# Questions about a scaling up, down, and resetting using a scale matrix

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Hey I have a quick question about a scale matrices

I have my matrices in column major order and I know a scale matrix looks like:

// Column order matrix. Data arragned in an array:
0 4 8  12
1 5 9  13
2 6 10 14
3 7 11 15

//Scale Matrix
x 0 0 0
0 y 0 0
0 0 z 0
0 0 0 1

And I know I need to multiple my matrix by the scale matrix in order to scale by the x, y, z values. But how am I supposed to actually scale my matrix back down/set it to a scale factor?

I have this code that is to scale my matrix the along the X access

//Scale the current matrix by X amount
void Matrix4::scaleX(float x)
{
data[0] *= x;
data[1] *= x;
data[2] *= x;
data[3] *= x;
}

And if I were to do something like this I could scale my matrix along the X axis by 2

//Scale the matrix along the x axis by 2
myMatrix.scaleX(2.0f);

But I'm honestly not sure how I'm supposed to scale back down from this point. I was hoping for something like:

//Scale the matrix along the x axis by 2
myMatrix.scaleX(2.0f);

//Scale the matrix down along the x axis by 2
myMatrix.scaleX(-2.0f);

But based on the current math that is not how it works

Also how should I go about "resetting/setting" a scale matrix to a certain value? Say I have a matrix that is at scale factor 1. Then over time I want to scale it up until it hits a scale factor of 5. Then later after some other conditions are met I want to reset/set the scale factor to 2

Edited by noodleBowl

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The inverse of multiplying by 2 is multiplying by 1/2, not -2.

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2 hours ago, alvaro said:

The inverse of multiplying by 2 is multiplying by 1/2, not -2.

I don't think I explained myself very well here. If I scale up by 2 then yes if I want to get back to my original number I would multiple by 0.5

I guess I'm really looking for a way to scale up / down easily using matrices. Easily in the sense that I have a single value that controls the scale factor I need to use. Example, something like:

//Declares somewhere, global or class memeber
float scaleFactor = 1.0f;

//Somewhere else in code
if(keyDown(W_KEY))
scaleFactor += 0.5f

if(keyDown(S_KEY))
scaleFactor -= 0.5f

//Scale the matrix up or down along the X axis based on the scaleFactor value
//See above post for implementation details
myMatrix.scaleX(scaleFactor); 

I'm not sure if adding / subtracting to a scale factor is possible using a scale matrix since it is multiplicative. Kind of throws me off since multiplying by a translation or rotation matrix seems to be additive

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I am having a hard time understanding what your problem is. But perhaps we can get to the bottom of it if by looking at your last line: "[...] multiplying by a translation or rotation matrix seems to be additive".

I can see how translations might seem additive: There is a very natural way to describe the translation using a vector, and composition of translations corresponds to addition of vectors.

In the case of rotations, they seem additive if you are thinking about them in terms of angles. Now, anything multiplicative can be made to look additive if you use logarithms, because log(a*b) = log(a) + log(b). In some sense, angles are logarithms of the transformations they represent.

Now, scaling things is the prototypical example of multiplication, and you generally want to use multiplicative updates. In the bit of code you posted, if you hit "S" twice the object will collapse to a point because you made the scaling factor zero. Also, if you have made the object very big already, hitting "W" again will have an almost imperceptible effect. My guess is that that is not what you wanted. An alternative would be to multiply the scale factor by some constant (say, 1.2) when you hit "W" and divide by the same constant when you hit "S". Try that and see if that's closer to the behavior you want.

As a side note, you could keep track of the logarithm of the scaling factor instead. To get the same effect, you would be adding log(1.2) [about 0.1823] or subtracting log(1.2) to a variable named "log_scale", and then the scaling factor would be computed as "exp(log_scale)". That's rather awkward and I don't recommend it, but it would make scaling seem additive. It gives me a similar feeling to code that uses angles.

Edited by alvaro

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11 hours ago, alvaro said:

Now, scaling things is the prototypical example of multiplication, and you generally want to use multiplicative updates. In the bit of code you posted, if you hit "S" twice the object will collapse to a point because you made the scaling factor zero. Also, if you have made the object very big already, hitting "W" again will have an almost imperceptible effect. My guess is that that is not what you wanted. An alternative would be to multiply the scale factor by some constant (say, 1.2) when you hit "W" and divide by the same constant when you hit "S". Try that and see if that's closer to the behavior you want.

I went back and tried this, but I don't think it will work

//Declares somewhere, global or class memeber
float scaleFactor = 1.0f;

//Somewhere else in code
if(keyDown(W_KEY))
scaleFactor *= 1.2f

if(keyDown(S_KEY))
scaleFactor /= 1.2f

//Scale the matrix up or down along the X axis based on the scaleFactor value
//See above post for implementation details
myMatrix.scaleX(scaleFactor); 

The scenario goes like this:
1. Press the W key. scaleFactor now has a value of 1.2f. The matrix is scaled up by 1.2f just like we wanted
2. Press the W key again. scaleFactor now has a value of 1.44f. The matrix is scaled up by 1.44f. This is a issue because we will now scale by double the amount we wanted
3. Press the S key. scaleFactor is now 1.2f. The matrix is scaled up by 1.2f. This is definitely an issue. We intended to scale down by 1.2f, but because the value for scaleFactor is 1.2f we will actually scale up our matrix by 1.2f

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Oh, you have a more basic problem. I imagined you were building your matrix from scratch every time. You should make the scaleFactor equal to 1.2 when W' is pressed, and 1/1.2 when 'S' is pressed, 1 otherwise. Either that, or build the matrix from scratch every time.

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Normalize the x vector, and then multiply it with the scale factor.

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6 hours ago, alvaro said:

Oh, you have a more basic problem. I imagined you were building your matrix from scratch every time. You should make the scaleFactor equal to 1.2 when W' is pressed, and 1/1.2 when 'S' is pressed, 1 otherwise. Either that, or build the matrix from scratch every time.

This will totally work! I think I will have to rebuild the matrix from scratch if I need to keep track of how much I scaled my matrix by. That or have another variable

5 hours ago, Hodgman said:

Normalize the x vector, and then multiply it with the scale factor.

Can you explain this? I'm curious, but I don't know what you really mean by normalize the X vector since I'm just using a single value and I don't know how you are supposed to normalize a single value

Also just a side question for confirmation, I didn't mess up the scale matrix math did I? The whole not adding or subtracting to an accumulator value and then passing that value to my functions makes me feel like I did it wrong

void Matrix4::scale(float x, float y, float z)
{
data[0] *= x;
data[1] *= x;
data[2] *= x;
data[3] *= x;

data[4] *= y;
data[5] *= y;
data[6] *= y;
data[7] *= y;

data[8]  *= z;
data[9]  *= z;
data[10] *= z;
data[11] *= z;
}

Edited by noodleBowl

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21 minutes ago, noodleBowl said:

Can you explain this? I'm curious, but I don't know what you really mean by normalize the X vector since I'm just using a single value and I don't know how you are supposed to normalize a single value

In your matrix, elements 0, 1, 2 and 3 are the X basis vector. If you want to scale that vector, you can multiply it with a single (scalar) value. If you want to set the scale of the X axis to some new value, you can first normalize the x basis vector (which sets the scale / length to 1.0), and then multiply it by your scalar.

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54 minutes ago, Hodgman said:

In your matrix, elements 0, 1, 2 and 3 are the X basis vector. If you want to scale that vector, you can multiply it with a single (scalar) value

Isnt this what I'm already doing?

55 minutes ago, Hodgman said:

If you want to set the scale of the X axis to some new value, you can first normalize the x basis vector (which sets the scale / length to 1.0), and then multiply it by your scalar.

So then I'm looking at something like this then?:

float length = sqrt(data[0] * data[0] + data[1] * data[1] + data[2] * data[2] + data[3] * data[3]);
data[0] = (data[0]/length) * newScaleValue;
data[1] = (data[1]/length) * newScaleValue;
data[2] = (data[2]/length) * newScaleValue;
data[3] = (data[3]/length) * newScaleValue;

Does just computing the length on the first 3 columns give me back the current scale values for x, y, z?
Can I just extract everything from the matrix then? Not just scale but rotation and transform too. Is it worth it (accurate)?

Assuming the answer to my first question is yes, you wouldn't be able to get an accurate scale value back if the scale was negative. Which in my mind is "wrong" since we are missing the sign information. Only makes me wonder what I wouldn't / couldn't get back trying to extract the rotation and transform values. Mainly just the rotation values since I'm pretty sure the last column of the matrix is everything needed for the transform values

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• Overview
Welcome to the 2D UFO game guide using the Orx Portable Game Engine. My aim for this tutorial is to take you through all the steps to build a UFO game from scratch.
The aim of our game is to allow the player to control a UFO by applying physical forces to move it around. The player must collect pickups to increase their score to win.
I should openly acknowledge that this series is cheekily inspired by the 2D UFO tutorial written for Unity.
It makes an excellent comparison of the approaches between Orx and Unity. It is also a perfect way to highlight one of the major parts that makes Orx unique among other game engines, its Data Driven Configuration System.
You'll get very familiar with this system very soon. It's at the very heart of just about every game written using Orx.
If you are very new to game development, don't worry. We'll take it nice and slow and try to explain everything in very simple terms. The only knowledge you will need is some simple C++.
I'd like say a huge thank you to FullyBugged for providing the graphics for this series of articles.

What are we making?
Visit the video below to see the look and gameplay of the final game:
Getting Orx
The latest up to date version of Orx can be cloned from github and set up with:
git clone https://github.com/orx/orx.git Once cloning has completed, the setup script in the root of the files will start automatically for you. This script creates an $ORX environment variable for your system. The variable will point to the code subfolder where you cloned Orx. Why? I'll get to the in a moment, but it'll make your life easier. The setup script also creates several projects for various IDEs and operating system: Visual Studio, Codelite, Code::Blocks, and gmake. You can pick one of these projects to build the Orx library. Building the Orx Library While the Orx headers are provided, you need to compile the Orx library so that your own games can link to it. Because the setup script has already created a suitable a project for you (using premake), you can simply open one for your chosen OS/IDE and compile the Orx library yourself. There are three configurations to compile: Debug, Profile and Release. You will need to compile all three. For more details on compiling the Orx lbrary at: http://orx-project.org/wiki/en/tutorials/cloning_orx_from_github at the Orx learning wiki. The$ORX Environment Variable
I promised I would explain what this is for. Once you have compiled all three orx library files, you will find them in the code/lib/dynamic folder:
orx.dll orxd.dll orxp.dll Also, link libraries will be available in the same folder:
orx.lib orxd.lib orxp.lib When it comes time to create our own game project, we would normally be forced to copy these library files and includes into every project.
A better way is to have our projects point to the libraries and includes located at the folder that the $ORX environment variable points to (for example: C:\Dev\orx\code). This means that your projects will always know where to find the Orx library. And should you ever clone and re-compile a new version of Orx, your game projects can make immediate use of the newer version. Setting up a 2D UFO Project Now the you have the Orx libraries cloned and compiled, you will need a blank project for your game. Supported options are: Visual Studio, CodeLite, Code::Blocks, XCode or gmake, depending on your operating system. Once you have a game project, you can use it to work through the steps in this tutorial. Orx provides a very nice system for auto creating game projects for you. In the root of the Orx repo, you will find either the init.bat (for Windows) or init.sh (Mac/Linux) command. Create a project for our 2D game from the command line in the Orx folder and running: init c:\temp\ufo or init.sh ~/ufo Orx will create a project for each IDE supported by your OS at the specified location. You can copy this folder anywhere, and your project will always compile and link due to the$ORX environment variable. It knows where the libraries and includes are for Orx.
Open your project using your favourite IDE from within the ufo/build folder.
When the blank template loads, there are two main folders to note in your solution:
config src Firstly, the src folder contains a single source file, ufo.cpp. This is where we will add the c++ code for the game. The config folder contains configuration files for our game.
What is config?
Orx is a data driven 2D game engine. Many of the elements in your game, like objects, spawners, music etc, do not need to be defined in code. They can be defined (or configured) using config files.
You can make a range of complex multi-part objects with special behaviours and effects in Orx, and bring them into your game with a single line of code. You'll see this in the following chapters of this guide.
There are three ufo config files in the config folder but for this guide, only one will actually be used in our game. This is:
ufo.ini All our game configuration will be done there.
Over in the Orx library repo folder under orx/code/bin, there are two other config files:
CreationTemplate.ini SettingsTemplate.ini These are example configs and they list all the properties and values that are available to you. We will mainly concentrate on referring to the CreationTemplate.ini, which is for objects, sounds, etc. It's good idea to include these two files into your project for easy reference.
Alternatively you can view these online at https://github.com/orx/orx/blob/master/code/bin/CreationTemplate.ini and here: https://github.com/orx/orx/blob/master/code/bin/SettingsTemplate.ini

The code template
Now to take a look at the basic ufo.cpp and see what is contained there.
The first function is the Init() function.
This function will execute when the game starts up. Here you can create objects have been defined in the config, or perform other set up tasks like handlers. We'll do both of these soon.
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The Exit() function is where memory is cleaned up when your game quits. Orx cleans up nicely after itself. We won't use this function as part of this guide.
The Bootstrap() function is an optional function to use. This is used to tell Orx where to find the first config file for use in our game (ufo.ini). There is another way to do this, but for now, we'll use this function to inform Orx of the config.
Then of course, the main() function. We do not need to use this function in this guide.
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Great. So now you have everything you need to start building the UFO game.
If you experience an issue compiling, check the troubleshooting article for Orx projects    for help.

Setting up the game assets
Our game will have a background, a UFO which the player will control, and some pickups that the player can collect.
The UFO will be controlled by the player using the cursor keys.
First you'll need the assets to make the game. You can download the file  assets-for-orx-ufo-game.zip which contains:
The background file (background.png😞

The UFO and Pickup sprite images (ufo.png and pickup.png😞

And a pickup sound effect (pickup.ogg😞
pickup.ogg
Copy the .png files into your data/texture folder
Copy the .ogg file into your data/sound folder.
Now these files can be accessed by your project and included in the game.

Setting up the Playfield
We will start by setting up the background object. This is done using config.
Open the ufo.ini config file in your editor and add the following:

[BackgroundGraphic] Texture = background.png Pivot = center
The BackgroundGraphic defined here is called a Graphic Section. It has two properties defined. The first is Texture which has been set as background.png.
The Orx library knows where to find this image, due to the properties set in the Resource section:

[Resource] Texture = ../../data/texture
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There are other values available for Pivot. To see the list of values, open the CreationTemplate.ini file in your editor. Scroll to the GraphicTemplate section and find Pivot in the list. There you can see all the possible values that could be used.
top left is also a typical value.
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The second property is the Position. In our world, this object will be created at (0, 0, 0). In Orx, the coordinates are (x, y, z). It may seem strange that Orx, being a 2D game engine has a Z axis. Actually Orx is 2.5D. It respects the Z axis for objects, and can use this for layering above or below other objects in the game.
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