Difference between revisions of "Distance Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
{{command|geometry}}
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;Distance( <Point>, <Object> ): Yields the shortest distance between a point and an object.
; Distance[Point A, Point B]: Yields the distance between two points ''A'' and ''B''.
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:{{example|1=<code><nowiki>Distance((2, 1), x^2 + (y - 1)^2 = 1)</nowiki></code> yields ''1''}}
; Distance[Point, Line]: Yields the distance between the point and the line.
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: {{Note| 1=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 g, Line h]: Yields the distance between the parallel lines ''g'' and ''h''.
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::{{example|Let ''f'' be a function and ''A'' be a point. <code><nowiki>Distance(A, f)</nowiki></code> yields the distance between ''A'' and ''(x(A), f(x(A)))''.}}
: {{Note| The distance between intersecting lines is 0. Thus, this command is only interesting for parallel lines.}}
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}}
: {{Note| See also [[Distance or Length Tool|Distance or Length]] tool .}}
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<br>
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;Distance( <Line>, <Line> ): Yields the distance between two lines.
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:{{examples|1=<div>
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:*<code><nowiki>Distance(y = x + 3, y = x + 1)</nowiki></code> yields ''1.41''
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:*<code><nowiki>Distance(y = 3x + 1, y = x + 1)</nowiki></code> yields ''0''</div>}}
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: {{Note| 1=The distance between intersecting lines is ''0''. Thus, this command is only interesting for parallel lines.}}
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{{Note| 1=See also [[File:Mode distance.svg|link=|20px]] [[Distance or Length Tool|Distance or Length]] tool .}}
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;Distance( <Point>, <Point> )
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: Yields the distance between the two points.
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:{{example|1=<code><nowiki>Distance((2, 1, 2), (1, 3, 0))</nowiki></code> yields ''3''}}
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;Distance( <Line>, <Line> )
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:Yields the distance between two lines.
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:{{example|1=Let ''a: X = (-4, 0, 0) + λ*(4, 3, 0)'' and ''b: X = (0, 0, 0) + λ*(0.8, 0.6, 0)''.  <code><nowiki>Distance(a, b)</nowiki></code> yields ''2.4''}}

Latest revision as of 10:16, 11 October 2017


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 Mode distance.svg 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
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