So I'm supposed to Texture Map a specific model I've loaded into a scene (with a Framebuffer and a Planar Pinhole Camera), however I'm not allowed to use OpenGL and I have no idea how to do it otherwise (we do use glDrawPixels for other functionality, but that's the only function we can use).
Is anyone here able enough to give me a run-through on how to texture map without OpenGL functionality?
I'm supposed to use these slides: https://www.cs.purdue.edu/cgvlab/courses/334/Fall_2014/Lectures/TMapping.pdf
But they make very little sense to me.
What I've gathered so far is the following:
You iterate over a model, and assign each triangle "texture coordinates" (which I'm not sure what those are), and then use "model space interpolation" (again, I don't understand what that is) to apply the texture with the right perspective.
I currently have my program doing the following:
TL;DR:
1. What is model space interpolation/how do I do it?
2. What explicitly are texture coordinates?
3. How, on a high level (in layman's terms) do I texture map a model without using OpenGL.
OK, let's start by making sure we're both on the same page about how the color interpolation works. Lines 125 through 143 set up three vectors redABC, greenABC and blueABC that are used to interpolate the colors across the triangle. They work one color component at a time, and each of the three vectors helps interpolate one color component.
By convention, s,t coordinates are in source texture space. As provided in the mesh data, they specify the position within the texture of that particular vertex of the triangle. The crucial thing to understand is that s,t coordinates need to be interpolated across the triangle just like colors.
So, what you want to do is set up two more ABC vectors: sABC and tABC, exactly duplicating the logic used to set up redABC, but instead of using the color components of each vertex, you just use the s,t coordinates of each vertex. Then for each pixel, instead of computing ssiRed etc. as unsigned int values, you compute ssis and ssit as floats, they should be in the range 0.0f through 1.0f assuming your source s,t values are well behaved.
Now that you have an interpolated s,t coordinate, multiply ssis by the texel width of the texture, and ssit by the texel height, and use those coordinates to fetch the texel. Then just put that on the screen.
Since you are not using OpenGL I assume you wrote your own software renderer to render that teapot?
A texture is simply an image. A texture coordinate is a 2D position in the texture. So (0,0) is bottom-left and (1,1) is top-right. For every vertex of your 3D model you should store a 2D position (u,v) in the texture. That means that at that vertex, you should use the colour the texture has at that point.
To know the UV texture coordinate of a pixel in between vertices you need to interpolate the texture coordinates of the vertices around it. Then you can use that UV to look up the colour in the texture.
Related
I have a texture of the earth which I want to map onto a sphere.
As it is a unit sphere and the model itself has no texture coordinates, the easiest thing I could think of is to just calculate spherical coordinates for each vertex and use them as texture coordinates.
textureCoordinatesVarying = vec2(atan(modelPositionVarying.y, modelPositionVarying.x)/(2*M_PI)+.5, acos(modelPositionVarying.z/sqrt(length(modelPositionVarying.xyz)))/M_PI);
When doing this in the fragment shader, this works fine, as I calculate the texture coordinates from the (interpolated) vertex positions.
But when I do this in the vertex shader, which I also would do if the model itself has texture coordinates, I get the result as shown in the image below. The vertices are shown as points and a texture coordinate (u) lower than 0.5 is red while all others are blue.
So it looks like that the texture coordinate (u) of two adjacent red/blue vertices have value (almost) 1.0 and 0.0. The variably is then smoothly interpolated and therefore yields values somewhere between 0.0 and 1.0. This of course is wrong, because the value should either be 1.0 or 0.0 but nothing in between.
Is there a way to work with spherical coordinates as texture coordinates without getting those effects shown above? (if possible, without changing the model)
This is a common problem. The seams between two texture coordinate topologies, where you want the texture coordinate to seamlessly wrap from 1.0 to 0.0 requires the mesh to properly handle this. To do this, the mesh must duplicate every vertex along the seam. One of the vertices will have a 0.0 texture coordinate and will be connected to the vertices coming from the right (in your example). The other will have a 1.0 texture coordinate and will be connected to the vertices coming from the left (in your example).
This is a mesh problem, and it is best to solve it in the mesh itself. The same position needs two different texture coordinates, so you must duplicate the position in question.
Alternatively, you could have the fragment shader generate the texture coordinate from an interpolated vertex normal. Of course, this is more computationally expensive, as it requires doing a conversion from a direction to a pair of angles (and then to the [0, 1] texture coordinate range).
As far as I understand, location of a point/pixel cannot be a fraction, at least on a raster graphics system where hardwares use pixels to display images.
Then, why and how does OpenGL use fractional values for plotting pixels?
For example, how is it possible: glVertex2f(0.15f, 0.51f); ?
This command does not plot any pixels. It merely defines the location of a point in 3D space (you'll notice that there are 3 coordinates, while for a pixel on the screen you'd only need 2). This is the starting point for the OpenGL pipeline. This point then goes through a lot of transformations before it ends up on the screen.
Also, the coordinates are unitless. For example, you can say that your viewport is between 0.0f and 1.0f, then these coordinates make a lot of sense. Basically you have to think of these point in terms of mathematics, not pixels.
I would suggest some reading on how OpenGL transformations work, for example here, here or the tutorial here.
The vectors you pass into OpenGL are not viewport positions but arbitrary numbers in some vector space. Only after a chain of transformations these numbers are mapped into viewport pixel positions. With the old fixed function pipeline this could be anything that can be represented by a vector–matrix multiplication.
These days, where everything is programmable (shaders) the mapping can very well be any kind of function you can think of. For example the values you pass into glVertex (immediate mode call, but available to shaders with OpenGL-2.1) may be interpreted as polar coordinates in the vertex shader:
This is a perfectly valid OpenGL-2.1 vertex shader that interprets the vertex position to be in polar coordinates. Note that due to triangles and lines being straight edges and polar coordinates being curvilinear this gives good visual results only for points or highly tesselated primitives.
#version 110
void main() {
gl_Position =
gl_ModelViewProjectionMatrix
* vec4( gl_Vertex.y*vec2(sin(gl_Vertex.x),cos(gl_Vertex.x)) , 0, 1);
}
As you can see here the valus passed to glVertex are actually arbitrary, unitless components of vectors in some vector space. Only by applying some transformation to the viewport space these vectors gain meaning. Hence it makes no way to impose a certain value range onto the values that go into the vertex attribute.
Vertex and pixel are very different things.
It's quite possible to have all your vertices within one pixel (although in this case you probably need help with LODing).
You might want to start here...
http://www.glprogramming.com/blue/ch01.html
Specifically...
Primitives are defined by a group of one or more vertices. A vertex defines a point, an endpoint of a line, or a corner of a polygon where two edges meet. Data (consisting of vertex coordinates, colors, normals, texture coordinates, and edge flags) is associated with a vertex, and each vertex and its associated data are processed independently, in order, and in the same way.
And...
Rasterization produces a series of frame buffer addresses and associated values using a two-dimensional description of a point, line segment, or polygon. Each fragment so produced is fed into the last stage, per-fragment operations, which performs the final operations on the data before it's stored as pixels in the frame buffer.
For your example, before glVertex2f(0.15f, 0.51f) is on the screen, there are many transforms to be done. Making complex thing crudely simpler, after moving your vertex to view space (applying camera position and direction), the magic here is (1) projection matrix, and (2) viewport setting.
Internally, OpenGL "screen coordinates" are in a cube (-1, -1, -1) - (1, 1, 1), :
http://www.matrix44.net/cms/wp-content/uploads/2011/03/ogl_coord_object_space_cube.png
Projection matrix 'squeezes' the frustum in this cube (which you do in vertex shader), assuming you have perspective transform - if projection is orthogonal, the projection is just a tube, limited by near and far values (and like in both cases, scaling factors):
http://www.songho.ca/opengl/files/gl_projectionmatrix01.png
EDIT: Maybe better example here:
http://www.opengl-tutorial.org/beginners-tutorials/tutorial-3-matrices/#The_Projection_matrix
(EDIT: The Z-coordinate is used as depth value) When fragments are finally transferred to pixels on texture/framebuffer/screen, these are multiplied with viewport settings:
https://www3.ntu.edu.sg/home/ehchua/programming/opengl/images/GL_2DViewportAspectRatio.png
Hope this helps!
So when drawing a rectangle on OpenGL, if you give the corners of the rectangle texture coordinates of (0,0), (1,0), (1,1) and (0, 1), you'll get the standard rectangle.
However, if you turn it into something that's not rectangular, you'll get a weird stretching effect. Just like the following:
I saw from this page below that this can be fixed, but the solution given is only for trapezoidal values only. Also, I have to be doing this over many rectangles.
And so, the questions is, what is the proper way, and most efficient way to get the right "4D" texture coordinates for drawing stretched quads?
Implementations are allowed to decompose quads into two triangles and if you visualize this as two triangles you can immediately see why it interpolates texture coordinates the way it does. That texture mapping is correct ... for two independent triangles.
That diagonal seam coincides with the edge of two independently interpolated triangles.
Projective texturing can help as you already know, but ultimately the real problem here is simply interpolation across two triangles instead of a single quad. You will find that while modifying the Q coordinate may help with mapping a texture onto your quadrilateral, interpolating other attributes such as colors will still have serious issues.
If you have access to fragment shaders and instanced vertex arrays (probably rules out OpenGL ES), there is a full implementation of quadrilateral vertex attribute interpolation here. (You can modify the shader to work without "instanced arrays", but it will require either 4x as much data in your vertex array or a geometry shader).
Incidentally, texture coordinates in OpenGL are always "4D". It just happens that if you use something like glTexCoord2f (s, t) that r is assigned 0.0 and q is assigned 1.0. That behavior applies to all vertex attributes; vertex attributes are all 4D whether you explicitly define all 4 of the coordinates or not.
What i'd like to do:
I have a 3d transformed, uvmapped object with a white texture as well as a screenspace image.
I want to bake the screenspace image into the texture of the object, such that it's 3d transformed representation on screen exactly matches the screenspace image (so i want to project it onto the uv space).
I'd like to do this with image_load_and store. I imagine it as:
1st pass: render the transformed 3d objects uvcoordinates into a offscreen texture
2nd pass: render screensized quad, on each pixel, check the value of the texture rendered in the first pass, if there are valid texturecoordinates there, look up the screenspace image with the screenspace quad's own uv textures and write this texel color with image_load_and_store into a texturebuffer by using the uv textures read from the input texture as index.
As I never worked with this feature before, I'd just like to ask whether someone who worked with it already considers this feasible and whether there maybe are already some examples that do something in this direction?
Your proposed way is certainly one method to do it, and actually it's quite common. The other way is to to a back projection from screen space to texture space. It's not that hard as it might sound at first. Basically for each triangle you have to find the transformation of the tangent space vectors (UV) on the models surface to their screen counterparts. In addition to that transform the triangle itself to find the boundaries of the screen space triangle in the picture. Then you invert that projection.
EDIT
glTexcoord4f allows to specif four dimensions of a texture, but how do you create 4-dimensional textures
The r component is used to specify either the depth in a 3D (volumetric) texture, or the layer in a 2D texture array.
The q component plays the same role, like the vertex position w element: It is used for scaling the perspective divide in perspective texture projection.
There isn't any real "meaning" to them. If you were using shaders, you can assign any meaning you want to them.
For example, in our game: we used the xy for the actual texcoords, the z for which texture to sample from, and the w (4th component) to control the brightness.
There is such thing as 3D and 4D textures which do actually require 3 and 4 texcoords respectively, I suppose that could be the "meaning" of them.
The main reason that they exist, is because graphics cards work with 4 component vectors. When you pass a 2D texcoord in, it's still a 4-vector behind the scenes (the other r and q components aren't set). OpenGL provides you with the functionality to use them, on the off chance that you might need it.
The r component is the 3rd coordinate for GL_TEXTURE_3D (for rendering volumes). I am not familiar with any method that uses the 4th coordinate.
But it seems reasonable to have that available as all homogeneous OpenGL vectors have 4 components.
There is no such thing as a 4-dimensional texture. At least, not without extensions.
The reason glTexCoord4D exists is to allow passing 4 values. In the modern shader-based rendering world, "texture coordinates" don't have to be texture coordinates at all. They're just values the shader uses to do whatever it does.
Many of the texture lookup functions in shaders take more texture coordinate dimensions than the dimensionality of the actual texture. All texture functions for shadow textures take an extra coordinate, which represents the comparison value. All of the Proj texture functions take an extra coordinate, which represents the homogeneous coordinate for a homogeneous coordinate system.
In fixed-function land, 4D texture coordinates can be used for projective texturing of 3D textures. So the 4D coordinate is in a homogeneous coordinate system.