I'm trying to implement tiled deferred rendering method and now I'm stuck. I'm computing min/max depth for each tile (32x32) and storing it in texture. Then I want to compute screen space bounding box (bounding square) represented by left down and top right coords of rectangle for every pointlight (sphere) in my scene (see pic from my app). This together with min/max depth will be used to check if light affects actual tile.
Problem is I have no idea how to do this. Any idea, source code or exact math?
Update
Screen-space is basically a 2D entity, so instead of a bounding box think of a bounding rectangle.
Here is a simple way to compute it:
Project 8 corner points of your world-space bounding box onto the screen using your ModelViewProjection matrix
Find a bounding rectangle of these points (which is just min/max X and Y coordinates of the points)
A more sophisticated way can be used to compute a screen-space bounding rect for a point light source. We calculate four planes that pass through the camera position and are tangent to the light’s sphere of illumination (the light radius). Intersections of each tangent plane with the image plane gives us 4 lines on the image plane. This lines define the resulting bounding rectangle.
Refer to this article for math details: http://www.altdevblogaday.com/2012/03/01/getting-the-projected-extent-of-a-sphere-to-the-near-plane/
Related
I am using orthographic projection glOrtho for my scene. I implemented a virtual trackball to rotate an object beside that I also implemented a zoom in/out on the view matrix. Say I have a cube of size 100 unit and is located at the position of (0,-40000,0) far from the origin. If the center of rotation is located at the origin once the user rotate the cube and after zoom in or out, it could be position at some where (0,0,2500000) (this position is just an assumption and it is calculated after multiplied by the view matrix). Currently I define a very big range of near(-150000) and far(150000) plane, but some time the object still lie outside either the near or far plane and the object just turn invisible, if I define a larger near and far clipping plane say -1000000 and 1000000, it will produce an ungly z artifacts. So my question is how do I correctly calculate the near and far plane when user rotate the object in real time? Thanks in advance!
Update:
I have implemented a bounding sphere for the cube. I use the inverse of view matrix to calculate the camera position and calculate the distance of the camera position from the center of the bounding sphere (the center of the bounding sphere is transformed by the view matrix). But I couldn't get it to work. can you further explain what is the relationship between the camera position and the near plane?
A simple way is using the "bounding sphere". If you know the data bounding box, the maximum diagonal length is the diameter of the bounding sphere.
Let's say you calculate the distance 'dCC' from the camera position to the center of the sphere. Let 'r' the radius of that sphere. Then:
Near = dCC - r - smallMargin
Far = dCC + r + smallMargin
'smallMargin' is a value used just to avoid clipping points on the surface of the sphere due to numerical precision issues.
The center of the sphere should be the center of rotation. If not, the diameter should grow so as to cover all data.
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 have a 3D mesh encoded in a .OFF file. Only vertices, coordinates of these vertices and connectivity are encoded. I read in some papers that a 3D mesh can be normalized in a unit bounding box. What this really means ? and how we can do this ?
That means the mesh will fit into space defined by axis aligned cube of size 1 for example defined by corners: A(-0.5,-0.5,-0.5) and B(+0.5,+0.5,+0.5).
To achieve this:
get actual bounding box
So loop through all used Vertexes and remember min and max coordinate for each axis A0(xmin,ymin,zmin),B0(xmax,ymax,zmax).
Normalize to bounding box A,B
So loop through each Vertex again and recompute them (by linear interpolation). For example like this:
Vertex[i].x=A.x + (B.x-A.x)*(Vertex[i].x-A0.x)/(B0.x-A0.x)
Vertex[i].y=A.y + (B.y-A.y)*(Vertex[i].y-A0.y)/(B0.y-A0.y)
Vertex[i].z=A.z + (B.z-A.z)*(Vertex[i].z-A0.z)/(B0.z-A0.z)
The problem is that this will not respect aspect ratios. In case you need the mesh preserves it then you need to change this to:
scale = min((B.x-A.x)/(B0.x-A0.x)),
(B.y-A.y)/(B0.y-A0.y),
(B.z-A.z)/(B0.z-A0.z))
Vertex[i].x=(Vertex[i].x-0.5*(A0.x+B0.x))*scale+0.5*(A.x+B.x)
Vertex[i].y=(Vertex[i].y-0.5*(A0.y+B0.y))*scale+0.5*(A.y+B.y)
Vertex[i].z=(Vertex[i].z-0.5*(A0.z+B0.z))*scale+0.5*(A.z+B.z)
Hope I did not make any mistake as I derived it right in the SO/SE editor. The idea is to compute the max scale that is not exceeding new bounding box size (largest mesh axis size will fit exactly into new bounding box) and then just rescale the Mesh while center of old bounding box will be center of new bounding box too.
Some meshes also include their own transform matrices. In that case you can encode this transformation directly to this matrix leaving the vertexes as are. But usually if mesh normalization is required then it is because some Vertexes manipulation needs it and is usually better to change the vertexes ...
I have a program displaying planes of cubes, like levels in a house, I have the planes displayed so that the display angle is consistent to the viewport projection plane. I would like to be able to allow the user to select them.
First I draw them relative to each other with the first square drawn at {0,0,0}
then I translate and rotate them, each plane has it's own rotate and translate.
Thanks to this this page I have code that can cast a ray using the user's last touch. If you notice in the picture above, there is a green square and blue square, this is debug graphic displaying the ray intersecting the near and far planes in the projection matrix after clicking in the centre (with z of zero in order to display them), so it appears to be working.
I can get a bounding box of the cube, but it's coordinates will think they are still up in the left corner.
My question is how do I use my ray to check intersections with the objects after they have been rotated and translated? I'm very confused as I once had this working when I was translating and rotating the whole grid as one, now each plane is being moved separately I can't work out how to do it.
I am working on voxelisation using the rendering pipeline and now I successfully voxelise the scene using vertex+geometry+fragment shaders. Now my voxels are stored in a 3D texture which has size, for example, 128x128x128.
My original model of the scene is centered at (0,0,0) and it extends in both positive and negative axis. The texure, however, is centered at (63,63,63) in tex coordinates.
I implemented a simple ray marcing for visualizing but it doesn't take into account the camera movements (I can render only from very fixed positions because my ray have to be generated taking into account the different coordinates of the 3D texture).
My question is: how can I map my rays so that they are generated at point Po with direction D in the coordinates of my 3D model but intersect the voxels at the corresponding position in texture coordinates and every movement of the camera in the 3D world is remapped in the voxel coordinates?
Right now I generate the rays in this way:
create a quad in front of the camera at position (63,63,-20)
cast rays in direction towards (63,63,3)
I think you should store your entire view transform matrix in your shader uniform params. Then for each shader execution you can use its screen coords and view transform to compute the view ray direction for your particular pixel.
Having the ray direction and camera position you just use them the same as currently.
There's also another way to do this that you can try:
Let's say you have a cube (0,0,0)->(1,1,1) and for each corner you assign a color based on its position, like (1,0,0) is red, etc.
Now for every frame you draw your cube front faces to the texture, and cube back faces to the second texture.
In the final rendering you can use both textures to get enter and exit 3D vectors, already in the texture space, which makes your final shader much simpler.
You can read better descriptions here:
http://graphicsrunner.blogspot.com/2009/01/volume-rendering-101.html
http://web.cse.ohio-state.edu/~tong/vr/