line/circle

[Lin-Rolover]

Why do this?
float len = sqrt( (distXdistX) + (distYdistY) );
And after this
float dot = ( ((cx-x1)(x2-x1)) + ((cy-y1)(y2-y1)) ) / pow(len,2);

You have scalar aa
float len2 = (distXdistX) + (distYdistY);
And
float dot = ( ((cx-x1)(x2-x1)) + ((cy-y1)(y2-y1)) ) / len2;

But what is that ? I am understand projection vector in other vector ab/|b|. But what is : ab/|b|*|b|?

[Jeff Thompson]

Thanks for noting this. It's been a looooong time since I researched this and my vector math isn't so good. I'm not sure I'm understanding you're question though?

[Lin-Rolover]

I found out. This is really a projection of a vector onto a vector, but also finding a collinear vector

1. 𝑝𝑟𝑥 (𝑌) = |𝑌| ∙ 𝑐𝑜𝑠(∠𝑋, 𝑌) = (𝑋∙ 𝑌) / |𝑋| this number, the length of the projection with a sign (+, -)
2. 𝑃𝑅𝑋 (𝑌) = ((𝑋∙ 𝑌) / |𝑋|) ∙ (𝑋/|𝑋|) = ((𝑋,𝑌) ∙ 𝑋) / |𝑋|∙|𝑋| - is a vector parallel (collinear) to the vector 𝑋.
   and |𝑋|∙|𝑋| <=>(𝑋∙𝑋) => ((𝑋∙ 𝑌)/(𝑋∙𝑋)) ∙ 𝑋

ab/|b|*|b| => ((𝑋∙ 𝑌)/(𝑋∙𝑋)) = dot => dot ∙ 𝑋 - But this is a vector

Then you find the point
x = x1 + (dot ∙ (x2 - x1) ) // x1 + dot ∙ Xx
y = y1 + (dot ∙ (y2 - y1) ) // y1 + dot ∙ Xy

[Jeff Thompson]

Sorry, I think you lost me! Does this mean the code on the site isn't working correctly or could be simplified?

[Lin-Rolover]

Honestly, I haven’t tested your code at all except on the page at the very top. I just read and took for an idea, a solution algorithm, for example, what steps, what to watch for. I really liked the point / polygon algorithm, I took the comparison logic, and did not analyze it.

In some solutions, I went from the opposite. For example, the intersection of a point and a line. I did not look for the intersection of a point with a line. I checked whether the point of the line belongs. Got this result

pointLine (px,py, l) {
l = l.arrVert;
// if the scalar product of vectors <= 0, the point belongs to the segment
return (
(l[0] - px) * ( l[2] - px) +
(l[1] - py) * (l[3] - py) <= 0
) ? {x:px, y:py} : false;
}
All

If think can put a buffer in, but now me no needed pointer
And my line / line algorithm is not very scary. Sorry.

But once again I want to thank you for great ideas
The code can be simplified, without doing unnecessary actions