# Combining matrix functions with applyMatrix()

**URL:** <https://discourse.processing.org/t/combining-matrix-functions-with-applymatrix/38475>\
**Category:** Beginners\
**Created:** [August 24, 2022, 10:07am UTC](https://discourse.processing.org/t/combining-matrix-functions-with-applymatrix/38475 "2022-08-24T10:07:07Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Sunt](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.processing.org/sunt/32/16827_2.png) [@Sunt](https://discourse.processing.org/u/Sunt)\
**Post date:** [August 24, 2022, 10:07am UTC](https://discourse.processing.org/t/combining-matrix-functions-with-applymatrix/38475/1 "2022-08-24T10:07:07Z")

</div>

Hi. In this code I have a rotating rectangle in the center of the canvas using the applyMatrix() function.  
In the reference it’s said that I can combine these functions into one.

> This is a powerful operation that can perform the equivalent of translate, scale, shear and rotate all at once.

I’ve read the provided links, but I can’t figure out how to do this. Summing the matrixes gives a different ‘scaling’ outcome.  
Thanks in advance.

```auto
  let a = 1 + cos_a;
  let b = sin_a;
  let c = -sin_a;
  let d = 1 + cos_a;
  let e = width / 2;
  let f = height / 2;
  // applyMatrix(1, 0, 0, 1, width / 2, height / 2);
  // rotate(angle);
  // applyMatrix(cos_a, sin_a, -sin_a, cos_a, 0, 0);
  applyMatrix(a, b, c, d, e, f);

```

```auto
function setup() {
  let c = createCanvas(250, 250);
  rectMode(CENTER);
}

function draw() {
  let step = frameCount % 200;
  let angle = map(step, 0, 200, 0, TWO_PI);
  let cos_a = cos(angle);
  let sin_a = sin(angle);
  background(200);
  // translate(width / 2, height / 2);
  applyMatrix(1, 0, 0, 1, width / 2, height / 2);
  // rotate(angle);
  applyMatrix(cos_a, sin_a, -sin_a, cos_a, 0, 0);
  rect(0, 0, 50, 50);
}

```

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<div class="post-metadata">

**Author:** ![Sunt](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.processing.org/sunt/32/16827_2.png) [@Sunt](https://discourse.processing.org/u/Sunt)\
**Post date:** [August 24, 2022, 10:45am UTC](https://discourse.processing.org/t/combining-matrix-functions-with-applymatrix/38475/2 "2022-08-24T10:45:40Z")

</div>

I managed to do it; you need to multiply the matrixes.  
But honestly, I don’t understand why. Can someone explain this?

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<div class="post-metadata">

**Author:** ![Sunt](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.processing.org/sunt/32/16827_2.png) [@Sunt](https://discourse.processing.org/u/Sunt)\
**Post date:** [August 25, 2022, 2:31pm UTC](https://discourse.processing.org/t/combining-matrix-functions-with-applymatrix/38475/3 "2022-08-25T14:31:09Z")

</div>

In my project I have lists of translation sequences using a vector array.  
I noticed that summing all vectors first and just use one translation is significantly faster.  
But since I also have rotations in between I thought to experiment combining them with the applyMatrix() function. This works, however doesn’t speed up the code. So, for what is this function actually used for?