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From: sund@tde.lth.se (Lars Sundstr|m)
Newsgroups: comp.sys.mac.programmer
Subject: Re: How do you grab lines like MacDraw?
Message-ID: <1990Aug10.085010.18302@lth.se>
Date: 10 Aug 90 08:50:10 GMT
References: <4176@dogie.macc.wisc.edu>
Sender: newsuser@lth.se (LTH network news server)
Organization: Dept. of Applied Electronics, Lund University, Sweden
Lines: 46

In article <4176@dogie.macc.wisc.edu> yahnke@vms.macc.wisc.edu (Ross Yahnke, MACC) writes:
>In programming a MacDraw style environment where the
>user can click-n-drag objects around, it's ez enuf to grab
>objects with mass like squares and rectangles. You just see if
>the clicked on pixel is in any of the regions defined by the
>objects, i.e., you do a "PtInRgn()" call. 
>
>But what if the object is a line? Can a region be defined to
>be a line, w/no thickness? I'm posting this for a friend who
>said he tried creating a region w/only a line in it and
>subsequent PtInRgn calls would fail... any ideas?
>
>>>> yahnke@macc.wisc.edu <<<



It's possible to calculate the distance between the line and the click
point by using the vector product of the line and the vector between
the click point and a endpoint of the line.

Define A=(Ax,Ay) as a vector between the startpoint and endpoint
of the line and B=(Bx,By) as a vector between the startpoint of the
line and the clickpoint. Now, there is a nice relationship that
can be used:

|A x B| = |A| |B| sin(alfa)

The angle alfa is the angle between the vectors and therefore, the
distance between the line and the clickpoint is |B| sin(alfa). But
according to the relationship above |B| sin(alfa) is equal to
|A x B| / |A| which is pretty simple to calculate because

|A x B| = abs(Ax By + Ay Bx) and |A| = sqrt(sqr(Ax) + sqr(Ay))

Because you get the distance to the line you can define your own
click margin. With the formulas above you get away with
4 multiplications, 1 division, 2 additions and and square root.
If you think the square root eats to much computer power then
square both the distance and the click margin.

I think that this approach saves both computer power and memory
compared to the Point-In-Region-approach.

Lars