Distance Command

Distance( <Point>, <Object> )

Yields the shortest distance between a point and an object.

Example: Distance((2, 1), x^2 + (y - 1)^2 = 1) yields 1

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.

Example: Let f be a function and A be a point. Distance(A, f) yields the distance between A and (x(A), f(x(A))).

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

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( <Point>, <Point> )

Yields the distance between the two points.

Example: Distance((2, 1, 2), (1, 3, 0)) yields 3

Distance( <Line>, <Line> )

Yields the distance between two lines.

Example: 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