Manipulating shapes and colors using expressions

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color wheel article

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Introduction

As an exercise to practice our expression coding skills, we would like to create a color wheel using a single shape layer and expressions. The wheel should be made with colored arcs of varying hue, saturation and lightness. We want 4 levels of tint and 12 arcs per level (subdivisions). The following figure shows the different parts of the wheel and the notation we’ll use in the expressions:

Constructing The Base Arc

We want to create an initial arc, add expressions to it, and then duplicate that arc to construct the entire wheel. The setup consists of a shape group containing a trimmed stroked ellipse:

Since the wheel is made of concentric circles, the size of each circle depends on the level. We apply the following expression to the ellipse size:

subdivs = 12;
idx = parseInt(thisProperty.propertyGroup(3).name.split(" ")[1]) - 1;
levelIdx = Math.floor(idx / subdivs);
strokeW = content("Arc " + (idx + 1)).content("Stroke 1").strokeWidth;
diam = 0.8 * thisComp.height - levelIdx * 2 * strokeW;
[diam,diam];

We add the following expression to the start property of the Trim Paths effector:

subdivs = 12;
idx = parseInt(thisProperty.propertyGroup(3).name.split(" ")[1]) - 1;
arcIdx = idx % subdivs;
arcIdx * (100 / subdivs);

The expression is the same for the end property, except the last line:

...
(arcIdx + 1) * (100 / subdivs);

The stroke width is set to 10% of the comp height:

0.1 * thisComp.height;

And finally we apply the following expression to the stroke color:

subdivs = 12;
numLevels = 4;
idx = parseInt(thisProperty.propertyGroup(3).name.split(" ")[1]) - 1;
levelIdx = Math.floor(idx / subdivs);
arcIdx = idx % subdivs;
h = arcIdx / subdivs; // hue
s = 1 - levelIdx / numLevels; // saturation (from high to low)
l = linear(levelIdx, 0, numLevels-1, 0.5, 0.3); // lightness (remap range)
a = 1; // alpha (doesn't affect the result here)
hslToRgb([h,s,l,a]);

This should produce something like this:

Duplicating The Base Arc

Quite a lot of code for drawing a simple arc, but now comes the fun part. We simply press Ctrl+D (Cmd+D on Mac) to duplicate the base arc until the wheel is complete:

When the number of arcs reaches 48 (i.e., 4 x 12), the wheel is complete:ession to the ellipse size:

Reveal Animation

As a bonus we would like to animate the construction of the wheel. To this end, we add a second Trim Paths effector to the base arc (don’t forget to remove every other arc):

We add the following trim end expression to sequentially reveal the arcs with a short delay:

arcRevealDur = 8; // duration in frames
delay = 2; // delay in frames
subdivs = 12;
numLevels = 4;
totalArcs = numLevels * subdivs;
idx = parseInt(thisProperty.propertyGroup(3).name.split(" ")[1]) - 1;
startT = idx * delay * thisComp.frameDuration;
endT = startT + arcRevealDur * thisComp.frameDuration;
linear(time, startT, endT, 0, 100);

The expression is the same for the out tangent except the vector points in the opposite direction:

Conclusion

Through this little exercise we have seen how we can manipulate shapes and colors using simple expressions. Hope you find it useful!

You can also check ConnectLayers PRO, a tool that create lines that are dynamically linked to the layers using powerful path expressions. No keyframes at all!

Creating and projecting a 3D cube onto a shape layer using expressions

Introduction

In this exercise we would like to create a 3D spinning cube and project it onto a 2D plane. All of that using a single shape layer and expressions.

This is a port of Daniel Shiffman’s Coding Challenge #112 (code for Processing).

Download the After Effects project with the code!

3D projection

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Setup

We want to draw the cube vertices with filled ellipses, and connect them with thin stroked lines. We would like to create a single point, apply an expression to its position, and then duplicate that point to create the other points. Once all points are created, we will draw the edges.

Math Utils

Manipulating 3D vectors (rotation, projection) is easier with matrices. Since there aren’t any built-in matrix utilities in the expression language, we must create our own. To avoid having a too long expression, we decide to put our matrix code in an external js file (e.g., “matrix.js”). This file can be imported into our our expression at runtime.

We only need basic stuff here: multiply a matrix and a vector, multiply two matrices… Here is our matrix library:

function vecToMatrix(v)
{
   var m = [];
   for (var i = 0; i < 3; i++)
   {
      m[i] = [];
   }
   m[0][0] = v[0];
   m[1][0] = v[1];
   m[2][0] = v[2];
   return m;
}

function matrixToVec(m)
{
   return [m[0][0], m[1][0], m.length > 2 ? m[2][0] : 0];
}

function matMatMul(a, b)
{
   var colsA = a[0].length;
   var rowsA = a.length;
   var colsB = b[0].length;
   var rowsB = b.length;
   var result = [];
   for (var j = 0; j < rowsA; j++)
   {
      result[j] = [];
      for (var i = 0; i < colsB; i++)
      {
         var sum = 0;
         for (var n = 0; n < colsA; n++)
         {
            sum += a[j][n] * b[n][i];
         }
         result[j][i] = sum;
      }
   }
   return result;
}

function matVecMul(a, v)
{
   var m = vecToMatrix(v);
   var r = matMatMul(a, m);
   return matrixToVec(r);
}

Creating The Vertices

$.evalFile("F:/Documents/JSX/matrix.js");

r = 200; // cube size
distance = 2; // affects perspective
rotSpeed = 0.06; // in radians per frame

idx = parseInt(thisProperty.propertyGroup(3).name.split(" ")[1]) - 1;

p = []; // 3D vertex position at start
bs = [];
for (i = 0; i < 3; i++)
{
	bs[i] = (idx >> i) & 1;
	p[i] = 0.5 * Math.pow(-1, bs[i]);
}

Now that we have found the 3D starting position of the vertices, we can dive into the main part of this exercise. We basically loop through every previous frame, setup rotation matrices based on the current angle, apply 3 successive rotations (around Y, X, and Z axis), and finally project the 3D vertex to find its 2D position inside the shape layer. Here is the beast:

angle = 0;
for (t = 0; t <= time; t += thisComp.frameDuration)
{
	// rotation matrices (https://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations)
	rxMatrix = [[1,0,0], [0,Math.cos(angle),-Math.sin(angle)], [0,Math.sin(angle),Math.cos(angle)]];
	ryMatrix = [[Math.cos(angle),0,-Math.sin(angle)], [0,1,0], [Math.sin(angle),0,Math.cos(angle)]];
	rzMatrix = [[Math.cos(angle),-Math.sin(angle),0], [Math.sin(angle),Math.cos(angle),0], [0,0,1]];

	// do rotations (the order matters, here we chose it arbitrarily)
	p3d = matVecMul(ryMatrix, p);
	p3d = matVecMul(rxMatrix, p3d);
	p3d = matVecMul(rzMatrix, p3d);

	// increase rotation angle
	angle += rotSpeed;
}
// handle perspective
z = 1 / (distance - p3d[2]);

// project 3D point
projectionMatrix = [[z, 0, 0], [0, z, 0]];
p2d = matVecMul(projectionMatrix, p3d);

// scale result
mul(p2d, r);

To create the cube vertices we just need to duplicate the first Ellipse group 7 times.

We obtain the following animation:

Great, our calculations seem correct. Now we need to connect those dots to finish the cube.

Creating The Edges

Since we cannot connect all vertices with a single path, we need to create multiple connecting lines. We want these lines to be constructed from the same unique expression, and control the connected vertices by specifying their indices in the shape’s group name.

Here is the first connecting path which connects the first four vertices (i.e., the front face):

We apply the following expression to the path property of the connection:

indices = thisProperty.propertyGroup(3).name.split("Connection ")[1].split(" ");
pts = [];
for (i = 0; i < indices.length; i++)
{
	idx = indices[i];
	pt = content("Ellipse " + idx).content("Ellipse Path 1").position;
	pts.push(pt);
}
createPath(pts, [], [], false);

For creating every other connection we duplicate the first connection and rename it with the appropriate indices list for that connection. The final timeline looks like this:

It’s time to press the 0 key on the numpad to preview the final animation.

Conclusion

In this exercise we have shown how to project a 3D object onto a 2D plane using expressions. We have created our own matrix library to facilitate 3D calculations, and imported it into our expression. We used it to setup and manipulate rotation and projection matrices. Hope you find it useful!

You can also check ConnectLayers PRO, a tool that create lines that are dynamically linked to the layers using powerful path expressions. No keyframes at all!