Beefy Boxes and Bandwidth Generously Provided by pair Networks
There's more than one way to do things
 
PerlMonks  

Comment on

( #3333=superdoc: print w/ replies, xml ) Need Help??
First of all the game is quite nice, but there's a simple method with which you can win every level pretty fast, which kind of kills the fun as it is now.
How can I tell whether the circular sprit intersects with an arbitrary line.

I don't know how familiar you are with linear algebra, it really helps ;-)

(Update: When I talk about "points", I really mean "position vectors to points". Thanks FunkyMonk)

I'll call the end points of your line A and B, the center of your sprite M, the point on the line which is the closest to M is called C (all those are vectors), the radius of the sprite is r (a scalar value).

Since C is on the line between A and B, it must be expressible in the form A + x * (B-A). Since it's the closest point to M, the connection line from C to M is perpendicular to the original line, or as a formula:

(B-A) . (M-C) = 0 or (B-A) . (M - A - x * (B-A)) = 0 # (that's a scalar product)

The only unknown part in this equation is x, which you can calculate from that equation, but to which I'm too tired at the moment.

If 0 <= x <= 1 and |M - C| < r, then it circle touches or intersects the line.

Likewise if |M-A| <= r or |M-B| <= r it also touches or intersects. In all other case it doesn't.

To get a realistic bouncing behaviour, the angle between (dx, dy) and (M-C) after the bounce has to be negative of what it was before the bounce.


In reply to Re: Some simple 2d game-related maths questions by moritz
in thread Some simple 2d game-related maths questions by skx

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":



  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.
  • Log In?
    Username:
    Password:

    What's my password?
    Create A New User
    Chatterbox?
    and the web crawler heard nothing...

    How do I use this? | Other CB clients
    Other Users?
    Others scrutinizing the Monastery: (9)
    As of 2015-07-07 00:57 GMT
    Sections?
    Information?
    Find Nodes?
    Leftovers?
      Voting Booth?

      The top three priorities of my open tasks are (in descending order of likelihood to be worked on) ...









      Results (86 votes), past polls