1. Anyone know anything about trigonometry?
- Posted by dstanger at belco.bc.ca
Sep 05, 2001
Hello all,
Does anyone know anything about trigonometry? I am interested in making a
"dueling artillery" game but cannot fathom the math needed to plot arcs. I
know that it has something to do with arc, tan, and cos (?) but what?!
So this is a call to all you mathematicians on the list ;)
Thanks a lot,
David S.
2. Re: Anyone know anything about trigonometry?
This is a multi-part message in MIME format.
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David,
they are not arcs. They are quite complex ballistic curves. But let's
assume we live in a complete vacuum, as some of us do, then we can
approximate them very well with parabolas. And parabolas are dead easy
to calculate, even to draw. The attached small demo is, I hope,
sufficiently commented to give you reasonable idea how to proceed.
jiri
----- Original Message -----
From: <dstanger at belco.bc.ca>
To: "EUforum" <EUforum at topica.com>
Sent: Thursday, 6 September 2001 16:57
Subject: Anyone know anything about trigonometry?
>
> Hello all,
>
> Does anyone know anything about trigonometry? I am interested in
making a
> "dueling artillery" game but cannot fathom the math needed to plot
arcs. I
> know that it has something to do with arc, tan, and cos (?) but
what?!
>
> So this is a call to all you mathematicians on the list ;)
>
> Thanks a lot,
> David S.
>
>
>
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Content-Type: application/octet-stream;
name="Gun.ex"
Content-Transfer-Encoding: quoted-printable
Content-Disposition: attachment;
filename="Gun.ex"
-- gun.ex
-- jiri babor
-- jbabor at paradise.net.nz
-- 6 Sep 2001
include graphics.e
constant d2r =3D PI/180 -- degrees-to-radians factor
constant g =3D 5 -- acceleration due to gravity
object o
sequence vc -- video configuration
atom hspeed,vspeed,x,x0,y,y0
integer angle, color, key, speed, toggle,xmax,ymax
procedure show_header()
text_color(BLUE)
puts(1, "enter : toggle lines/dots\n")
puts(1, "up : increase angle\n")
puts(1, "down : decrease angle\n")
puts(1, "right : increase speed\n")
puts(1, "left : decrese speed\n")
puts(1, "c : change trace color\n")
puts(1, "delete: clear screen\n")
puts(1, "space : fire\n")
puts(1, "esc : quit\n")
text_color(RED)
position(11, 1)
if toggle then
puts(1, "lines")
else
puts(1, "dots ")
end if
position(12, 1)
printf(1, "angle : %2d", angle)
position(13, 1)
printf(1, "speed :%3d", speed)
position(14, 1)
printf(1, "color : %2d", color)
end procedure
procedure fire()
hspeed =3D speed * cos(angle*d2r) -- horizontal speed component
vspeed =3D -speed * sin(angle*d2r) -- vertical speed component
x0 =3D 0 -- initial projectile position
y0 =3D ymax -- also gun position
x =3D x0 -- projectile hor. position
y =3D y0 -- projectile ver. position
while x <=3D xmax and y <=3D ymax do
vspeed +=3D g -- new vertical speed
x +=3D hspeed -- new projectile position
y +=3D vspeed
if toggle then
draw_line(color, {{x0, y0},{x, y}})
else
pixel(color, {x, y})
end if
x0 =3D x
y0 =3D y
end while
end procedure
-- initial (default) parameters:
angle =3D 60 -- gun angle from horizontal
speed =3D 60 -- nozzle speed
toggle =3D 1 -- draw lines
color =3D 15 -- BRIGHT_WHITE, initial trace color
o =3D graphics_mode(18) -- 640x480x16
vc =3D video_config()
xmax =3D vc[5]-1
ymax =3D vc[6]-1
show_header()
ellipse(7,1,{-5,ymax-5},{5,ymax+5}) -- gun
key =3D get_key()
while key !=3D 27 do -- escape
if key =3D 328 then -- up arrow
if angle < 80 then
angle +=3D 1
position(12, 9)
printf(1, "%2d", angle)
end if
elsif key =3D 336 then -- down arrow
if angle > 10 then
angle -=3D 1
position(12, 9)
printf(1, "%2d", angle)
end if
elsif key =3D 333 then -- right arrow
if speed < 100 then
speed +=3D 1
position(13, 8)
printf(1, "%3d", speed)
end if
elsif key =3D 331 then -- left arrow
if speed > 10 then
speed -=3D 1
position(13, 8)
printf(1, "%3d", speed)
end if
elsif key =3D 13 then -- enter: dots/lines toggle
toggle =3D not toggle
position(11, 1)
if toggle then
puts(1, "lines")
else
puts(1, "dots ")
end if
elsif key =3D 32 then -- space: fire!
fire()
elsif key =3D 'c' then -- change trace color
color +=3D 1
if color > BRIGHT_WHITE then
color =3D GREEN
end if
position(13, 9)
printf(1, "%2d", color)
elsif key =3D 339 then -- delete: clear screen
clear_screen()
show_header()
ellipse(7,1,{-5,ymax-5},{5,ymax+5})
end if
key =3D get_key()
end while
o =3D graphics_mode(-1) -- back to text mode
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4. Re: Anyone know anything about trigonometry?
Unless you really want it to be fairly accurate, I wouldn't worry about
calculating trajectories.
In fact, more often than not, I find it looks more realistic, taking the
approach I mention, rather than actually trying to calculate the trajectory.
Like others said, you need to consider gravity, resistance (friction and
wind force), inertia, mass, aerodynamics (that's being very petty :P).
If you were making a golf game, I would say that tracjectory calculations
would be crutial.
If you look at any fireworks demos, they should give you an idea of what to
do. Most use arcs for the path of the flare and the sparks, they will even
take into account GRAVITY and trajectory SPEED.
I haven't looked at the workings of the EU fireworks demos, but I suspect it
would be similar.
I know that there are numerous fireworks examples for BASIC, that
demonstrate how to do the arced paths.
The main concept is to change the position incrementally(the increment can
be whatever realistic value you choose), multiplying the increment by SPEED,
and subtracting (or dividing) GRAVITY every time. Once you've made your
calculation for that increment, you decrement SPEED. Eventually, speed will
be 0 and the trajectory will end.
For fireworks, I would have static values for increment and gravity, and
speed is random. For your purposes, speed wouldn't be random.
This should give you an idea of how to proceed
EG.
INCREMENT=10
GRAVITY=0.6
SPEED=50
while SPEED>0 do
pos_x+=INCREMENT*SPEED*GRAVITY
pos_y+=INCREMENT*SPEED*GRAVITY
SPEED-=1
end while
Chris
5. Re: Anyone know anything about trigonometry?
hello David,
When the user tells the program the angle to shoot at, you should convert
the angle and speed to component vector form. It is easier to work with (x,
y) than (angle, speed) internally. First, get the x and y components for
the velocity vector of the projectile as follows:
xspeed = cos(angle) * speed
yspeed = sin(angle) * speed
When the projectile is in motion, move the ball by an amount proportional to
the x and y speed. Then decrease the y speed by a number that tells the
acceleration due to gravity.
It gets a bit more complicated than this. A knowledge of maths (and
physics) would help for this. I made a small program that simulates
projuctile motion, and you can download it at
http://www.geocities.com/daryl_vdb/euphoria
Sorry if the code is hard to understand, or the program is buggy. Email me
again if you want to know more.
regards,
Daryl van den Brink
>Hello all,
>
>Does anyone know anything about trigonometry? I am interested in making a
>"dueling artillery" game but cannot fathom the math needed to plot arcs. I
>know that it has something to do with arc, tan, and cos (?) but what?!
>
>So this is a call to all you mathematicians on the list ;)
>
>Thanks a lot,
>David S.
