This is one of the best if not the best computer graphics course on TH-cam. Prof. Ken Joy really makes complex concepts simple. I've been doing OpenGL game/simulation and many things fall into places after watching this video series. Thank you so much for putting it out.
I think there is a mistake. At 44:30, he says in the case that j > 0, P_i^j = (1-t)P_i^(j-1) + tP_(i-1)^(j-1). By his previous example, when he expanded P_2^2 he said it was equal to (1-t)P_1^1 + tP_2^1 which doesn't follow the rule he stated here. I think it should say P_i^j = (1-t)P_(i-1)^(j-1) + tP_i^(j-1) in this case.
@44:06 I believe the respective subscripts i and i-1 are in the wrong order according to the notation he established earlier it should be p_i-1 and p_i
I think I have some fundamental holes in my understanding. Why do need to get an equation of the curve we want to draw? Does this have something to do with how the computer draws programatically? Or did he derive this out of curiosity? Previously I thought we would give the computer just a few lines like at 8:00 and then the computer works to make a curve out of it by basically adding more points. But I got lost at around 28:00 when he was trying to get an equation for the curve (or at least that's what I think he's doing). Can someone enlighten me?
How would the computer know where to add the points? A parametric equation is super useful because u can define the perfect spacing and LOD for the vertices you generate since you are only varying t and the equation of the line figure out the actual shape to be drawing
You are right, he is only very briefly covering why you would want the curve equation in the first place. My answer would be: Because otherwise you would have to save the curve as pixels laying on the curve. If you want to zoom in or rotate, you would enlarge these pixels and have to translate them on ur screen. The parametric curve however can grab for you any point on the curve in a scale and rotation of your chosing. Besides solving the scaling problem, its a bit of a trade-off between memory space and calculating time when chosing how to display a line on the screen. Even if you have no intuition for the math behind it or designing car pieces or other engineering disciplines, the issue is immediately clear, when you want to use a drawing as a magazine graphic. You can't just enlarge pixel-art and expect it to look good on a high dpi print. The human eye will see pixels and attempts to smooth the pixel remnants will look less crisp and sort of sloppy. So either you decide to recreate the digital art on a digital canvas large enough to have small enough pixels for the printout, or you display the lineart by parametric curves to get the scaling done.
Confusion in Algo at 17:40 , we are here to draw the curve , we select points on the curve, now on the next step is to draw tangents. but how can we draw tangents by using points only??
This reminds me of Zeno's Dichotomy paradox... en.wikipedia.org/wiki/Zeno%27s_paradoxes#Dichotomy_paradox ...as well as of the concept of a limit encountered in Calculus.
It is incredible to access this material free of charge.
Problem Statement- 5:10
Chaikin Algorithm- 7:08 by George Chaikin
Bezier Algorithm(Geometric)- 25:05
Bezier Algorithm(Mathematical)- 32:05
15:30 - 17:20 Utah graduates
@@gordonlim2322 😂
instaBlaster...
This is one of the best if not the best computer graphics course on TH-cam. Prof. Ken Joy really makes complex concepts simple. I've been doing OpenGL game/simulation and many things fall into places after watching this video series. Thank you so much for putting it out.
Your patience with the chalk is admirable.
Ken Joy: Destroyer Of Chalk
University management have been saving (shaving) on chalks!
Virgin Ken Joy vs. Chad Walter Lewins
If you apply relaxation to those point with a given radius, you can get a nice diffrential grow effect ❤
Thank you for great lecture ~ 감사합니다
I think there is a mistake. At 44:30, he says in the case that j > 0, P_i^j = (1-t)P_i^(j-1) + tP_(i-1)^(j-1). By his previous example, when he expanded P_2^2 he said it was equal to (1-t)P_1^1 + tP_2^1 which doesn't follow the rule he stated here. I think it should say P_i^j = (1-t)P_(i-1)^(j-1) + tP_i^(j-1) in this case.
You are correct. He made a mistake.
How does Bezier's curve relate to Chaikin's curve?
Thank you, I love that
@44:06 I believe the respective subscripts i and i-1 are in the wrong order according to the notation he established earlier it should be p_i-1 and p_i
Thank you! Best explanation out there!
Great course😘
I think I have some fundamental holes in my understanding. Why do need to get an equation of the curve we want to draw? Does this have something to do with how the computer draws programatically? Or did he derive this out of curiosity? Previously I thought we would give the computer just a few lines like at 8:00 and then the computer works to make a curve out of it by basically adding more points. But I got lost at around 28:00 when he was trying to get an equation for the curve (or at least that's what I think he's doing). Can someone enlighten me?
How would the computer know where to add the points? A parametric equation is super useful because u can define the perfect spacing and LOD for the vertices you generate since you are only varying t and the equation of the line figure out the actual shape to be drawing
You are right, he is only very briefly covering why you would want the curve equation in the first place.
My answer would be: Because otherwise you would have to save the curve as pixels laying on the curve. If you want to zoom in or rotate, you would enlarge these pixels and have to translate them on ur screen. The parametric curve however can grab for you any point on the curve in a scale and rotation of your chosing. Besides solving the scaling problem, its a bit of a trade-off between memory space and calculating time when chosing how to display a line on the screen.
Even if you have no intuition for the math behind it or designing car pieces or other engineering disciplines, the issue is immediately clear, when you want to use a drawing as a magazine graphic. You can't just enlarge pixel-art and expect it to look good on a high dpi print. The human eye will see pixels and attempts to smooth the pixel remnants will look less crisp and sort of sloppy. So either you decide to recreate the digital art on a digital canvas large enough to have small enough pixels for the printout, or you display the lineart by parametric curves to get the scaling done.
where is the auto-titles? I lost them : (
Confusion in Algo at 17:40 ,
we are here to draw the curve , we select points on the curve, now on the next step is to draw tangents. but how can we draw tangents by using points only??
I believe we should manually find out the Chaikin's points from an image. Then draw it using a program utilizing the algorithm.
What topic should be checked in the library to read further
does anyone know where to get the homework files? I could not get through the the link on the first video
+Tesla Vortex graphics.cs.ucdavis.edu/~joy/ecs175/
Thanks dude!
thank you, cheers!!!
the website is not working anymore ?
为啥没有字母了呀
anyone know full course videos
Great lecture
Very nice
This reminds me of Zeno's Dichotomy paradox...
en.wikipedia.org/wiki/Zeno%27s_paradoxes#Dichotomy_paradox
...as well as of the concept of a limit encountered in Calculus.
As a non english speaker, subtitle please!
The curve of 1.618 , As in the curve of space and time.
Try that one!!! It's real and also a Cosmic constant...
"He's the only person on the planet that we know of to have started 3 billion dollar companies"
Elon Musk: *_hold my rocket_*
Bezier died in 1999
They couldn't afford coloured chalk. 🙁
drinking game: take a shot every time he says "okay?"
😞