Difference between revisions of "Distance Command"

Revision as of 11:05, 16 December 2022

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

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
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.

@@ Line 1: / Line 1: @@
 <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
 ;Distance( <Point>, <Object> ): Yields the shortest distance between a point and an object.
-:{{example|1=<code><nowiki>Distance((2, 1), x^2 + (y - 1)^2 = 1)</nowiki></code> yields ''1''}}
+:{{examples|1=<div>
-: {{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.
+:*<code><nowiki> Distance((2, 1), x^2 + (y - 1)^2 = 1)</nowiki></code> yields ''1''
-::{{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)))''.}}
+:*<code><nowiki>Distance((2, 1, 2), (1, 3, 0))</nowiki> </code> yields ''3''</div>}}
+: {{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.
+::{{example|Let ''f'' be a function and ''A'' be a point. <code><nowiki>Distance(A, f)</nowiki></code> yields the distance between ''A'' and <div> ''(x(A), f(x(A)))''.}}
 }}
 <br>
 ;Distance( <Line>, <Line> ): Yields the distance between two lines.
 :{{examples|1=<div>
 :*<code><nowiki>Distance(y = x + 3, y = x + 1)</nowiki></code> yields ''1.41''
-:*<code><nowiki>Distance(y = 3x + 1, y = x + 1)</nowiki></code> yields ''0''</div>}}
+:*<code><nowiki>Distance(y = 3x + 1, y = x + 1)</nowiki></code> yields ''0''
+:* 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''</div>}}
 : {{Note| 1=The distance between intersecting lines is ''0''. Thus, this command is only interesting for parallel lines.}}
@@ Line 15: / Line 19: @@
+;Distance( <Plane>, <Plane> )
-;Distance( <Point>, <Point> )
+: Yields the distance between the two planes.
-: Yields the distance between the two points.
+:{{example|1=Let ''eq1: x + y 2x = 1'' and ''eq2: 2x + 2y +4z = -2''.  <code><nowiki>Distance(eq1, eq2)</nowiki></code> yields ''0.82''}}
-:{{example|1=<code><nowiki>Distance((2, 1, 2), (1, 3, 0))</nowiki></code> yields ''3''}}
+: {{Note| 1=The distance between intersecting planes is 0. Thus, this command is only meaningful for parallel planes.}}
-;Distance( <Line>, <Line> )
-:Yields the distance between two lines.
-:{{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''}}

Difference between revisions of "Distance Command"

Revision as of 11:05, 16 December 2022

Distance

Command Categories (All commands)