Salomonsson.se
Oct 31 2016

Creative Parental Leave!

Today is the last day of my parental leave. For 6 months I’ve been home with my twin daughters (they were almost 9 months old when I started, and soon 16 months).

I’ve spent a lot of time with them, but I have managed to stay creative in the few hours every now and then when they were taking naps. I have to say I’m a bit impressed in retrospect!

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Oct 31 2016

Math - Triangle Rasterizer

Warning: lengthy post ahead! But lots of really cool stuff!

Been a while since I posted now. There are a couple of reasons for this:

  • First of all, I decided to write my own software triangle rasterizer (I’ll get to explain what that is in a bit)
  • It’s a lot of math involved. And a lot of diagrams with pen and paper. I has spent several hours to get it to its current working state
  • My parental leave is getting close to the end. My kids are now almost 16 months and require a lot of attention! Have not gotten any computer time at all for the past three weeks

But now I finally have something to show, so lets show it!

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Oct 12 2016

Markdeep

A few days ago I came across Markdeep. A simple way to write formatted documents using markdown syntax.

I think markdown syntax is nice, and I’m already using it for all content on this site.

The idea is that you only need a small snippet of javascript text in the bottom of the document. You edit it in your regular notepad app, and view it through a browser. It will fall back to unformatted markdown text (still pretty readable) if it cannot fetch the javascript file.

However the original markdeep.js has a big flaw. At least for me!
It cannot detect single line breaks!
Like this one.
So I modified it a bit.

If you want to use it, just copy and paste the following snippet in the bottom of a text document, and make sure the file ending is .html.

<!-- Markdeep: --><style class="fallback">body{visibility:hidden;white-space:pre;font-family:monospace}</style><script src="http://salomonsson.se/md/markdeep.min.js"></script><script src="http://salomonsson.se/md/markdeep.min.js"></script><script>window.alreadyProcessedMarkdeep||(document.body.style.visibility="visible")</script>

You might want to paste the following at the very top
<meta charset="utf-8">

View a demo page with all the features

Oct 05 2016

Math - Backface Culling And Directional Lighting

Up to this point I’ve only drawn wireframes. To create colored 3d objects I need two things. Backface Culling and Z Sorting.
Time to start with the first: Backface Culling.

  • First of all I changed to using triangles instead of just points/lines.
  • Then I calculate the cross product on two of the sides to get a normal vector.
  • Compare the normal with your viewing vector (a line from the camera to the middle of the triangle) to see if the triangle is facing towards you or away from you
  • Don’t draw if the triangle is facing away from you

Now you no longer see any lines “behind” the cubes.
I also draw the normal vectors for each triangle.

Spinning cube with normals

From this point I just filled the triangles with a single color.

Red spinning cub

With the normal vectors already calculated on each triangle, I tried to implement some directional lighting as well.
It went much smoother than I would ever have thought.

Yay, lighting!

Pretty interesting! I made a spinning cube with lighting almost exactly ten years ago. However I did not understand much of it, and going back to that tutorial it seems to be full of weird tricks. This time however I did it all by myself =D.

Next up is Z-Sorting so we can have more than just one cube at once

Sep 22 2016

Math - The Camera Matrix

We can move around in our 3d world!

I’m doing serious progress! Today I managed to get the camera matrix working!

The coolest thing about this is that just a few months ago I would have thought that this was too much math for me to ever be able to understand! Remember that I have written everything from scratch - except for the line render code, which is basically just a lineTo(x,y) function. Even the matrix implementation.

There’s no frustum culling in there yet (except for any z-values behind the camera) so pretty much everything gets drawn all the time.

Resources for camera matrix:
Camera View Transform Matrix
Faster Matrix Inversions

Sep 15 2016

Math - 3D and Perspective

In our last blog post we used matrices to translate, rotate and scale vectors, but so far only in 2D.

Transforming vectors in 3D is pretty much the same thing. The only difference is that we cannot directly plot those vectors out on the screen since each vector will come in a triplet of {x,y,z} and the screen only consists of {x,y}.

We could just ignore the Z-coordinate, but that would look weird!

No Perspective

To get it to look right we need to apply perspective. Perspective means that an object that is further away from our eye will appear smaller than an object that is closer!

Perspective

Applying perspective to 3D-points is something I’ve been able to do for a long time, but now we’re working with matrices, and of course there is something called a perspective projection matrix!

Another great resource I found on the subject is scratchpixel.com, here on Perspective Matrix Projection.

In the past when I’ve been playing with 3D, I’ve used trigonometry for all transformations. It works, but has several drawbacks!

  • More computation heavy! Needs to do Sine and Cosine lookup for each point!
  • Much more complex to nest parent/child-relationship!!
  • Viewing from a camera… I don’t think so!
3D with trigonometry (and fancy blur), made 2006

Using matrices is superior by far. The image below is just a couple of matrices combined, using vectors forming a cube and a pyramid. This would not have been possible using my old 2006 methods!

3D with matrices

If you want to read up on this too, then check out:

Math for game developers youtube channel
And http://www.scratchapixel.com/index.php?nocategory

Sep 04 2016

Math - Matrices and Vectors

After my Shader Week I decided to try to re-wake the math part of my brain that feels like it has numbed of a bit in recent years of Android app development. I have actually been doing this for several weeks now, but have not had anything to show until now.

So I started reading up on Linear Algebra, and is currently writing my own custom implementation of Vector and Matrix-classes from scratch in Haxe. And it’s super interesting!

Rotation Matrix

If you have a 2x2 matrix you can put an up-vector in the first column and a right-vector in the second column. When multiplying a vector with this rotation-matrix it will transform the vector into that coordinate space!
If you rotate the up and right-vector clockwise each frame you get a rotation matrix!

Matrix rotation

In this first image I multiply four 2d-vectors through a rotation matrix. The unmodified vectors are shown to the left.


TRS Matrix (Translate Rotate Scale)

Another interesting thing with matrices is that you can combine them!
If you have one matrix for translation, one for rotation and one matrix for scaling, you can get a single matrix containing all those values by multiplying them! Just remember to multiply them in the correct order!

Translate, Rotate, Scale

In this image I changed the four vectors to form a square instead of that cross.
Then just multiplying each vector through my single TRS-matrix.


Parenting

If you have a TRS-matrix named M1, and another TRS-matrix named M2, you can move the transformation of M2 into the local coordinate space of M1 by multiplying M2 with M1! By doing this M2 will be “parented” to M1! It’s so simple!

Parenting

The big square is rotating and the second, smaller square is parented to the big one, therefore inheriting its rotation. Same with the third square (it inherits both the rotation and scale of it’s parent before applying its own rotation).

The vectors (points) for all three squares are just a single unmodified array. All the transformations are done though a single matrix multiplication (for each point).


I will keep working through the math, so expect more posts on this.
In the mean time, these two youtube playlists are really great resources:

Math for game developers
Khan academy: Linear Algebra

Jul 28 2016

TLDR - Part 4: Component filtering BLAZING fast with macros!

Made a huge optimization in the way Seagal filters list of entities that contains specific components!

Using the macro I’ve written two days ago as a base I now use bitflags instead of multiple for-loops and several Std.is(classA, classB). I now just use simple bit-flag comparison as the macro auto-generates a unique bitflag for each component class, and the result is stunning!

I actually had to go back to my old test and change the number of entities from 10,000 to 100,000!!!

The critical part is the last test, taking 0.0469 seconds
The optimized code! 0.012 seconds! Thats 391% faster!!!

Note 1: Both test 2 and test 3 took 0.001 seconds when running 10,000 entities. That’s why I had to increase the number of entities.

Note 2: Test 2 now takes only 0.007 seconds with that huge amount of entities!

Note 3: Running identical test 3 with 100,000 entities on Edge gives an approx time of 0.049 seconds, even slower than my own old solution…

High fiving myself

Jul 26 2016

Haxe Macros, Part 1

When reading up on the Edge-entity system in the post about TLDR I got an idea on how to speed up my Seagal enging a lot using macros.
The problem is that macros is a subject with few tutorials and resources online, and it seems a lot of people are afraid to look into it.

I will try to explain what macros are, some good places to start learning more, and a cool example that I’ll expand upon to improve the speed of Seagal!

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Jul 22 2016

TLDR - Part 3

I’ve downloaded and tried a new exciting ECS-framework called Edge. The interesting thing about it is that it relies heavily on haxe macros to generate code at compile time that will remove of the costly runtime type checking.

I did a similar test to test number 3 in my TLDR - Part 2. Only the third test was interesting to me.

And look! It’s taking between 4 and 5 milliseconds here as well! That was surprising, I really though you had to try hard to be slower than my current implementation.

However, using macros seems super interesting. and I just got an idea on how I could use macros in seagal that might speed the matching up quite a bit!

Jul 11 2016

Shader Week 1, Conclusion

The source code for all 7 days can be found here: https://github.com/Tommislav/unity_shaderweek

It has been a successful and interesting experiment, commiting 7 days to shader programming. As I’m on parental leave I could only spend about an hour a day for this, but I think I managed to get quite far!
Apart from what’s visible here, I spent 3-4 days reading or researching, but did not count those as I wanted visible examples for each day.

One problem with only having about an hour a day, and only doing tutorials is that you don’t get much time to modify/experiment/fix bugs. But I early decided that my focus this week would be learning, and that I will do a second shader week where I experiment and create my own shader effects instead.

To conclude

  • I have learned a ton!
  • Need a second shader week, where I write my own shader effects
  • A superb resource for learning shaders is this link: http://www.alanzucconi.com/
Jul 11 2016

Shader Week, Day 7

Last day on my shader week. Not sure what to do when a friend of mine suggested that I do a “wobbly water shader”. Well, I guess you could do it pretty simple by using a displacement map as in day 2, so I used another approach manipulating the vertexes with a sine-wave instead.

I used this tutorial as base
http://www.alcove-games.com/opengl-es-2-tutorials/vertex-shader-for-tiled-water/
but re-wrote it in CG

Jun 30 2016

Shader Week, Day 6

Todays shader tutorial was about keeping an offscreen buffer which we can update continually.

http://www.alanzucconi.com/2016/03/02/4539/

In the image to the left we invert the colors every second.

The right image was supposed to be smoke, but the tutorial was very math heavy but thin on how to do the implementation. So I skipped the smoke tutorial and made a script myself that draws a circle at the mouse position (cursor not visible in gif) and fades the image by 0.9 every frame.

Good thing the cursor isn’t visible though. Somehow the mouse X/Y-movement was inverted, and coordinates messed up.
But not enough time to fix tonight, as I’m only using an hour a day.

Jun 29 2016

Shader Week, Day 5

Finally started on vertex and fragment shaders again!
http://www.alanzucconi.com/2015/07/01/vertex-and-fragment-shaders-in-unity3d/

Using a GrabPass to grab a texture of what’s underneath we can manipulate whats underneath.
The red rectangle is just taking the rgb + r*1.5, applied to a quad.

Underneath we’re using a bumpmap to apply something that looks like glass.

Very cool, but a lot of new concepts here. Will have to play around with this more. But now I’m out of time for today…

Jun 29 2016

Shader Week, Day 4

Still playing around with surface shaders from this link:
http://www.alanzucconi.com/2015/06/17/surface-shaders-in-unity3d/

We got two new knights. One with extruded vertices, and a pink one.

The pink one uses dot product to calculate the light for each fragment, as we’ve written our own lightning implementation.