! this uses u for time and t for the moving "current" time

! a simple discrete convolution

! Invest 1 dollar a day in internet stock, and each day a dollar loses half its value.
! There are two discrete functions:
!    f(u) = 1           ! (signal)  invest one dollar per day
!    g(u) = (1/2)^u     ! (weight)  reduce value by half each day

! The discrete convolution, f*g, is the sum of the products, f(u) g(t-u)
! for current day, t, and time from u=0 to u=t.  
! g(u) has values 1, 1/2, 1/4, 1/8, etc.

! On any given day, we have a sum of products. Suppose the day, t, is 2, 
! and we look at each day from u=t or u=2, back to u=0.

! day 0:  1               = 1
! day 1: 1/2   1          = 1.5
! day 2: 1/4  1/2   1     = 1.75
! day 3: 1/8  1/4  1/2  1 = 1.875

! or more graphically

!                  1
!             1   1/2
!        1   1/2  1/4
!   1   1/2  1/4  1/8
! -------------------> u
!   0    1    2    3
!             t

! If the current day, t, is 2:
! On day u=2, the new dollar is multiplied by 1, which is g(t-u) or g(0), so its value is 1.
! The day u=1 dollar is multiplied by 1/2, which is g(t-u) or g(1), so its value is now 1/2.
! The day u=0 dollar is multiplied by 1/4, which is g(t-u) or g(2), so its value is now 1/4.

! g(0) or 1, is the weight for day 2, and g(2), or 1/4 is the weight for day 0.
! So the weighting function, g, is reversed in time to find the daily products.

! The products on day 2 are f(2)*g(2-2) = 1*1, f(2)*g(2-1) = 1*1/2, f(2)*g(2-0) = 1*1/4
! The sum of products on day 2 is 1 + 1/2 + 1/4 = 1.75.

! The points on the convolution curve are the sums of the products to each day:
! (0,1), (1,1.5), (2,1.75), (3,1.875)
! The discrete convolution curve records the history of the sums of the products.

! Using continuous functions, the products form a continuous curve, and 
! the convolution curve records the history of the area under the product curve.


!! File: ConvolutionBack
!! January 13, 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 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

! DECLARE DEF quitWithin,infoWithin

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

LET title$ = "Convolution: Looking Back"

SUB ThisProgram
    CALL ConvolutionBack
    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 51a\TBLibs\TrueCtrl.trc"     ! windows
LIBRARY "c:\TB Gold 51a\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 ConvolutionBack
    DECLARE PUBLIC worklft,workrgt,workbas,worktop,workmid      ! work area
    DECLARE PUBLIC black,drkgry,drkmid,midgry,litmid,litgry,white
    DECLARE PUBLIC red,yellow,green,cyan,blue,magenta,colorscheme
    DECLARE PUBLIC slideclr,axislabelclr,true,false

    DECLARE DEF InfoWithin, QuitWithin


    ! ------- help screen array -------

    DIM  info$(1:1)
    MAT READ info$
    DATA "Information on convolution"


    ! ------- color -------

    LET sigClr = red
    LET wgtClr = green
    LET cnvClr = cyan
    LET prdClr = yellow
    LET areaClr= blue

    SET COLOR MIX(areaClr) 0,.5,.4               ! remix blue fill


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

    DECLARE DEF clamp,roundn,e


    ! --- functions and parameters -----------

    !    SUB SetConstants(signum,wgtnum, a,b,k)
    !        SELECT CASE signum
    !        CASE 1
    !             SELECT CASE wgtnum
    !             CASE 1
    !             CASE 2
    !             CASE 3
    !             CASE 4
    !             END SELECT
    !        CASE 2
    !             SELECT CASE wgtnum
    !             CASE 1
    !             CASE 2
    !             CASE 3
    !             CASE 4
    !             END SELECT
    !        CASE 3
    !             SELECT CASE wgtnum
    !             CASE 1
    !             CASE 2
    !             CASE 3
    !             CASE 4
    !             END SELECT
    !        CASE 4
    !             SELECT CASE wgtnum
    !             CASE 1
    !             CASE 2
    !             CASE 3
    !             CASE 4
    !             END SELECT
    !        END SELECT
    !    END SUB

    ! ----------------------------------------

    !For reference: the LTI differential operators with these weight functions are:
    !w1:  Lx = x' + ax
    !w2:  Lx = x'
    !w3:  Lx = x" + b^2 x
    !w4:  Lx = x" + 2a x' + a^2 x

    !The convolution equals the solution to  Lx = f(t)  with rest initial cond's:
    !x(0) = 0             in the first order cases
    !x(0) = 0, x'(0) = 0  in the second order cases.

    !Here are the convolutions: (notation:  c^2 = a^2 + b^2)

    !f1*w1(t) = (1/c^2)(a sin(bt) - b cos(bt) + b e^{-at}).
    !f1*w2(t) = (1/b)(1 - cos(bt))
    !f1*w3(t) = (-1/2b) t cos(bt) + (1/2b^2) sin(bt).
    !f1*w4(t) = ((a^2-b^2)/c^4) sin(bt) - (2ab/c^4) cos(bt) + ((b/c^2)t + 2ab/c^4) e^{-at} 

    !f2*w1(t) = (1/a)(1 - e^{-at}).
    !f2*w2(t) = t
    !f2*w3(t) = (1/b)(1 - cos(bt)).
    !f2*w4(t) = (1/a^2) - (t/a + 1/a^2) e^{-at}

    !f3*w1(t) = (1/a)(1 - e^{-at})                   for  t < t0
    !           (1/a)(1 - e^{-a(t0)}) e^{-a(t-t0))   for  t > t0
    !f3*w2(t) = t    for t < t0
    !           t0   for t > t0
    !f3*w3(t) = (1/b)(1 - cos(bt))                   for  t < t0
    !           (1/b)(1 - cos(b t0)) cos(b(t-t0)) + (1/b) sin(b t0) sin(b(t-t0))  for  t > t0
    !f3*w4(t) = (1/a^2) - (t/a + 1/a^2) e^{-at}      for  t < t0
    !           (c1(t-t0) + c0) e^{-a(t-t0)}         for  t > t0           
    !           where   c1 = (1/a)(1 - e^{-a t0})
    !                   c0 = (1/a^2) - (t0/a + 1/a^2) e^{-a t0).

    !f4*w1(t) = (1/h^2) (a sin(wt) - w cos(wt) + w e^{-at}).
    !f4*w2(t) = (1/w) (1 - cos(wt))
    !f4*w3(t) = (1/(w^2-b^2)) (sin(wt) - (w/b) sin(bt))
    !f4*w4(t) = ((a^2-w^2)/h^4) sin(wt) - (2aw/h^4) cos(wt) + ((w/h^2)t + 2aw/h^4) e^{-at} 
    !           where  h^2 = a^2 + w^2.

    DIM CnvVals(1:1)

    !f4(t) = sin(wt)  where  w  differs from  b.
    !The "b"s here are intentionally the same. You took  b = 2, and w = 1, and
    !this looks good. 

    SUB SetConstants(signum,wgtnum, a,b,k)
        IF signum=4 then
           LET a= 1
           LET b= 1
           LET k= 2                              ! haynes used w
           !        ELSE IF signum=3 and wgtnum=5 then
           !           LET a= 0.2
           !           LET b= 2
           !           LET k= 1                              ! haynes used w
        ELSE
           LET a= 1
           LET b= 1
           LET k= 1
        END IF
    END SUB


    ! ----- weights -----

    !w1(t) = e^{-at}       (t > 0)
    !w2(t) = 1             (t > 0)
    !w3(t) = (1/b) sin(bt) (t > 0)
    !w4(t) = t e^{-at}     (t > 0)

    DEF w(wgtnum,t)
        IF t>=0 then
           SELECT CASE wgtnum
           CASE 1
                LET w= e^(-a*t)
           CASE 2
                LET w= 1
           CASE 3
                LET w= 1/b * sin(b*t)
           CASE 4
                LET w= t * e^(-a*t)
           CASE 5
                LET w= 1/b * sin(b*t) * e^(-a*t)
           END SELECT
        ELSE
           LET w= 0
        END IF
    END DEF


    !w5(t) = (1/b) e^{-at} sin(bt) 
    !
    !(a and b will have the same values as they did for the other weights.)



    ! ----- signals -----

    !f1(t) = sin(bt)
    !f2(t) = 1
    !f3(t) = 1  for  0 < t < 3
    !f4(t) = sin(kt)   where  k  differs from  b.

    LET f3Step= 3
    DEF f(signum,t)
        IF signum<>3 then
           IF t<0 then
              LET f= 0
           ELSE
              SELECT CASE signum
              CASE 1
                   LET f= sin(b*t)
              CASE 2
                   LET f= 1
              CASE 4
                   LET f= sin(k*t)
              END SELECT
           END IF
        ELSE IF signum=3 then
           IF t>=0 and t<f3step then
              LET f= 1
           ELSE
              LET f= 0
           END IF
        END IF
    END DEF


    ! ------- convolution equations -------


    !f1*w5(t) = (1/(a^4 + 4a^2b^2)) ((a^2) sin(bt) - 2ab cos(bt) + e^{-at} (2ab cos(bt) + (a^2) sin(bt)))
    !
    !f2*w5(t) = (1/(a^2+b^2)) (1 - e^{-at} (cos(bt) + (a/b) sin(bt)))
    !
    !  Let c0 = (1/(a^2+b^2)) (1 - e^{-a(t0)} (cos(b(t0)) + (a/b) sin(b(t0)))) 
    !      c1 = (1/b) e^{-a(t0)} sin(b(t0))
    !f3*w5(t) = (1/(a^2+b^2)) (1 - e^{-at} (cos(bt) + (a/b) sin(bt)))             for  t < t0
    !         = e^{a(t-t0)} (c0 cos(b(t-t0)) + ((a(c0) + c1)/b) sin(b(t-t0)))     for  t > t0
    !
    !  Let  d = (a^2+b^2-w^2)^2 + 4a^2w^2 .
    !f4*w5(t) = (1/d) ((a^2+b^2-w^2) sin(wt) - 2aw cos(wt) + e^{-at} (2aw cos(bt) + (a^2-b^2+w^2)(w/b) sin(bt)))

    DEF cnv(signum,wgtnum,t)
        LET c2 = a^2 + b^2
        LET c4 = c2^2
        LET h2 = a^2 + k^2
        LET h4 = h2^2

        IF t<0 then
           LET cnv= 0
        ELSE
           SELECT CASE signum
           CASE 1
                !f1*w1(t) = (1/c^2)(a sin(bt) - b cos(bt) + b e^{-at})
                !f1*w2(t) = (1/b)(1 - cos(bt))
                !f1*w3(t) = (-1/2b) t cos(bt) + (1/2b^2) sin(bt)
                !f1*w4(t) = ((a^2-b^2)/c^4) sin(bt) - (2ab/c^4) cos(bt) + ((b/c^2)t + 2ab/c^4) e^{-at} 
                !f1*w5(t) = (1/(a^4 + 4a^2b^2)) ((a^2) sin(bt) - 2ab cos(bt) + e^{-at} (2ab cos(bt) + (a^2) sin(bt)))

                SELECT CASE wgtnum
                CASE 1
                     LET cnv = (1/c2) * (a*sin(b*t) - b*cos(b*t) + b*e^(-a*t))
                CASE 2
                     LET cnv = (1/b)*(1-cos(b*t))
                CASE 3
                     LET cnv = (-1/(2*b))*t*cos(b*t) + 1/(2*b^2)*sin(b*t)
                CASE 4
                     LET cnv = ((a^2-b^2)/c4)*sin(b*t) - (2*a*b/c4)*cos(b*t) + ((b/c2)*t + 2*a*b/c4)*e^(-a*t)
                CASE 5
                     LET cnv = (1/(a^4 + 4*a^2*b^2))  *  ((a^2)*sin(b*t) - 2*a*b*cos(b*t)  +  e^(-a*t) * (2*a*b*cos(b*t)+(a^2)*sin(b*t)))
                END SELECT
           CASE 2
                !f2*w1(t) = (1/a)(1 - e^{-at}).
                !f2*w2(t) = t
                !f2*w3(t) = (1/b)(1 - cos(bt)).
                !f2*w4(t) = (1/a^2) - (t/a + 1/a^2) e^{-at}

                SELECT CASE wgtnum
                CASE 1
                     LET cnv = (1/a) * (1-e^(-a*t))
                CASE 2
                     LET cnv = t
                CASE 3
                     LET cnv = (1/b) * (1-cos(b*t))
                CASE 4
                     LET cnv = (1/a^2) - (t/a + 1/a^2)*e^(-a*t)
                CASE 5
                     LET cnv = (1/(a^2+b^2)) * (1 - e^(-a*t) * (cos(b*t) + (a/b)*sin(b*t)))
                END SELECT
           CASE 3
                !f3*w1(t) = (1/a)(1 - e^{-at})                   for  t < t0
                !           (1/a)(1 - e^{-a(t0)}) e^{-a(t-t0))   for  t > t0
                !f3*w2(t) = t    for t < t0
                !           t0   for t > t0
                !f3*w3(t) = (1/b)(1 - cos(bt))                   for  t < t0
                !           (1/b)(1 - cos(b t0)) cos(b(t-t0)) + (1/b) sin(b t0) sin(b(t-t0))  for  t > t0
                !f3*w4(t) = (1/a^2) - (t/a + 1/a^2) e^{-at}      for  t < t0
                !           (c1(t-t0) + c0) e^{-a(t-t0)}         for  t > t0           
                !           where  c1 = (1/a)(1 - e^{-a t0})
                !                  c0 = (1/a^2) - (t0/a + 1/a^2) e^{-a t0).
                !f3*w5(t) = (1/(a^2+b^2)) (1 - e^{-at} (cos(bt) + (a/b) sin(bt)))             for  t < t0
                !         = e^{a(t-t0)} (c0 cos(b(t-t0)) + ((a(c0) + c1)/b) sin(b(t-t0)))     for  t > t0
                !           where  c0 = (1/(a^2+b^2)) (1 - e^{-a(t0)} (cos(b(t0)) + (a/b) sin(b(t0)))) 
                !                  c1 = (1/b) e^{-a(t0)} sin(b(t0))

                SELECT CASE wgtnum
                CASE 1
                     IF t<f3step then
                        LET cnv = (1/a)*(1-e^(-a*t))
                     ELSE
                        LET cnv = (1/a)*(1-e^(-a*(f3step)))*e^(-a*(t-f3step))
                     END IF
                CASE 2
                     IF t<f3step then
                        LET cnv = t
                     ELSE
                        LET cnv = f3step
                     END IF
                CASE 3
                     IF t<f3step then
                        LET cnv = (1/b)*(1-cos(b*t))
                     ELSE
                        LET cnv = (1/b)*(1-cos(b*f3step))*cos(b*(t-f3step)) + (1/b)*sin(b*f3step)*sin(b*(t-f3step))
                     END IF
                CASE 4
                     LET c1 = (1/a) * (1-e^(-a*f3step))
                     LET c0 = (1/a^2) - (f3step/a + 1/a^2)*e^(-a*f3step)

                     IF t<f3step then
                        LET cnv = (1/a^2) - (t/a + 1/a^2)*e^(-a*t)
                     ELSE
                        LET tdif= t-f3step
                        LET cnv = (c1*tdif + c0) * e^(-a*tdif)
                     END IF
                CASE 5
                     ! signal is a step function from 0 to 3
                     ! f3step is your t0
                     ! k is your w         (the weight function is w and that conflicts)

                     LET c1 = (1/(a^2+b^2)) * (1 - e^(-a*f3step) * (cos(b*f3step) + (a/b)*sin(b*f3step)) )
                     LET c0 = (1/b) * e^(-a*f3step) * sin(b*f3step)

                     IF t<f3step then
                        ! this is ok
                        LET cnv = (1/(a^2+b^2)) * (1 - e^(-a*t)*(cos(b*t) + (a/b)*sin(b*t)))
                     ELSE
                        LET tdif= t-f3step

                        ! this breaks very badly - needs a negative exponent for e and a c1 for cos amplitude
                        ! LET cnv = e^(a*tdif) * ( c0*cos(b*tdif) + (a*c0+c1)/b * sin(b*tdif) )

                        LET cnv = e^(-a*tdif) * ( c1*cos(b*tdif) + (a*c0+c1)/b * sin(b*tdif) )
                     END IF
                END SELECT
           CASE 4                                ! sin(2t)
                !f4*k1(t) = (1/h^2) (a sin(kt) - k cos(kt) + k e^{-at}).
                !f4*k2(t) = (1/k) (1 - cos(kt))
                !f4*k3(t) = (1/(k^2-b^2)) (sin(kt) - (k/b) sin(bt))
                !f4*k4(t) = ((a^2-k^2)/h^4) sin(kt) - (2ak/h^4) cos(kt) + ((k/h^2)t + 2ak/h^4) e^{-at} 
                !           where  h^2 = a^2 + k^2
                !f4*w5(t) = (1/d) ((a^2+b^2-k^2) sin(kt) - 2ak cos(kt) + e^(-at) (2ak cos(bt) + (a^2-b^2+k^2)(k/b) sin(bt)))
                !           where  d = (a^2+b^2-k^2)^2 + 4a^2k^2

                SELECT CASE wgtnum
                CASE 1
                     LET cnv = (1/h2) * (a*sin(k*t) - k*cos(k*t) + k*e^(-a*t))
                CASE 2
                     LET cnv = (1/k)*(1-cos(k*t))
                CASE 3
                     LET cnv = -(1/(k^2-b^2)) * (sin(k*t)-(k/b)*sin(b*t))
                CASE 4
                     LET cnv = ((a^2-k^2)/h4)*sin(k*t) - (2*a*k/h4)*cos(k*t) + ((k/h2)*t + 2*a*k/h4)*e^(-a*t)
                CASE 5
                     LET d   = (a^2 + b^2 - k^2)^2 + 4*a^2*k^2
                     LET cnv = (1/d)*((a^2+b^2-k^2)*sin(k*t) - 2*a*k*cos(k*t) + e^(-a*t)*(2*a*k*cos(b*t) + (a^2-b^2+k^2)*(k/b) * sin(b*t)))
                END SELECT
           END SELECT
        END IF
    END DEF



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

    LET wwid      = 360
    LET fwid      =  12
    LET pixperunit= wwid/fwid
    LET pixstep   = 1/pixperunit                 ! .025
    LET whgt      = 120
    LET wyStp     =  50                          ! vertical space between graph planes

    LET vrule1= workLft + 45
    LET vrule2= vrule1 + wwid + 85

    ! --- plane 1 ---

    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  w1xPiFlag, w1xMult, w1yPiFlag, w1yMult

    DECLARE DEF w1Fncx,w1Fncy,w1Wndx,w1Wndy
    DECLARE DEF w1wWithin,w1Within

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

    LET w1Lft    = vrule1                        ! 180
    LET w1Rgt    = w1Lft + wwid
    LET w1Top    = workTop + 32
    LET w1Bas    = w1Top + whgt

    LET w1fLft   =  -1
    LET w1fRgt   =  fwid
    LET w1fBas   =  -1.5
    LET w1fTop   =   1.5

    LET w1xax$   = "u"
    LET w1xSTik  = 0
    LET w1xLTik  = 1
    LET w1xLabel = 1
    LET w1xFirst = w1fLft

    LET w1yax$   = "(f*g)(t)"
    LET w1ySTik  =  0.5
    LET w1yLTik  =  1
    LET w1yLabel =  1
    LET w1yFirst = -1

    LET w1yGridstep= 0
    LET w1xGridstep= 0

    CALL w1Variables

    SUB w1Init
        CALL w1DrawPlane(1,1,1)
        CALL SetTextFont(1,12,"bold")

        CALL PlotTextLJ(w1Rgt+8,w1y0+3,w1xax$,5)

        CALL StringWidth("(f * g)(t)",cw)
        CALL SetConvolutionTypeRJ(w1x0+cw/2+2,w1Top-12,cnvClr)
        CALL w1KeepGridLayer
    END SUB

    SUB w1SetBounds(signum,wgtnum)
        SELECT CASE signum
        CASE 1
             SELECT CASE wgtnum
             CASE 1,4,5
                  LET w1fBas  = -1.0
                  LET w1fTop  =  1.0
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  1.0
                  LET w1yFirst= -1.0
             CASE 2
                  LET w1fBas  = -0.5
                  LET w1fTop  =  2.5
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  1.0
                  LET w1yFirst=  0
             CASE 3
                  LET w1fBas  = -6.0
                  LET w1fTop  =  6.0
                  LET w1yStik =  0
                  LET w1yLtik =  1.0
                  LET w1yLabel=  2.0
                  LET w1yFirst= -6.0
             END SELECT
        CASE 2
             SELECT CASE wgtnum
             CASE 1,4
                  LET w1fBas  = -0.5
                  LET w1fTop  =  1.5
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  0.5
                  LET w1yFirst= -0.5
             CASE 2
                  LET w1fBas  = -1.0
                  LET w1fTop  = 14.0
                  LET w1yStik =  0
                  LET w1yLtik =  1.0
                  LET w1yLabel=  2.0
                  LET w1yFirst=  0
             CASE 3
                  LET w1fBas  = -0.5
                  LET w1fTop  =  2.5
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  1.0
                  LET w1yFirst=  0
             CASE 5
                  LET w1fBas  = -0.5
                  LET w1fTop  =  1.0
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  0.5
                  LET w1yFirst= -0.5
             END SELECT
        CASE 3
             SELECT CASE wgtnum
             CASE 1,4,5
                  LET w1fBas  = -0.5
                  LET w1fTop  =  1.0
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  0.5
                  LET w1yFirst= -0.5
             CASE 2
                  LET w1fBas  = -1.0
                  LET w1fTop  =  4.0
                  LET w1yStik =  0
                  LET w1yLtik =  1.0
                  LET w1yLabel=  1.0
                  LET w1yFirst= -1.0
             CASE 3
                  LET w1fBas  = -3.0
                  LET w1fTop  =  3.0
                  LET w1yStik =  0
                  LET w1yLtik =  1.0
                  LET w1yLabel=  1.0
                  LET w1yFirst= -3.0
             END SELECT
        CASE 4
             SELECT CASE wgtnum
             CASE 1,3
                  LET w1fBas  = -1.0
                  LET w1fTop  =  1.0
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  1.0
                  LET w1yFirst= -1.0
             CASE 2
                  LET w1fBas  = -0.5
                  LET w1fTop  =  1.5
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  1.0
                  LET w1yFirst=  0
             CASE 4,5
                  LET w1fBas  = -0.5
                  LET w1fTop  =  0.5
                  LET w1yStik =  0
                  LET w1yLtik =  0.5
                  LET w1yLabel=  0.5
                  LET w1yFirst= -5.5
             END SELECT
        CASE else
        END SELECT
        CALL w1Variables
    END SUB

    ! --- window 2 ---

    DECLARE PUBLIC  w2Lft, w2Rgt, w2Bas, w2Top, w2Midx, w2Midy
    DECLARE PUBLIC  w2fLft, w2fRgt, w2fBas, w2fTop, w2x0, w2y0
    DECLARE PUBLIC  w2xFirst, w2xSTik, w2xLTik, w2xLabel, w2xGridstep
    DECLARE PUBLIC  w2yFirst, w2ySTik, w2yLTik, w2yLabel, w2yGridstep
    DECLARE PUBLIC  w2xPiFlag, w2xMult, w2yPiFlag, w2yMult

    DECLARE DEF w2Fncx,w2Fncy,w2Wndx,w2Wndy
    DECLARE DEF w2wWithin,w2Within

    LET w2xPiFlag= 0
    LET w2xMult  = 1
    LET w2yPiFlag= 0
    LET w2yMult  = 1

    LET w2Lft    = w1Lft
    LET w2Rgt    = w2Lft + wwid
    LET w2Top    = w1Bas + wyStp
    LET w2Bas    = w2Top + 108

    LET w2fLft   = w1fLft
    LET w2fRgt   = w1fRgt
    LET w2fTop   = w1fTop
    LET w2fBas   = w1fBas

    LET w2xax$   = "u"
    LET w2xSTik  = 0
    LET w2xLTik  = 1
    LET w2xLabel = 1
    LET w2xFirst = w2fLft

    LET w2yax1$  = "f(u)"
    LET w2yax2$  = "g(t-u)"
    LET w2ySTik  = 0.5
    LET w2yLTik  =  1
    LET w2yLabel =  1
    LET w2yFirst = -1

    LET w2yGridstep= 0
    LET w2xGridstep= 0

    CALL w2Variables

    SUB w2Init
        CALL w2DrawPlane(1,1,1)
        CALL SetTextFont(1,12,"bold")

        CALL PlotTextLJ(w2Rgt+8,w2y0+3,w2xax$,axisLabelClr)

        CALL PlotTextRJ(w2x0,w2Top-12,w2yax1$,prdClr)
        CALL PlotTextLJ(w2x0+3,w2Top-12,w2yax2$,prdClr)
        CALL w2KeepGridLayer
    END SUB


    ! --- window 3 ---

    DECLARE PUBLIC  w3Lft, w3Rgt, w3Bas, w3Top, w3Midx, w3Midy
    DECLARE PUBLIC  w3fLft, w3fRgt, w3fBas, w3fTop, w3x0, w3y0
    DECLARE PUBLIC  w3xFirst, w3xSTik, w3xLTik, w3xLabel, w3xGridstep
    DECLARE PUBLIC  w3yFirst, w3ySTik, w3yLTik, w3yLabel, w3yGridstep
    DECLARE PUBLIC  w3xPiFlag, w3xMult, w3yPiFlag, w3yMult

    DECLARE DEF w3Fncx,w3Fncy,w3Wndx,w3Wndy
    DECLARE DEF w3wWithin,w3Within

    LET w3xPiFlag= 0
    LET w3xMult  = 1
    LET w3yPiFlag= 0
    LET w3yMult  = 1

    LET w3Lft = w1Lft
    LET w3Rgt = w3Lft + wwid
    LET w3Top = w2Bas + wyStp
    LET w3Bas = w3Top + 108

    LET w3fLft= w1fLft
    LET w3fRgt= w1fRgt
    LET w3fTop=  1.5
    LET w3fBas= -1.5

    LET w3xax$  = "u"
    LET w3xSTik = 0
    LET w3xLTik = 1
    LET w3xLabel= 0
    LET w3xFirst= w3fLft

    LET w3yax1$ = "f(u)"
    LET w3yax2$ = "g(t-u)"
    LET w3ySTik =  0.5
    LET w3yLTik =  1
    LET w3yLabel=  1
    LET w3yFirst= -1

    LET w3yGridstep= 0
    LET w3xGridstep= 0

    CALL w3Variables

    SUB w3Init
        CALL w3DrawPlane(1,1,1)
        CALL SetTextFont(1,12,"bold")

        CALL PlotTextLJ(w3Rgt+8,w3y0+3,w3xax$,5)

        CALL PlotTextRJ(w3x0- 7,w3Top-12,w3yax1$,sigClr)
        CALL PlotTextLJ(w3x0+10,w3Top-12,w3yax2$,wgtClr)
        CALL w3KeepGridLayer
    END SUB


    ! --- window 4 ---

    DECLARE PUBLIC  w4Lft, w4Rgt, w4Bas, w4Top, w4Midx, w4Midy
    DECLARE PUBLIC  w4fLft, w4fRgt, w4fBas, w4fTop, w4x0, w4y0
    DECLARE PUBLIC  w4xFirst, w4xSTik, w4xLTik, w4xLabel, w4xGridstep
    DECLARE PUBLIC  w4yFirst, w4ySTik, w4yLTik, w4yLabel, w4yGridstep
    DECLARE PUBLIC  w4xPiFlag, w4xMult, w4yPiFlag, w4yMult

    DECLARE DEF w4Fncx,w4Fncy,w4Wndx,w4Wndy
    DECLARE DEF w4wWithin,w4Within

    LET w4xPiFlag= 0
    LET w4xMult  = 1
    LET w4yPiFlag= 0
    LET w4yMult  = 1

    LET w4Lft    = vrule2
    LET w4Rgt    = w4Lft + 240
    LET w4Top    = w3Top
    LET w4Bas    = w3Bas

    LET w4fLft   = -1.0
    LET w4fRgt   =  7
    LET w4fTop   =  1.5
    LET w4fBas   = -1.5

    LET w4xax$   = "u"
    LET w4xSTik  = 0
    LET w4xLTik  = 1
    LET w4xLabel = 1
    LET w4xFirst = w4fLft

    LET w4yax$   = "g(u)"
    LET w4ySTik  =  0.5
    LET w4yLTik  =  1
    LET w4yLabel =  1
    LET w4yFirst = -1

    LET w4yGridstep= 0
    LET w4xGridstep= 0

    CALL w4Variables

    SUB w4Init
        CALL w4DrawPlane(1,1,1)
        CALL SetTextFont(1,12,"bold")

        CALL PlotTextLJ(w4Rgt+8,w4y0+3,w4xax$,axisLabelClr)
        CALL PlotTextCJ(w4x0,w4Top-12,w4yax$,wgtClr)
        CALL w4KeepGridLayer
        CALL Plane4Graph
    END SUB


    ! ----- Slider parameters and methods -----
    ! ----------- h1 slider - time -------

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

    DECLARE DEF h1within
    DECLARE DEF h1AnimWithin, h1AnimStopWithin, h1LStpWithin, h1RStpWithin

    LET h1PiAxis= 0
    LET h1mult  = 1

    LET h1clr   = slideclr
    LET h1name$ = "t"
    LET h1form$ = "--%.##"
    LET h1Places= 2

    LET h1axis  = w3Bas + 22
    LET h1wLft  = w3Lft
    LET h1wRgt  = w3Rgt
    LET h1fLft  = w1fLft
    LET h1fRgt  = w1fRgt

    LET h1STik  = 0                              ! short tick marks
    LET h1LTik  = 1                              ! long tick marks
    LET h1Label = 1                              ! labels
    LET h1First = h1fLft                         ! first tick mark
    LET h1Click = 1

    CALL h1SliderVariables

    LET h1AnimStep= .1                           ! 3 pixels

    SUB h1Init
        CALL h1DrawSlider(h1name$,tm)
        CALL h1AnimButtons
    END SUB

    SUB h1SetZero
        LET tm= 0
        CALL h1Mark(tm)
    END SUB


    ! ---------- text output routines ----------
    ! --- t1 - Convolution Formula and value ---

    LET t1BasLn1= w1Top - 12
    LET t1BasLn2= t1BasLn1 + 30
    LET t1Eqx   = vrule2 + 78
    LET t1Lft   = t1Eqx + 8
    LET t1Rgt   = t1Lft + 100
    LET t1Bas   = t1BasLn2 +  5
    LET t1Top   = t1BasLn2 - 12
    LET t1Clr   = cnvClr

    SUB t1Init
        CALL SetTextFont(1,12,"bold")
        CALL StringWidth(" = ",ew)

        CALL PlotTextRJ(t1Eqx,t1BasLn1,"=",t1clr)
        CALL SetConvolutionTypeRJ(t1Eqx-ew,t1BasLn1,t1clr)
        CALL PlotTextRJ(t1Eqx,t1BasLn2,"=",t1clr)

        LET intx= t1Eqx + 8
        DRAW IntegralSign(t1clr) with shift(intx,t1BasLn1)
        CALL SetTextFont(1, 9,"bold")
        CALL PlotTextLJ(intx+6,t1BasLn1-8,"t", t1clr)
        CALL PlotTextLJ(intx+5,t1BasLn1+7,"0", t1clr)

        CALL SetTextFont(1,12,"bold")
        CALL PlotTextLJ(intx+20,t1BasLn1,"f(u) g(t-u) du", t1clr)
    END SUB

    SUB SetConvolutionTypeRJ(tx,ty,clr)
        LET length$= "(f*g)(t)"
        CALL StringWidth(length$,sw)
        CALL StringWidth("(f",fw)
        LET lft= tx-sw
        CALL SwapMultiplication(lft,ty,"(f*g)(t)",clr)
    END SUB

    SUB t1SetValue(a,b,t)
        CALL SetTextFont(1,12,"bold")
        BOX CLEAR t1Lft,t1Rgt,t1Bas,t1Top
        LET sum = cnv(signum,wgtnum,t)
        CALL PlotTextLJ(t1Lft,t1BasLn2,trim$(using$("-%.###",sum)),t1clr)
    END SUB


    ! -------- menu data and methods ----------
    ! ----------- menu 1: signals -------------

    !f1(t) = sin(bt)
    !f2(t) = 1
    !f3(t) = 1  for  0 < t < 3
    !f4(t) = sin(kt)   where  k  differs from  b.

    DECLARE PUBLIC m1Lft, m1Rgt, m1Bas, m1Top, m1Equation, m1Prefix$, m1Menu1$()
    DECLARE PUBLIC m1Name$, m1tClr
    DECLARE DEF m1Within

    MAT redim m1Menu1$(1:4)
    MAT READ m1Menu1$

    DATA "sin(u)"
    DATA "1 u>0"
    DATA "1 0<u<3"
    DATA "sin(2u)"

    LET m1Prefix$ = "f(u) = "
    LET m1Lft     = vrule2
    LET m1Top     = w2Top - 92
    LET m1Name$   = "Signal"
    LET m1tClr    = sigclr
    LET m1Equation= 1

    SUB m1Init
        CALL m1ResetMenu(m1State)
    END SUB

    ! ----- menu 2: weights -----

    !w1(t) = e^{-at}                (t > 0)
    !w2(t) = 1                      (t > 0)
    !w3(t) = (1/b) sin(bt)          (t > 0)
    !w4(t) = t e^{-at}              (t > 0)
    !w4(t) = (1/b) sin(bt) e^{-at}  (t > 0)

    DECLARE PUBLIC m2Lft, m2Rgt, m2Bas, m2Top, m2Equation, m2Prefix$, m2Menu1$()
    DECLARE PUBLIC m2Name$, m2tClr
    DECLARE DEF m2Within

    MAT redim m2Menu1$(1:4)
    MAT READ m2Menu1$
    DATA "e^[-u]"
    DATA "1"
    DATA "sin(u)"
    DATA "u e^[-u]"
    ! DATA "sin(u) e^[-u]"

    LET m2Prefix$ = "g(u) = "
    LET m2Lft     = m1Lft
    LET m2Top     = m1Top + 115
    LET m2Name$   = "Weight"
    LET m2tClr    = wgtClr
    LET m2Equation= 1

    SUB m2Init
        CALL m2ResetMenu(m2State)
    END SUB

    ! -------- end of design and layout ---------


    ! --- set default parameters ---

    LET m1State   = 0
    LET m2State   = 0
    LET m1Equation= 1                            ! signals
    LET m2Equation= 1                            ! weights
    LET signum    = m1Equation
    LET wgtnum    = m2Equation
    LET tm        = 0

    ! --- initialize screen ---

    CALL InitScreen
    CALL m1InitMenu1
    CALL m2InitMenu1
    CALL SetTimer

    SUB InitScreen
        BOX CLEAR workLft,workRgt,workBas,workTop
        CALL SetConstants(signum,wgtnum, a,b,k)

        CALL w1SetBounds(signum,wgtnum)
        CALL w1Init
        CALL w2Init
        CALL w3Init
        CALL w4Init

        CALL t1Init
        CALL t1SetValue(a,b,tm)

        CALL h1Init

        CALL m1Init
        CALL m2Init

        CALL BackGroundGraphs
        CALL DrawGraphs(tm)
    END SUB


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

    DO
       CALL MouseDown(mx,my,ms)

       IF w1wWithin(mx,my)=true or w2wWithin(mx,my)=true or w3wWithin(mx,my)=true then
          DO                                     ! drag t within a plane
             GET MOUSE: mx,my,ms
             LET mx = clamp(mx,w3Lft,w3Rgt)
             LET tm = w3Fncx(mx)
             CALL h1Action
          LOOP until ms=3

       ELSE IF h1Within(mx,my)=true then         ! h1 - t slider
          IF my<h1axis then
             CALL h1MouseClick
          ELSE
             CALL h1MouseDrag
          END IF

       ELSE IF h1AnimWithin(mx,my)=true then     ! h1 - t animation
          CALL h1AnimButtonUp(ms)
          CALL h1Animate
       ELSE IF h1LstpWithin(mx,my)=true then     ! h1 - t step left
          CALL h1LstpButtonUp(ms)
          CALL h1LeftStep(tm,h1AnimStep)
          CALL h1Action
       ELSE IF h1RstpWithin(mx,my)=true then     ! h1 - t step right
          CALL h1RstpButtonUp(ms)
          CALL h1RightStep(tm,h1AnimStep)
          CALL h1Action

       ELSE IF m1Within(mx,my)=true then         ! menu 1 - signals
          CALL MouseButtonUp(m1Lft,m1Rgt,m1Bas,m1Top,ms)
          CALL m1ReadMenu
          LET signum= m1Equation
          CALL ChangeEquation
       ELSE IF m2Within(mx,my)=true then         ! menu 2 - weights
          CALL MouseButtonUp(m2Lft,m2Rgt,m2Bas,m2Top,ms)
          CALL m2ReadMenu
          LET wgtnum= m2Equation
          CALL ChangeEquation

       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                                      ! meaningless click
          CALL MouseUp(mx,my,ms)
       END IF
    LOOP

    ! ------- response to events --------
    ! -------- h1 slider events ---------

    SUB h1MouseClick
        CALL h1GetClickVal(ms,h1Click,tm)
        CALL h1Action
    END SUB
    SUB h1MouseDrag
        DO
           CALL h1GetDragVal(ms,h1Places,tm)
           CALL h1Action
        LOOP until ms=3
    END SUB
    SUB h1Action
        IF tm<>oldtm then
           CALL h1Mark(tm)
           CALL t1SetValue(a,b,tm)
           CALL DrawGraphs(tm)
           LET oldtm= tm
        END IF
    END SUB

    SUB h1Animate
        LET start= tm
        FOR tm= start to h1fRgt step 2*pixstep
            CALL h1Action
            GET MOUSE: mx,my,ms                  ! check for mouse event
            IF ms=2 then                         ! stop on mousedown
               CALL h1AnimStopButtonUp(ms)       ! get mouse up
               EXIT FOR
            END IF
            CALL Delay(1/30)
        NEXT tm
        CALL h1StopButtonClear
    END SUB

    ! --- menu event ---

    SUB ChangeEquation
        CALL h1SetZero
        CALL w1SetBounds(signum,wgtnum)
        CALL w1Init
        CALL SetConstants(signum,wgtnum, a,b,k)
        CALL BackGroundGraphs
        CALL DrawGraphs(tm)
    END SUB


    ! --- Tool specific drawing and typesetting routines ---
    ! ------------------------------------------------------

    ! --- response to real-time change ---

    SUB DrawT(wx,wBas,wTop)                      ! moving vertical rule at t
        CALL PlotLine(wx,wTop+1, wx,wBas-1, litgry)
    END SUB

    SUB DrawGraphs(tm)
        ! --- plane 3 - overlay weight from tm back to zero

        CALL w3ShowGraphLayer
        LET wxTm= w3Wndx(tm)
        CALL DrawT(wxTm,w3Bas,w3Top)             ! vertical rule

        SET COLOR wgtClr                         ! now the weight
        FOR wx= w3Lft to wxTm
            LET u  = w3Fncx(wx)
            LET wgt= w(wgtnum,tm-u)
            LET wy = w3Wndy(wgt)
            PLOT wx,wy
        NEXT wx

        ! --- plane 2 - product curve and area

        CALL w2ShowGridLayer
        FOR u= tm to 0 step -pixstep
            LET u  = round(u,3)                  ! time
            LET y1 = f(signum,u)                 ! signal
            LET y2 = w(wgtnum,tm-u)              ! weight
            LET y  = y1*y2                       ! product

            CALL w2MathToPixels(u,y, wx,wy)
            CALL PlotPoint(wx,wy,prdclr)         ! product curve value

            ! now area within product curve if there is space
            IF wy<w2y0 then                      ! above zero
               IF wy<w2y0-2 then
                  CALL PlotLine( wx,wy+2, wx,w2y0-1, areaClr)
               END IF
            ELSE                                 ! below zero
               IF wy>w2y0+2 then
                  CALL PlotLine( wx,w2y0+1, wx,wy-2, areaClr)
               END IF
            END IF
        NEXT u
        CALL DrawT(wxTm,w2Bas,w2Top)             ! vertical rule


        ! --- plane 1 - top plane - convolution curve line and point

        CALL w1ShowGraphLayer

        LET yi= cnv(signum,wgtnum,tm)            ! find convolution y
        ! CALL w1NumericalIntegral(tm,yi)          ! for debugging

        LET wy= w1Wndy(yi)
        IF wy<w1y0 then                          ! up?
           CALL PlotLine( wxTm,wy+1, wxTm,w1y0-1, cnvClr)
        ELSE                                     ! down
           CALL PlotLine( wxTm,wy-1, wxTm,w1y0+1, cnvClr)
        END IF
        DRAW diamond7(cnvClr) with shift(wxTm,wy)
    END SUB

    ! ----------------------------------
    ! ----- draw background graphs -----

    SUB BackgroundGraphs
        ! plane 3 - signal to buffer
        CALL w3ShowGridLayer
        CALL Plane3Graph
        CALL w3KeepGraphLayer

        ! plane 4 - weight

        CALL w4ShowGridLayer
        CALL Plane4Graph

        ! plane 1 - convolution
        ! CALL DrawNumericalIntegral               ! for debugging
        CALL DrawIntegral                        ! convolution to buffer
    END SUB

    ! --- plane 1 - convolution integral curve ---

    SUB DrawIntegral
        SET COLOR cnvClr
        FOR wx= w1x0 to w1Rgt
            LET t = w1Fncx(wx)
            LET y = cnv(signum,wgtnum,t)
            LET wy= w1Wndy(y)
            PLOT wx,wy;
        NEXT wx
        PLOT
        CALL w1KeepGraphLayer
    END SUB

    ! ----- plane 3 - background signal ---

    SUB Plane3Graph                              ! lower right plane - signal (f)
        SET COLOR sigClr
        IF signum=2 then                         ! 1 for t>0
           LET wy= w3Wndy(1)
           PLOT w3Lft,w3y0; w3x0,w3y0; w3x0,wy; w3Rgt,wy
        ELSE IF signum=3 then                    ! step to one for 0<=t<=3
           CALL w2MathToPixels(f3step,1,wRgt,wy)
           LET wRgt= w3Wndx(f3step)
           LET wy  = w3Wndy(1)
           PLOT w3Lft,w3y0; w3x0,w3y0; w3x0,wy; wRgt,wy; wRgt,w3y0; w3Rgt,w3y0
        ELSE
           FOR wx= w3Lft to w3Rgt
               LET u = w3Fncx(wx)
               LET wy= w3Wndy(f(signum,u))
               PLOT wx,wy;
           NEXT wx
           PLOT
        END IF
    END SUB

    ! --- plane 4 - weight function ---

    SUB Plane4Graph
        ! lower left plane - weight function
        SET COLOR wgtClr
        FOR wx= w4x0+1 to w4Rgt
            LET u = w4Fncx(wx)
            LET wy= w4Wndy(w(wgtnum,u))
            PLOT wx,wy;
        NEXT wx
        PLOT
    END SUB

    ! ------------------------------------

    ! --- numerical routines for debugging and absence of closed form solutions ---

    SUB DrawNumericalIntegral
        CALL w1ShowGridLayer
        SET COLOR cnvClr
        CALL NumericalIntegral
        CALL w1KeepGraphLayer
    END SUB

    SUB w1NumericalIntegral(t,sum)
        ! returns one convolution value at t
        LET sum= 0
        FOR u= w1fLft to t step pixstep
            LET y1  = f(signum,u)
            LET y2  = w(wgtnum,t-u)
            LET y   = y1*y2
            LET area= y*pixstep
            LET sum = sum+area
        NEXT u
        ! LET sum= sum*pixstep
    END SUB

    SUB NumericalIntegral
        ! draws a graph of the convolution
        SET COLOR litgry
        !           FOR wx= w1Lft to w1Rgt ! use stored values
        !               LET wy= CnvVals(wx)
        !               PLOT wx,wy
        !           NEXT wx
        FOR wx= w1Lft to w1Rgt
            LET x = w1Fncx(wx)
            CALL w1NumericalIntegral(x,sum)
            LET wy= w1Wndy(sum)
            PLOT wx,wy;
        NEXT wx
        PLOT
    END SUB

    SUB IntegralValues
        ! stores numerical integration for quik access
        MAT redim CnvVals(w1Lft:w1Rgt)
        FOR wx= w1Lft to w1Rgt
            LET x = w1Fncx(wx)
            CALL w1NumericalIntegral(x,sum)
            LET wy= w1Wndy(sum)
            LET CnvVals(wx)= wy
        NEXT wx
    END SUB
END SUB

! ---- end of backward convolution code --------------------------------