Perpendicular to an infinite line & distance to line segment

Calculate the foot point of perpendiculars on infinite lines and calculate the minimal distances D from a point P to a 2D or 3D line segment

FEATURES

• 2D or 3D infinite lines and line segments
• Output of perpendicular foot coordinates for infinite lines and distance to point
• Output of minimal distances to line segments
• Indicator for perpendicular foot position for line segments
• Process multiple lines at once

Manual

INPUT:

2D 3D

P : Reference point, P=[xp, xp] or P=[xp, yp, zp]

A1: Starting points of line segments, A1=[X1, Y 1] or A1=[X1, Y1, Z1]

A2: Ending points of line segments, A2=[X2, Y 2] or A2=[X2, Y2, Z2]

OUTPUT:

F: Foot points X, Y where the perpendiculars hits the infinite line.

D: Distances from P to lines (length of perpendiculars)

Fs: Point on line segment closest to P. May be, but must not be the foot point F.

Ds: Shortest distance from P to line segments

outside: Indicator for perpendicular position

outside 0: Perpendicular inside line segment

outside 1: Perpendicular outside start of line segment

outside 2: Perpendicular outside end of line segment

EXAMPLE 2D, three line segments:

P=[0,0]; %Reference point

A1=[ -4, 1 ; %x1 and y1 of 1st segment

-4, 2 ; %x1 and y1 of 2nd segment

-1, 2 ]; %x1 and y1 of 3rd segment

A2=[ -2, 1 ; %x2 and y2 of 1st segment

-2, 4 ; %x2 and y2 of 2nd segment

1, 2 ]; %x2 and y2 of 3rd segment

[F, D, Fs, Ds, outside]=Perpendicular2Line(P, A1, A2)

See also the demonstration file Examples.m and ReadMe.pdf