Author : Grant Smith
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we have DrawPoints then
RotatePoints. The variables used in DrawPoints are set in RotatePoints,
so if you put RotatePoints before DrawPoints, the program should work
fine. Alternatively, turn off error checking 8-)
Fourthly, I have had a surprisingly large number of people saying that
"I get this, like, strange '286 instructions not enabled' message!
What's wrong with your code, dude?" To all of you, get into Pascal, hit
Alt-O (for options), hit enter and a 2 (for Enable 286 instructions). Hard
hey? Doesn't anyone EVER set up their version of Pascal?
Now, on to todays tutorial! 3D solids. That is what the people wanted,
that is what the people get! This tutorial is mainly on how to draw the
polygon on screen. For details on how the 3D stuff works, check out tut
8.
If you would like to contact me, or the team, there are many ways you
can do it : 1) Write a message to Grant Smith/Denthor/Asphyxia in private mail
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3) Write to : Grant Smith
P.O.Box 270 Kloof
3640
Natal
4) Call me (Grant Smith) at (031) 73 2129 (leave a message if you
call during varsity)
5) Write to mcphail@beastie.cs.und.ac.za on InterNet, and
mention the word Denthor near the top of the letter.
NB : If you are a representative of a company or BBS, and want ASPHYXIA
to do you a demo, leave mail to me; we can discuss it.
NNB : If you have done/attempted a demo, SEND IT TO ME! We are feeling
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How to draw a polygon
Sounds easy enough, right? WRONG! There are many, many different ways to
go about this, and today I'll only be showing you one. Please don't take
what is written here as anything approaching the best method, it is just
here to get you on your way...
The procedure I will be using here is based on something most of us
learned in standard eight ... I think. I seem to recall doing something
like this in Mrs. Reids maths class all those years ago ;)
Take two points, x1,y1 and x2,y2. Draw them :
+ (x1,y1)
\
\ <-- Point a somewhere along the line
\
+ (x2,y2)
Right, so what we have to do is this : if we know the y-coord of a, what
is it's x-coord? To prove the method we will give the points random
values.
+ (2,10)
\
\ <-- a.y = 12
\
+ (15,30)
Right. Simple enough problem. This is how we do it :
(a.y-y1) = (12 - 10) {to get a.y as though y1 was zero}
*(x2-x1) = *(15 - 2) {the total x-length of the line}
/(y2-y1) = /(30 - 10) {the total y-length of the line}
+x1 = +2 { to get the equation back to real coords}
So our equation is : (a.y-y1)*(x2-x1)/(y2-y1)+x4 or
(12-10)*(15-2)/(30-10)+2
which gives you :
2*13/20+2 = 26/20+2
= 3.3
That means that along the line with y=12, x is equal to 3.3. Since we
are not concerned with the decimal place, we replace the / with a div,
which in Pascal gives us an integer result, and is faster too. All well
and good, I hear you cry, but what does this have to do with life and
how it relates to polygons in general. The answer is simple. For each of
the four sides of the polygon we do the above test for each y line. We
store the smallest and the largest x values into separate variables for
each line, and draw a horizontal line between them. Ta-Dah! We have a
cool polygon!
For example : Two lines going down :
+ +
/ <-x1 x2->| <--For this y line
/ |
+ +
Find x1 and x2 for that y, then draw a line between them. Repeat for all
y values.
Of course, it's not as simple as that. We have to make sure we only
check those y lines that contain the polygon (a simple min y, max y test
for all the points). We also have to check that the line we are
calculating actually extends as far as where our current y is (check
that the point is between both y's). We have to compare each x to see
weather it is smaller then the minimum x value so far, or bigger then
the maximum (the original x min is set as a high number, and the x max
is set as a small number). We must also check that we only draw to the
place that we can see ( 0-319 on the x ; 0-199 on the y (the size of the
MCGA screen))
To see how this looks in practice, have a look at the sample code
provided. (Mrs. Reid would probably kill me for the above explanation,
so when you learn it in school, split it up into thousands of smaller
equations to get the same answer ;))
Okay, that's it! What's that? How do you draw a vertical line? Thats
simple ...
Drawing a vertical line
Right, this is a lot easier than drawing a normal line (Tut 5 .. I
think), because you stay on the same y value. So, what you do is you set
ES to the screen you want to write to, and get DI to the
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