Re: geometric problem
Get a book called "Fundamentals of Interavtive Computer Graphics" by
J.D. Foley & A. Van Dam ... It has all the math and some good short
-cuts in it... Its not a quick read but very helpfull ... It also has a
reference to other books and papers(some are able to be found on the
net.. the urls excape me right now)....
GV
>From: Nick <metcalfn at ALPHALINK.COM.AU>
>Reply-To: Euphoria Programming for MS-DOS
<EUPHORIA at LISTSERV.MUOHIO.EDU>
>To: EUPHORIA at LISTSERV.MUOHIO.EDU
>Subject: geometric problem
>Date: Fri, 19 Mar 1999 03:30:59 +1000
>
>Hi all. I have a small problem which has evaded every attempt I have
>made to solve it. I need a routine that does the folowing:
>
>* Given an arbitrary rectangular polygon {V1, V2, V3, V4} where Vx
is
>a vertex point {x, y} and the vertexes are ordered clockwise on the
>rectangle starting at the top left, so that the line V1 -> V2 might be
>called the top,
>* Also given a point {x, y} that could be inside or outside the
polygon
>
>* Evaluates two expressions mag_x and mag_y such that both expressions
>will be linearly interpolated between opposing lines on the polygon
>(left side and right side for mag_x and top to bottom for mag_y) to
>provide a value in the range of 0 to 1 while the point is inside the
>polygon on either 'axis', and < 0 or > 1 when it is outside.
>
>Phew! Basically I want to project a point in an arbitrary polygon into
>a cartesian space that is the equivalent of a unit square, keeping
track
>of orientation. This is the reverse of a procedure I use to map such a
>coordinate system into an arbitrary polygon. That was easy. Now I
need
>it back!
>
>I have had so little success coming up with capable code that i decided
>to ask better minds than mine. I have tried seriously twice, enough
>times to realize I don't really know whats going on. My first attempt
>tried to weight vectors orthagonal to opposing sides (dont laugh) and
>was a complete failure. My second attempt found the intercept between
>opposing lines, and their angles, then found the angle of a line
>connecting the point to the intercept and then evaluated the mag by
>comparing the angles. This procedure had more success, but needed to
>deal with so many 'special cases', i.e. paralell, and worse, near
>paralell lines, angle quadrant problems, etc. that I eventually gave
up
>on it in despair. I really need something that can handle any weird
>input.
>
>I'm sure there is a simple solution, some kind of simultaneous
equation,
>but I slept through that class at school (doh!) Please would somebody
>with more math than me help me out please. Um, if I havent explained
>this very well and you need more information don't hesitate to mail me.
>
>Thanks,
>Nick
>
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