in the example of two bezier curves with meeting endpoints, you say you have 8 vector constrains, but you only have 4 right? I mean at the very least you should be left with two vector degrees of freedom representing the base transform of the curve
in which case 2 quadratic bezier curves should be able to make a closed loop. But as you only have two degrees of freedom left, there should only be one possible such curve, up to solid transformations. But with more quadratic bezier curves you should be able to get more flexibility no? Number of d.o.f.s growing as 3N, while number of constraints growing as 2N
thank you for uploading this..am trying to build a game engine and I kinda lack in complex math in computer graphics..so this is really helpful... please do a video on sign distance fields nd functions..
In th-cam.com/video/MakhXtIX2YM/w-d-xo.html, I do not understand how the control coordinates can be degrees of freedom. I thought the purpose of the Bezier curve is to interpolate among a given set of fixed points, which define control points. So it seems that you cannot "change" where your control points go.
To find out how to make an implicit heart shape you can watch this: th-cam.com/video/aNR4n0i2ZlM/w-d-xo.html ;) (reacting to: th-cam.com/video/MakhXtIX2YM/w-d-xo.html)
Now I come back to the lecture I've left behind since this August!
Excellent lecture.
What are the branches of algebraic geometry, how do I study it
in the example of two bezier curves with meeting endpoints, you say you have 8 vector constrains, but you only have 4 right? I mean at the very least you should be left with two vector degrees of freedom representing the base transform of the curve
in which case 2 quadratic bezier curves should be able to make a closed loop. But as you only have two degrees of freedom left, there should only be one possible such curve, up to solid transformations. But with more quadratic bezier curves you should be able to get more flexibility no? Number of d.o.f.s growing as 3N, while number of constraints growing as 2N
thank you for uploading this..am trying to build a game engine and I kinda lack in complex math in computer graphics..so this is really helpful... please do a video on sign distance fields nd functions..
I don't think these things will be discussed carefully in a "Intro" level class. You should go to ShaderToy for references
In th-cam.com/video/MakhXtIX2YM/w-d-xo.html, I do not understand how the control coordinates can be degrees of freedom. I thought the purpose of the Bezier curve is to interpolate among a given set of fixed points, which define control points. So it seems that you cannot "change" where your control points go.
Isn't it the reason that we call them 'control' points because we can 'change' them?
To find out how to make an implicit heart shape you can watch this: th-cam.com/video/aNR4n0i2ZlM/w-d-xo.html ;)
(reacting to: th-cam.com/video/MakhXtIX2YM/w-d-xo.html)