I'm trying to keep a simple cube a fixed size on screen no matter how far it translates into the scene (slides along the z axis).
I know that using an orthogonal projection, I could draw an object at fixed size, but I'm not interested in just having it look right. I need to read out the x and z coordinates (in world space) at any given time.
So the further along the -z axis the cube translates, the larger are its x and z values getting in order for the cube to still be a defined pixel size on screen (let's say the cube should be 50x50x50 pixel).
I'm not sure how to begin tackling this, any suggestions?
Related
I am trying to draw a 3D cuboid by clicking on one of the corner points and then extending it based on the dimensions provided by the user, and then rotating it about any axis. However, I am not sure about how I can specify the (x, y, z) tuple after the mouse-click, since the output window is on 2D. Also, I cannot understand how to extend the point to form a cuboid.
What you want is called 3D Picking. Usually, this is done using Raycasting.
However, there is an easy solution (with acceptable performance) that involves rendering the scene off-screen on a framebuffer with 32-bit floats for the R/G/B values.
In the shader you use the x, y and z coordinates of that pixel as the color values.
Then, when the user clicks somewhere, you simply read out that pixels color to get its position.
Im making an editor in which I want to build a terrain map. I want to use the mouse to increase/decrease terrain altitude to create mountains and lakes.
Technically I have a heightmap I want to modify at a certain texcoord that I pick out with my mouse. To do this I first go from screen coordinates to world position - I have done that. The next step, going from world position to picking the right texture coordinate puzzles me though. How do I do that?
If you are using a simple hightmap, that you use as a displacement map in lets say the y direction. The base mesh lays in the xz plain (y=0).
You can discard the y coordinate from world coordinate that you have calculated and you get the point on the base mesh. From there you can map it to texture space the way, you map your texture.
I would not implement it that way.
I would render the scene to a framebuffer and instead of rendering a texture the the mesh, colorcode the texture coordinate onto the mesh.
If i click somewhere in screen space, i can simple read the pixel value from the framebuffer and get the texture coordinate directly.
The rendering to the framebuffer should be very inexpensive anyway.
Assuming your terrain is a simple rectangle you first calculate the vector between the mouse world position and the origin of your terrain. (The vertex of your terrain quad where the top left corner of your height map is mapped to). E.g. mouse (50,25) - origin(-100,-100) = (150,125).
Now divide the x and y coordinates by the world space width and height of your terrain quad.
150 / 200 = 0.75 and 125 / 200 = 0.625. This gives you the texture coordinates, if you need them as pixel coordinates instead simply multiply with the size of your texture.
I assume the following:
The world coordinates you computed are those of the mouse pointer within the view frustrum. I name them mouseCoord
We also have the camera coordinates, camCoord
The world consists of triangles
Each triangle point has texture coordiantes, those are interpolated by barycentric coordinates
If so, the solution goes like this:
use camCoord as origin. Compute the direction of a ray as mouseCoord - camCoord.
Compute the point of intersection with a triangle. Naive variant is to check for every triangle if it is intersected, more sophisticated would be to rule out several triangles first by some other algorithm, like parting the world in cubes, trace the ray along the cubes and only look at the triangles that have overlappings with the cube. Intersection with a triangle can be computed like on this website: http://www.lighthouse3d.com/tutorials/maths/ray-triangle-intersection/
Compute the intersection points barycentric coordinates with respect to that triangle, like that: https://www.scratchapixel.com/lessons/3d-basic-rendering/ray-tracing-rendering-a-triangle/barycentric-coordinates
Use the barycentric coordinates as weights for the texture coordinates of the corresponding triangle points. The result are the texture coordinates of the intersection point, aka what you want.
If I misunderstood what you wanted, please edit your question with additional information.
Another variant specific for a height map:
Assumed that the assumptions are changed like that:
The world has ground tiles over x and y
The ground tiles have height values in their corners
For a point within the tile, the height value is interpolated somehow, like by bilinear interpolation.
The texture is interpolated in the same way, again with given texture coordinates for the corners
A feasible algorithm for that (approximative):
Again, compute origin and direction.
Wlog, we assume that the direction has a higher change in x-direction. If not, exchange x and y in the algorithm.
Trace the ray in a given step length for x, that is, in each step, the x-coordinate changes by that step length. (take the direction, multiply it with step size divided by it's x value, add that new direction to the current position starting at the origin)
For your current coordinate, check whether it's z value is below the current height (aka has just collided with the ground)
If so, either finish or decrease step size and do a finer search in that vicinity, going backwards until you are above the height again, then maybe go forwards in even finer steps again et cetera. The result are the current x and y coordinates
Compute the relative position of your x and y coordinates within the current tile. Use that for weights for the corner texture coordinates.
This algorithm can theoretically jump over very thin tops. Choose a small enough step size to counter that. I cannot give an exact algorithm without knowing what type of interpolation the height map uses. Might be not the worst idea to create triangles anyway, out of bilinear interpolated coordinates maybe? In any case, the algorithm is good to find the tile in which it collides.
Another variant would be to trace the ray over the points at which it's x-y-coordinates cross the tile grid and then look if the z coordinate went below the height map. Then we know that it collides in this tile. This could produce a false negative if the height can be bigger inside the tile than at it's edges, as certain forms of interpolation can produce, especially those that consider the neighbour tiles. Works just fine with bilinear interpolation, though.
In bilinear interpolation, the exact intersection can be found like that: Take the two (x,y) coordinates at which the grid is crossed by the ray. Compute the height of those to retrieve two (x,y,z) coordinates. Create a line out of them. Compute the intersection of that line with the ray. The intersection of those is that of the intersection with the tile's height map.
Simplest way is to render the mesh as a pre-pass with the uvs as the colour. No screen to world needed. The uv is the value at the mouse position. Just be careful though with mips/filtering etv
I need to have a 2D layer in my OpenGL application.I have implemented it first using a typical ortho projection like this:
Mat4 ortho =Glm.ortho(0,viewWidth , 0 ,viewHeight);
The 2d worked fine except the fact that when running in different screen sizes the 2d shapes are scaled relatively to a new aspect.That is not what I want (opposite to what usually people need). I need the 2d shapes to get stretched or squeezed according to the new screen size.
I tried not to use the ortho matrix but just an identity.This one works but in such a case I have to use numbers in range 0 -1 to manipulate the objects in the visible frustum area.And I need to use numbers in regular (not normalized ) ranges.So it is sort of forcing me to get back to ortho projection which is problematic because of what already said.
So the question is how do I transform 2d object without perspective staying in the world coordinates system.
UPDATE:
The best example is 2D layers in Adobe AfterEffects. If one changes composition dimension ,2d layers don't get scaled according to new dimensions.That is what I am after.
It's tricky to know how to answer this, because to some degree your requirements are mutually exclusive. You don't want normalised coordinates, you want to use screen coordinates. But by definition, screen coordinates are defined in pixels, and pixels are usually square... So I think you need some form of normalised coordinates, albeit maybe uniformly scaled.
Perhaps what you want is to fix the ratio for width and height in your ortho. That would allow you to address the screen in some kind of pseudo-pixel unit, where one axis is "real" pixels, but the other can be stretched. So instead of height, pass 3/4 of the width for a 4:3 display, or 9/16ths on a 16:9, etc. This will be in units of pixels if the display is the "right" dimension, but will stretch in one dimension only if it's not.
You may need to switch which dimension is "real" pixels depending on the ratio being less or greater than your "optimal" ratio, but it's tricky to know what you're really shooting for here.
I want to draw a spaceship in the centre of a window as it powers through space. To scroll the world window, I compute the new position of the ship and centre a 4000x3000 window around this using glOrtho. My test is to press the forward button and move the ship upwards. On most machines there is no problem. On a slower linux laptop, where I am getting only 30 frames per second, the ship shudders back and forth. Comparing its position relative to the mouse pointer (which does not move), the ship can clearly be seen jumping forward and back by a couple of pixels. The stars are also shown to be blurred into short lines.
I would like to query the pixel value of the centre of the ship to see if it is changing.
Is there an OpenGL way to supply a world point and get back the pixel point it will be transformed to?
I'd consider doing it the other way around. Keep the ship at 0,0 world coordinates, and move the world relative to it. Then you only need the glOrtho call when the size of the window changes (the camera is in a fixed position). Apart from not having to calculate the projection matrix every time, you also have the benefit that if your world ends up being massive in the future then you have the option of using double precision positions, since large offsets on floats results in inaccurate positioning.
To draw your space scene, you then manipulate the modelview matrix before drawing any objects, and use a different matrix when drawing the ship.
To get a pixel coordinate from a world coordinate, take the point and multiply it by the projection matrix multiplied by the modelview matrix (make sure you get the multiplication around the right way). You'll then have a value that has x and y in the ranges -1 to 1. You can add [1,1] and multiply by half the screen size to get the pixel position. (if you wanted, you could add this into the matrix transformation).
I'm implementing a rasterizer for a class project, and currently im stuck on what method/how i should convert vertex coordinates to viewing pane coordinates.
I'm given a list of verticies of 2d coordinates for a triangle, like
0 0 1
2 0 1
0 1 1
and im drawing in a viewing pane (using OpenGL and GLUT) of size 400X400 pixels, for example.
My question is how do i decide where in the viewing pane to put these verticies, assuming
1) I want the coordinate's to be centered around 0,0 at the center of the screen
2) I want to fill up most of the screen (lets say for this example, the screen is the maximum x coordinate + 1 lengths wide, etc)
3) I have any and all of OpenGL's and GLUT's standard library functions at my disposal.
Thanks!
http://www.opengl.org/sdk/docs/man/xhtml/glOrtho.xml
To center around 0 use symmetric left/right and bottom/top. Beware the near/far which are somewhat arbitrary but are often chosen (in examples) as -1..+1 which might be a problem for your triangles at z=1.
If you care about the aspect ratio make sure that right-left and bottom-top are proportional to the window's width/height.
You should consider the frustum which is your volumetric view and calculate the coordinates by transforming the your objects to consider their position, this explains the theory quite thoroughly..
basically you have to project the object using a specified projection matrix that is calculated basing on the characteristics of your view:
scale them according to a z (depth) value: you scale both y and x in so inversely proportionally to z
you scale and shift coordinates in order to fit the width of your view