Kristoffer Dyrkorn, November 4, 2022

5. We’ve got to move it

(This article is part of a series. You can jump to the previous section or the next section if you would like to.)

In this section, we will start animating our triangles - we will make them rotate on the screen!

The application code

To make our triangles rotate, it is sufficient to make the vertices rotate. Remember, the triangle objects themselves just contain references to vertex coordinates, so as long as the values in the vertex coordinate array are updated, everything will be correct.

Also, the notion of sharing edges and vertices might become clearer now: By making triangles share vertices, we save calculations: It is sufficient to rotate a vertex just once, and all triangles that use that vertex will then be updated. Also, if we instead had chosen to duplicate vertices among triangles, there is a risk that small errors in calculations might move duplicate vertices apart, thus creating cracks or overlaps between the triangles. We would very much like to avoid that. (We will return to the topic of precision later on in this tutorial.)

Now, back to the code. We start by keeping our existing vertex coordinate array as it is. In addition, we create an array that will hold our rotated vertices, and we initialize it to contain empty Vector objects.

const rotatedVertices = Array.from({ length: 4 }, () => new Vector());

To rotate the vertices, we first move them so all vertices are centered around the origin, then do the rotation, and then move them back to where they originally were centered. This way we make them rotate around their own centers. (If we don’t move them to the origin before rotating, they would instead rotate around the screen coordinates’ origin, which is the top left corner of the screen.) Finally, we round the result to the nearest integer value, and store the coordinates in the array containing rotated vertices.

function rotate(angle) {
    const DEG_TO_RAD = Math.PI / 180;

    for (let i = 0; i < 4; i++) {
        const v = new Vector(vertices[i]);

        const r = rotatedVertices[i];
        r[0] = Math.round(v[0] * Math.cos(angle * DEG_TO_RAD) - v[1] * Math.sin(angle * DEG_TO_RAD));
        r[1] = Math.round(v[0] * Math.sin(angle * DEG_TO_RAD) + v[1] * Math.cos(angle * DEG_TO_RAD));


In each full screen repaint, we base all our calculations on the same non-rotated vertices, and just increase the rotation angle a little bit per frame. This way we make the vertices (that is, the triangles) rotate. We could also have decided to start with the coordinates from the previous screen paint, and rotated them with some fixed, small amount, but that would mean that small errors in the calculations would accumulate. So doing everything from scratch is more precise - and has no performance penalty. (The work to rotate vertices stays the same, only the rotation angle changes.)

In the code, we set up a function that will be run each frame. Inside the function, we first rotate the vertices, clear the pixel buffer, draw the triangles into the buffer, and then put the buffer onto the screen - and increase the rotation angle.

We use the requestAnimationFrame method to synchronise the drawing and rotation with the screen refresh rate. The code looks like this:

 function draw() {

    greenTriangle.draw(rotatedVertices, greenColor);

    if (drawBlue) {
        blueTriangle.draw(rotatedVertices, blueColor);

    ctx.putImageData(screenBuffer, 0, 0);
    angle += angleSpeed;

We are now ready to inspect the results. Not bad - the triangles are indeed rotating, but notice: The movement is not smooth. The triangles seem to jump around a bit as they rotate.

This can be improved! We will have a look at that in the next section.

The code for this section is available here along with the utility classes. The demo app could also be interesting to look at. Press space to show/hide the blue triangle, and p to turn the animation on/off.