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LineScaledCoordinate[{{x1,y1},{x2,y2},…,{xk,yk}},r]

gives the coordinate of a point in the polyline {{x1,y1},{x2,y2},…,{xk,yk}}, at a scaled distance of r from point {x1,y1}.

LineScaledCoordinate[{{x1,y1},{x2,y2},…,{xk,yk}}]

is the same as LineScaledCoordinate[{{x1,y1},{x2,y2},…,{xk,yk}},0.5].

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Interactive Examples  
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GraphUtilities`
GraphUtilities`

LineScaledCoordinate

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

LineScaledCoordinate[{{x1,y1},{x2,y2},…,{xk,yk}},r]

gives the coordinate of a point in the polyline {{x1,y1},{x2,y2},…,{xk,yk}}, at a scaled distance of r from point {x1,y1}.

LineScaledCoordinate[{{x1,y1},{x2,y2},…,{xk,yk}}]

is the same as LineScaledCoordinate[{{x1,y1},{x2,y2},…,{xk,yk}},0.5].

Details and Options

  • To use LineScaledCoordinate, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • LineScaledCoordinate works for both two and three dimensions.

Examples

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Basic Examples  (1)

Wolfram Language code: Needs["GraphUtilities`"]

This displays the vertices that form the edges at a point 60% of the way down the arrow:

Wolfram Language code: LayeredGraphPlot[{1 -> 2, 2 -> 3, 1 -> 3, 1 -> 1, 2 -> 1}, EdgeRenderingFunction -> ({Arrow[#1], Text[#2, LineScaledCoordinate[#1, 0.6], Background -> White]}&)]

This adds edge labels in GraphPlot3D:

Wolfram Language code: GraphPlot3D[{{1 -> 2, "Edge 12"}, 1 -> 3, 1 -> 4, {1 -> 5, "Edge 15"}, 2 -> 3, 2 -> 4, 2 -> 5, 3 -> 4, 3 -> 5, 4 -> 5}, VertexLabeling -> True, EdgeRenderingFunction -> ({RGBColor[0.5, 0, 0], Line[#1], Black, If[#3 =!= None, Text[#3, LineScaledCoordinate[#1, 0.5], Background -> White], {}]}&)]

Interactive Examples  (1)

Wolfram Language code: Manipulate[ LayeredGraphPlot[{4 -> 3, 5 -> 3, 5 -> 4, 6 -> 1, 6 -> 2, 6 -> 4, 6 -> 5, 6 -> 3}, VertexLabeling -> True, EdgeRenderingFunction -> ({Line[#1], Text[#2, LineScaledCoordinate[#1, t], Background -> White]}&), ImageSize -> 500], {{t, 0.5}, 0.1, 0.9}, Initialization :> Needs["GraphUtilities`"]]
Wolfram Research (2007), LineScaledCoordinate, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/LineScaledCoordinate.html.

Text

Wolfram Research (2007), LineScaledCoordinate, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/LineScaledCoordinate.html.

CMS

Wolfram Language. 2007. "LineScaledCoordinate." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/LineScaledCoordinate.html.

APA

Wolfram Language. (2007). LineScaledCoordinate. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/LineScaledCoordinate.html

BibTeX

@misc{reference.wolfram_2026_linescaledcoordinate, author="Wolfram Research", title="{LineScaledCoordinate}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/LineScaledCoordinate.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_linescaledcoordinate, organization={Wolfram Research}, title={LineScaledCoordinate}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/LineScaledCoordinate.html}, note=[Accessed: 13-June-2026]}