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Convex hull, quick algorithm
#1
I need to calculate and display the convex hull of 2D polygons in the editor for that 3d thing, so I implemented a quick (as in "divide and conquer") algorithm for it. I remember writing a quick algorithm for the convex hull of a set of random points in 3D at the university, which is a bit trickier.

If you ever need to calculate the convex hull for a polygon or a bunch of points, you can use this Smile

Code:
' Convex hull test
' ----------------

set window "test", 640, 480
set redraw off

do
    set color 0, 0, 0
    cls
    ' Create 100 random points.
    points = []
    for i = 1 to 100
        a = rnd()*2*PI
        r = rnd(200)
        points[sizeof(points)] = 320 + cos(a)*r
        points[sizeof(points)] = 240 + sin(a)*r
    next
    ' Draw points.
    set color 255, 255, 255
    pcount = sizeof(points)/2
    for i = 0 to pcount - 1
        draw pixel points[i*2], points[i*2 + 1]
    next
    ' Display and wait one second.
    redraw
    wait 1000
    ' Calculate convex hull and display it.
    hull = ConvexHull(points)
    draw poly hull
   
    set caret width(primary)/2, 4
    center "Press space bar to continue ..."
   
    redraw
    while not keydown(KEY_SPACE, true)  fwait 60
loop

' ConvexHull
' ----------
' Calculate the convex hull for a set of points in an array [x0, y0, x1, y1 ..], return as a polygon
' in the same format.
function ConvexHull(points)
    pcount = sizeof(points)/2
    xminIndex = 0; xmaxIndex = 0
    for i = 1 to pcount - 1
        x = points[i*2]
        if x < points[xminIndex*2] xminIndex = i
        if x > points[xmaxIndex*2] xmaxIndex = i
    next
    lpoints = []; rpoints = []
    for i = 0 to pcount - 1
        if i <> xminIndex and i <> xmaxIndex
            cp = CrossProd(points[xminIndex*2], points[xminIndex*2 + 1],
                    points[xmaxIndex*2], points[xmaxIndex*2 + 1],
                    points[i*2], points[i*2 + 1])
            if cp < 0
                lpoints[sizeof(lpoints)] = points[i*2]
                lpoints[sizeof(lpoints)] = points[i*2 + 1]
            elseif cp > 0
                rpoints[sizeof(rpoints)] = points[i*2]
                rpoints[sizeof(rpoints)] = points[i*2 + 1]
            endif
        endif
    next
    hull = []
    hull[sizeof(hull)] = points[xminIndex*2]
    hull[sizeof(hull)] = points[xminIndex*2 + 1]
    HullRec(hull, lpoints, points[xminIndex*2], points[xminIndex*2 + 1], points[xmaxIndex*2], points[xmaxIndex*2 + 1])
    hull[sizeof(hull)] = points[xmaxIndex*2]
    hull[sizeof(hull)] = points[xmaxIndex*2 + 1]
    HullRec(hull, rpoints, points[xmaxIndex*2], points[xmaxIndex*2 + 1], points[xminIndex*2], points[xminIndex*2 + 1])
   
    return hull
   
    function HullRec(hull, points, x0, y0, x1, y1)
        if not sizeof(points)  return
        pcount = sizeof(points)/2
        maxd = 0; maxdIndex = -1
        for i = 0 to pcount - 1
            x = points[i*2]; y = points[i*2 + 1]
            d = LinePointDist(x0, y0, x1, y1, x, y)
            if d > maxd
                maxd = d
                maxdIndex = i
            endif
        next
           
        npoints = []
        for i = 0 to pcount - 1
            if i <> maxdIndex
                x = points[i*2]; y = points[i*2 + 1]
                cp = CrossProd(x0, y0, points[maxdIndex*2], points[maxdIndex*2 + 1], x, y)
                if cp < 0
                    npoints[sizeof(npoints)] = x
                    npoints[sizeof(npoints)] = y
                endif
            endif
        next
        if sizeof(npoints)
            HullRec(hull, npoints, x0, y0, points[maxdIndex*2], points[maxdIndex*2 + 1])
        endif
        hull[sizeof(hull)] = points[maxdIndex*2]
        hull[sizeof(hull)] = points[maxdIndex*2 + 1]
       
        npoints = []
        for i = 0 to pcount - 1
            if i <> maxdIndex
                x = points[i*2]; y = points[i*2 + 1]
                cp = CrossProd(points[maxdIndex*2], points[maxdIndex*2 + 1], x1, y1, x, y)
                if cp < 0
                    npoints[sizeof(npoints)] = x
                    npoints[sizeof(npoints)] = y
                endif
            endif
        next
        if sizeof(npoints)
            HullRec(hull, npoints, points[maxdIndex*2], points[maxdIndex*2 + 1], x1, y1)
        endif
    endfunc
   
    function CrossProd(ax, ay, bx, by, cx, cy)
        return (bx - ax)*(cy - ay) - (by - ay)*(cx - ax)
    endfunc
   
    function LinePointDist(x0, y0, x1, y1, px, py)
        dx = x1 - x0; dy = y1 - y0; d = dx*dx + dy*dy
        if d <= 0  return 0
        return |(x1 - x0)*(py - y0) - (px - x0)*(y1 - y0)|/sqr(d)
    endfunc   
endfunc
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#2
CONVEX HULL

   
click image to zoom in

Convex Hull is very useful. 
It can be used in 3D graphics, which you are working now ... and it can be used also to simulate football in 2D game.
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#3
(05-03-2024, 05:18 AM)1micha.elok Wrote: CONVEX HULL


click image to zoom in

Convex Hull is very useful. 
It can be used in 3D graphics, which you are working now ... and it can be used also to simulate football in 2D game.

I didn't know it was used in soccer, haha! But then, my interest in sports happens to be pretty much equal to zero Smile

I need it in the editor because portals/doorways between sectors/rooms must only exist on the convex hull of the sectors, else you're doomed to get rendering errors (like seeing other sectors through walls).
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#4
Doomed! Doom! Great idea... Time to play!
Logic is the beginning of wisdom.
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#5
(05-03-2024, 08:28 AM)johnno56 Wrote: Doomed! Doom! Great idea... Time to play!

Just curious, what version of doom do you prefer?
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#6
My favourite is classic... out of the box Doom and Doom2... Of course I have many, many mods and total conversions... I use GZDoom as my front-end...
Logic is the beginning of wisdom.
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#7
(05-04-2024, 12:25 PM)johnno56 Wrote: My favourite is classic... out of the box Doom and Doom2... Of course I have many, many mods and total conversions... I use GZDoom as my front-end...

Any way to play the doom 64 levels (originally on the N64 console) on that? They're very different from the original doom, creepier somehow, unsettling.
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#8
Doom 64 is one of the files I have... As I had never played the N64 version I cannot compare Doom 64 with N64... I also have "creepy" doom files... Not my "cup of tea" but good for a chuckle... lol
Logic is the beginning of wisdom.
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