Ternary diagram / ternary plot calculations

[Patrick Grossien]

Yes, the sliders are just there to store the results so that I can easily use these as text sources to display the percentage in the animation.

I used the 3 slider controls in the dot layer so that the expression can always easily reference to it’s own layer position and that it’s all in one place.

[Kalleheikki Kannisto]

The distance calculation between a point and a line can be found here:
Mathwold, Point-Line Distance

Since we know all the points (the corners that create the line and the point that we want to know the distance of), the solution lies here:

and in this formula:

[Patrick Grossien]

oh my 🙂

[Xavier Gomez]

The expression below is for a text layer (display all 3 coordinates in 1 single text) :

A = thisComp.layer("A").transform.position.value;
B = thisComp.layer("B").transform.position.value;
C = thisComp.layer("C").transform.position.value;
M = thisComp.layer("Point").transform.position.value;
AB = sub(B,A); if (AB.length<3) AB.push(0);
BC = sub(C,B); if (BC.length<3) BC.push(0);
CA = sub(A,C); if (CA.length<3) CA.push(0);
AM = sub(M,A); if (AM.length<3) AM.push(0);
u = cross(AB, CA);
U = dot(u,u);

c = dot(u, cross(AM, AB))/U*100;
b = dot(u, cross(AM, CA))/U*100;
a = 100-(b+c);

letters= ["a", "b", "c"];
values = [a,b,c];
for (k=0; k<3; k++) letters[k] += " : " + (values[k]<10 ? " " : "") + values[k].toFixed(1) + "%";
letters.join("\n");

It’s not optimal as it does unnecessary calculations, but trying to optimize would make it less compact.

Xavier

[Kalleheikki Kannisto]

Xavier got there before me 🙂

Anyways, attached is my humble approach which is not quite as compact.

I’ve used the coordinates that show on the diagram, so they need to be modified for a triangle that has different corner coordinates.

Also, there’s no code checking that the dot is not outside the triangle, but I figured you will animate it so that that doesn’t occur.

9698_ternarydiagram.aep.zip

[Patrick Grossien]

Wow! Both you guys are amazing. You just made my day.

Now I need to backtrace what you did, trying to understand the math and expressions behind it, but it’s awesome already. I tried both solutions and they both work nicely!

I have the problem that I didn’t get Xaviers solution to work. I tried this one first, because I could easily integrate into my existing comp. Now the percentages are all of. In a clean composition it works like a charm. But I’ll go ahead and try to figure out what’s going on there.

Just to be sure, @Xavier: I could also just add [x,y] values for each one of the ABC variables instead of linking layers to the expression, correct?

[Patrick Grossien]

Thank you, thank you, thank you, for your generous help!

Next beer’s on me! 🙂

[Patrick Grossien]

PS.

OK direct input of the coordinates works of course.
I just wanted to let you know whats happening where I integrated it into my comp:

In the center of the triangle I get
a: 100, b: 100, and c:-100

and for example at the lower left corner (A) I get
a: 164, b: 65, and c: -129

I’ll continue to search for what happens. But maybe this already triggers for you what could be going wrong here.

[Patrick Grossien]

OK I found it: I was relying on getting the summits XY positions from INFO window XY values, which were not the same as the true positions of the summits inside the comp

I got this working now, but how can the Info window be wrong? Any clue?

[Xavier Gomez]

I can’t tell.
The expression i gave assumes that all point coordinates A, B, C and M are in the same system. Depending on your set up you might have to use one of the space transform functions (toComp/fromComp etc).

Also, that expression is unnecessarily heavy. If you have lots of points you can change it to this one, which does the same thing without extra stuff:

A = thisComp.layer("A").transform.position.value;
B = thisComp.layer("B").transform.position.value;
C = thisComp.layer("C").transform.position.value;
M = thisComp.layer("Point").transform.position.value;
AB = sub(B,A);
BC = sub(C,B);
CA = sub(A,C);
AM = sub(M,A);
u = AB[0]*CA[1]-AB[1]*CA[0];

c = 100 * (AM[0]*AB[1]-AM[1]*AB[0]) / u;
b = 100 * (AM[0]*CA[1]-AM[1]*CA[0]) / u;
a = 100-(b+c);

letters= ["a", "b", "c"];
values = [a,b,c];
for (k=0; k<3; k++) letters[k] += " : " + (values[k]<10 ? " " : "") + values[k].toFixed(1) + "%";
letters.join("\n");

Xavier