Point on line closest to two points outside that line

[Walt-D]

@Walt-D

I know this is getting a bit off topic --but since it came up… does anyone know why curves are NOT automatically parameterized 0 to 1 like lines? Like for example why doesn’t a circle just default to 0-1? I use the Pufferfish “reparameterize curve” tool all the time… is there something I’m missing?

In partial answer to my own question here is a very informative posts by David (see link below).

Most to the point:
“When Rhino makes curves it typically picks a domain from zero to the length of the curve. There is no stringent need for such a choice, except that many algorithms ‘like’ it when the physical size of a curve is roughly equal to its parametric size.”

and also:
“Certain special types of curves have an intrinsic domain. Lines are always (0,1), circles are always (0,π), arcs are always (α0,α1), where the α’s represent the start and end angles of the arc.”

Thanks again everyone for your help!

Shatter component / Crv-Crv intersection: does not always work

Some basic info on curve parameters: The curve domain is a non-zero-length, increasing numeric interval. An interval is delineated by two extremes and these values could be anything, as long as they aren’t the same and as long as the domain start value is less than the domain end value. The curve ‘exists’ everywhere inside this domain. The first (i.e. smallest) value represents the curve start point. The last (i.e. largest) value represents the curve end point. Any value (or parameter) in bet…