Math God needed

[Shadowing]

Every year I run into some math that is over my head lol.

 

Say I have a circle with a radius of 600 and I want to place 20 objects around the circle perfectly spaced.

 

I need to figure out what the x and y would be for each object.

[requinix]

"Perfectly" spaced how? 20 isn't a nice number like 19 (hexagonal) or 25 (square).

[Barand]

If you want them spaced around the circumference then the attached diagram will tell you what you need to know

[Shadowing]

Thanks for thee responses guys.

 

Ya I meant spaced around its circumference. So together all 20 objects forms a circle.

 

I think this is the formula I saw when I was trying to google it Barand.

 

I'm confused about the theta part

Do I use pie for that?

 

Also not sure how this would give me 20 spaced out. But I guess the theta would determine that.

 

so really I need 20 slices of pie and a object in the middle of each slice on the circumference.

 

Maybe I need to find the circumference first then divide it out by 20.

Then find what each one would be spaced out on the circumference.

Then some how use that number with a formula to find my x and y?

Edited February 14, 2016 by Shadowing

[Barand]

All you need is theta. You have 20 objects so theta will start at zero and increase by 2*PI/20 for each one. Then, as in the diagram, if the circle has radius R and its centre is at cx,cy the x,y coordinates for each object are

x = cx + R * cos(theta)
y = cy - R * sin(theta)

[Shadowing]

Ahh OK. Thanks now I know how to find theta.

 

I can just ignore cy and CX right since that's always going to be 0,0?

[Barand]

0,0 is usually at the top left corner of the image.

[Shadowing]

Actually this is for unity game engine. Atm center is 0,0

So I'm dealing with negative numbers

[Shadowing]

Actually the zero probably affects if the vakue is negative or not

Edited February 14, 2016 by Shadowing

[Barand]

Here's an example

<?php
$width = 140;
$height = 140;
$rad = 60;
$dtheta = M_PI/10;

$im = "<svg width=\"$width\" height=\"$height\" viewBox=\"0 0 $width $height\" >\n
        <rect x='1' y='1' width='$width' height='$height' fill='black' />\n
        <g transform='translate(70,70)'>\n
        <circle cx='0' cy='0' r='$rad' stroke='white' fill='none' />\n";
for  ($theta=0; $theta<2*M_PI; $theta+=$dtheta) {
    $x = $rad*cos($theta);
    $y = $rad*sin($theta);
    $im .= "<circle cx='$x' cy='$y' r='5' fill='cyan' />\n";
}      
$im .= "</g></svg>\n";

echo $im;
?>