELECT
        ELSE IF PCFlag=1 then
           IF largefonts=1 then
              IF size<12 then
                 LET size=  6
              ELSE IF size=14 then
                 LET size= 10
              ELSE IF size=18 then
                 LET size= 12
              ELSE IF size=24 then
                 LET size= 14
              ELSE IF size=12 then
                 LET size=  8
              ELSE
                 LET size= round(72/96 * size * .8)
              END IF
           ELSE
              IF size<12 then
                 LET size=  7
              ELSE IF size=14 then
                 LET size= 12
              ELSE IF size=12 then
                 LET size=  9
              ELSE IF size=18 then
                 LET size= 14
              ELSE IF size=24 then
                 LET size= 18
              ELSE
                 LET size= round(72/96 * size)
              END IF
           END IF
           SELECT CASE font
           CASE 4
                LET font$= "Courier New"
           CASE 16
                LET font$= "Times New Roman"
           CASE else
                LET font$= "Verdana"
           END SELECT
        END IF
        IF style$= "normal" then LET style$= "plain"
        CALL TC_Win_SetFont(WinID,font$,size,style$)
    END SUB

    SUB BoxDisk(Lft,Rgt,Bas,Top)
        BOX DISK Lft,Rgt,Bas,Top
    END SUB
END MODULE

!  --- End TB5 Cross-platform header and subs ---
!! ---------------------------------------------------------

!! --- Start Unix Header and Subs ---

!library "HHLib.unix"
!LET UnixFlag= 1
!ASK PIXELS winWid,winHgt
!LET winLft= 0
!LET winTop= 0
!LET winRgt= winWid-1
!LET winBas= winHgt-1
!SET WINDOW 0,winRgt,winBas,0
!CALL Palette
!
!CALL ToolPanel
!CALL ThisProgram
!
!END
!EXTERNAL
!
!MODULE UnixParts
!    SHARE CharWidth
!
!    SUB SetTextFont(font,size,style$)
!        LET font$= "-adobe-courier-"
!        IF style$= "normal" then
!           LET style$= "medium-r-normal--"
!        ELSE
!           LET style$= "bold-r-normal--"
!        END IF
!        IF size=9 then
!           LET size$= str$(10)
!        ELSE
!           LET size$= str$(size)
!        END IF
!        LET test= SetFont(font$&style$&size$&"*")
!
!        IF size=9 then
!           LET CharWidth=  6
!        ELSE IF size=12 then  ! numeric output - axis labels
!           LET CharWidth=  7
!        ELSE IF size=14 then  ! rare
!           LET CharWidth=  8
!        ELSE IF size=18 then  ! rare
!           LET CharWidth= 10
!        END IF
!    END SUB
!
!    SUB StringWidth(sw$,sl)                      ! string width in pixels
!        ! LET sl= StrWidth(sw$)
!        LET chars= len(sw$)
!        LET sl   = chars*CharWidth
!    END SUB
!
!    SUB SetLineWeight(wgt)
!        ! CALL PenSize(wgt,wgt)
!    END SUB
!
!    SUB BoxDisk(Lft,Rgt,Bas,Top)
!        CALL Fill_Circle(Lft,Rgt,Bas,Top)
!    END SUB
!END MODULE

!! ------ End of TB Unix Header and Subs ------
! -----------------------------------------------------------


! ***

SUB TrochoidCurves
    DECLARE PUBLIC workLft,workRgt,workBas,workTop,workMidx     ! work area
    DECLARE PUBLIC black,drkgry,drkmid,midgry,litmid,litgry,white
    DECLARE PUBLIC red,yellow,green,cyan,blue,magenta,colorscheme
    DECLARE PUBLIC slideclr,axisclr,axislabelclr,true,false

    DECLARE DEF InfoWithin,QuitWithin

    ! LET axisclr= drkmid

    ! --- help screen array ---

    DIM info$(1:14)
    MAT READ info$

    DATA "Cycloid Curves"
    DATA ""
    DATA "This tool supports visual exploration of the relationship between the velocity vector and the trajectory of a particle, and of the formation of complex parametrized curves as sums of simpler ones."
    DATA "The time parameter is 'theta' and the two parameterized curves being summed are:"
    DATA "a straight line, or horizontal translation"
    DATA "-x = a theta"
    DATA "-y = a"
    DATA "and a circle, or rotation."
    DATA "-x = -b sin(theta)"
    DATA "-y = -b cos(theta)"
    DATA ""
    DATA "The sum parametrizes the path of a point at a distance, b, from the center of a circle of radius, a, as it rolls along the x axis."
    DATA "A green circle of radius a is centered on a purple point that marks the position along the straight line, and the radial vector for the translated circle is blue."
    DATA "The point on the curve that is parametrized by the vector sum is yellow."

    DIM info2$(1:11)
    MAT READ info2$

    DATA "Cycloid Curves"
    DATA ""
    DATA "Click or drag the theta slider to move the circle. Click among the hash marks to round theta to the nearest half pi. You can also move the circle by dragging the mouse on the drawing plane."
    DATA "Click one of the [<][>] buttons to step the value of theta, and click the [>>>] button to animate the value of theta. Click the stop button to interrupt the animation."
    DATA ""
    DATA "Click or drag the  b  slider to set the distance of the yellow point from the center. Click among the hash marks to round b to the nearest 0.25."
    DATA "Click or drag the  a  slider to set the radius of the circle. Click among the hash marks to round b to the nearest 0.25."
    DATA ""
    DATA "Click the [Reset] button to clear the plane and move the circle to (0,a)."
    DATA "Click the trace checkbox to leave a trace of the point as the circle rolls."
    DATA "Click the velocity vector checkbox to display the velocity vector at the yellow point."

    !    DATA "Trochoid Curves"
    !    DATA "Trochoids are curves drawn by a point at a distance, b, from the center of circle of radius, a, that is rolling along a straight line. A reflector on a spoke of a bicycle wheel draws a trochoid."
    !    DATA "If b=a the trochoid is a cycloid."
    !    DATA "If b>a the trochoid is an extended, or prolate, cycloid."
    !    DATA "If b<a the trochoid is a contracted, or curtate, cycloid."
    !    DATA ""
    !    DATA "If t is the angle through which the circle has rotated, the center of the circle is (at,a) and the parametric equations for points on the trochoid are:"
    !    DATA "-x = at - b sin(t)"
    !    DATA "-y = a - b cos(t)"
    !    DATA ""
    !    DATA "Click or drag the  b  slider to set the distance of the drawing point from the center. Click above the b slider axis to round b to the nearest 0.25."
    !    DATA "Click or drag the  a  slider to set the radius of the circle. Click above the a slider axis to round a to the nearest 0.25."
    !    DATA "Click or drag the theta slider to move the circle. Click above the theta slider axis to round theta to the nearest half pi. You can also move the circle by dragging the mouse on the drawing plane."
    !    DATA "Click the [Roll] button to roll the circle without leaving a trace of the point. Click the [Stop] button to interrupt the animation."
    !    DATA "Click the [Trace] button to leave a trace of the point as the circle rolls.  Click the [Stop] button to interrupt the animation."
    !    DATA "Click the [Reset] button to clear the plane and move the circle to (0,a)."


    ! -------- Utility functions ------

    DECLARE DEF clamp,roundn
    LET sixPi= 6*pi

    ! ---- Trochoid Functions ----

    !    U. North Dakota - works if b is expansion or contraction of r
    !    DEF fxt(r,b,theta)= r*(theta - b*sin(theta))
    !    DEF fyt(r,b,theta)= r*(1 - b*cos(theta))
    !    Mathematica - mathworld.wolfram.com - b is an independent parameter

    DEF fxt(r,b,theta)= r*theta - b*sin(theta)   ! trochoid points
    DEF fyt(r,b,theta)= r - b*cos(theta)

    DEF dxt(r,b,theta) = (r-b*cos(theta))/2
    DEF dyt(r,b,theta) =    b*sin(theta) /2

    DEF dst(theta,r)= theta*r                    ! convert rotation angle to horizontal distance
    DEF ang(xc,r)   = xc/r                       ! convert horizontal distance to rotation angle

    ! ---------- Graphing plane parameters and methods ----------

    ! --- w1 plane data ---

    DECLARE PUBLIC w1Lft,w1Rgt,w1Bas,w1Top,w1Midx,w1Midy
    DECLARE PUBLIC w1fLft,w1fRgt,w1fBas,w1fTop,w1x0,w1y0
    DECLARE PUBLIC w1xFirst, w1xSTik, w1xLTik, w1xLabel, w1xGridstep
    DECLARE PUBLIC w1yFirst, w1ySTik, w1yLTik, w1yLabel, w1yGridstep
    DECLARE PUBLIC w1wWid,w1wHgt,w1fWid,w1fHgt
    DECLARE PUBLIC w1fxRatio,w1fyRatio,w1wxRatio,w1wyRatio,w1Aspect
    DECLARE PUBLIC w1xPiFlag, w1xMult, w1yPiFlag, w1yMult

    LET w1Flag   = 1
    LET w1xPiFlag= 0
    LET w1xMult  = 1
    LET w1yPiFlag= 0
    LET w1yMult  = 1

    LET w1Top = workTop+35                       ! window bounds
    LET w1Bas = w1Top+275
    LET w1Lft = workLft+40
    LET w1Rgt = w1Lft+700

    LET w1fTop=  7                               ! window bounds
    LET w1fBas= -4
    LET w1fLft= -4
    LET w1fRgt= 24

    LET w1Xax$= "x"                              ! axis labels
    LET w1Yax$= "y"

    LET w1xGridstep= 0                           ! horizontal grid intervals
    LET w1yGridstep= 0                           ! vertical grid intervals

    LET w1xSTik = 0.5                            ! horizontal axis Tik marks
    LET w1xLTik = 1
    LET w1xLabel= 1
    LET w1xFirst= w1fLft

    LET w1ySTik = 0.5                            ! vertical axis Tik marks
    LET w1yLTik = 1
    LET w1yLabel= 1
    LET w1yFirst= w1fBas

    ! --- w1 Plane methods ---

    DECLARE DEF w1fncx,w1fncy,w1wndx,w1wndy      ! window/function transforms
    DECLARE DEF w1wWithin,w1Within,w1fWithin

    CALL w1Variables

    SUB w1Init
        CALL w1DrawPlane(1,1,1)                  ! grid, axes, zeroaxes

        CALL SetTextFont(1,12,"bold")
        SET COLOR drkmid                         ! pi grid
        FOR i= 1 to 6 step 1
            PLOT w1Wndx(i*pi),w1Bas-1; w1Wndx(i*pi),w1Top+1
        NEXT i

        CALL PlotTextLJ(w1Rgt+8,w1y0+3,w1Xax$,axislabelclr)     ! axis labels
        CALL PlotTextCJ(w1x0,w1Top-11,w1Yax$,axislabelclr)
        CALL w1KeepGridLayer
        CALL w1KeepGraphLayer
    END SUB

    SUB w1KeepTempLayer
        BOX KEEP w1Lft,w1Rgt,w1Bas,w1Top in temp$
    END SUB

    SUB w1ShowTempLayer
        BOX SHOW temp$ at w1Lft,w1Bas
    END SUB

    ! ----------- horizontal sliders ------------

    ! --- h1 horizontal slider - b ---

    DECLARE PUBLIC h1axis,h1wLft,h1wRgt,h1wBas,h1wTop,h1fLft,h1fRgt
    DECLARE PUBLIC h1name$,h1form$,h1clr,h1First,h1STik,h1LTik,h1Label
    DECLARE PUBLIC h1PiAxis,h1Mult,h1fMin,h1fMax

    LET h1PiAxis= 0
    LET h1Mult  = 1

    LET h1clr   = cyan
    LET h1name$ = "b"
    LET h1form$ = "-%.##"
    LET h1Places= 2
    LET h1Click = 0.25                           ! click steps

    LET h1axis  = w1Bas + 150
    LET h1wLft  = w1Lft
    LET h1wRgt  = h1wLft + 400

    LET h1fLft  = 0
    LET h1fRgt  = 4.0

    LET h1STik  = 0.25                           ! short tick marks
    LET h1LTik  = 0.50                           ! long tick marks
    LET h1Label = 0.50                              ! labels
    LET h1First = 0                              ! first tick mark

    DECLARE DEF h1Within

    CALL h1SliderVariables

    SUB h1Init
        CALL h1DrawSlider(h1name$,b)
    END SUB


    ! --- h2 horizontal slider - theta ---

    DECLARE PUBLIC h2axis,h2wLft,h2wRgt,h2wBas,h2wTop,h2fLft,h2fRgt
    DECLARE PUBLIC h2name$,h2form$,h2clr,h2First,h2STik,h2LTik,h2Label
    DECLARE PUBLIC h2PiAxis,h2Mult,h2fMin,h2fMax

    LET h2PiAxis= 1
    LET h2Mult  = pi

    LET h2clr   = slideclr
    LET h2name$ = ""                             ! will be theta
    LET h2form$ = "--%.##"
    LET h2Places= 2
    LET h2Click = 0.5*pi                         ! click steps

    LET h2axis  = h1axis -  55
    LET h2wLft  = h1wLft
    LET h2wRgt  = h1wRgt

    LET h2fLft  = 0
    LET h2fRgt  = 6

    LET h2STik  = 0.5                            ! short tick marks
    LET h2LTik  = 1                              ! long tick marks
    LET h2Label = 1                              ! labels
    LET h2First = h2fLft                         ! first tick mark

    DECLARE DEF h2Within,h2AnimWithin,h2LstpWithin,h2RstpWithin

    CALL h2SliderVariables
    LET h2AnimStep= pi/16

    SUB h2Init
        CALL h2DrawSlider(h2name$,theta)
        CALL DrawTheta12(h2wLft-16,h2wBas-2,h2clr)
        CALL h2AnimMoveStep(1,0,1)
    END SUB


    ! --- h3 horizontal slider - a ---

    DECLARE PUBLIC h3axis,h3wLft,h3wRgt,h3wBas,h3wTop,h3fLft,h3fRgt
    DECLARE PUBLIC h3name$,h3form$,h3clr,h3First,h3STik,h3LTik,h3Label
    DECLARE PUBLIC h3PiAxis,h3Mult,h3fMin,h3fMax

    LET h3PiAxis= 0
    LET h3Mult  = 1

    LET h3clr   = slideclr
    LET h3name$ = "a"
    LET h3form$ = "--%.##"
    LET h3Places= 2
    LET h3Click = 0.25                           ! click steps

    LET h3axis  = h1axis + 45
    LET h3wLft  = h1wLft
    LET h3wRgt  = h3wLft + 150
    LET h3fLft  = 0.5
    LET h3fRgt  = 2

    LET h3STik  = 0.25                           ! short tick marks
    LET h3LTik  = 0.5                            ! long tick marks
    LET h3Label = 0.5                            ! labels
    LET h3First = h3fLft                         ! first tick mark

    DECLARE DEF h3Within

    CALL h3SliderVariables

    SUB h3Init
        CALL h3DrawSlider(h3name$,r)
    END SUB


    ! --- Text Output Rects ----------

    ! --- text rectangle 1 ---

    LET t1BasLn = w1Bas +  40
    LET t1Lft   = w1Rgt - 125
    LET t1Rgt   = t1Lft + 130
    LET t1Bas   = t1BasLn +  5
    LET t1Top   = t1BasLn - 15
    LET t1Eqx   = t1lft + 24

    LET t1a$ = "x"
    LET t1b$ = " = "
    LET t1c$ = "a0"
    LET t1d$ = " - "
    LET t1e$ = "b sin(0)"

    SUB t1Set
        CALL StringWidth(t1b$,swb)
        CALL StringWidth(t1c$,swc)
        CALL StringWidth(t1d$,swd)
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextRJ(t1Eqx-swb,t1BasLn,t1a$,yellow)
        CALL PlotTextRJ(t1Eqx,t1BasLn,t1b$,litgry)
        CALL SwapTheta(t1Eqx,t1BasLn,"at","t",magenta)
        CALL PlotTextLJ(t1Eqx+swc,t1BasLn,t1d$,litgry)
        CALL SwapTheta(t1Eqx+swc+swd,t1BasLn,"b sin(t)","t",cyan)
    END SUB

    SUB t1Clear
        BOX CLEAR t1Lft-2,t1Rgt,t1Bas,t1Top
    END SUB

    SUB t1Init
        CALL t1Set
    END SUB


    ! --- text rectangle 2 ---

    LET t2BasLn = t1BasLn + 20
    LET t2Lft   = w1Rgt - 125
    LET t2Rgt   = t2Lft + 130
    LET t2Bas   = t2BasLn +  5
    LET t2Top   = t2BasLn - 15
    LET t2Eqx   = t2lft + 24

    LET t2a$ = "y"
    LET t2b$ = " = "
    LET t2c$ = "a"
    LET t2d$ = " - "
    LET t2e$ = "b cos(0)"

    SUB t2Set
        CALL StringWidth(t2b$,swb)
        CALL StringWidth(t2c$,swc)
        CALL StringWidth(t2d$,swd)
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextRJ(t2Eqx-swb,t2BasLn,t2a$,yellow)
        CALL PlotTextRJ(t2Eqx,t2BasLn,t2b$,litgry)
        CALL PlotTextLJ(t2Eqx,t2BasLn,"a",magenta)
        CALL PlotTextLJ(t2Eqx+swc,t2BasLn,t2d$,litgry)
        CALL SwapTheta(t2Eqx+swc+swd,t2BasLn,"b cos(t)","t",cyan)
    END SUB

    SUB t2Clear
        BOX CLEAR t2Lft-2,t2Rgt,t2Bas,t2Top
    END SUB

    SUB t2Init
        CALL t2Set
    END SUB


    ! --- text rectangle 3 ---

    LET t3BasLn = w1Bas +  40
    LET t3Lft   = w1Lft
    LET t3Rgt   = t3Lft + 150
    LET t3Bas   = t3BasLn +  5
    LET t3Top   = t3BasLn - 15
    LET t3Label$= ""

    SUB t3Label
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextRJ(t3Lft,t3BasLn,t3Label$,white)
    END SUB

    SUB t3Set
        CALL t3Clear
        CALL SetTextFont(1,12,"bold")
        IF b>r then
           LET txt$= "Prolate Cycloid"
        ELSE IF b<r then
           LET txt$= "Curtate Cycloid"
        ELSE
           LET txt$= "Cycloid"
        END IF
        CALL PlotTextLJ(t3Lft,t3BasLn,txt$,troClr)
    END SUB

    SUB t3Clear
        BOX CLEAR t3Lft-2,t3Rgt,t3Bas,t3Top
    END SUB

    SUB t3Init
        CALL t3Set
    END SUB


    ! --- text rectangle 4 ---

    LET t4BasLn1 = w1Bas + 40
    LET t4BasLn2 = t4BasLn1 + 20
    LET t4Lft    = w1Lft + 200
    LET t4Rgt    = t4Lft + 100
    LET t4Bas    = t4BasLn2 +  5
    LET t4Top    = t4BasLn1 - 15
    LET t4Label1$= "x ="
    LET t4Label2$= "y ="
    LET t4Clr    = white

    SUB t4Label
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextRJ(t4Lft,t4BasLn1,t4Label1$,t4Clr)
        CALL PlotTextRJ(t4Lft,t4BasLn2,t4Label2$,t4Clr)
    END SUB

    SUB t4Set
        CALL SetTextFont(1,12,"bold")
        LET txt1$ = trim$(using$("--%.##",xc))
        LET txt2$ = trim$(using$("--%.##",yc))
        CALL t4Clear
        CALL PlotTextRJ(t4Lft+45,t4BasLn1,txt1$,t4Clr)
        CALL PlotTextRJ(t4Lft+45,t4BasLn2,txt2$,t4Clr)
    END SUB

    SUB t4Clear
        BOX CLEAR t4Lft-2,t4Rgt,t4Bas,t4Top
    END SUB

    SUB t4Init
        CALL t4Label
        CALL t4Set
    END SUB


    !    ! --- text rectangle 5 ---
    !
    !    LET t5BasLn = t4BasLn + 20
    !    LET t5Lft   = t4Lft
    !    LET t5Rgt   = t4Rgt
    !    LET t5Bas   = t5BasLn +  5
    !    LET t5Top   = t5BasLn - 15
    !    LET t5Label$= "y ="
    !
    !    SUB t5Label
    !        CALL SetTextFont(1,12,"bold")
    !        CALL PlotTextRJ(t5Lft,t5BasLn,t5Label$,circlr)
    !    END SUB
    !
    !    SUB t5Set
    !        CALL t5Clear
    !        CALL SetTextFont(1,12,"bold")
    !        LET txt$ = trim$(using$("--%.##",yc))
    !        CALL PlotTextRJ(t5Lft+45,t5BasLn,txt$,circlr)
    !    END SUB
    !
    !    SUB t5Clear
    !        BOX CLEAR t5Lft-2,t5Rgt,t5Bas,t5Top
    !    END SUB
    !
    !    SUB t5Init
    !        CALL t5Label
    !        CALL t5Set
    !    END SUB


    !    ! ---
    !
    !    SUB SetCoords
    !        CALL t4Set
    !        CALL t5Set
    !    END SUB
    !
    !    SUB ClearCoords
    !        CALL t4Clear
    !        CALL t5Clear
    !    END SUB


    ! --- checkbox 1 ---

    DECLARE PUBLIC cb1Lft,cb1Rgt,cb1Bas,cb1Top,cb1Txt$,cb1Clr,cb1State
    DECLARE DEF cb1Within

    LET cb1Lft = w1Rgt - 166
    LET cb1Bas = h1WBas - 1
    LET cb1Txt$= "trace"
    LET cb1Clr = yellow

    CALL cb1Variables

    ! --- checkbox 2 ---

    DECLARE PUBLIC cb2Lft,cb2Rgt,cb2Bas,cb2Top,cb2Txt$,cb2Clr,cb2State
    DECLARE DEF cb2Within

    LET cb2Lft = w1Rgt - 166
    LET cb2Bas = cb1Bas + 18
    LET cb2Txt$= "velocity vector"
    LET cb2Clr = red

    CALL cb2Variables


    ! --- user interface buttons ---

    LET btnHgt= 18
    LET clLft = w1Rgt - 166
    LET clRgt = clLft +  50
    LET clTop = h2wBas - 17
    LET clBas = clTop + btnHgt

    LET trLft = w1Rgt - 166
    LET trRgt = trLft + 50
    LET trTop = h1wBas - 17
    LET trBas = trTop + btnHgt

    SUB Buttons
        CALL SetTextFont(1,12,"bold")
        CALL DrawButton(clLft,clRgt,clBas,clTop,5,"reset")
    END SUB

    SUB StopButton(StopState)
        CALL SetTextFont(1,9,"bold")
        IF StopState=1 then
           CALL DrawButton(stLft,stRgt,stBas,stTop,5,"stop")
        ELSE
           BOX CLEAR stLft,stRgt,stBas,stTop
        END IF
    END SUB


    ! --- Initialize parameters ---

    LET troClr= yellow                           ! cycloid trace
    LET crcClr= green                            ! circle
    LET cirClr= green

    LET r     =  1                               ! radius
    LET b     =  r                               ! inside or outside circumference
    LET oldr  = -9999
    LET oldb  = -9999

    LET crcBas= w1y0                             ! circle Base
    LET crcTop= w1Wndy(2*r)                      ! circle Top
    LET w6pi  = round(w1Wndx(sixPi)+.49999)

    LET theta =  0
    LET oldth = -99999
    LET xc    =  0
    LET yc    =  r

    LET cb1State  = 0
    LET traceState= cb1State
    LET cb2State  = 0
    LET velocityState= cb1State


    ! --- Draw the screen ---

    CALL InitScreen
    CALL SetTimer

    SUB InitScreen
        BOX CLEAR workLft,workRgt,workBas,workTop
        CALL w1Init

        CALL t1Init
        CALL t2Init
        CALL t3Init
        CALL t4Init

        CALL h1Init
        CALL h2Init
        CALL h3Init

        CALL SetMax
        CALL Buttons
        CALL cb1Init
        CALL cb2Init

        CALL h1Action
        CALL DrawCircle
    END SUB


    ! ----------------- Event manager -----------------

    DO
       CALL CopyCoords(xc,yc,oldxc,oldyc)

       IF ms<>2 then                             ! mouse state down?
          CALL CopyCoords(-999,-999,oxc,oyc)
          CALL w1KeepTempLayer
          DO
             GET MOUSE: mx,my,ms
             CALL w1RollOver
          LOOP until ms=2
          CALL w1ClearRollOver
       END IF

       ! mouse down events

       IF w1Within(mx,my)=true then              ! drag circle in plane
          LET oldmx= 9999
          DO
             GET MOUSE: mx,my,ms
             CALL w1MouseDrag
          LOOP until ms=3
          CALL t4Clear

       ELSE IF h1Within(mx,my)=true then         ! h1 radial trochoid point
          CALL ResetTrace
          IF my<h1axis then
             CALL h1MouseClick
          ELSE
             CALL h1MouseDrag
          END IF
          CALL h1h3Reset

       ELSE IF h2Within(mx,my)=true then         ! theta
          IF my<h2axis then
             CALL h2MouseClick
          ELSE
             CALL h2MouseDrag
          END IF
       ELSE IF h2animWithin(mx,my)=true then     ! h2 theta animation
          CALL h2animButtonUp(ms)
          IF xc=maxdist then
             CALL ResetVars
             CALL Position(theta)
             CALL h2Action
          END IF
          CALL cycle(traceState)
       ELSE IF h2LstpWithin(mx,my)=true then     ! h2 left step
          CALL h2LstpButtonUp(ms)
          CALL h2LeftStep(theta,h2AnimStep)
          CALL Position(theta)
       ELSE IF h2RstpWithin(mx,my)=true then     ! h2 right step
          CALL h2RstpButtonUp(ms)
          CALL h2RightStep(theta,h2AnimStep)
          CALL Position(theta)

       ELSE IF h3Within(mx,my)=true then         ! h3 r
          CALL ResetTrace
          IF my<h3axis then
             CALL h3MouseClick
          ELSE
             CALL h3MouseDrag
          END IF
          CALL h1h3Reset

       ELSE IF mx>=clLft and mx<=clRgt and my>=clTop and my<=clBas then   ! reset
          CALL MouseButtonUp(clLft,clRgt,clBas,clTop,ms)
          CALL w1ShowGridLayer
          CALL w1KeepGraphLayer
          CALL ResetVars
          CALL Position(theta)
          CALL h2Action

       ELSE IF cb1Within(mx,my)=true then        ! trace
          CALL cb1MouseUp(ms)
          LET traceState= cb1State

       ELSE IF cb2Within(mx,my)=true then        ! velocity vector
          CALL cb2MouseUp(ms)
          LET velocityState= cb2State
          CALL w1ShowGridLayer
          CALL Position(theta)

       ELSE IF InfoWithin(mx,my,ms)=true then    ! help page
          CALL InfoButtonUp(ms)
          CALL InfoPage(Info$())
          CALL InfoPage(Info2$())
          CALL InitScreen
       ELSE IF QuitWithin(mx,my,ms)=true then    ! Quit
          CALL QuitButtonUp(ms)
          EXIT SUB
       ELSE
          CALL MouseUp(mx,my,ms)
       END IF
    LOOP

    SUB ResetTrace
        CALL w1ShowGridLayer
        CALL w1KeepGraphLayer
        !        LET traceState,cb1State= 0
        !        CALL cb1SetState
        LET theta= 0
        CALL Position(theta)
        CALL t3Set
    END SUB

    ! ---

    SUB w1RollOver
        IF w1wWithin(mx,my)=true then            ! rollover in plane
           CALL w1PixelsToMath(mx,my,xc,yc)
           IF xc<>oxc or yc<>oyc then
              SET COLOR litmid
              CALL w1ShowTempLayer

              PLOT mx,w1Top+1; mx,w1Bas-1
              PLOT w1Lft+1,my; w1Rgt-1,my

              CALL t4Set
              CALL CopyCoords(xc,yc,oxc,oyc)
              LET clearflag= 1
           END IF
        ELSE IF clearflag=1 then
           CALL w1ClearRollOver
        END IF
    END SUB
    SUB w1ClearRollOver
        CALL w1ShowTempLayer
        CALL t4Clear
        LET clearflag= 0
    END SUB

    SUB w1RollOverClear
        CALL w1ShowTempLayer
        LET w1Clear= 0
        CALL t3Clear
    END SUB

    SUB w1MouseDrag
        LET mx= Clamp(mx,w1x0,w6pi)
        LET my= Clamp(my,w1Top,w1Bas)
        IF mx<>oldmx or my<>oldmy then
           LET xc   = w1Fncx(mx)
           LET xc   = min(xc,maxdist)
           LET theta= ang(xc,r)
           LET yc   = w1Fncx(my)
           LET oldmx= mx
           LET oldmy= my
           CALL h2Action
        END IF
    END SUB


    ! ---

    SUB h1MouseClick
        CALL h1GetClickVal(ms,h1Click,b)
        CALL h1Action
    END SUB
    SUB h1MouseDrag
        DO
           CALL h1GetDragVal(ms,h1Places,b)
           CALL h1Action
        LOOP until ms=3
    END SUB
    SUB h1Action                                 ! b
        IF b<>oldb then
           LET theta= 0
           CALL Position(theta)
           CALL t3Set
           LET oldb= b
        END IF
    END SUB

    ! ---

    SUB h2MouseClick
        CALL h2GetClickVal(ms,h2Click,theta)
        CALL h2Action
    END SUB
    SUB h2MouseDrag
        DO
           CALL h2GetDragVal(ms,h2Places,theta)
           CALL h2Action
        LOOP until ms=3
    END SUB
    SUB h2Action                                 ! theta
        LET theta= Clamp(theta,0,maxtheta)
        IF theta<>oldth then
           CALL h2mark(theta)                    ! needed for adjusted theta
           CALL Position(theta)
           CALL t4Set
           LET oldth= theta
        END IF
    END SUB

    ! ---

    SUB h3MouseClick
        CALL h3GetClickVal(ms,h3Click,r)
        CALL h3Action
    END SUB
    SUB h3MouseDrag
        DO
           CALL h3GetDragVal(ms,h3Places,r)
           CALL h3Action
        LOOP until ms=3
    END SUB
    SUB h3Action                                 ! r
        IF r<>oldr then
           LET crcTop= w1Wndy(2*r)               ! circle Top
           LET theta= 0
           CALL Position(theta)
           CALL t3Set
           LET oldr= r
        END IF
    END SUB

    SUB h1h3Reset
        CALL ResetVars
        CALL SetMax
    END SUB

    ! ---

    SUB SetVars(theta)
        LET oldwxc= wxc
        LET oldwyc= wyc
        LET oldwxt= wxt
        LET oldwyt= wyt

        LET xt    = fxt(r,b,theta)               ! trochoid coords
        LET yt    = fyt(r,b,theta)
        CALL w1MathToPixels(xt,yt,wxt,wyt)

        LET xc    = dst(theta,r)
        CALL w1MathToPixels(xc,r,wxc,wyc)

        LET crcLft= round(w1Wndx(xc-r))          ! circle edges
        LET crcRgt= round(w1Wndx(xc+r))
    END SUB

    SUB SetMax                                   ! when r changes
        LET maxdist = sixPi*r
        LET maxdist = min(maxdist,sixPi)
        LET wmax    = w1Wndx(maxdist)
        LET maxtheta= min(sixPi,sixPi/r)
    END SUB

    SUB ResetVars
        LET theta=  0
        LET oldth= -99999
        LET xc   =  0
        LET yc   =  r
        LET oldr = -9999
        LET oldb = -9999
        CALL h2mark(theta)
    END SUB

    SUB Position(theta)
        IF traceState=0 then
           CALL w1ShowGridLayer
           CALL SetVars(theta)
           CALL DrawCircle
        ELSE
           CALL w1ShowGraphLayer
           CALL SetVars(theta)
           LET wxt= w1Wndx(xt)
           LET wyt= w1Wndy(yt)
           SET COLOR yellow
           PLOT wxt,wyt
           CALL w1KeepGraphLayer
           CALL DrawCircle
        END IF
    END SUB

    SUB DrawCircle
        SET COLOR  crcClr
        BOX CIRCLE crcLft,crcRgt,crcBas,crcTop
        BOX CIRCLE crcLft+1,crcRgt-1,crcBas-1,crcTop+1
        CALL PlotLine(wxc,wyc, wxt,wyt, cyan)
        CALL PlotDiamondClr(wxt,wyt,yellow)
        SET COLOR magenta
        PLOT wxc,wyc
        BOX CIRCLE wxc-1,wxc+1,wyc+1,wyc-1
        BOX CIRCLE wxc-2,wxc+2,wyc+2,wyc-2

        IF velocityState=1 then
           LET vx  = dxt(r,b,theta)
           LET vy  = dyt(r,b,theta)
           SET COLOR red
           LET wvxt= w1Wndx(xt+vx)
           LET wvyt= w1Wndy(yt+vy)
           PLOT wxt,wyt; wvxt,wvyt

           IF vx<>0 or vy<>0 then
              LET a = angle(vx,-vy)
              DRAW arrow with rotate(a) * shift(wvxt,wvyt)
           END IF
        END IF
    END SUB

    PICTURE arrow
        PLOT -2,-2; 2,0; -2,2
    END PICTURE

    SUB Cycle(trace)
        CALL w1ShowGridLayer
        CALL w1KeepGraphLayer
        CALL SetVars(theta)
        CALL DrawCircle

        LET exit= 0
        IF trace=1 then                          ! trace = 1
           FOR wx= wxc to wmax+1 step 2          ! roll from current position
               LET xc= w1Fncx(wx)
               IF xc>maxdist then
                  LET xc  = maxdist
                  LET exit= 1
               END IF
               LET theta= ang(xc,r)
               CALL SetVars(theta)
               CALL w1ShowGraphLayer

               CALL PlotLine(oldwxc,oldwyc, wxc,wyc, magenta)
               CALL PlotLine(oldwxt,oldwyt, wxt,wyt, troClr)
               CALL w1KeepGraphLayer

               CALL DrawCircle
               CALL h2mark(theta)

               GET MOUSE: mx,my,ms
               IF ms=2 then
                  CALL h2AnimStopButtonUp(ms)
                  EXIT FOR
               END IF
               IF exit=1 then EXIT FOR
               CALL Delay(1/60)
           NEXT wx
        ELSE                                     ! trace = 0
           FOR wx= wxc to wmax+1 step 2          ! roll from current position
               LET xc= w1Fncx(wx)
               IF xc>maxdist then
                  LET xc  = maxdist
                  LET exit= 1
               END IF
               LET theta= ang(xc,r)
               CALL SetVars(theta)
               CALL w1ShowGraphLayer

               CALL DrawCircle
               CALL h2mark(theta)

               GET MOUSE: mx,my,ms
               IF ms=2 then
                  CALL h2AnimStopButtonUp(ms)
                  EXIT FOR
               END IF
               IF exit=1 then EXIT FOR
               CALL Delay(1/30)
           NEXT wx
        END IF
        CALL h2StopButtonClear
    END SUB
END SUB

! -------- end of trochoid curves code ---------