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## #1 2010-01-09 15:46:20

brod
Member
From: NY, United States
Registered: 2008-12-14
Posts: 9
Website

### point_in_ellipse

Expand//point_in_ellipse(point_x, point_y, x1, y1, x2, y2);

var x1, y1, x2, y2, cenx, ceny, major, minor, foc1, foc2, R1, R2;
x1 = min(argument2, argument4); y1 = min(argument3, argument5);
x2 = max(argument2, argument4); y2 = max(argument3, argument5);

cenx  = x1 +(x2-x1)/2;
ceny  = y1 +(y2-y1)/2;
major = max(x2-x1, y2-y1);
minor = min(x2-x1, y2-y1);

if(major==(x2-x1)) {
foc1  = cenx -sqrt(sqr(major/2) - sqr(minor/2));
foc2  = cenx +sqrt(sqr(major/2) - sqr(minor/2));

R1    = point_distance(argument0, argument1, foc1, ceny);
R2    = point_distance(argument0, argument1, foc2, ceny);
} else {
foc1  = ceny -sqrt(sqr(major/2) - sqr(minor/2));
foc2  = ceny +sqrt(sqr(major/2) - sqr(minor/2));

R1    = point_distance(argument0, argument1, cenx, foc1);
R2    = point_distance(argument0, argument1, cenx, foc2);
}

return(R1+R2 <= major);

I'm sure there are plenty of things that can be made more efficient, but it still works, so there.

Last edited by brod (2010-01-09 15:51:39)

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## #2 2010-01-09 17:16:35

xot
Registered: 2007-08-18
Posts: 1,240

### Re: point_in_ellipse

This is a great idea for a script. It could be done a lot simpler, though, if the ellipse is axis-aligned (which it is).

Expandreturn sqr((2*argument0-(argument4+argument2))/(argument4-argument2)) + sqr((2*argument1-(argument5+argument3))/(argument5-argument3)) < 1;

The problem with that, besides being hard to read, is that it will fail if (x1 == x2) or (y1 == y2) because of a divide by zero. Even with checks it's still far fewer operations.

Expand//  point_in_ellipse(point_x, point_y, x1, y1, x2, y2);
{
if ((x1==x2) || (y1==y2)) return false;
return sqr((2*argument0-(argument4+argument2))/(argument4-argument2)) + sqr((2*argument1-(argument5+argument3))/(argument5-argument3)) < 1;
}

I think that's something like 17 operations compared to your 48. I couldn't find a way to simplify it more but I'm not a math whiz.

edit: Hey, I just noticed you are from NY. I lived on Long Island for 10 years of my yoot. I miss it but not right now. It's snowing here in Florida, I'm not sure I could handle NY anymore. Winters suck.

Last edited by xot (2010-01-09 17:26:54)

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## #3 2010-01-09 17:34:22

brod
Member
From: NY, United States
Registered: 2008-12-14
Posts: 9
Website

### Re: point_in_ellipse

Wow impressive stuff, although what the script is doing is way over my head >_<. Thanks a lot, though!

Yeah I'm from long island too, I'll probably be moving out to college next year, but then again I'm not sure which college I plan on attending. All "iffy" stuff.

Last edited by brod (2010-01-09 17:35:40)

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## #4 2010-01-09 17:43:50

xot
Registered: 2007-08-18
Posts: 1,240

### Re: point_in_ellipse

Well, it's over my head too. I read this, wrote a script based on it, and then tried to optimize it as much as possible ... which completely destroyed its normal elegance.

$$\frac{x^2}{a^2}+\frac{y^2}{b^2} < 1$$

What's good about yours is that it could be adapted for ellipses of arbitrary position and orientation.

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## #5 2010-01-09 18:08:16

xot
Registered: 2007-08-18
Posts: 1,240

### Re: point_in_ellipse

There is some interesting discussion about ellipses in this blog post by Yourself.

http://blog.ultimatepronoun.com/?p=11#more-11

Way, way, way, way over my head.

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## #6 2010-01-09 18:32:19

brod
Member
From: NY, United States
Registered: 2008-12-14
Posts: 9
Website

### Re: point_in_ellipse

Definitely
But for simple, GM standards, I think your script is perfect (Since it has the same arguments as draw_ellipse)

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## #7 2010-01-10 22:36:19

Marchal_Mig12
Member
Registered: 2009-05-21
Posts: 75

### Re: point_in_ellipse

xot wrote:

edit: Hey, I just noticed you are from NY. I lived on Long Island for 10 years of my yoot. I miss it but not right now. It's snowing here in Florida, I'm not sure I could handle NY anymore. Winters suck.

Yeah New York's winter suck. I went there for 2-3 days during winter and it really sucked because it was enough cold to snow and enough hot to... suck heh. I think if you really want to enjoy winter you should come to Quebec someday .

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## #8 2010-01-14 18:42:42

paul23
Member
Registered: 2007-10-17
Posts: 110

### Re: point_in_ellipse

Well xot: one could also add the inverse translation to the point first (asume the circle is the origin, and it's axis-aligned to the x' and y' axis: then calculate the x' and y' coordinate of the point and use the simple formula above. - I used a similar method for describing how much "percent" of a cell is filled by an ellipse...

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## #9 2010-01-14 20:08:41

xot
Registered: 2007-08-18
Posts: 1,240

### Re: point_in_ellipse

It already does that, unless you meant inverse transform so it could handle rotations as well. I would agree that that is probably best way to handle arbitrary ellipses.

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