According to my understanding, modern computer monitors mainly display images in raster ways, that is, what we see on the screen are all dots or pixels. What confused me is that we often said ray tracing is not rasterization, but no matter how the 3D world is calculated, shouldn't everything rendered in the computer be finally converted to pixels forming a raster image on the screen? Or if it is that I misunderstood some critical concepts.
As you said correctly, after the calculations, the whole scene is placed in a raster image.
Putting pixels in a raster is done after the calculation of each pixel's color.
It's the same procedure for any rendering method.
Ray tracing and rasterization are techniques for processing primitives and projecting the above mentioned calculation.
When you make a distinction between ray tracing and rasterization you ask yourself how the input (primitives, mostly triangles) gets processed.
Rasterization is part of the graphics pipeline and determines the pixels covered by a primitive.
The main goal is to convert a set of vertices into a raster image.
Rasterization is used more often because it is much faster than ray tracing.
The complexity is proportional to the number of primitives.
The image below shows the procedure of rasterizing using the top-left rule.
Ray tracing takes a different approach than rasterization.
You start by shooting rays out of an imaginary camera into the scene.
The scene is processed per pixel and not per primitive.
That means the complexity is proportional to the resolution.
The advantage is that we can simulate optical effects such as reflection, refraction and scattering.
The advantages come with the disadvantage of ray tracing being significantly slower than rasterization.
The image below shows the process of shooting rays through the image plane into the scene.
More information:
Wikipedia | Rasterisation
Wikibooks | Cg Programming/Rasterization
Wikipedia | Ray tracing (graphics)
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This is a question to understand the principles of GPU accelerated rendering of 2d vector graphics.
With Skia or Direct2D, you can draw e.g. rounded rectangles, Bezier curves, polygons, and also have some effects like blur.
Skia / Direct2D offer CPU and GPU based rendering.
For the CPU rendering, I can imagine more or less how e.g. a rounded rectangle is rendered. I have already seen a lot of different line rendering algorithms.
But for GPU, I don't have much of a clue.
Are rounded rectangles composed of triangles?
Are rounded rectangles drawn entirely by wild pixel shaders?
Are there some basic examples which could show me the basic prinicples of how such things work?
(Probably, the solution could also be found in the source code of Skia, but I fear that it would be so complex / generic that a noob like me would not understand anything.)
In case of direct2d, there is no source code, but since it uses d3d10/11 under the hood, it's easy enough to see what it does behind the scenes with Renderdoc.
Basically d2d tends to have a policy to minimize draw calls by trying to fit any geometry type into a single buffer, versus skia which has some dedicated shader sets depending on the shape type.
So for example, if you draw a bezier path, Skia will try to use tesselation shader if possible (which will need a new draw call if the previous element you were rendering was a rectangle), since you change pipeline state.
D2D, on the other side, tends to tesselate on the cpu, and push to some vertexbuffer, and switches draw call only if you change brush type (if you change from one solid color brush to another it can keep the same shaders, so it doesn't switch), or when the buffer is full, or if you switch from shape to text (since it then needs to send texture atlases).
Please note that when tessellating bezier path D2D does a very great work at making the resulting geometry non self intersecting (so alpha blending works properly even on some complex self intersecting path).
In case on rounded rectangle, it does the same, just tessellates into triangles.
This allows it to minimize draw calls to a good extent, as well as allowing anti alias on a non msaa surface (this is done at mesh level, with some small triangles with alpha). The downside of it is that it doesn't use much hardware feature, and geometry emitted can be quite high, even for seemingly simple shapes).
Since d2d prefers to use triangle strips instead or triangle list, it can do some really funny things when drawing a simple list of triangles.
For text, d2d use instancing and draws one instanced quad per character, it is also good at batching those, so if you call some draw text functions several times in a row, it will try to merge this into a single call as well.
I know that there are 4 techniques to draw 3D objects:
(1) Wireframe Modeling and rendering, (2) Additive Modeling, (3) Subtractive Modeling, (4) Splines and curves.
Then, those models go through hidden surface removal algorithm.
Am I correct?
Be that way, What formula or algorithm can I use to draw a 3D Sphere?
I am using a low-level library named WinBGIm from colorado university.
there are 4 techniques to draw 3D objects:
(1) Wireframe Modeling and rendering, (2) Additive Modeling, (3) Subtractive Modeling, (4) Splines and curves.
These are modelling techniques and not rendering techniques. They allow you to mathematically define your mesh's geometry. How you render this data on to a 2D canvas is another story.
There are two fundamental approaches to rendering 3D models on a 2D canvas.
Ray Tracing
The basic idea of ray tracing is to pass a ray from the camera's origin, through the point on the canvas whose colour needs to be determined. Determine which models get hit by it and pick the closest one, determine how it's lit to compute the colour there. This is done by further tracing rays from the hit point to all the light sources in the scene. If you notice, this approach eliminates the need to use hidden surface determination algorithms like the back face culling, z-buffer, etc. since the basic idea is rooted on a hidden surface algorithm (ray tracing).
There are packages, libraries, etc. that help you do this. However, it's common that ray tracers are written from scratch as a college-level project. However, this approach takes more time to render (not to code), but the results are generally more pleasing than the below one. This approach is more popular when you want to render non-interactive visuals like movies.
Rasterization
This approach takes primitives (triangles and quads) that define the models in the scene and sample them at regular intervals (screen pixels they cover) and write it on to a colour buffer. Here hidden surface is usually eliminated using the Z-buffer; a buffer that stores the z-order of the fragment and the closer one wins, when writing to the colour buffer.
Rasterization is the more popular approach with cheap hardware support for it available on most modern computers due to years of research and money that has gone in to it. Libraries like OpenGL and Direct3D are readily available to facilitate development. Although the results are less pleasing than ray tracing, it's faster to render and thus is widely used in interactive, real-time rendering like games.
If you want to not use those libraries, then you have to do what is commonly known as software rendering i.e. you will end up doing what these libraries do.
What formula or algorithm can I use to draw a 3D Sphere?
Depends on which one of the above you choose. If you simply rasterize a 3D sphere in 2D with orthographic projection, all you have to do is draw a circle on the canvas.
If you are looking for hidden lines removal (drawing the edges rather than the inside of the faces), the solution is easy: "back face culling".
Every edge of your model belongs to two faces. For every face you can compute the normal vector and check if it is facing to the observer (by the sign of the dot product of the normal and the direction of the projection line); in other words, if the observer is located in the outer half-space defined by the plane of the face. Then an edge is wholly visible if and only if it belongs to at least one front face.
Usual discretization of the sphere are made by drawing equidistant parallels and meridians. It may be advantageous to adjust the spacing of the parallels so that all tiles are about the same area.
I'd like to know what's reason to use Ray Marching/Ray casting over rasterization? Is it better only in specific cases?
Thanks for your answers.
Ray casting and rasterization are two totally different methods of rendering. Rasterization is designed to be very fast, and lighting is typically computed on a per-fragment basis in a fragment shader (or pixel shader). Ray casting (a type of ray tracing) actually simulates light rays in a sense, creating a more accurate render, with a much larger computation time.
The main advantage of ray tracing(in general) is in the quality of the image.ray traced image vs rasterized. Ray tracing actually simulates a ray of light from the camera through each and every pixel of your screen while also taking into effect natural phenomena like reflection and refraction while computing the final color for the pixel,whereas in rasterization the 3D objects are simple squashed onto the pixels of the screen.
Commonly, techniques such as supersampling or multisampling are used to produce high fidelity images.
I've been messing around on mobile devices with CSS3 3D lately and this trick does a fantastic job of obtaining high quality non-aliased edges on quads.
The way the trick works is that the texture for the quad gains two extra pixels in each dimension forming a transparent one-pixel-wide outline outside the border. Due to texture sampling interpolation, so long as the transformation does not put the camera too close to an edge the effect is not unlike a pre-filtered antialiased rendering approach.
What are the conceptual and technical limitations of taking this sort of approach to render a 3D model, for example?
I think I already have one point that precludes using this kind of trick in the general case. Whenever geometry is not rectangular it does nothing to reduce aliasing: The fact that the result with a transparent 1px outline border is smooth for HTML5 with CSS3 depends on those elements being rectangular so that they rasterize neatly into a pixel grid.
The trick you linked to doesn't seem to have to do with texture interpolation. The CSS added a border that is drawn as a line. The rasterizer in the browser is drawing polygons without antialiasing and is drawing lines with antialiasing.
To answer your question of why you wouldn't want to blend into transparency over a 1 pixel border is that transparency is very difficult to draw correctly and could lead to artifacts when polygons are not drawn from back to front. You either need to presort your polygons based on distance or have opaque polygons that you check occlusion of using a depth buffer and multisampling.
From the oldest games to the very modern, it seems like you can still see through walls or most often the ground in some camera positions.
Why is collision difficult to effectively compute in graphics engines?
Is it rounding/loss of precision accumulating leading to a mis-rendered view?
This is not actually collision in the explicit sense. The camera position is probably not actually "inside" the wall or the ground in those situations, but it is simply very close to it.
In computer 3D graphics the camera has a concept of a near plane and a far plane. Only geometry located between these two planes will be visible, while the rest will be clipped. If you are too close to something and align the camera correctly, then chances are that some parts of the geometry will be too close to the camera as defined by the near plane and as a result that geometry will not be rendered.
Now, the distance to this near plane can be set by the developers, and it can be set to be very short - short enough to ensure that situations like these cannot occur. However, the depth buffer or z buffer that is used to determine which objects are closest to the camera during rendering, and thus which objects to render and which not to render, is closely related to the near and far plane distances.
In graphics hardware the depth buffer is represented using a fixed amount of bits for each pixel, for example 32 bits. These 32 bits must be enough to accurately represent the entire span between the near plane and the far plane. It is also not linear, but will use more precision closer to the camera. As a result, choosing a very small near plane distance will greatly reduce the overall precision of the depth buffer. This can cause annoying flickering throughout the entire scene wherever two objects are very close to each others.
You can read more about this issue here as well as section 12.040 here.
It's not about difficulty (of course, it's not easy to compute collision/clipping of non-convex object), but you still have only like ~33ms to compute whole frame, so some compromise have to be made (collision mesh is not the same like mesh you really see). If there is no time for precise solution (to fulfill all conditions - camera distance, object which have to be seen, collision avoidance), you have to fallback to some "easy" solution like see through the wall.