Distance Command

Distance( <Point>, <Object> )

Yields the shortest distance between a point and an object.

Examples:

• Distance((2, 1), x^2 + (y - 1)^2 = 1) yields 1
• Distance((2, 1, 2), (1, 3, 0)) yields 3
• Let f be a function and A be a point. Distance(A, f) yields the distance between A and (x(A), f(x(A))).

Note: The command works for points, segments, lines, conics, functions, and implicit curves. For functions, it uses a numerical algorithm which works better for polynomials. 

Distance( <Line>, <Line> )

Yields the distance between two lines.

Examples:

• Distance(y = x + 3, y = x + 1) yields 1.41
• Distance(y = 3x + 1, y = x + 1) yields 0
• Let a: X = (-4, 0, 0) + λ*(4, 3, 0) and b: X = (0, 0, 0) + λ*(0.8, 0.6, 0).  Distance(a, b) yields 2.4

Note: The distance between intersecting lines is 0. Thus, this command is only interesting for parallel lines.

Note: See also Distance or Length tool .

Distance( <Plane>, <Plane> )

Yields the distance between the two planes.

Example: Let eq1: x + y 2x = 1 and eq2: 2x + 2y +4z = -2.  Distance(eq1, eq2) yields 0.82

Note: The distance between intersecting planes is 0. Thus, this command is only meaningful for parallel planes.