File:Barycentriccoordinates.gif
Summary
| Description |
English: Barycentric coordinates are a way to identify a point inside a triangle with three numbers, which can be thought as masses on the triangle vertices, and the point inside the triangle as their center of mass. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1127866653981724672 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
p1 = {-1, 0};
p2 = {1, 0};
p3 = {0, 1};
c1 = 1;
c2 = 1;
c3 = 1;
plot1 = Table[
c1 = j;
Graphics[{Black, Disk[p1, 0.1], Disk[p2, 0.1], Disk[p3, 0.1], Line[{p1, p2, p3, p1}], White, Text[NumberForm[c1, {3, 2}], p1], Text[NumberForm[c2, {3, 2}], p2], Text[NumberForm[c3, {3, 2}], p3], Red,
Disk[(c1 p1 + c2 p2 + c3 p3)/(c1 + c2 + c3), 0.05]}, PlotRange -> {{-1.1, 1.1}, {-0.1, 1.1}}]
, {j, 1, 2, 0.02}];
plot2 = Table[
c2 = j;
Graphics[{Black, Disk[p1, 0.1], Disk[p2, 0.1], Disk[p3, 0.1], Line[{p1, p2, p3, p1}], White, Text[NumberForm[c1, {3, 2}], p1], Text[NumberForm[c2, {3, 2}], p2], Text[NumberForm[c3, {3, 2}], p3], Red,
Disk[(c1 p1 + c2 p2 + c3 p3)/(c1 + c2 + c3), 0.05]}, PlotRange -> {{-1.1, 1.1}, {-0.1, 1.1}}]
, {j, 1, 2.5, 0.02}];
plot3 = Table[
p2 = {1, 0} - {j, 0};
Graphics[{Black, Disk[p1, 0.1], Disk[p2, 0.1], Disk[p3, 0.1], Line[{p1, p2, p3, p1}], White, Text[NumberForm[c1, {3, 2}], p1], Text[NumberForm[c2, {3, 2}], p2], Text[NumberForm[c3, {3, 2}], p3], Red,
Disk[(c1 p1 + c2 p2 + c3 p3)/(c1 + c2 + c3), 0.05]}, PlotRange -> {{-1.1, 1.1}, {-0.1, 1.1}}]
, {j, 0, 0.5, 0.01}];
ListAnimate[Join[plot1, plot2, plot3]]
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