[Gambas-user] more trigonometry fun (not)

[wally]

On Tuesday, May 24, 2011 05:44:14 Kevin Fishburne wrote:
> I was already helped graciously in figuring out how to translate a point
> in a plane along its local axes at a given orientation, but now need a
> bit of the inverse of the equation.
> 
> I need to know the (x, y) offset of a point at a given orientation and
> velocity. For example if a point is moving at an angle of 45 degrees (or
> radians, take your pick), what would its x and y coordinate be
> increased/decreased by? The variables I can think of would be:
> 
> x1 (point's current x coordinate)
> y1 (point's current y coordinate)
> a (point's angle/orientation in degrees/radians)
> v (point's velocity)
> x2 (x coordinate offset of point's new position)
> y2 (y coordinate offset of point's new position)
> 
> The calculation would take x1, y1 a and v as inputs and produce x2 and
> y2 as offsets (x1 + x2, y1 + y2 = point's new position).
> 
> There really should be a list of basic things like this for graphics
> programmers. I've searched for years and found practically nothing.
> Weird, considering this has probably been done thousands of times since
> the days of DOS. :/
> 
> In case anyone's wondering why I need this, the equation will allow
> particles and projectiles to follow logical paths. Currently they're
> bound to local coordinates and ignore player orientation. Digging,
> shooting arrows, throwing objects, etc. can't work without it.

Hello Kevin,

the problem seems pretty easy to solve, so I'm not sue i understand 
the question correctly. 
A good idea would be to use polar coordinates for this:  

P( r, a) where r = radial distance to (0,0) offset and a the angle a .
r = sqrt( x^2 + y^2) 

r(p2) = r(p1) + vt  , 
new radius point 2 = 1st radius + distance to move (velocity *  time)
a does not change

in cartesian coordinates:
x2 = x1 + cos(a) * v * t
y2 = y1 + sin(a) * v * t

if you need more complex paths, using matrices is a good way.

but always time is needed to calculate. You did not mention time t
so i assume i did not understand the question. 

wally