apatriarca

Implementing a complete or even incomplete modeler takes a lot of time. I suggest using Blender or other free tools instead.

I'm not an expert, but there should be a rotation of the torso and abdomen which should also be visible in 2D. I think that the animation looks weird without it.

Ciao m3rlino. Where do you live in Italy? There are some game studios in Italy (for example there are Ubisoft and Milestone in Milan), but if you really want to have more job opportunities in the game industry you probably have to move to another country.

After reading Cornstalks reply I have decided to test it and it comes out quite unsurprisingly that the last version of add is two order of magnitude slower than the naive method on my computer (release mode and all optimizations and SSE turned on).

I think it's basically what you are doing already plus lighting, models for grass/rocks/trees... , more detailed textures (maybe with some procedural details added).

It is the dot product between the vector perpendicular to the direction and the difference between the points. If (x, y) is a vector, (-y, x) is perpendicular to it (it's the vector rotated by 90°). It works because the projection of one vector v along the direction of another vector d is defined to be (dot(d, v)/dot(d, d))d, but since we are only interested if the projection of the difference vector has the same direction of the perpendicular vector we have chosen, it is enough to determine the sign of the dot product between these two vectors.

As long as you are consistent you should be ok with either conventions. I think it's more common to use (-y,x) since it represents a “positive” rotation of 90° and { (x,y), (-y,x) } is a positively oriented basis (it has the same orientation of the current basis). It also corresponds to the multiplication by the imaginary unit when using complex numbers.

You can use   barycentric coordinates like in the following pseudocode:

a = rand(0,1)
b = rand(0,1 - a)
c = 1 - a - b
P = a*P1 + b*P2 + c*P3

EDIT: Corrected a typo

I don't know what book are you following, but Sedgewick have recently given some talks about left-leaning red-black trees (here for example) which I think may be interesting if you are interested in learning about these trees. The left leaning part of his variant is an additional constraints in the colors of the tree which simplifies the code.

First of all, VAO is probably not what you are thinking about (look here). It's VA (vertex arrays) without the O.

What do you mean by changing the size of the buffer every frame? What you should do is using a fixed size VBO (the maximum size you want to support) and then only use a part of it (sending the data with glBufferSubData). How do you create the VBO? Are you using the correct GL_STREAM_DRAW usage flag?

I think it needs a little more structure. You should probably separate your tutorial in different sections like Tools, Library dependencies.. and maybe make use of lists to better separate the various steps to do things like building the libraries or installing some tools. Moreover, you should probably includes some images to make the tutorial easier to follow.

You will probably also need multi-variate calculus since in graphics and physics you often have to integrate on 2 or 3 dimensional domains (for example on surfaces).

I suggest looking at this blog post about sorting algorithms. It discuss the implementation of sorting algorithms on the PS3. It doesn't discuss parallel quicksort, but I think the suggested parallel sorting algorithm (Parallel AA-Sort) described at the end of that post is superior.

EDIT: Some ideas of this algorithm are particularly important on clusters. You probably want to break the data in chunk and then send each part to a computer in the network to sort. Once a part is sorted, you can then merge the various parts trying to minimize network traffic.

I think the easier way to learn about more advanced and specific topics is to use them. Once you relearn the basics of C++, it's probably better to jump directly in making simple games. You will learn by yourself what you will need to create your game.

Technically, an expression like

cos⁴(x) + 2cos²(x)sin²(x) + sin⁴(x)

is not a polynomial, but a transcendental function. In this particular case, you can simply consider sin²(x) and cos²(x) as indeterminate and then use a polynomial factorization algorithm to simplify it, but it is not always possible or useful to use such an algorithm. Sometimes, it is better to use some trigonometric identity for example. Moreover, the algorithm in that book is designed for polynomials with rational coefficients (actually integer) and you may have expressions with transcendental numbers like pi or with square roots. You have to consider them as "indeterminate" if you want to use that algorithm, but the results may not be particularly good. A factorization algorithm which works on reals or complex numbers may however introduce bad looking factorizations and also contains some approximations of the real roots.

I'm not an expert of this field, but I know there are some ACM journal on mathematical softwares. You may search for papers on expression simplification and polynomial factorization at the ACM portal (http://portal.acm.org/) to find additional material on the subject. To read the paper there you have to pay, but the preprints of several papers are freely available on internet. Note however that some papers may require advanced knowledge of algebra (in particular of field or ring theory).