!   I was just playing with some of the tools, which I will domo for 
!   Dan Freedman's class tomorrow. Isoclines has a bug! - and could
!   use some work anyway. 
!   
!   The bug occurs when  x' = x(1-x) . Try dragging c; the program vanishes.
!   I am using the sunos implementation; I don't know whether that matters.
!   
!   While we are about it, though, let's simplify a little, and make the
!   display under the c slider just say  x' = c  for each of the cases.
!   Those solutions are misleading.

!Isoclines: I hadn't noticed the equation for the isocline in terms
!of  c  before. I don't think this is a good idea; I'd prefer to have
!the students think of the isocline as given by the EQUATION  y' = c,
!rather than solving explicity for y as a function of x.
!
!Hubbard and West at Cornell wanted their students to attend to
!how to draw the graph of the isocline as a function of t.  Whatever
!students need to know in an engineering context is fine with me. Perhaps
!the equations for isoclines is not an issue. I will kill the equations for 
!the isocline and put the generic "y' = c" for all examples.

! needs homemade pointers everywhere
! last example - use plotlines?
! do we need heads on arrows if they only designate slope?
! does direction matter?
! needed for visibility? use triple weight lines instead?

!! File: Isoclines
!! May 26, 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$ = "Isoclines"

SUB ThisProgram
    CALL Isoclines
    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 Isoclines
    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 quitWithin, infoWithin

    ! --- info page ---

    DIM Info$(1:15)
    MAT READ Info$

    DATA "Isoclines"
    DATA ""
    DATA "This tool supports visual exploration of isoclines, curves in the tx-plane along which the solution slopes are equal."
    DATA ""
    DATA "Drag the slider handle or click above the slider axis to change C and draw isoclines."
    DATA ""
    DATA "Click the (t,x) plane to draw solutions."
    DATA ""
    DATA "Click the pop-up menu button [v] to open the list of equations."
    DATA "Click an equation to select it."
    DATA ""
    DATA "Click [ ] Slope Field to toggle the slope field on or off."
    DATA "Click [Clear All] to remove solutions and isoclines from the plane."
    DATA "Click [Clear Solutions] to remove solutions from the plane."
    DATA "Click [Clear Isoclines] to remove isoclines from the plane."

    ! --- utility functions ---

    DECLARE DEF clamp,roundn,e
    LET bignum= 10^10

    DEF SetColor(n) = red + n

    ! --- Functions ---

    ! Equation list panel

    LET eqcnt= 6
    DEF dxdt1(t,x) = 1
    DEF dydt1(t,x) = x*(1-x)
    DEF dxdt2(t,x) = 1
    DEF dydt2(t,x) = t-2*x
    DEF dxdt3(t,x) = 1
    DEF dydt3(t,x) = x*x-t
    DEF dxdt4(t,x) = 1
    DEF dydt4(t,x) = x*x-t*t
    DEF dxdt5(t,x) = 1
    DEF dydt5(t,x) = -t/x
    DEF dxdt6(t,x) = 1
    DEF dydt6(t,x) = x/t

    SUB FetchEq(eq,t,x,dx,dy)
        SELECT CASE eq
        CASE 1
             LET dx= dxdt1(t,x)
             LET dy= dydt1(t,x)
        CASE 2
             LET dx= dxdt2(t,x)
             LET dy= dydt2(t,x)
        CASE 3
             LET dx= dxdt3(t,x)
             LET dy= dydt3(t,x)
        CASE 4
             LET dx= dxdt4(t,x)
             LET dy= dydt4(t,x)
        CASE 5
             IF x<>0 then
                LET dx= dxdt5(t,x)
                LET dy= dydt5(t,x)
             ELSE
                LET dx= 1
                LET dy= bignum
             END IF
        CASE 6
             IF t<>0 then
                LET dx= dxdt6(t,x)
                LET dy= dydt6(t,x)
             ELSE
                LET dx= 1
                LET dy= bignum
             END IF

        END SELECT
        IF dy=99999 then LET err= 1 else LET err= 0
    END SUB

    ! Graphing window

    LET wsize = 300
    LET pisize= 176

    ! --- plane 1 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 w1yPiFlag= 0
    LET w1xMult  = 1
    LET w1yMult  = 1

    LET w1Top = worktop + 35
    LET w1Bas = w1Top + 400
    LET w1Lft = worklft + 70
    LET w1Rgt = w1Lft + 400

    LET fsz    =  4
    LET w1fTop =  fsz
    LET w1fBas = -fsz
    LET w1fLft = -fsz
    LET w1fRgt =  fsz

    LET w1xAx$= "t"                              ! axis labels
    LET w1yAx$= "x"

    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

    ! --- Plane 1 methods ---

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

    CALL w1Variables

    LET vrule1= w1Rgt + 70

    SUB w1Init(eqnum)
        CALL w1Bounds(eqnum)
        CALL w1DrawPlane(1,1,1)                  ! x axis, y axis, zeroaxes
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(w1Rgt+8,w1y0+3,w1xAx$,axislabelclr)     ! axis labels
        CALL PlotTextCJ(w1x0,w1Top-10,w1yAx$,axislabelclr)
        CALL w1KeepGridLayer
        CALL w1KeepGraphLayer
    END SUB

    SUB w1Bounds(eqnum)
        IF eqnum=1 then
           LET w1fTop =  2
           LET w1fBas = -1
        ELSE
           LET w1fTop =  4
           LET w1fBas = -4
        END IF
        LET w1yFirst= w1fBas
        CALL w1Variables
    END SUB


    ! --- horizontal slider 1 ---

    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   = yellow
    LET h1name$ = "C"
    LET h1form$ = "-%.###"
    LET h1Places= 3

    LET h1axis = w1Midy-50
    LET h1wLft = vrule1 + 20
    LET h1wRgt = h1wLft+120

    LET h1fLft = -3                              ! h0flft
    LET h1fRgt =  3                              ! h0frgt

    LET h1STik =  0.25                           ! short tick marks
    LET h1LTik =  0.50                           ! long tick marks
    LET h1Label=  1.00                           ! labels
    LET h1First= h1fLft                          ! first tick mark
    LET h1Click=  1

    DECLARE DEF h1Within                         ! window/function transforms

    CALL h1SliderVariables

    SUB h1Bounds(eqnum)
        IF eqnum=1 then
           LET h1fLft = -2.00
           LET h1fRgt =  0.25

           LET h1STik =  0.25                    ! short tick marks
           LET h1LTik =  0.50                    ! long tick marks
           LET h1Label=  1.00                    ! labels
           LET h1First= -2.00                    ! first tick mark
           LET h1Click=  0.25
        ELSE
           LET h1fLft = -3
           LET h1fRgt =  3

           LET h1STik =  0.25                    ! short tick marks
           LET h1LTik =  0.50                    ! long tick marks
           LET h1Label=  1.00                    ! labels
           LET h1First= h1fLft                   ! first tick mark
           LET h1Click=  0.50
        END IF
        CALL h1SliderVariables
    END SUB

    SUB h1Init(eqnum)
        CALL h1Bounds(eqnum)
        CALL h1DrawSlider(h1name$,c)
    END SUB

    ! -------- popup menu -------
    ! ----- menu parameters -----

    DECLARE PUBLIC m1Lft, m1Rgt, m1Bas, m1Top, m1Equation, m1Prefix$, m1Menu1$(), m1tClr
    DECLARE DEF m1Within

    MAT redim m1Menu1$(1:eqcnt)
    MAT READ m1Menu1$
    DATA "x(1-x)"
    DATA "t-2x"
    DATA "x^[2]-t"
    DATA "x^[2]-t^[2]"
    DATA "-t/x"
    DATA "x/t"

    LET m1Prefix$= "x' = "
    LET m1Lft    = vrule1
    LET m1Top    = w1Midy + 30
    LET m1tClr   = cyan

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

    ! --- t1 - dynammic output of initial conditions ---

    LET t1LnSpc = 20
    LET t1BasLn1= w1Top + t1Lnspc
    LET t1BasLn2= t1BasLn1 + t1Lnspc
    LET t1Lft   = vrule1
    LET t1Rgt   = t1Lft + 80
    LET t1Eqx   = t1Lft + 27
    LET t1Dot   = t1Lft + 50
    LET t1Top   = t1BasLn1 - 15
    LET t1Bas   = t1BasLn2 +  5
    LET t1Clr   = cyan
    LET t1f$    = "---%.##"

    SUB t1OutputLabels
        CALL SetTextFont(1,12,"bold")
        CALL PlotTextRJ(t1Eqx,t1BasLn1,"t = ",t1Clr)
        CALL PlotTextRJ(t1Eqx,t1BasLn2,"x = ",t1Clr)
    END SUB

    SUB t1CursorValues(x,y)
        CALL t1ClearOutput
        CALL SetTextFont(1,12,"bold")
        CALL AlignDot(t1Dot,t1BasLn1,using$(t1f$,x),t1Clr)
        CALL AlignDot(t1Dot,t1BasLn2,using$(t1f$,y),t1Clr)
    END SUB

    SUB t1ClearOutput
        BOX CLEAR t1Eqx-2,t1Rgt,t1Bas,t1Top+5
    END SUB

    SUB t1Init
        CALL t1OutputLabels
    END SUB

    ! --- t2 - the isocline equations ---

    DIM ClineEq$(0:5)
    MAT READ ClineEq$
    DATA "(1 +- sqrt(1-4c))/2"
    DATA "(t-c)/2"
    DATA "+- sqrt(c+t)"
    DATA "+- sqrt(c-t)"
    DATA "-t/c"
    DATA "c/t"

    LET t2Lft   = h1wLft
    LET t2Rgt   = workrgt
    LET t2BasLn = h1wBas + 20
    LET t2Top   = t2BasLn - 12
    LET t2Bas   = t2BasLn + 5
    LET t2Eqx   = t2Lft + 30
    LET t2Label$= "x' = "

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

    SUB t2ClineEq(ce)
        CALL SetTextFont(1,12,"bold")
        CALL t2Clear
        CALL PlotTextRJ(t2Eqx,t2BasLn,t2Label$,yellow)
        CALL PlotTextLJ(t2Eqx,t2BasLn,"c",yellow)
    END SUB

    !    SUB t2ClineEq(ce)
    !        CALL SetTextFont(1,12,"bold")
    !        CALL t2Clear
    !        CALL PlotTextRJ(t2Eqx,t2BasLn,t2Label$,yellow)
    !        SELECT CASE ce
    !        CASE 2,5,6
    !             CALL PlotTextLJ(t2Eqx,t2BasLn,ClineEq$(ce-1),yellow)
    !        CASE 1
    !             CALL PlotTextLJ(t2Eqx,t2BasLn,"(1 ",yellow)
    !             CALL StringWidth("(1 ",sw)
    !             CALL PlusMinus12(t2Eqx+sw+2,t2BasLn,yellow)
    !             CALL StringWidth("(1 +",sw)
    !             CALL PlotTextLJ(t2Eqx+sw+3,t2BasLn,"sqrt(1-4c)) / 2",yellow)
    !        CASE 3
    !             CALL PlusMinus12(t2Eqx+3,t2BasLn,yellow)
    !             CALL PlotTextLJ(t2Eqx+9,t2BasLn,"sqrt(c+t)",yellow)
    !        CASE 4
    !             CALL PlusMinus12(t2Eqx+3,t2BasLn,yellow)
    !             CALL PlotTextLJ(t2Eqx+9,t2BasLn,"sqrt(c-t)",yellow)
    !        END SELECT
    !    END SUB


    ! --- single check box ---

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

    LET cb1Lft = w1Lft
    LET cb1Bas = w1Bas + 40
    LET cb1Clr = litgry
    LET cb1Txt$= "Slope Field"

    CALL cb1Variables


    ! --- buttons ---

    LET bwid= 135
    LET bhgt= 18

    LET clft= w1Lft
    LET crgt= clft +  90
    LET ctop= w1Bas + 60
    LET cbas= ctop + bhgt

    LET cslft= crgt + 2
    LET csrgt= cslft + bwid
    LET cstop= ctop
    LET csbas= cstop + bhgt

    LET cclft= csrgt + 2
    LET ccrgt= cclft + bwid
    LET cctop= ctop
    LET ccbas= cctop + bhgt

    SUB Buttons
        CALL SetTextFont(1,12,"bold")
        CALL DrawButton(clft,crgt,cbas,ctop,5,"Clear All")
        CALL DrawButton(cslft,csrgt,csbas,cstop,5,"Clear Solutions")
        CALL DrawButton(cclft,ccrgt,ccbas,cctop,5,"Clear Isoclines")
    END SUB

    ! --- default parameters ---

    DIM cValues(0:50),icValues(0:50,0:1)
    LET cCount = 0
    LET ivCount= 0

    LET fieldclr  = drkmid
    LET  cb1State = 1
    LET fieldState= 1
    LET menuState = 0
    LET dt,tstep  = 1/16
    LET f$        = "-%.##"
    LET elft      = t1Lft+32
    LET c         = 1
    LET m1Equation= 3

    CALL SetTimer

    ! --- draw screen ---

    CALL InitScreen
    CALL m1InitMenu1

    SUB InitScreen
        BOX CLEAR worklft,workrgt,workbas,worktop

        CALL w1Init(m1Equation)
        CALL t1Init
        CALL Buttons
        CALL m1ResetMenu(menuState)
        CALL VectorField
        CALL h1Init(m1Equation)
        CALL t2ClineEq(m1Equation)

        CALL w1KeepGraphLayer
        CALL cb1Init
    END SUB

    ! --- event loop ---

    DO
       CALL SetTextFont(1,12,"bold")
       LET clearflag= 0
       IF ms<>2 then
          DO
             GET MOUSE: mx,my,ms
             IF w1Within(mx,my)=true then
                CALL w1wClamp(mx,my)
                IF mx<>oldx or my<>oldy then
                   LET t= w1Fncx(mx)
                   LET x= w1Fncy(my)
                   CALL CopyCoords(mx,my,oldx,oldy)
                   CALL t1CursorValues(t,x)
                   LET clearflag= 1
                END IF
             ELSE
                IF clearflag=1 then
                   CALL CleanUp
                END IF
             END IF
          LOOP until ms=2
       END IF

       IF w1wWithin(mx,my)=true then             ! set initial values and draw
          CALL MouseUp(mx,my,ms)
          CALL w1PixelsToMath(mx,my,t0,x0)
          CALL Trajectory(t0,x0)
          LET icCount= icCount+1
          LET icValues(icCount,0)= t0
          LET icValues(icCount,1)= x0

       ELSE IF h1Within(mx,my)=1 then            ! c slider
          IF my<h1axis then
             CALL h1MouseClick
          ELSE
             CALL h1MouseDrag
          END IF

       ELSE IF m1Within(mx,my)=true then         ! menu
          CALL MouseButtonUp(m1lft,m1rgt,m1bas,m1top,ms)
          CALL m1ReadMenu
          CALL w1Init(m1equation)                ! redraw window for new function

          IF m1Equation=1 then
             LET c= 0
          ELSE
             LET c= 0.2
          END IF
          CALL h1Init(m1Equation)
          CALL t2ClineEq(m1Equation)
          CALL VectorField

          MAT cValues = Zer
          MAT icValues= Zer
          LET cCount  = 0
          LET ivCount = 0

       ELSE IF mx>clft and mx<crgt and my>ctop and my<cbas then      ! clear all
          CALL MouseButtonUp(clft,crgt,cbas,ctop,ms)
          MAT cValues = ZER
          LET cCount  = 0
          MAT icValues= ZER
          LET icCount = 0
          CALL VectorField
          CALL w1KeepGraphLayer

       ELSE IF mx>cslft and mx<csrgt and my>cstop and my<csbas then  ! clear solutions
          CALL MouseButtonUp(cslft,csrgt,csbas,cstop,ms)
          CALL VectorField
          FOR ci= 1 to cCount
              LET c= cValues(ci)
              CALL Cline(1)
          NEXT ci
          CALL w1KeepGraphLayer
          MAT icValues= ZER
          LET icCount = 0

       ELSE IF mx>cclft and mx<ccrgt and my>cctop and my<ccbas then  ! clear clines
          CALL MouseButtonUp(cclft,ccrgt,ccbas,cctop,ms)
          CALL VectorField
          FOR ci= 1 to icCount
              LET t0= icValues(ci,0)
              LET x0= icValues(ci,1)
              CALL Trajectory(t0,x0)
          NEXT ci
          CALL w1KeepGraphLayer
          MAT cValues= ZER
          LET cCount = 0

       ELSE IF cb1Within(mx,my)=true then        ! toggle field state
          CALL cb1MouseUp(ms)
          LET fieldState= cb1State
          CALL VectorField
          FOR ci= 1 to icCount
              LET t0= icValues(ci,0)
              LET x0= icValues(ci,1)
              CALL Trajectory(t0,x0)
          NEXT ci
          FOR ci= 1 to cCount
              LET c= cValues(ci)
              CALL Cline(1)
          NEXT ci
          CALL w1KeepGraphLayer

       ELSE IF infoWithin(mx,my,ms)=true then    ! info page
          CALL infoButtonUp(ms)
          CALL InfoPage(Info$)
          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 CleanUp
        LET clearflag= 0
        CALL t1ClearOutput
    END SUB

    SUB h1MouseClick
        CALL h1GetClickVal(ms,h1Click,c)
        CALL Cline(1)
        CALL w1KeepGraphLayer
        LET oldc= c

        LET cCount= cCount+1
        LET cValues(cCount)= c
    END SUB
    SUB h1MouseDrag
        DO
           CALL h1GetDragVal(ms,h1Places,c)
           IF c<>oldc then
              CALL Cline(1)
              LET oldc= c
           END IF
        LOOP until ms=3
        CALL w1KeepGraphLayer

        LET cCount= cCount+1
        LET cValues(cCount)= c
    END SUB

    ! ----- trajectory routines -----

    SUB Trajectory(t0,x0)
        LET dt=  tstep                           ! reset to default
        CALL DrawTraj(t0,x0)
        IF ms=2 then EXIT SUB
        LET dt= -tstep                           ! reset to default
        CALL DrawTraj(t0,x0)
        CALL w1KeepGraphLayer
    END SUB

    SUB DrawTraj(t0,x0)
        SET COLOR cyan
        CALL CopyCoords(t0,x0,t,x)
        IF m1Equation<>5 then
           DO
              CALL w1MathToPixels(t,x,wx,wy)
              IF wx<w1Rgt and wx>w1Lft and wy>w1Top and wy<w1Bas then
                 IF x<>badarg then
                    PLOT wx,wy;
                 ELSE
                    PLOT
                 END IF
              ELSE
                 PLOT
              END IF
              CALL CopyCoords(wx,wy,oldwx,oldwy)
              CALL AdjustStep(oldwx,oldwy)

              CALL RungeKutta4(t,x)
              CALL w1MathToPixels(t,x,wx,wy)

              IF abs(x)>5 or abs(t)>5 then EXIT DO    ! leaving the window?
              GET MOUSE: mx,my,ms
              IF ms=2 then EXIT DO
           LOOP
           PLOT
        ELSE                                     ! m1equation is 5: circles
           LET r= sqr(t*t+x*x)
           IF x<>0 or t<>0 then
              LET a= angle(t,x)
           ELSE
              LET a= 0
           END IF

           IF r>0 then
              LET stp= 1/(50*r)
              IF r<w1fTop then
                 FOR ang= a to a+2*pi step stp
                     CALL PolarToCartesian(r,ang,xx,yy)
                     PLOT w1Wndx(xx),w1Wndy(yy)
                 NEXT ang
              ELSE
                 FOR i= 0 to 3
                     LET a1= a + i*pi/2
                     FOR ang= a1 to a1+pi/2 step stp

                         CALL PolarToCartesian(r,ang,xx,yy)
                         IF w1fWithin(xx,yy)=1 then
                            PLOT w1Wndx(xx),w1Wndy(yy)
                         ELSE
                            EXIT FOR
                         END IF
                     NEXT ang
                     FOR ang= a1 to a1-pi/2 step -stp
                         CALL PolarToCartesian(r,ang,xx,yy)
                         IF w1fWithin(xx,yy)=1 then
                            PLOT w1Wndx(xx),w1Wndy(yy)
                         ELSE
                            EXIT FOR
                         END IF
                     NEXT ang
                 NEXT i
              END IF
           END IF
        END IF
    END SUB

    SUB AdjustStep(oldwx,oldwy)
        FOR i= 1 to 6
            CALL CopyCoords(x,t,tx,tt)
            CALL RungeKutta4(tt,tx)              ! check the next values
            CALL w1MathToPixels(tt,tx,wtt,wtx)
            LET pixels= max(abs(abs(wtt)-abs(oldwx)),abs(abs(wtx)-abs(oldwy)))
            IF pixels>=2 and pixels<=4 then
               EXIT FOR
            ELSE
               IF pixels<2 then
                  LET dt= dt*2
               ELSE IF pixels>4 then
                  LET dt= dt/2
               END IF
            END IF
        NEXT i
    END SUB

    SUB RungeKutta4(t,x)
        CALL FetchEq(m1Equation,t,x,dx,dy)
        LET dx1= dx
        LET dy1= dy
        LET x1 = t + .5*dx1*dt
        LET y1 = x + .5*dy1*dt
        CALL FetchEq(m1Equation,x1,y1,dx,dy)
        LET dx2= dx
        LET dy2= dy
        LET x2 = t + .5*dx2*dt
        LET y2 = x + .5*dy2*dt
        CALL FetchEq(m1Equation,x2,y2,dx,dy)
        LET dx3= dx
        LET dy3= dy
        LET x3 = t + dx3*dt
        LET y3 = x + dy3*dt
        CALL FetchEq(m1Equation,x3,y3,dx,dy)
        LET dx4= dx
        LET dy4= dy

        LET dy = (dy1 + 2*dy2 + 2*dy3 + dy4) / 6
        LET dx = (dx1 + 2*dx2 + 2*dx3 + dx4) / 6
        LET x  = x + dt*dy
        LET t  = t + dt*dx
    END SUB

    ! ----- end of trajectory routines -----
    ! ----- isocline graph routines -----

    SUB Cline(vctflag)
        CALL w1ShowGraphLayer

        SET COLOR yellow
        SELECT CASE m1Equation
        CASE 1
             LET n   = 1-4*c
             LET sqrn= sqr(n)
             IF n>=0 then
                LET x = (1 + sqrn)/2
                LET wx= w1Wndy(x)
                PLOT w1Lft,wx; w1Rgt,wx

                LET x = (1 - sqrn)/2
                LET wx= w1Wndy(x)
                PLOT w1Lft,wx; w1Rgt,wx
             END IF
        CASE 2
             FOR wx= w1Lft to w1Rgt
                 LET t = w1Fncx(wx)
                 LET x = (t-c)/2
                 LET wy= w1Wndy(x)
                 IF wy>w1Top and wy<w1Bas then
                    PLOT wx,wy;
                 ELSE
                    PLOT
                 END IF
             NEXT wx
             PLOT
        CASE 3
             FOR wy= w1Top to w1Bas
                 LET x = w1Fncy(wy)
                 LET t = x*x - c
                 LET wx= w1Wndx(t)
                 IF wx>w1Lft and wx<w1Rgt then
                    PLOT wx,wy;
                 ELSE
                    PLOT
                 END IF
             NEXT wy
             PLOT
        CASE 4
             IF c>0 then
                CALL DrawFt( 1)
                CALL DrawFt(-1)
             ELSE IF c<0 then
                CALL DrawFx( 1)
                CALL DrawFx(-1)
             ELSE IF c=0 then
                CALL DrawFt( 1)
                CALL DrawFt(-1)
                CALL DrawFx( 1)
                CALL DrawFx(-1)
             END IF
        CASE 5
             IF c<>0 then
                FOR wx= w1Lft to w1Rgt
                    LET t = w1Fncx(wx)
                    LET x = -t/c
                    LET wy= w1Wndy(x)
                    IF wy>w1Top and wy<w1Bas then
                       PLOT wx,wy;
                    ELSE
                       PLOT
                    END IF
                NEXT wx
                PLOT
             ELSE
                PLOT w1x0,w1Top; w1x0,w1Bas
             END IF
        CASE 6
             FOR wx= w1Lft to w1Rgt
                 LET t = w1Fncx(wx)
                 LET x = t*c
                 LET wy= w1Wndy(x)
                 IF wy>w1Top and wy<w1Bas then
                    PLOT wx,wy;
                 ELSE
                    PLOT
                 END IF
             NEXT wx
             PLOT
        END SELECT

        IF vctflag=1 then
           CALL ClineVectors
        END IF
    END SUB

    SUB DrawFt(sign)
        FOR wx= w1Lft to w1Rgt step 2
            LET t = w1Fncx(wx)
            LET n = c+t*t
            IF n>=0 then
               LET x = sign*sqr(n)
               LET wy= w1Wndy(x)
               IF wy>w1Top and wy<w1Bas then
                  PLOT wx,wy;
               ELSE
                  PLOT
               END IF
            END IF
        NEXT wx
        PLOT
    END SUB

    SUB DrawFx(sign)
        FOR wy= w1Top to w1Bas step 2
            LET x = w1Fncy(wy)
            LET t = sign * sqr(x*x-c)
            LET wx= w1Wndx(t)
            IF wx>w1Lft and wx<w1Rgt then
               PLOT wx,wy;
            ELSE
               PLOT
            END IF
        NEXT wy
        PLOT
    END SUB

    SUB ClineVectors
        SET COLOR cyan
        SELECT CASE m1Equation
        CASE 1
             !    DEF f1(x) = x*(1-x)
             FOR t= w1fLft to w1fRgt
                 LET wx= w1Wndx(t)
                 IF 1-4*c>=0 then
                    LET n = sqr(1-4*c)
                    LET x = (1+n)/2
                    CALL DrawPointerX
                    LET x = (1-n)/2
                    CALL DrawPointerX
                 END IF
             NEXT t
        CASE 2
             !    DEF f2(x) = t-2x
             FOR t= w1fLft+1 to w1fRgt-1
                 LET wx= w1Wndx(t)
                 LET x = (t-c)/2
                 CALL DrawPointerX
             NEXT t
        CASE 3
             !    DEF f3(x) = x*x-t
             FOR t= w1fLft to w1fRgt
                 LET wx= w1Wndx(t)
                 IF c+t>=0 then
                    LET n = sqr(c+t)
                    LET x = n
                    CALL DrawPointerX
                    LET x = -n
                    CALL DrawPointerX
                 END IF
             NEXT t
        CASE 4
             !    DEF f4(x) = x*x-t*t
             IF c>0 then
                FOR t= w1fLft+1 to w1fRgt-1
                    LET wx= w1Wndx(t)
                    IF c+t*t>=0 then
                       LET n = sqr(c+t*t)
                       LET x =  n
                       CALL DrawPointerX
                       LET x = -n
                       CALL DrawPointerX
                    END IF
                NEXT t
             ELSE IF c<=0 then
                FOR x= w1fBas+1 to w1fTop-1
                    LET wy= w1Wndy(x)
                    IF x*x-c>=0 then
                       LET n = sqr(x*x-c)
                       LET t =  n
                       CALL DrawPointerT
                       LET t = -n
                       CALL DrawPointerT
                    END IF
                NEXT x
             END IF
        CASE 5
             IF c<>0 then
                LET ang   =  angle(1,-1/c)
                LET angle1= -pi/2-ang
                LET angle2=  pi/2-ang

                FOR r= -3.5 to 3.5
                    CALL PolarToCartesian(r,ang,x,y)
                    CALL w1MathToPixels(x,y,wx,wy)
                    IF c>0 then
                       DRAW pointer with rotate(angle1) * shift(wx,wy)
                    ELSE
                       DRAW pointer with rotate(angle2) * shift(wx,wy)
                    END IF
                NEXT r
             ELSE
                LET wx= w1x0
                FOR r= -3.5 to 3.5
                    LET wy= w1Wndy(r)
                    DRAW pointer with shift(wx,wy)
                NEXT r
             END IF
        CASE 6
             IF c<>0 then
                LET ang= angle(1,c)
                FOR r= -3.5 to 3.5
                    CALL PolarToCartesian(r,ang,x,y)
                    CALL w1MathToPixels(x,y,wx,wy)
                    IF c>0 then
                       DRAW pointer with rotate(-ang) * shift(wx,wy)
                    ELSE
                       DRAW pointer with rotate(-ang) * shift(wx,wy)
                    END IF
                NEXT r
             ELSE
                LET wy= w1y0
                FOR r= -3.5 to 3.5
                    LET wx= w1Wndx(r)
                    DRAW pointer with shift(wx,wy)
                NEXT r
             END IF
        END SELECT
    END SUB

    SUB DrawPointerX
        CALL FetchEq(m1Equation,t,x,dx,dy)
        LET dx= dx*w1aspect
        LET wy= w1Wndy(x)
        CALL AngleRadians(dx,-dy,a)
        ! PRINT a
        !CALL DrawIsoPointer(wx,wy,a)
        DRAW pointer with rotate(a) * shift(wx,wy)
    END SUB

    SUB DrawPointerT
        CALL FetchEq(m1Equation,t,x,dx,dy)
        LET dx  = dx*w1aspect
        LET wx  = w1Wndx(t)
        ! LET ang = angle(dx,-dy)
        CALL AngleRadians(dx,-dy,a)
        !CALL DrawIsoPointer(wx,wy,a)
        DRAW pointer with rotate(a) * shift(wx,wy)
    END SUB

    SUB SlopeMark(sx,sy)
        CALL FetchEq(m1Equation,sx,sy,dx,dy)
        ! LET ang= angle(dx,-dy)
        CALL AngleRadians(dx,-dy,ang)
        LET sa = 4*sin(ang)
        LET wy1= wy+sa
        LET wy2= wy-sa
        LET ca = 4*cos(ang)
        CALL VectorHead(ang,wx,wy,wvx0,wvy0)
    END SUB

    SUB VectorHead(ang,wx,wy,wvx0,wvy0)
        CALL SetVMat(ang)
        CALL Rotate(6, 2,vx1,vy1)
        CALL Rotate(6,-2,vx2,vy2)
        LET wvx1= wx+vx1
        LET wvy1= wy+vy1
        LET wvx2= wx+vx2
        LET wvy2= wy+vy2
        PLOT wvx1,wvy1; wvx0,wvy0; wvx2,wvy2
    END SUB

    SUB Rotate(xin,yin,xout,yout)
        LET xout= xin*vcta + yin*vctc
        LET yout= xin*vctb + yin*vctd
    END SUB

    SUB SetVMat(ang)
        LET vcta=  cos(ang)
        LET vctb=  sin(ang)
        LET vctc= -vctb
        LET vctd=  vcta
    END SUB

    PICTURE pointer
        PLOT 2,-4;  6,0; 2,4
        PLOT 6, 0; -6,0
    END PICTURE

    SUB DrawIsoPointer(wxp,wyp,a)
        CALL SetVMat(a)
        CALL Rotate(-3, 0,lftx,lfty)
        CALL Rotate(+3, 0,rgtx,rgty)
        CALL Rotate( 0,-3,waxm,waym)
        CALL Rotate( 0,+3,waxp,wayp)

        PLOT w1Wndx(lftx), w1Wndy(lfty); w1Wndx(rgtx), w1Wndy(rgty)
        !        PLOT waxm,waym; wrgtx,wrgty
        !        PLOT waxp,wayp; wrgtx,wrgty
    END SUB

    SUB AngleRadians(x,y,a)
        IF x>0 then
           LET a= atn(y/x)
        ELSE IF x<0 and y<>0 then
           LET a= atn(y/x)+sgn(y) * 180
        ELSE IF x<0 and y=0 then
           LET a= 180
        ELSE IF y<>0 then
           LET a= sgn(y)*90
        ELSE
        END IF
    END SUB

    ! ----- end of isocline graph routines -----

    SUB VectorField
        CALL w1ShowGridLayer
        IF fieldState=1 then
           SET COLOR fieldclr                    ! vector field
           LET vstp  = 20
           LET hstp  = vstp/2
           FOR wy= w1top+hstp to w1bas-hstp step vstp
               FOR wx= w1Lft+hstp to w1Rgt-hstp step vstp
                   CALL w1PixelsToMath(wx,wy,x,y)
                   IF round(y,2)<>0 then
                      CALL FetchEq(m1Equation,x,y,dx,dy)
                      LET dx = dx*w1aspect
                      LET ang= angle(dx,-dy)
                      LET sa = 4*sin(ang)
                      LET wy1= wy+sa
                      LET wy2= wy-sa
                      LET ca = 4*cos(ang)
                      PLOT wx-ca,wy2; wx+ca,wy1
                   END IF
               NEXT wx
           NEXT wy
           CALL w1KeepGraphLayer
        ELSE
           CALL w1KeepGraphLayer
        END IF
    END SUB
END SUB

! ----- end of isoclines code -----