[Gambas-user] translating planar coordinates relative to point's angle

[Caveat]

Hi Kevin
Great to hear you got it working.  I was having a discussion with a
developer friend of mine who needs to do a lot of "math stuff" in his
work and he came up with the suggestion to use affines, just a little
after Doriano came up with the working solution (which is actually based
on affines).

If you want more background (and it looks like you may need it), he
suggested you try this link:

http://en.wikipedia.org/wiki/Rotation_%28mathematics%29

Regards,
Caveat


On Thu, 2011-03-17 at 00:40 -0400, Kevin Fishburne wrote:
> On 03/15/2011 05:03 PM, Doriano Blengino wrote:
> > Kevin Fishburne ha scritto:
> >>     Just to be clear on what -should- be happening, here's an example.
> >>     Player is facing up (0 degrees): left stick pushed up moves up, pushed down
> >>     moves down, pushed left moves left, pushed right moves right.
> >>     Player is facing right (90 degrees): left stick pushed up moves right,
> >>     pushed down moves left, pushed left moves up, pushed right moves down.
> >>
> > Well, you need to rotate the data from the left joystick around the
> > player. This is the formula of rotation:
> >    xr := xp*g92cos - yp*g92sin;
> >    yr := xp*g92sin + yp*g92cos;
> >
> > Sorry, I took them from an old pascal program, but I explain.
> > The above code rotates a point (xp; yp) around the origin, by a given
> > angle "g92", of which g92cos and g92sin are the cosine and sine. The new
> > rotated point is (xr; yr). Please note that 0 degrees is toward right,
> > 90° up, 180 left, but a computer screen is flipped up side down (which
> > is not a rotation but a mirror), so the y coordinates must be mirrored
> > (choose the opposite sign if a coordinate is relative, or subtract the
> > coordinate from the maximum Y coordinate if absolute). In addition, you
> > say that 0° is up, and 90° right, which is both mirrored and rotated in
> > respect to the canonical trigonometry... this kind of things can drive
> > me crazy... :-)
> >
> > Back to the problem. If I well understand, at every frame you take the
> > left joystick, and apply its "command" to the player. But the direction
> > of the movement depends on the orientation of the player. Well, you take
> > the left joystick data (x and y) and rotate them using the formulas
> > above, basin on current player orientation. This way, when the left
> > joystick slides up, the player will always move ahead, along its current
> > direction. Now I will make an example.
> >
> > Suppose your player is at X=0 and Y=0, facing up (0 degrees), and you
> > move the left joystick "up". You receive y=10 and x=0 from the left
> > joystick. The above formula gives (cos(0)=1, sin(0)=0):
> >    xr := xp*g92cos - yp*g92sin    = 0*1 - 10*0 = 0
> >    yr := xp*g92sin + yp*g92cos   = 0*0 + 10*1 = 10
> >
> > So you add 0 to X and subtract 10 from Y (or add "-yr" to Y). The player
> > moves up. Note that X is added and Y is subtracted because of the screen.
> >
> > Now, suppose that the player instead is facing right (90°). The formulawe came up with 
> > gives (cos(90)=0, sin(90)=1:
> >    xr := xp*g92cos - yp*g92sin    = 0*0 - 10*1 = -10
> >    yr := xp*g92sin + yp*g92cos   = 0*1 + 10*0 = 0
> >
> > So you add -10 to X, and subtract 0 from Y. The player moves left. Why
> > not to the right? Because if you rotate your head to the left, you turn
> > 90 degrees, and if you turn your head to the right, you turn -90°. So if
> > you say that 0° is up and 90° is right, there is something wrong. I hope
> > that what I write is comprehensible...
> >
> > I don't know at which extent your program is already using this strange
> > coordinates, so I prefer to elaborate no more (a little tired this
> > night), but by inverting the readings from the joystick, and/or swapping
> > X and Y from the joystick, or by using "90-angle" instead of "angle"
> > when calculating cos() and sin(), you should quickly solve without
> > touching the rest of the program. I presume you should use both
> > "90-angle" and subtract from Y instead of adding to it, but I am not
> > sure - sorry. In a few days I will go to visit those URLs you posted, I
> > am always curious about math and videogames :-)
> 
> Doriano, you a genius. =) I adjusted my calculations based on your 
> formulas and I'll be damned it if didn't work perfect on the first try. 
> Amazing... Here's the code in gb:
> 
> ' Move player relative to player's orientation.
> worldx = worldx + (Interface.stick_leftx / 131072) * 
> Cos(Rad(orientation)) - (Interface.stick_lefty / 131072) * 
> Sin(Rad(orientation))
> worldy = worldy + (Interface.stick_leftx / 131072) * 
> Sin(Rad(orientation)) + (Interface.stick_lefty / 131072) * 
> Cos(Rad(orientation))
> 
> For others who may read this in the future, the division by 131072 just 
> compresses the movement range to -0.25 to 0.25 since the gamepad stick 
> input goes from -32767 to 32767, so apply your own number as necessary.
> 
> Of course as soon as my celebration ended I realized I was now deep in 
> the swamp of getting full-screen rotation working. I've made pretty good 
> progress so far and surprisingly am actually learning a little new math 
> (namely how to rotate point A around point B by angle X).
> 
> Thanks again Doriano.
>