If all of maths was taught this way, we'd be looking at a bright future (in terms of education).
The Continuity of Splines [video]
11–20 of 43 posts
Re: The Continuity of Splines [video]
#12this is almost a 1:1 copy of the Bezier curve video posted some months ago. how is this video getting attention? Even has the same graphics...
It's the same creator, but longer video.
I wonder if the beginning can be skipped if the first video was already seen?
Re: The Continuity of Splines [video]
#13If all of maths was taught this way, we'd be looking at a bright future (in terms of education).
I sure hope YouTube or some other similar video streaming service keeps existing far into the future.
Re: The Continuity of Splines [video]
#14I think the secret to get the C2 splines that pass through the control points right is to not just increase the degree but also add two more points, i.e. not 4 but 6 segments.
> add two more points, i.e. not 4 but 6 segments.
If I understand your suggestion correctly, I believe what this buys you is directional control of your spline at the spline endpoints and a more constant parameterization (one that doesn’t accelerate or decelerate at the spline endpoints). Perhaps the most common alternative is to insert duplicate knots at the spline endpoints, inserting as many extra knots as you need to reach the support requirements of your segment (degree minus one, right?). The problem with this is that you end up with several segments decreasing in size to zero, so the parameterization decelerates to zero. The derivatives also shrink to zero, which can cause problems depending on what you’re doing. Another common technique is to pretend the control points keep going straight after they end, meaning insert implicit ‘phantom’ control points beyond the first & last control point of a spline that matches the direction & magnitude of the first & last explicit segments. (Freya discusses this at 46 minutes into the video.) If your spline was degree 2 and starts with control point p1, then you could insert the phantom point p0 where p1-p0 = p2-p1. This gives you enough control points to evaluate the spline up to your explicit endpoint p1, but you lose a little bit of control over the tangent at the endpoint. If you wanted a different tangent than p2-p1, then you could, as you suggest, add explicit phantom control points. The continuity is the same in all three cases here, but the direction and tangent magnitude are unique to each approach with your suggestion offering the most control.
Re: The Continuity of Splines [video]
#15this is almost a 1:1 copy of the Bezier curve video posted some months ago. how is this video getting attention? Even has the same graphics...
The beginning has a recap of Bezier curves as a refresher before going into splines in more detail.
It looks similar because it's a sequel to the original video.
Re: The Continuity of Splines [video]
#16Truly a masterpiece of technical communication! Mind blowing to think about how much work went into this video.
So. Much. Work. And really well done. I loved the discussion on geometric continuity, starts at around 28 minutes in.
Re: The Continuity of Splines [video]
#17Truly a masterpiece of technical communication! Mind blowing to think about how much work went into this video.
So. Much. Work. And really well done. I loved the discussion on geometric continuity, starts at around 28 minutes in.
All very calm and cool until "it yeets off into fucking wherever" on C2 continuity. I LOLed at that.
Re: The Continuity of Splines [video]
#18I’ve been following Freya’s work [0] for a while. She works in the game industry working with Unity, hosts a bunch of Discord channels, and live streams about game math and shaders. This video is relatively long, but it’s one year in the making. If you ever wanted to understand a bit more about Béziers vs B-Splines and G2 vs C2, this is great place to start. PS. I would also highly recommend these sources which have…
As the author of [2], I strongly recommend everyone watch Freya's video summary of Bezier curves in addition to this tour de force. They're both authoritative works.
Re: The Continuity of Splines [video]
#19this is almost a 1:1 copy of the Bezier curve video posted some months ago. how is this video getting attention? Even has the same graphics...
It really isn't. It starts with Bezier curves because that's how you start a talk about splines, and then the majority of the video is new information.
Re: The Continuity of Splines [video]
#20This video is fucking amazing.