This is just a general, high-level question.
In computer graphics, why is it better to use clipping instead of scan-converting each line and then activating only those pixels that are within the viewport?
Some reasons:
culling invisible (pieces of) primitives: a primitive or a part of a primitive fully outside the viewport (or behind the near plane) will not have to be rasterized at all post-clipping.
rasterization performance: with clipping, even for the pieces that are still visible, no additional visibility computation has to be done post-clipping per scanline (i.e. computing the scanline spans that are within the viewport / between the near/far planes).
accuracy: rasterization is based on interpolation with incremental computations which are more difficult/expensive to make accurate if the range of allowed input coordinates is not restricted to the viewport.
Related
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.
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)
I know the Bresenham and related algorithms, and I found a good algorithm to draw a circle with a 1-pixel wide border. Is there any 'standard' algorithm to draw a circle with an n-pixel wide border, without restoring to drawing n circles?
Drawing the pixel and n2 surrounding pixels might be a solution, but it draws many more pixels than needed.
I am writing a graphics library for an embedded system, so I am not looking for a way to do this using an existing library, although a library that does this function and is open source might be a lead.
Compute the points for a single octant for both radii at the same time and simultaneously replicate it eight ways, which is how Bresenham circles are usually drawn anyway. To avoid overdrawing (e.g., for XOR drawing), the second octant should be constrained to draw outside the first octant's x-extents.
Note that this approach breaks down if the line is very thick compared to the radius.
Treat it as a rasterization problem:
Take the bounding box of your annulus.
Consider the image rows falling in the bounding box.
For each row, compute the intersection with the 2 circles (ie solve x^2+y^2=r^2, so x=sqrt(r^2-y^2) for each, for x,y relative to the circle centres.
Fill in the spans. Repeat for next row.
This approach generalizes to all sorts of shapes, can produce sub-pixel coordinates useful for anti-aliasing and scales better with increasing resolution than hacky solutions involving multiple shifted draws.
If the sqrt looks scary for an embedded system, bear in mind there are fast approximate algorithms which would probably be good enough, especially if you're rounding off to the nearest pixel.
Does anyone know of a graphics system which handles composition of multiple anti-aliased lines well?
I'm showing a dependency diagram and have a bunch of curves emanating from a point. These are drawn anti-aliased in the usual way, of blending partially covered pixels. So if two lines would occupy the same half of a pixel, the antialiasing blends it to 75% filled rather than 50% filled. With enough lines drawn on top of each other, the pixel blend clamps and you end up with aliased lines.
I know anti-grain geometry has algorithms for calculating blends which cater for lines which abut, and that oversampling might work, but are there any other approaches?
Handling this form of line composition well is going to be slow (you have to consider all the lines that impinge upon each pixel using a deferred rendering approach). I doubt that there are many (if any) libraries out there that will do it for you.
The quickest and easiest method (and possibly the only realistic and cost effective solution for your case), which will work with virtually any drawing library would be to supersample it - draw to an offscreen bitmap at much higher resolution (e.g. 4 times wider and higher, with lines of 4 pixels width. Disable antialiasing when drawing this as it'll only slow it down) and then scale the result down with bilinear filtering. The main down-side is that it uses a lot of memory for the offscreen bitmap.
If you need an existing system that gets antialiased lines "visually correct", you might try using one of several existing RenderMan-compliant 3D renderers. The REYES algorithm, which many of these renderers use, works by breaking up primitives into micropolygons, then sampling them at several random point locations within each pixel. So even if you have a million lines collectively obscuring 50% of a pixel, the resulting image value will show roughly 50% coverage. (This is, for example, how the millions of antialiased hairs are drawn on characters in many animated movies.)
Of course, using a full-blown 3D renderer to draw 2D lines is like driving nails with a sledgehammer. You'd need a fairly pathological scenario for the 3D renderer to be any more efficient than simply supersampling with a traditional 2D renderer.
It sounds like you want a premade drawing library, which I do not know of.
However, to answer your question of knowing any approach that would work, you can consider a pixel to be a square. You can then approximate any shape that you draw as a polygon that intersects the pixel box. By clipping these polygons against the box of the pixel and against each other, you can get a very good estimate of the areas associated with each color that intersects the pixel for accurate antialiasing. This is, of course, very slow to calculate and is not suitable for interactive drawing.
An old Direct3D book says
"...you can achieve an acceptable frame
rate with hardware acceleration while
displaying between 2000 and 4000
polygons per frame..."
What is one polygon in Direct3D? Do they mean one primitive (indexed or otherwise) or one triangle?
That book means triangles. Otherwise, what if I wanted 1000-sided polygons? Could I still achieve 2000-4000 such shapes per frame?
In practice, the only thing you'll want it to be is a triangle because if a polygon is not a triangle it's generally tessellated to be one anyway. (Eg, a quad consists of two triangles, et cetera). A basic triangulation (tessellation) algorithm for that is really simple; you just loop though the vertices and turn every three vertices into a triangle.
Here, a "polygon" refers to a triangle. All . However, as you point out, there are many more variables than just the number of triangles which determine performance.
Key issues that matter are:
The format of storage (indexed or not; list, fan, or strip)
The location of storage (host-memory vertex arrays, host-memory vertex buffers, or GPU-memory vertex buffers)
The mode of rendering (is the draw primitive command issued fully from the host, or via instancing)
Triangle size
Together, those variables can create much greater than a 2x variation in performance.
Similarly, the hardware on which the application is running may vary 10x or more in performance in the real world: a GPU (or integrated graphics processor) that was low-end in 2005 will perform 10-100x slower in any meaningful metric than a current top-of-the-line GPU.
All told, any recommendation that you use 2-4000 triangles is so ridiculously outdated that it should be entirely ignored today. Even low-end hardware today can easily push 100,000 triangles in a frame under reasonable conditions. Further, most visually interesting applications today are dominated by pixel shading performance, not triangle count.
General rules of thumb for achieving good triangle throughput today:
Use [indexed] triangle (or quad) lists
Store data in GPU-memory vertex buffers
Draw large batches with each draw primitives call (thousands of primitives)
Use triangles mostly >= 16 pixels on screen
Don't use the Geometry Shader (especially for geometry amplification)
Do all of those things, and any machine today should be able to render tens or hundreds of thousands of triangles with ease.
According to this page, a polygon is n-sided in Direct3d.
In C#:
public static Mesh Polygon(
Device device,
float length,
int sides
)
As others already said, polygons here means triangles.
Main advantage of triangles is that, since 3 points define a plane, triangles are coplanar by definition. This means that every point within the triangle is exactly defined as a linear combination of polygon points. More vertices aren't necessarily coplanar, and they don't define a unique curved plane.
An advantage more in mechanical modeling than in graphics is that triangles are also undeformable.