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^3               T R I G   S C R E E N   E F F E C T S 

^2                     An Insight By Paul Townsend

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^4 So  you  want  to  know  how  to produce those Sin and Cos generated
^4effects that keep appearing from Technical Fred Software.  This short
^4introduction  should  give  you an idea on how to get started.  I get
^4the  impression that many people seem to have a fear of using Sin and
^4Cos  in  their  programs  (Trigophobia  ?), this is not too suprising
^4really  as  their  seems  to  be very little explanation of what they
^4really do, so here I am to try to make sense of it all.

^2                             First Steps

^5 When you run my programs that use Sin and Cos, if you look carefully
^5then  you  will  realize  that most of the effects are based upon the
^5circle,  or multiple circles interacting with each other.  The reason
^5for  this  is that I use Sin and Cos to produce circles, with is what
^5they  are  good at (They probably have many other uses, but I haven't
^5found any that are interesting enough to bother about).

^2                             The Theory

^4 The  circle can be split up into 360 points which can be imagined to
^4be  positioned,  equally  spaced around the circumference.  So if you
^4start  at  any  place on the circumference and move 360 points in any
^4direction, you will end up back where you started from.

^5 What  we  need to know is how to work out where all these points are
^5so  that  we can do something at that particular point on the screen,
^5i.e plot a point, paste a bob etc.

^4 When  typing  in these examples, dont type in the <---- and comments
^4or  the  computer  will spit them back at you, (You could use Rems if
^4you want, but I'm just too lazy !), Just type in the bits before them
^4and press RETURN

^5 The way to do this is to choose which points on the circle you want,
^5for our purposes we will just plot the entire circle, a program to do
^5this could be:

^7Screen Open 0,320,256,32,Lowres

^7Degree           <----Tell the computer we want to work in degrees

^7For F=0 To 360   <----Set up a loop 

^7X#=Sin(F)        <----Work out the Co-ords

^7Y#=Cos(F)        <---- "    "   "   "  "

^7Plot X#,Y#       <----Plot the point

^7Next F           <----Loop ? 

^4If  you  try  it,  don't  be  surprised  if you get nothing at all on
^4screen, the reason for this is that
^4 1) The co-ords are just off screen at the top left and
^4 2) the circle is only 1 pixel wide.

^5This calls for some minor changes to the above program :-

^4Firstly let's add the centre of the screen to the points plotted.

^7Screen Open 0,320,256,32,Lowres

^7Degree           <----Tell the computer we want to work in degrees

^7For F=0 To 360   <----Set up a loop 

^7X#=160+Sin(F)    <----Work out the Co-ords

^7Y#=128+Cos(F)    <---- "    "   "   "  "

^7Plot X#,Y#       <----Plot the point

^7Next F           <----Loop ? 

^5 This  program  will  appear  to  plot  a  point in the centre of the
^5screen,  this  is  because  the  circle  is  still only 1 pixel wide,
^5therefore one final change is needed to get the circle to look like a
^5circle.

^7Screen Open 0,320,256,32,Lowres

^7Degree              <----Tell the computer we want to work in degrees

^7For F=0 To 360       <----Set up a loop 

^7X#=160+(100*Sin(F))  <----Work out the Co-ords

^7Y#=128+(100*Cos(F))  <---- "    "   "   "  "

^7Plot X#,Y#           <----Plot the point

^7Next F               <----Loop ? 

^4 This  program  should  now work, it should draw a circle that is 100
^4pixels wide.  (Why not try other numbers other than 100 for different
^4sizes of circles)

^5 Hopefully  you  should  now  have a circle on the screen, it may not
^5look  much,  but  if you can understand why the circle is there, then
^5that is the first hurdle over with.

^4 OK,  I  think we should make this program a little more interesting,
^4what about making the circle appear to move.

^5The  method  I  will use is a palette switch, try this, don't type in
^5the comments though

^7Screen Open 0,320,256,32,Lowres

^7Flash off            <----Needed for Shift Up to work

^7Degree               <----Tell the computer we want to work in degrees

^7For F=0 To 360       <----Set up a loop 

^7Add rgb,1,1 to 31

^7X#=160+(100*Sin(F))  <----Work out the Co-ords

^7Y#=128+(100*Cos(F))  <---- "    "   "   "  "

^7Plot X#,Y#,RGB       <----Plot the point in the selected colour.

^7Next F               <------Loop ? 

^7Shift Up 2,1,31,1    <------set up a palette switch (or colour cycle)

^7Direct

^4 If you run this program you should have a revolving circle.

^5 You  can  now  plot  a circle, each point in a different colour, and
^5then to make it move.

^4 In  the  next part of this tutorial, we will try to use what we have
^4learned  to  produce  some  more  interesting effects, but until then
^4please don't be afraid to experiment, try changing any of the numbers
^4in  the  above programs, just to see what happens.  After all, that's
^4how all of the effects I have written in the past started off.  (i.e.
^4see Screen Wipes in previous editions of TA) I just guess at a number
^4to  change  in a program run it and hope for the best.  If the effect
^4looks  good then I save the program, if not, I change it to something
^4else.  (How's that for a structured approach to programming?)

^5 So  until  next time, have fun.  If you have anything you would like
^5to see in these tutorials, why not drop a line to Totally Amos at the
^5usual address.

                             ^3T T F N 

                  ^2Paul (Technical Fred) Townsend.

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