I'm encountering a problem trying to replicate the OpenGL behaviour in an ambient without OpenGL.
Basically I need to create an SVG file from a list of lines my program creates. These lines are created using an othigraphic projection.
I'm sure that these lines are calculated correctly because if I try to use them with a OpenGL context with orthographic projection and save the result into an image, the image is correct.
The problem raises when I use the exactly same lines without OpenGL.
I've replicated the OpenGL projection and view matrices and I process every line point like this:
3D_output_point = projection_matrix * view_matrix * 3D_input_point
and then I calculate it's screen (SVG file) position like this:
2D_point_x = (windowWidth / 2) * 3D_point_x + (windowWidth / 2)
2D_point_y = (windowHeight / 2) * 3D_point_y + (windowHeight / 2)
I calculate the othographic projection matrix like this:
float range = 700.0f;
float l, t, r, b, n, f;
l = -range;
r = range;
b = -range;
t = range;
n = -6000;
f = 8000;
matProj.SetValore(0, 0, 2.0f / (r - l));
matProj.SetValore(0, 1, 0.0f);
matProj.SetValore(0, 2, 0.0f);
matProj.SetValore(0, 3, 0.0f);
matProj.SetValore(1, 0, 0.0f);
matProj.SetValore(1, 1, 2.0f / (t - b));
matProj.SetValore(1, 2, 0.0f);
matProj.SetValore(1, 3, 0.0f);
matProj.SetValore(2, 0, 0.0f);
matProj.SetValore(2, 1, 0.0f);
matProj.SetValore(2, 2, (-1.0f) / (f - n));
matProj.SetValore(2, 3, 0.0f);
matProj.SetValore(3, 0, -(r + l) / (r - l));
matProj.SetValore(3, 1, -(t + b) / (t - b));
matProj.SetValore(3, 2, -n / (f - n));
matProj.SetValore(3, 3, 1.0f);
and the view matrix this way:
CVettore position, lookAt, up;
position.AssegnaCoordinate(rtRay->m_pCam->Vp.x, rtRay->m_pCam->Vp.y, rtRay->m_pCam->Vp.z);
lookAt.AssegnaCoordinate(rtRay->m_pCam->Lp.x, rtRay->m_pCam->Lp.y, rtRay->m_pCam->Lp.z);
up.AssegnaCoordinate(rtRay->m_pCam->Up.x, rtRay->m_pCam->Up.y, rtRay->m_pCam->Up.z);
up[0] = -up[0];
up[1] = -up[1];
up[2] = -up[2];
CVettore zAxis, xAxis, yAxis;
float length, result1, result2, result3;
// zAxis = normal(lookAt - position)
zAxis[0] = lookAt[0] - position[0];
zAxis[1] = lookAt[1] - position[1];
zAxis[2] = lookAt[2] - position[2];
length = sqrt((zAxis[0] * zAxis[0]) + (zAxis[1] * zAxis[1]) + (zAxis[2] * zAxis[2]));
zAxis[0] = zAxis[0] / length;
zAxis[1] = zAxis[1] / length;
zAxis[2] = zAxis[2] / length;
// xAxis = normal(cross(up, zAxis))
xAxis[0] = (up[1] * zAxis[2]) - (up[2] * zAxis[1]);
xAxis[1] = (up[2] * zAxis[0]) - (up[0] * zAxis[2]);
xAxis[2] = (up[0] * zAxis[1]) - (up[1] * zAxis[0]);
length = sqrt((xAxis[0] * xAxis[0]) + (xAxis[1] * xAxis[1]) + (xAxis[2] * xAxis[2]));
xAxis[0] = xAxis[0] / length;
xAxis[1] = xAxis[1] / length;
xAxis[2] = xAxis[2] / length;
// yAxis = cross(zAxis, xAxis)
yAxis[0] = (zAxis[1] * xAxis[2]) - (zAxis[2] * xAxis[1]);
yAxis[1] = (zAxis[2] * xAxis[0]) - (zAxis[0] * xAxis[2]);
yAxis[2] = (zAxis[0] * xAxis[1]) - (zAxis[1] * xAxis[0]);
// -dot(xAxis, position)
result1 = ((xAxis[0] * position[0]) + (xAxis[1] * position[1]) + (xAxis[2] * position[2])) * -1.0f;
// -dot(yaxis, eye)
result2 = ((yAxis[0] * position[0]) + (yAxis[1] * position[1]) + (yAxis[2] * position[2])) * -1.0f;
// -dot(zaxis, eye)
result3 = ((zAxis[0] * position[0]) + (zAxis[1] * position[1]) + (zAxis[2] * position[2])) * -1.0f;
// Set the computed values in the view matrix.
matView.SetValore(0, 0, xAxis[0]);
matView.SetValore(0, 1, yAxis[0]);
matView.SetValore(0, 2, zAxis[0]);
matView.SetValore(0, 3, 0.0f);
matView.SetValore(1, 0, xAxis[1]);
matView.SetValore(1, 1, yAxis[1]);
matView.SetValore(1, 2, zAxis[1]);
matView.SetValore(1, 3, 0.0f);
matView.SetValore(2, 0, xAxis[2]);
matView.SetValore(2, 1, yAxis[2]);
matView.SetValore(2, 2, zAxis[2]);
matView.SetValore(2, 3, 0.0f);
matView.SetValore(3, 0, result1);
matView.SetValore(3, 1, result2);
matView.SetValore(3, 2, result3);
matView.SetValore(3, 3, 1.0f);
The results I get from OpenGL and from the SVG output are quite different, but in two days I couldn't come up with a solution.
This is the OpenGL output
And this is my SVG output
As you can see, it's rotation isn't corrent.
Any idea why? The line points are the same and the matrices too, hopefully.
Pasing the matrices I was creating didn't work. I mean, the matrices were wrong, I think, because OpenGL didn't show anything.
So I tryed doing the opposite, I created the matrices in OpenGL and used them with my code. The result is better, but not perfect yet.
Now I think the I do something wrong mapping the 3D points into 2D screen points because the points I get are inverted in Y and I still have some lines not perfectly matching.
This is what I get using the OpenGL matrices and my previous approach to map 3D points to 2D screen space (this is the SVG, not OpenGL render):
Ok this is the content of the view matrix I get from OpenGL:
This is the projection matrix I get from OpenGL:
And this is the result I get with those matrices and by changing my 2D point Y coordinate calculation like bofjas said:
It looks like some rotations are missing. My camera has a rotation of 30° on both the X and Y axis, and it looks like they're not computed correctly.
Now I'm using the same matrices OpenGL does. So I think that I'm doing some wrong calculations when I map the 3D point into 2D screen coordinates.
Rather than debugging your own code, you can use transform feedback to compute the projections of your lines using the OpenGL pipeline. Rather than rasterizing them on the screen you can capture them in a memory buffer and save directly to the SVG afterwards. Setting this up is a bit involved and depends on the exact setup of your OpenGL codepath, but it might be a simpler solution.
As per your own code, it looks like you either mixed x and y coordinates somewhere, or row-major and column-major matrices.
I've solved this problem in a really simple way. Since when I draw using OpenGL it's working, I've just created the matrices in OpenGL and then retrieved them with glGet(). Using those matrices everything is ok.
You're looking for a specialized version of orthographic (oblique) projections called isometric projections. The math is really simple if you want to know what's inside the matrix. Have a look on Wikipedia
OpenGL loads matrices in column major(opposite of c++).for example this matrix:
[1 ,2 ,3 ,4 ,
5 ,6 ,7 ,8 ,
9 ,10,11,12,
13,14,15,16]
loads this way in memory:
|_1 _|
|_5 _|
|_9 _|
|_13_|
|_2 _|
.
.
.
so i suppose you should transpose those matrices from openGL(if you`re doing it row major)
Related
I try to use what many people seem to find a good way, I call gluUnproject 2 times with different z-values and then try to calculate the direction vector for the ray from these 2 vectors.
I read this question and tried to use the structure there for my own code:
glGetFloat(GL_MODELVIEW_MATRIX, modelBuffer);
glGetFloat(GL_PROJECTION_MATRIX, projBuffer);
glGetInteger(GL_VIEWPORT, viewBuffer);
gluUnProject(mouseX, mouseY, 0.0f, modelBuffer, projBuffer, viewBuffer, startBuffer);
gluUnProject(mouseX, mouseY, 1.0f, modelBuffer, projBuffer, viewBuffer, endBuffer);
start = vecmath.vector(startBuffer.get(0), startBuffer.get(1), startBuffer.get(2));
end = vecmath.vector(endBuffer.get(0), endBuffer.get(1), endBuffer.get(2));
direction = vecmath.vector(end.x()-start.x(), end.y()-start.y(), end.z()-start.z());
But this only returns the Homogeneous Clip Coordinates (I believe), since they only range from -1 to 1 on every axis.
How to actually get coordinates from which I can create a ray?
EDIT: This is how I construct the matrices:
Matrix projectionMatrix = vecmath.perspectiveMatrix(60f, aspect, 0.1f,
100f);
//The matrix of the camera = viewMatrix
setTransformation(vecmath.lookatMatrix(eye, center, up));
//And every object sets a ModelMatrix in it's display method
Matrix modelMatrix = parentMatrix.mult(vecmath
.translationMatrix(translation));
modelMatrix = modelMatrix.mult(vecmath.rotationMatrix(1, 0, 1, angle));
EDIT 2:
This is how the function looks right now:
private void calcMouseInWorldPosition(float mouseX, float mouseY, Matrix proj, Matrix view) {
Vector start = vecmath.vector(0, 0, 0);
Vector end = vecmath.vector(0, 0, 0);
FloatBuffer modelBuffer = BufferUtils.createFloatBuffer(16);
modelBuffer.put(view.asArray());
modelBuffer.rewind();
FloatBuffer projBuffer = BufferUtils.createFloatBuffer(16);
projBuffer.put(proj.asArray());
projBuffer.rewind();
FloatBuffer startBuffer = BufferUtils.createFloatBuffer(16);
FloatBuffer endBuffer = BufferUtils.createFloatBuffer(16);
IntBuffer viewBuffer = BufferUtils.createIntBuffer(16);
//The two calls for projection and modelView matrix are disabled here,
as I use my own matrices in this case
// glGetFloat(GL_MODELVIEW_MATRIX, modelBuffer);
// glGetFloat(GL_PROJECTION_MATRIX, projBuffer);
glGetInteger(GL_VIEWPORT, viewBuffer);
//I know this is really ugly and bad, but I know that the height and width is always 600
// and this is just for testing purposes
mouseY = 600 - mouseY;
gluUnProject(mouseX, mouseY, 0.0f, modelBuffer, projBuffer, viewBuffer, startBuffer);
gluUnProject(mouseX, mouseY, 1.0f, modelBuffer, projBuffer, viewBuffer, endBuffer);
start = vecmath.vector(startBuffer.get(0), startBuffer.get(1), startBuffer.get(2));
end = vecmath.vector(endBuffer.get(0), endBuffer.get(1), endBuffer.get(2));
direction = vecmath.vector(end.x()-start.x(), end.y()-start.y(), end.z()-start.z());
}
I'm trying to use my own projection and view matrix, but this only seems to give weirder results.
With the GlGet... stuff I get this for a click in the upper right corner:
start: (0.97333336, -0.98, -1.0)
end: (0.97333336, -0.98, 1.0)
When I use my own stuff I get this for the same position:
start: (-2.4399707, -0.55425626, -14.202201)
end: (-2.4399707, -0.55425626, -16.198204)
Now I actually need a modelView matrix instead of just the view matrix, but I don't know how I am supposed to get it, since it is altered and created anew in every display call of every object.
But is this really the problem? In this tutorial he says "Normally, to get into clip space from eye space we multiply the vector by a projection matrix. We can go backwards by multiplying by the inverse of this matrix." and in the next step he multiplies again by the inverse of the view matrix, so I thought this is what I should actually do?
EDIT 3:
Here I tried what user42813 suggested:
Matrix view = cam.getTransformation();
view = view.invertRigid();
mouseY = height - mouseY - 1;
//Here I only these values, because the Z and W values would be 0
//following your suggestion, so no use adding them here
float tempX = view.get(0, 0) * mouseX + view.get(1, 0) * mouseY;
float tempY = view.get(0, 1) * mouseX + view.get(1, 1) * mouseY;
float tempZ = view.get(0, 2) * mouseX + view.get(1, 2) * mouseY;
origin = vecmath.vector(tempX, tempY, tempZ);
direction = cam.getDirection();
But now the direction and origin values are always the same:
origin: (-0.04557252, -0.0020000197, -0.9989586)
direction: (-0.04557252, -0.0020000197, -0.9989586)
Ok I finally managed to work this out, maybe this will help someone.
I found some formula for this and did this with the coordinates that I was getting, which ranged from -1 to 1:
float tempX = (float) (start.x() * 0.1f * Math.tan(Math.PI * 60f / 360));
float tempY = (float) (start.y() * 0.1f * Math.tan(Math.PI * 60f / 360) * height / width);
float tempZ = -0.1f;
direction = vecmath.vector(tempX, tempY, tempZ); //create new vector with these x,y,z
direction = view.transformDirection(direction);
//multiply this new vector with the INVERSED viewMatrix
origin = view.getPosition(); //set the origin to the position values of the matrix (the right column)
I dont really use deprecated opengl but i would share my thought,
First it would be helpfull if you show us how you build your View matrix,
Second the View matrix you have is in the local space of the camera,
now typically you would multiply your mouseX and (ScreenHeight - mouseY - 1) by the View matrix (i think the inverse of that matrix sorry, not sure!) then you will have the mouse coordinates in camera space, then you will add the Forward vector to that vector created by the mouse, then you will have it, it would look something like that:
float mouseCoord[] = { mouseX, screen_heihgt - mouseY - 1, 0, 0 }; /* 0, 0 because we multipling by a matrix 4.*/
mouseCoord = multiply( ViewMatrix /*Or: inverse(ViewMatrix)*/, mouseCoord );
float ray[] = add( mouseCoord, forwardVector );
My Question
Can someone please link a good article/tutorial/anything or maybe even explain how to correctly cast a ray from the mouse coordinates to pick objects in 3D?
I already have the Ray and intersection works, now I only need to create the ray from the mouse click.
I would just like have something which I know actually should work, thats why I ask the professionals here, not something where I am unsure if it is even correct in the first place.
State right now
I have a ray class, which actually works and detects intersection if I set the origin and direction to be the same as the camera, so when I move the camera it actually selects the right thing.
Now I would like to actually have 3D picking with the mouse, not camera movement.
I have read so many other questions about this, 2 tutorials, and especially so much different math stuff, since I am really not good at it.
But that didn't help me much, because the people there often use some "unproject" functions, which seem to actually be deprecated and which I have no idea how to use and also don't have access to.
Right now I set the ray origin to the camera position and then try to get the direction of the ray from the calculations in this tutorial.
And it works a little bit, meaning the selection works when the camera is pointed at the object and also sometimes along the whole y-axis, I have no idea what is happening.
If someone wants to take a look at my code right now:
public Ray2(Camera cam, float mouseX, float mouseY) {
origin = cam.getEye();
float height = 600;
float width = 600;
float aspect = (float) width / (float) height;
float x = (2.0f * mouseX) / width - 1.0f;
float y = 1.0f - (2.0f * mouseX) / height;
float z = 1.0f;
Vector ray_nds = vecmath.vector(x, y, z);
Vector4f clip = new Vector4f(ray_nds.x(), ray_nds.y(), -1.0f, 1.0f);
Matrix proj = vecmath.perspectiveMatrix(60f, aspect, 0.1f, 100f);
proj = proj.invertRigid();
float tempX = proj.get(0, 0) * clip.x + proj.get(1, 0) * clip.y
+ proj.get(2, 0) * clip.z + proj.get(3, 0) * clip.w;
float tempY = proj.get(0, 1) * clip.x + proj.get(1, 1) * clip.y
+ proj.get(2, 1) * clip.z + proj.get(3, 1) * clip.w;
float tempZ = proj.get(0, 2) * clip.x + proj.get(1, 2) * clip.y
+ proj.get(2, 2) * clip.z + proj.get(3, 2) * clip.w;
float tempW = proj.get(0, 3) * clip.x + proj.get(1, 3) * clip.y
+ proj.get(2, 3) * clip.z + proj.get(3, 3) * clip.w;
Vector4f ray_eye = new Vector4f(tempX, tempY, tempZ, tempW);
ray_eye = new Vector4f(ray_eye.x, ray_eye.y, -1.0f, 0.0f);
Matrix view = cam.getTransformation();
view = view.invertRigid();
tempX = view.get(0, 0) * ray_eye.x + view.get(1, 0) * ray_eye.y
+ view.get(2, 0) * ray_eye.z + view.get(3, 0) * ray_eye.w;
tempY = view.get(0, 1) * ray_eye.x + view.get(1, 1) * ray_eye.y
+ view.get(2, 1) * ray_eye.z + view.get(3, 1) * ray_eye.w;
tempZ = view.get(0, 2) * ray_eye.x + view.get(1, 2) * ray_eye.y
+ view.get(2, 2) * ray_eye.z + view.get(3, 2) * ray_eye.w;
tempW = view.get(0, 3) * ray_eye.x + view.get(1, 3) * ray_eye.y
+ view.get(2, 3) * ray_eye.z + view.get(3, 3) * ray_eye.w;
Vector ray_wor = vecmath.vector(tempX, tempY, tempZ);
// don't forget to normalise the vector at some point
ray_wor = ray_wor.normalize();
direction = ray_wor;
}
First,unproject() method is the way to go.It is not deprecated at all.You can find it implemented in GLM math library for example.Here is my implementation of Ray based 3D picking:
// let's check if this renderable's AABB is clicked:
const glm::ivec2& mCoords = _inputManager->GetMouseCoords();
int mouseY = _viewportHeight - mCoords.y;
//unproject twice to build a ray from near to far plane"
glm::vec3 v0 = glm::unProject(glm::vec3(float(mCoords.x), float(mouseY), 0.0f),_camera->Transform().GetView(),_camera->Transform().GetProjection(), _viewport);
glm::vec3 v1 = glm::unProject(glm::vec3(float(mCoords.x), float(mouseY), 1.0f),_camera->Transform().GetView(),_camera->Transform().GetProjection(), _viewport);
glm::vec3 dir = (v1 - v0);
Ray r(_camera->Transform().GetPosition(),dir);
float ishit ;
//construct AABB:
glm::mat4 aabbMatr = glm::translate(glm::mat4(1.0),renderable->Transform().GetPosition());
aabbMatr = glm::scale(aabbMatr,renderable->Transform().GetScale());
//transforms AABB vertices(need it if the origianl bbox is not axis aligned as in this case)
renderable->GetBoundBox()->RecalcVertices(aabbMatr);
//this method makes typical Ray-AABB intersection test:
if(r.CheckIntersectAABB(*renderable->GetBoundBox().get(),&ishit)){
printf("HIT!\n");
}
But I would suggest you also to take a look at color based 3d picking which is pixel perfect and even easier to implement.
This function is supposed to give me the exact size of my near clipping plane.
public Vector2 NearplaneSize
{
get
{
float w = 2 * Mathf.Tan(Mathf.Deg2Rad(Fov) / 2) * ZNear;
return new Vector2(w, w / AspectRatio);
}
}
I'm creating a plane like this:
Vector2 s = cam.NearplaneSize;
Mesh = PrimitiveFactory.CreatePlane(s.X / -2, s.Y / -2, -(cam.ZNear + 0.1f), s.X, s.Y, 1, 1, Quaternion.FromAxisAngle(Vector3.UnitX, Mathf.Deg2Rad(90)));
in front of the camera, but its slightly larger than half the screen. So obviously the calculation is wrong. I can't seem to find a better formula though.
Any ideas? Thanks
I don't know OpenTK, but due to old gluPerspective call, "Fov" is generally understood as fov y, not fovx.
So I assume that
float h = 2 * Mathf.Tan(Mathf.Deg2Rad(Fov) / 2) * ZNear;
return new Vector2(h * AspectRatio, h);
should do the trick.
So I have this piece of code, which pretty much draws various 2D textures on the screen, though there are multiple sprites that have to be 'dissected' from the texture (spritesheet). The problem is that rotation is not working properly; while it rotates, it does not rotate on the center of the texture, which is what I am trying to do. I have narrowed it down to the translation being incorrect:
glTranslatef(x + sr->x/2 - sr->w/2,
y + sr->y/2 - sr->h/2,0);
glRotatef(ang,0,0,1.f);
glTranslatef(-x + -sr->x/2 - -sr->w/2,
-y + -sr->y/2 - -sr->h/2,0);
X and Y is the position that it's being drawn to, the sheet rect struct contains the position X and Y of the sprite being drawn from the texture, along with w and h, which are the width and heights of the 'sprite' from the texture. I've tried various other formulas, such as:
glTranslatef(x, y, 0);
The below three switching the negative sign to positive (x - y to x + y)
glTranslatef(sr->x/2 - sr->w/2, sr->y/2 - sr->h/2 0 );
glTranslatef(sr->x - sr->w/2, sr->y - sr->h/2, 0 );
glTranslatef(sr->x - sr->w, sr->y - sr->w, 0 );
glTranslatef(.5,.5,0);
It might also be helpful to say that:
glOrtho(0,screen_width,screen_height,0,-2,10);
is in use.
I've tried reading various tutorials, going through various forums, asking various people, but there doesn't seem to be a solution that works, nor can I find any useful resources that explain to me how I find the center of the image in order to translate it to '(0,0)'. I'm pretty new to OpenGL so a lot of this stuff takes awhile for me to digest.
Here's the entire function:
void Apply_Surface( float x, float y, Sheet_Container* source, Sheet_Rect* sr , float ang = 0, bool flipx = 0, bool flipy = 0, int e_x = -1, int e_y = -1 ) {
float imgwi,imghi;
glLoadIdentity();
glEnable(GL_TEXTURE_2D);
glBindTexture(GL_TEXTURE_2D,source->rt());
// rotation
imghi = source->rh();
imgwi = source->rw();
Sheet_Rect t_shtrct(0,0,imgwi,imghi);
if ( sr == NULL ) // in case a sheet rect is not provided, assume it's width
//and height of texture with 0/0 x/y
sr = &t_shtrct;
glPushMatrix();
//
int wid, hei;
glGetTexLevelParameteriv(GL_TEXTURE_2D,0,GL_TEXTURE_WIDTH,&wid);
glGetTexLevelParameteriv(GL_TEXTURE_2D,0,GL_TEXTURE_HEIGHT,&hei);
glTranslatef(-sr->x + -sr->w,
-sr->y + -sr->h,0);
glRotatef(ang,0,0,1.f);
glTranslatef(sr->x + sr->w,
sr->y + sr->h,0);
// Yeah, out-dated way of drawing to the screen but it works for now.
GLfloat tex[] = {
(sr->x+sr->w * flipx) /imgwi, 1 - (sr->y+sr->h *!flipy )/imghi,
(sr->x+sr->w * flipx) /imgwi, 1 - (sr->y+sr->h * flipy)/imghi,
(sr->x+sr->w * !flipx) /imgwi, 1 - (sr->y+sr->h * flipy)/imghi,
(sr->x+sr->w * !flipx) /imgwi, 1 - (sr->y+sr->h *!flipy)/imghi
};
GLfloat vertices[] = { // vertices to put on screen
x, (y + sr->h),
x, y,
(x +sr->w), y,
(x +sr->w),(y +sr->h)
};
// index array
GLubyte index[6] = { 0,1,2, 2,3,0 };
float fx = (x/(float)screen_width)-(float)sr->w/2/(float)imgwi;
float fy = (y/(float)screen_height)-(float)sr->h/2/(float)imghi;
// activate arrays
glEnableClientState(GL_VERTEX_ARRAY);
glEnableClientState(GL_TEXTURE_COORD_ARRAY);
// pass verteices and texture information
glVertexPointer(2, GL_FLOAT, 0, vertices);
glTexCoordPointer(2, GL_FLOAT, 0, tex);
glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_BYTE, index);
glDisableClientState(GL_VERTEX_ARRAY);
glDisableClientState(GL_TEXTURE_COORD_ARRAY);
glPopMatrix();
glDisable(GL_TEXTURE_2D);
}
Sheet container class:
class Sheet_Container {
GLuint texture;
int width, height;
public:
Sheet_Container();
Sheet_Container(GLuint, int = -1,int = -1);
void Load(GLuint,int = -1,int = -1);
float rw();
float rh();
GLuint rt();
};
Sheet rect class:
struct Sheet_Rect {
float x, y, w, h;
Sheet_Rect();
Sheet_Rect(int xx,int yy,int ww,int hh);
};
Image loading function:
Sheet_Container Game_Info::Load_Image(const char* fil) {
ILuint t_id;
ilGenImages(1, &t_id);
ilBindImage(t_id);
ilLoadImage(const_cast<char*>(fil));
int width = ilGetInteger(IL_IMAGE_WIDTH), height = ilGetInteger(IL_IMAGE_HEIGHT);
return Sheet_Container(ilutGLLoadImage(const_cast<char*>(fil)),width,height);
}
Your quad (two triangles) is centered at:
( x + sr->w / 2, y + sr->h / 2 )
You need to move that point to the origin, rotate, and then move it back:
glTranslatef ( (x + sr->w / 2.0f), (y + sr->h / 2.0f), 0.0f); // 3rd
glRotatef (0,0,0,1.f); // 2nd
glTranslatef (-(x + sr->w / 2.0f), -(y + sr->h / 2.0f), 0.0f); // 1st
Here is where I think you are getting tripped up. People naturally assume that OpenGL applies transformations in the order they appear (top-to-bottom), that is not the case. OpenGL effectively swaps the operands everytime it multiplies two matrices:
M1 x M2 x M3
~~~~~~~
(1)
~~~~~~~~~~
(2)
(1) M2 * M1
(2) M3 * (M2 * M1) --> M3 * M2 * M1 (row-major / textbook math notation)
The technical term for this is post-multiplication, it all has to do with the way matrices are implemented in OpenGL (column-major). Suffice it to say, you should generally read glTranslatef, glRotatef, glScalef, etc. calls from bottom-to-top.
With that out of the way, your current rotation does not make any sense.
You are telling GL to rotate 0 degrees around an axis: <0,0,1> (the z-axis in other words). The axis is correct, but a 0 degree rotation is not going to do anything ;)
I am trying to understand what the following code does:
glm::mat4 Projection = glm::perspective(35.0f, 1.0f, 0.1f, 100.0f);
Does it create a projection matrix? Clips off anything that is not in the user's view?
I wasn't able to find anything on the API page, and the only thing I could find in the pdf on their website was this:
gluPerspective:
glm::mat4 perspective(float fovy, float aspect, float zNear,
float zFar);
glm::dmat4 perspective(
double fovy, double aspect, double zNear,
double zFar);
From GLM_GTC_matrix_transform extension: <glm/gtc/matrix_transform.hpp>
But it doesn't explain the parameters. Maybe I missed something.
It creates a projection matrix, i.e. the matrix that describes the set of linear equations that transforms vectors from eye space into clip space. Matrices really are not black magic. In the case of OpenGL they happen to be a 4-by-4 arrangement of numbers:
X_x Y_x Z_x T_x
X_y Y_y Z_y T_y
X_z Y_z Z_z T_z
X_w Y_w Z_w W_w
You can multply a 4-vector by a 4×4 matrix:
v' = M * v
v'_x = M_xx * v_x + M_yx * v_y + M_zx * v_z + M_tx * v_w
v'_y = M_xy * v_x + M_yy * v_y + M_zy * v_z + M_ty * v_w
v'_z = M_xz * v_x + M_yz * v_y + M_zz * v_z + M_tz * v_w
v'_w = M_xw * v_x + M_yw * v_y + M_zw * v_z + M_tw * v_w
After reaching clip space (i.e. after the projection step), the primitives are clipped. The vertices resulting from the clipping are then undergoing the perspective divide, i.e.
v'_x = v_x / v_w
v'_y = v_y / v_w
v'_z = v_z / v_w
( v_w = 1 = v_w / v_w )
And that's it. There's really nothing more going on in all those transformation steps than ordinary matrix-vector multiplication.
Now the cool thing about this is, that matrices can be used to describe the relative alignment of a coordinate system within another coordinate system. What the perspective transform does is, that it let's the vertices z-values "slip" into their projected w-values as well. And by the perspective divide a non-unity w will cause "distortion" of the vertex coordinates. Vertices with small z will be divided by a small w, thus their coordinates "blow" up, whereas vertices with large z will be "squeezed", which is what's causing the perspective effect.
This is a c standalone version of the same function. This is roughly a copy paste version of the original.
# include <math.h>
# include <stdlib.h>
# include <string.h>
typedef struct s_mat {
float *array;
int width;
int height;
} t_mat;
t_mat *mat_new(int width, int height)
{
t_mat *to_return;
to_return = (t_mat*)malloc(sizeof(t_mat));
to_return->array = malloc(width * height * sizeof(float));
to_return->width = width;
to_return->height = height;
return (to_return);
}
void mat_zero(t_mat *dest)
{
bzero(dest->array, dest->width * dest->height * sizeof(float));
}
void mat_set(t_mat *m, int x, int y, float val)
{
if (m == NULL || x > m->width || y > m->height)
return ;
m->array[m->width * (y - 1) + (x - 1)] = val;
}
t_mat *mat_perspective(float angle, float ratio,
float near, float far)
{
t_mat *to_return;
float tan_half_angle;
to_return = mat_new(4, 4);
mat_zero(to_return);
tan_half_angle = tan(angle / 2);
mat_set(to_return, 1, 1, 1 / (ratio * tan_half_angle));
mat_set(to_return, 2, 2, 1 / (tan_half_angle));
mat_set(to_return, 3, 3, -(far + near) / (far - near));
mat_set(to_return, 4, 3, -1);
mat_set(to_return, 3, 4, -(2 * far * near) / (far - near));
return (to_return);
}