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MathGroup Archive 1998

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Re: help with trig(?) calculation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13234] Re: [mg13155] help with trig(?) calculation
  • From: Robert Pratt <rpratt at math.unc.edu>
  • Date: Fri, 17 Jul 1998 03:17:34 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Unless your screen is square (which I doubt), the example (320,240) 
with 45 degrees hits the point (560,0), not (640,0).  Use the angle 
ArcTan[240/320]=ArcTan[3/4] if you want to hit (640,0).

The following commands seem to do what you want, if you enter alpha  in
radians (convert if necessary).

WithinBoundaryQ[{x_,y_}]:=(0<=x<=640) && (0<=y<=480)

intersect[{x_,y_},alpha_]:=Module[{u,v,t,sol},
		{u,v}={x-320,240-y}+t{Cos[alpha],Sin[alpha]};
    sol=Select[Union[Solve[Abs[u]==320,t],Solve[Abs[v]==240,t]],
        Positive[t/.#]&];
    Select[Transpose[{(u/.sol)+320,240-(v/.sol)}],WithinBoundaryQ[#]&]]

intersect[{320,240},45 Pi/180]

{{560,0}}

intersect[{320,240},ArcTan[240/320]]

{{640,0}}

intersect[{320,0},3 Pi/2]

{{320,480}}

intersect[{0,240},0]

{{640,240}}

Rob Pratt
Department of Mathematics
The University of North Carolina at Chapel Hill CB# 3250, 331 Phillips
Hall
Chapel Hill, NC  27599-3250

rpratt at math.unc.edu

http://www.math.unc.edu/Grads/rpratt/

On Mon, 13 Jul 1998, Leon Bryant wrote:

> i need some help from the "gurus". i am a multimedia programmer working
> in San Antonio, and need help with a programming idea that involves
> some simple(?) trig.
> 
> the problem:
> 
> i have a display area (computer screen) that has the dimensions 640 by
> 480 units (pixels).
> my program sets the dimensions of this rectangle to:
> 
> TL - 0,0
> TR - 640,0
> BL - 0,480
> BR - 640,480
> 
> what i would like to do is give the coordinates of a point on the
> screen, an angle (or a second point), and devise an algorithm that will
> plot where the imaginary line would inintersect the boundaries of the
> display area. 
> for instance:
> 
> point:  (320,240) (centered on screen) angle: 45 degrees
> intersection point: (640,0)
> 
> this one's intuitive since the starting point is centered on the screen,
> and the angle is 25% of 360 degrees, but i'm stumped with anything more
> irregular.
> 
> can you explain how i'd do this? can it be put into a simple formual?
> 
> email: leon.bryant at usaa.com



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