I'm trying to learn multiple importance sampling (MIS) where I need to calculate the weight of a sample based on the PDF of each sampling technique. I understand the PDF from the BRDF, and the PDF of hitting a particular spherical light based on the light's radius. But for a mesh emitter, how do I calcuate the PDF of hitting the emitter? Is it just the solid angle of the emitting triangle?
The answer depends on what type of light it is. For example a mesh that is an area light has a pdf = 1.f / Area(); where Area() is the surface area of that shape.
This is a naive implementation and to improve this, you could get the surface area of the mesh that is only visible from the point of intersection. This would mean a solid angle measurement.
For more details with implementation, refer to PBRT Chapter 14.6, "Sampling Shapes" in the 2nd edition of the book.
Related
Summary
This is a question about how to map light intensity values, as calculated in a raytracing model, to color values percieved by humans. I have built a ray tracing model, and found that including the inverse square law for calculation of light intensities produces graphical results which I believe are unintuitive. I think this is partly to do with the limited range of brightness values available with 8 bit color images, but more likely that I should not be using a linear map between light intensity and pixel color.
Background
I developed a recent interest in creating computer graphics with raytracing techniques.
A basic raytracing model might work something like this
Calculate ray vectors from the center of the camera (eye) in the direction of each screen pixel to be rendered
Perform vector collision tests with all objects in the world
If collision, make a record of the color of the object at the point where the collision occurs
Create a new vector from the collision point to the nearest light
Multiply the color of the light by the color of the object
This creates reasonable, but flat looking images, even when surface normals are included in the calculation.
Model Extensions
My interest was in trying to extend this model by including the distance into the light calculations.
If an object is lit by a light at distance d, then if the object is moved a distance 2d from the light source the illumination intensity is reduced by a factor of 4. This is the inverse square law.
It doesn't apply to all light models. (For example light arriving from an infinite distance has intensity independent of the position of an object.)
From playing around with my code I have found that this inverse square law doesn't produce the realistic lighting I was hoping for.
For example, I built some initial objects for a model of a room/scene, to test things out.
There are some objects at a distance of 3-5 from the camera.
There are walls which make a boundry for the room, and I have placed them with distance of order 10 to 100 from the camera.
There are some lights, distance of order 10 from the camera.
What I have found is this
If the boundry of the room is more than distance 10 from the camera, the color values are very dim.
If the boundry of the room is a distance 100 from the camera it is completely invisible.
This doesn't match up with what I would expect intuitively. It makes sense mathematically, as I am using a linear function to translate between color intensity and RGB pixel values.
Discussion
Moving an object from a distance 10 to a distance 100 reduces the color intensity by a factor of (100/10)^2 = 100. Since pixel RGB colors are in the range of 0 - 255, clearly a factor of 100 is significant and would explain why an object at distance 10 moved to distance 100 becomes completely invisible.
However, I suspect that the human perception of color is non-linear in some way, and I assume this is a problem which has already been solved in computer graphics. (Otherwise raytracing engines wouldn't work.)
My guess would be there is some kind of color perception function which describes how absolute light intensities should be mapped to human perception of light intensity / color.
Does anyone know anything about this problem or can point me in the right direction?
If an object is lit by a light at distance d, then if the object is moved a distance 2d from the light source the illumination intensity is reduced by a factor of 4. This is the inverse square law.
The physical quantity you're describing here is not intensity, but radiant flux. For a discussion of radiometric concepts in the context of ray tracing, see Chapter 5.4 of Physically Based Rendering.
If the boundary of the room is more than distance 10 from the camera, the color values are very dim.
If the boundary of the room is a distance 100 from the camera it is completely invisible.
The inverse square law can be a useful first approximation for point lights in a ray tracer (before more accurate lighting models are implemented). The key point is that the law - radiant flux falling off by the square of the distance - applies only to the light from the point source to a surface, not to the light that's then reflected from the surface to the camera.
In other words, moving the camera back from the scene shouldn't reduce the brightness of the objects in the rendered image; it should only reduce their size.
I aim to make an object detection model and I labelled data with a square box
If I label the images with polygon, will it be better than square?
(labelling on image of people wearing safety helmet or not)
I did try label with polygon shape on a few images and after export txt file for YOLO
why it has only 4 points in the text file as same as labelled with a square shape
how those points will represent an area that I label accurately?
1 0.573748 0.018953 0.045332 0.036101
1 0.944520 0.098375 0.108931 0.167870
You have labeled your object in a polygonial format, but when you had made a conversion to YOLO-format the information in the labelings has reduced. The picture below shows how I suppose has happend;
...where you have done polygon shape annotation (black shape). But, the conversion has "searched" the smallest x-value from the polygonial coordinate points and smallest y-value from corresponding polygonial coordinate points. And, those are the "first two" values of your YOLO-format. The same logic has happend with the "width" and "heigth" -parameters.
A good description about the idea behind the labelling and dataset is shown in https://www.youtube.com/watch?v=h6s61a_pqfM.
In short; for your purpose (for efficiency) I propose you make fast & convenient annotation using rectangles only - no time consuming polygon annotation.
The YOLO you are using very likely only has square annotation support.
See this video showing square vs polygon quality of results for detection, and the problem of annotation time required to create custom data sets.
To use polygonal masks can I suggest switching to use YOLOv3-Polygon or YOLOv5-Polygon
I have a 3D shape (primitive shapes like cuboid, sphere, pyramid etc.). The shape is described by a set of necessary geometric parameters. For example, for a cube, I have information about the vertices, dimensions and orientation of the cube. Now, I have a voxel (kind of 3D grid of pixels). How can I determine which cells of the voxel needs to be filled and which will remain empty for "rendering" the cube in 3D?
Are there existing libraries for the same? Or, can someone point out the approach/algorithm that would help in this task? Also, what is this process exactly called, so that I can search on the Internet in the right direction?
It is called "Mesh to Voxel conversion" or "Mesh voxelization" or to be a bit more general "Volume Visualization".
If you are interested in math here is some good articles about it:
cs.swansea.ac.uk/~csmark/PDFS/cgfvoxel.pdf
Complete Polygonal Scene Voxelization
Ray Cast Methods
A bit of background
I am writing a simple ray tracer in C++. I have most of the core complete but don't understand how to retrieve the world coordinate of a pixel on the image plane. I need this location so that I can cast the ray into the world.
Currently I have a Camera with a position(aka my perspective reference point), a direction (vector) which is not normalized. The directions length signifies the center of the image plane and which way the camera is facing.
There are other values associated with the camera but they should not be relevant.
My image coordinates will range from -1 to 1 and the perspective(focal length), will change based on the distance of the direction associated with the camera.
What I need help with
I need to go from pixel coordinates (say [0, 256] in an image 256 pixels on each side) to my world coordinates.
I will also want to program this so that no matter where the camera is placed and where it is directed, that I can find the pixel in the world coordinates. (Currently the camera will almost always be centered at the origin and will look down the negative z axis. I would like to program this with the future changes in mind.) It is also important to know if this code should be pushed down into my threaded code as well. Otherwise it will be calculated by the main thread and then the ray will be used in the threaded code.
(source: in.tum.de)
I did not make this image and it is only there to give an idea of what I need.
Please leave comments if you need any additional info. Otherwise I would like a simple theory/code example of what to do.
Basically you have to do the inverse process of V * MVP which transforms the point to unit cube dimensions. Look at the following urls for programming help
http://nehe.gamedev.net/article/using_gluunproject/16013/ https://sites.google.com/site/vamsikrishnav/gluunproject
I'm using DirectX10 to simulate a water surface, and I'm now with a height map,which is a 2D array of the heights(y) at the points (x,z). But to draw it on the screen, I must turn it into a mesh or have a index to draw triangle topology.
But the data is too large to do it manually. Are there any methods for me to draw it on the screen. I hope it's easy to implement. If there is function included in DirectX10 which can make it, the it's the best one for me.
Create a mesh that format a grid of squares (each made of two triangles) and set all vertices y = 0. In the vertex shader sample the heightmap and add the value stored in the heightmap to the y of the vertice.
This might help you.
P.S: If the area you want it to cover is too big you should take a look at terrain LOD techniques (should work the same for water).
I'm sure you can make a mesh out of it. I doubt you can generate the heightmap for a water surface that is too large to "meshify".
Why are you looking at Diamond square. For a 512x512 heightmap all you need to do is define a set of point and then generate the triangles for it. Its really very simple.