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Member Since 17 Apr 2012
Offline Last Active Jun 26 2014 08:34 AM

Topics I've Started

Help on learning OpenGL! (Especially perspective projection)

23 June 2014 - 07:58 PM

I'm going slightly mad on this.


I've been trying to learn OpenGL. I've never learnt 3D programming / math (in a very solid way, anyway). I do know some basics about vectors, matrices, matrix multiplication, the identity matrix, how matrices store rotations, scaling and other transformations. I've read a couple hundred pages from 3D Math Primer for Graphics and Game Development, but that was at least a year ago. Furthermore, I guess there probably are some gaps in my 3D knowledge.


Lately, I tried to learn OpenGL through the Red Book. However, the book isn't very beginner-friendly. So after googling for a while I tried to learn from the arcsynthesis.com tutorials. I was doing very good until the perspective projection tutorial (http://www.arcsynthesis.org/gltut/Positioning/Tut04%20Perspective%20Projection.html). I don't get all that math on the "Camera perspective" section, tbh I think it's poorly explained (the rest of the tutorial is top-quality, though, gotta be fair).


From arcsynthesis I jumped to scratchapixel.com. The perspective projection matrix lesson (http://scratchapixel.com/lessons/3d-advanced-lessons/perspective-and-orthographic-projection-matrix/perspective-projection-matrix/) got me understanding things a bit better, but I'm starting to get really confused as scratchapixel.com and arcsynthesis.com seem to take slightly different approaches.


From what I understand, the homogeneous coordinates (as scratchapixel.com calls them) are acquired by dividing x,y and z by w. Those will then be the NDC (normalized device coordinates, as arcsynthesis calls them), right? Arcsynthesis seems to say that we "prepare" the perspective projection by setting the correct w coordinates for each vertex and letting the hardware do the rest:



The basic perspective projection function is simple. Really simple. Indeed, it is so simple that it has been built into graphics hardware since the days of the earliest 3Dfx card and even prior graphics hardware.

You might notice that the scaling can be expressed as a division operation (multiplying by the reciprocal). And you may recall that the difference between clip space and normalized device coordinate space is a division by the W coordinate. So instead of doing the divide in the shader, we can simply set the W coordinate of each vertex correctly and let the hardware handle it.

This step, the conversion from clip-space to normalized device coordinate space, has a particular name: the perspective divide. So named because it is usually used for perspective projections; orthographic projections tend to have the W coordinates be 1.0, thus making the perspective divide a no-op.


Suffice it to say that there are very good reasons to put the perspective term in the W coordinate of clip space vertices.


However, the same Arcsynthesis states:


Recall that the divide-by-W is part of the OpenGL-defined transform from clip space positions to NDC positions. Perspective projection defines a process for transforming positions into clip space, such that these clip space positions will appear to be a perspective projection of a 3D world. This transformation has well-defined outputs: clip space positions. But what exactly are its input values?

We therefore define a new space for positions; let us call this space camera space.

...then it proceeds to explain how to feed the clip space with already-processed vertex coordinates (in a way that gives the sense of perspective). I'm confused... Isn't that effect achieved by setting the correct w values for the perspective divide, which happens during the conversion from clip space to NDC???


Scratchapixel.com, on the other hand, defines the perspective divide as some sort of process of making w equal to z, so that dividing the coordinates by w will simultaneously make them homogeneous and fit into the z = 1 plane (which is considered the image plane in their example, or projection plane as arcsynthesis calls it).




Also remember from the beginning of this lesson, that point Ps, i.e. the projection of P onto the image plane, can be computed by dividing the x- and y-coordinates of P by its z-coordinate. So how do we compute Ps using point-matrix multiplication? First, we set x', y' and z' (the coordinates of Ps) to x, y and z (the coordinates of P). Then we need to divide x', y' and z' by z. Transforming x', y' and z' into x, y, and z is easy enough. First set the matrix to the identity matrix (The identity matrix is where the pivot coefficients, or the coefficients along the diagonal of the matrix, equal 1. All others coefficients equal 0). But why do we divide x', y' and z' by z? We explained in the previous section that a point expressed the homogeneous coordinate system (instead of in the Cartesian coordinate system) has a w-coordinate that equals 1. When the value of w is different than 1, we must divide the x-,y-,z-,w-coordinates of the point by w to reset it back to 1. The trick of the perspective projection matrix thus consists of making the w'-coordinate in Ps be different than 1, so that we have to divide x', y', and z' by w'. When we set w' to z (z cannot equal 1), we divide x', y' and z' by w' (which is equal to z). Through division by z, the resulting x'- and y'-coordinates form the projection of P onto the image plane. This operation is usually known in the literature as the z or perspective divide.


So technically, the perspective projection occurs from the conversion from clip space into NDC, NOT before feeding the clip space coordinates (as arcsynthesis stated)! Am I right?


Things are starting to get really messy in my mind, and I'm wondering if I should just pick a textbook on this subject and learn it all the hard way. Subsequent concepts mentioned by scratchapixel.com like far view and near view are also unclear to me, though there are previous tutorials on scratchapixel.com that should enlighten me about those. The question is... should I keep on hopping from place to place to figure out stuff one thing at a time, or would I better grab a textbook? If so, which one?


Any help would be very appreciated. This is starting to harm my motivation to learn OpenGL. It really gives the sense of overwhelmingness (just made up a new word).

Fellow beginner game programmers

20 December 2013 - 07:10 PM

I'd enjoy programming with other people while we learn, and/or share ideas and thoughts. [snip]
Who's interested? You can add me on skype, my email is [deleted]
I've tried posting this in the classifieds but didn't get replies, so I'm trying here now, [snip]

Please tell me there's a way to set line width in SDL

17 December 2013 - 01:09 PM

I can't find a way to set a line width for the SDL_RenderDrawLine function, but I can't believe there's no way to set it. That's just... basic. Is there really no way to do so? Are the lines always 1 pixel wide, or what?


EDIT: Found an extension library (SDL_GFX) that provides that feature. It's wierd native SDL doesn't have that, though...

Quick question - problems declaring an SDL_Texture container

16 December 2013 - 01:17 PM

I want to define a class with a member map container that maps strings to SDL_Textures. The purpose is to hold loaded textures for reusage.

class A
   map<std::string, SDL_Texture> textures;

When I try this, I get this error:

error: 'std::pair<_T1, _T2>::second' has incomplete type

How do I enforce the definition of SDL_Texture before the declaration of the textures map, to stop this error?

Can't pass string literal to constructor

15 December 2013 - 07:13 AM

Hello there.


I've been trying to make my very first game smile.png. Right now I'm at the menubuilding stage.


I'm trying to have a button class that can be initialized with its caption, X and Y relative coordinates, width and height. However, when I try to create an instance and initialize its caption, I get a compiler error:

error: expected identifier before string constant

Here's the code that matters (I'll point out with a comment the line where the error occurs).



class Button
    Button(string c, int pX, int pY, int w, int h) :    caption(c),
                                                        height(h) {}

    int width;
    int height;

    // The percentage of X and Y displacement relative to total screen width/height.
    // Counting from the left/up.
    int percX;
    int percY;

    string caption;


class Game
    // blablabla

    // more blablabla

    // GUI elements
    Button bSstart(     "StartGame",   50, 20, 50, 5); // --> ERROR OCCURS HERE
    Button bOptions(    "GameOptions", 50, 25, 50, 5);
    Button bHighScores( "HighScores",  50, 30, 50, 5);
    Button bAbout(      "About",       50, 35, 50, 5);
    Button bExitAll(    "ExitGame",    50, 40, 50, 5);

I can't figure out what's wrong... I'm passing a string literal to initialize a string (the button's caption). Why would I need an identifier?