2d geometry problem .... ?

[Brian Peacock]

Figure A:



Given the coordinates of A, B, and C and some arbitrary point within the triangle P ...


Figure B:



... and given some arbitrary angle a, how can I work out the distance d to the boundary of the triangle?

Cheers in advance


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[Brian Peacock]

Fixed the attachment issue above. So the problem is calculating the distance to the boundary of a triangle from any point within it it, in any direction, when the points of the triangle are three sets of {x, y} 2d coordinates relative to top-left {0, 0}.

[laklak]

I don't think you can.

[Brian Peacock]

Bum.

[Brian Peacock]

I was hoping there'd be some kind of formula, but perhaps I need to break it down into smaller triangles or something.

[Scot Dutchy]

Nope.

[Brian Peacock]

Surely I haven't stumbled upon an unsolvable Trigonometry problem?

[NineBerry]

Connect the dot to all three corners. That creates three triangles. The height of these triangles is the distance of the point to the borders.

[Svartalf]

it's not a trig problem. to calculate a distance, you need measurements. If you knew the length of the sides of the triangle, and the point's distance to the other two sides, you might have a prayer of doing it, but in a triangle of indeterminate size and with an undefined point, calculating a distance is impossible.

[NineBerry]

it's not a trig problem. to calculate a distance, you need measurements. If you knew the length of the sides of the triangle, and the point's distance to the other two sides, you might have a prayer of doing it, but in a triangle of indeterminate size and with an undefined point, calculating a distance is impossible.

Rubbish. You do that in 7th grade at school

[laklak]

You can get the lengths of the big triangle legs because you're got the coordinates. With all three legs you can get the internal angles. But that's still not solving the problem. To do that you'd need either the coordinates where two legs of the cross intersect the big triangle, or 2 angles and one length on the smaller triangle to calculate d. The smaller triangle has one 90 angle, and one equal to 360 -(a + 90). But you still need a length.

You could move point P anywhere within the big triangle and angle a would remain the same, but d would change.

[NineBerry]

https://en.m.wikipedia.org/wiki/Distanc ... two_points

[Brian Peacock]

Connect the dot to all three corners. That creates three triangles. The height of these triangles is the distance of the point to the borders.

The figure may be misleading. The angle a is arbitrary, therefore h = 2A/b only guarantees d = h when a is a specific value - imagine how it'd look with a ± 20°

[Brian Peacock]

https://en.m.wikipedia.org/wiki/Distanc ... two_points

I think I need this explained in a simpler form that the Wiki page offers.

[JimC]

9B has nailed it. You actually don't need the angle you mentioned in your OP, Brian, simply all 4 coordinates, then use 3 different versions of the formula, one for the perpendicular distance to each of the 3 sides. You could, additionally, calculate the angle if you wanted.