Відео

What a load of BS! 🎉

I like the video but it’s kinda strange when you choose to through all those steps with showing the binomials and taking 10 seconds just to get from 2x + 1 + y + y to 2(x + y) + 1 and then not explain the filling of the circle to the audience.

i got to know about the trailing one thing and the infinity and nan thing only. well i had studied this topic before. and yes this is a good guide.

im making a graphics library rn your videos really help

Amazing video. One tip though when explaining math... use allot of pauses to allow the words to transform from noise to comprehension in our minds. For example at this point: ua-cam.com/video/f3Rs20k-hcI/v-deo.html when you say "the change in y" add a pause and then continue to say "for one step in x". These two pieces of information are seperate and have different meaning. Allow your listeners and viewers a chance to recognise the distinct meaning of each piece of information your conveying.

0:15 is this really "perfectly anti-aliased" line? It seems like a good approximation. Perfectly anti-aliased should calculate orthogonal distance to the line, and not just delta X or Y. This requires more compute power

Why did you build that circle?

Why not multiply every term by 4 to get p = 1 - 4r? Multiplication by 4 is quite cheap.

Still waiting for the Digital Differential Analyzer, or DDA, it could also be used with floats. It's most popular application would be in psuedo 3D, raycasting, present in Wolfenstein 3D and other games when they weren't powerful enough to render true 3D

I think there is something wrong with the opacity and blending, causing dark spots on the line. the alpha should be A^(1/2.2) (or 1-(1-A)^2.2 idk), where A is the original alpha from 0 to 1.

this method uses approximate distances from the lune to rhe center of the pixel. There's going to be less distortion for a line that is nearly zero slipe compared to a line that is nearly diagonal. I wonder how better it would look to do a proper perpendicular distance from the line to the center point of the cell.

This channel has so much potential!! Amazing ❤️

There is also the probably more efficient DDA algorithm. It also uses floating point arithmetic. DDA stands for "digital differencial analyzer". The derivatives are predetermined. Add the correct slope/derivative to get to the next integer pixel. The difference to Xiaolin Wu is, only the pixels the line goes through are considered/affected.

I think the reason this line looks pretty mediocre is that you are assigning color values in the sRGB colorspace, which is *not linear*. If you redid the code using a linear color space (linear RGB would probably be fine here), I think it would look much better. Wikipedia has very good pages talking about this, you can also search for "converting to and from linear RGB".

fantastic series <3

Love it!

There are two debatable assumptions here: first, that Bresenham looks worse than Xiaolin Wu (in my opinion Bresenham looks better); and more importantly, that it is worthwhile to draw single-pixel-wide lines. With modern displays having three or four hundred dots per inch, you can’t see a line one pixel wide. A better approach is to draw lines that have a zero-width centre line and a non-zero width, by stroking a path using a circular or sometimes non-circular pen. Graphics systems compute the envelope of the line, which is the Minkowski sum of the pen and the zero-width line, and then fill it using a suitable anti-aliasing system.

Are you using something/some program to represent those pixels or are they just edited in?

I'd really appreciate a video on AA lines with thickness

Hello!

amazing, hidden gem

olm kanalını daha bugün gördüm ne kadar az video var diye üzüldüm ya allahu teala sesimi duymuş demek ki

Ok now this is some timing. I was watching your video on Bresenham per a friend's recommendation and now that I'm trying to understand Xaiolin Wu you post a video on it.

5:03 I implemented the 2 last algorithms in assembly (TASM 8086x) for fun (the version that was used for doom), I was so happy when I realized you have created another video, but man there is not chance I'm doing this under the conditions of ASSEMBLY. on another note... I absolutely LOVE your videos, keep them up! I've not seen a better explanation of those algorithms anywhere, and your videos made my day!

Can we improve this algorithm to work only with integers?

Can't wait for the next videos of this series!

I had no idea how UTF-8 worked for years and in one minute I got a sense of how it worked. Great job with the video

i think you explain that "Bresenham's line algorithm"

Whoever made this algorithm is a genius for me

16:09 dx needs to be positive for the range(dx+1) to work, but y, and thus m, being negative doesn't hurt the algorithm. Because the signs are inter-related, there are only 4 combinations, not 8. dx being negative is solved by simply swapping the points. With that simple change, you've already covered the left and right quadrants. 8:15 Had you simplified at 7:49 *before* substituting the definition of py, the doubling would ha been much simpler to handle. 10:26 pInitial, being an initial value, should have been set *before* the for loop, not in it. 12:12 When simplifying, you missed (i+1-i) becoming just 1. Likewise, I would have made (yNext-y) into (y+yP-y) [where yP is 0 or 1, indicating the increment in y], which simplifies to just yP. 14:10 Now here it's true that the algorithm assumes positive m. I suspect you were anticipating this when you claimed the floating point version couldn't handle negative m.

Optical instructions exist for monitors and tv. For example, Sonic Master System gameplay last level instructs the computer to speed up the fan, to prevent overheating. Just by watching the video, the level turns on the S5 power mode, when watching videos, the phone will be cold, and was hot before.

Could you please explain the algorithm for constructing a line with antialiasing?

I dont see where is use p to draw

-> Lowercase char |= 32

Why not just put drawline(y0, x0, y1, x1) instead of copy the entire function and swap x and y?

linear interpolation

how add "stroke" to that?=)

this is something intuitive that i was able to implement it in desmos in about two minutes

years ago I have implemented this algorithm on ZX Spectrum in Z80 assembly, using only integers and with no multiplications. Boy, that was fast

I interviewed at IMVU back in... God, 2010? And the tech part of the interview was just "derive this algorithm". It was a lot of fun, but this video really would have helped!

Since python has many version. It's a WARNING/ CRITICAL to do graphical computer science or low programming in python.

It can easily be generalized to line for zero-level set coverage finding

I wrote an assembly version of the algo for some Amiga demos back in the days. Used it to draw vector graphics.

At first I didn’t like you showing the steps to shorten the equation… but, I then realized it actually answered my usual question when viewing these equations which is “why are there hardcoded numbers?!”, this is great! Thank you!

u can just solve y++, not x++, it is just 3 step.

8:25 or you could change the > into >=, removing that slight difference. This is what I thought you were gonna do all along. Since yMid is always a half integer, and x is always an integer, the sum of their squares is always 1/4 greater than an integer. So if k+1/4>r², and both k and r² are integers, that's the same as saying k>=r².

With a few modifications, you can also draw ellipses using the same general approach. It's important to mention, because in many cases the aspect ratio of the pixels is not 1:1, so your "circle" is actually drawn as an ellipse anyway.

Cringing hard at the camelCase in Python code 😖😛 Awesome vid though, always love seeing more CS content!

this is great, thank you! a thick line modification of this or line algorithm would be great too

Can you please continue this with the ellipse drawing algorithm