Great explanation, thank you. I really appreciated the pictorial representation of the formula changing as the value of t changes - gave me a really helpful insight.
So helpful! I was doing a deep dive to figure out the Bézier curves in a drawing program (and why the control points/curves don't do what I want/expect them to do). This helped immensely!
Hello and thank you very much for your comment! That's exactly what I aimed to do, and I'm so very happy to hear I've achieved it =) Very happy to have been of help!
+Simon Lam Hmmm... I'm gonna need a bit more information about what exactly you're trying to achieve! For a bezier curve of degree n, groups of (n+1) points come together to form the "outer shell" of one curve, as demonstrated in the video. If you want to have a spline (ie. Multiple bezier curves stuck together), the last point and first point of two adjacent curves should coincide.
I think i have the idea but not sure is it correct. Please correct me thanks.. The last point of one curve and the first point of the second curve is the mid point from the adjacent point.
+Simon Lam Hmmm... I'm not really sure what you're saying I'm afraid. Sorry. Here, have a diagram: www.dropbox.com/s/5bnpp6s8gt7yz8v/bezier%20midpoint.jpg?dl=0 The last control point of the red curve segment and the first control point of the green curve segment must share the same location. Since a bezier curve goes through its first and last point, that shared point should appear on the curve. However, it does not have to be the midpoint of anything, as each individual curve can be of arbitrary length.
I think I'd like the the cubic bezier best honestly. Its the easiest for my brain to wrap around when editing.... but then you showed me that thing at the end so Ill stick with what premiere pro gives me! Thanks!
Hi, Your video and explanation was very clear, even explaining the Bezier curve equation. That was fun how your explanation was on par with animated graphics. Thank you very much!
+Anisha Roy You're welcome! Glad you liked the video =) Unfortunately it's not very likely for me to explore other curve types due to my own lack of familiarity with them. But I'll look them over and see what I can do.
You're welcome! Very happy to be of help! My channel is at th-cam.com/users/lcc0612, I have over 700 videos now, I'm sure you can find other things that interest you!
we just started doing motion of bars/cams that are moving with endpoints attached to collars on control rods. When we got to discussing the instantaneous center method for calculating the velocity vectors of the collars and the angular velocities/accelerations of the cams, I got curious if anything described the path of the collars in a more interesting way. damned if that's not a bezier curve IRL!
+onlyAerik Thanks for sharing! I can't say I've heard of that, but that sounds interesting! It would be cool to be able to model a real life problem with Bezier curves!
Also I hear that bezier curves were invented just for car design. Imagine some of those "incorrectly" sharp points and abruptly straight edges were actually placed carefully in the design of a car. Like where the trunk lid closes. Or the engine hood. Seams like bezier curves are useful for placing flush seams, and as few seams as possible in sheet metal construction.
+onlyAerik Very interesting, I have to look deeper into this in the future when I have more time. And, while I'm not sure if Bezier curves were specifically invented _for_ car design, its use _in_ car design is a classic application. C1 and higher level continuities are used to ensure "smooth surfaces" for good aerodynamics.
Hello and thank you very much for your comment! I wouldn't worry too much about the dislikes, at the end of the day what's the most important is I'm doing what I love and people are benefiting =)
Hello and thank you for your comment! Unfortunately, the definition is quite technical so I'll point you to an external source: www-isl.ece.arizona.edu/ACIS-docs/HTM/DATA/ACIS/FCG/03MATH/0003.HTM
Great video for fundemental understanding. I have one question. Why do some implementations of Bezier curve alghorithm use combination (nCk) in the formula before (1-t)?
Hello and thank you for your comment! You should be seeing derivatives of the bezier curve function, the coefficients are sometimes expressed as combinations.
@@NERDfirst Hell yeah. I just haven't noticed that 2 is made from the combination. So in fact, there is 2C2, 2C1 and 2C0 before these multiplications in the equation, right? Thanks a lot.
MisterMumkin Sorry about that! From time to time I fall into a rut of continuously reusing one particular word. I've even changed the words on several occasions =P Glad you found the video useful anyway!
Hello and thank you for your comment! The handwriting was done in Windows Journal and screencaptured with CamStudio. I used a Wacom graphics tablet for the handwriting.
Love the demonstration :) I have one question if you wouldn't mind helping me. How do I calculate the 'n of segments for a given bezier to draw in order for it to appear smooth when rasterized? I was thinking the number of segments would be equal to the arc-length? If so, is there a standard formula to calculate this for cubic bezier curves? Thank-you!
+Mr.Kian Hello and thank you very much for your comment! That is a very interesting problem - I searched around and as far as I can see, there doesn't seem to be any cut-and-dried solution to compute an "ideal" number of segments. You are very likely right in approaching this from the point of view of arc length. I have found some pretty scary looking math here for that: math.stackexchange.com/questions/12186/arc-length-of-b%C3%A9zier-curves However, I wonder if you really need to calculate things this precisely to achieve what you want. I believe a high-resolution approximation would suffice, and there probably isn't a need to compute one segment for every pixel onscreen. Here's a suggestion - Perhaps try using the euclidean distance between two control points to decide how much resolution you want that segment of the curve to have. I think that would be a pretty decent heuristic, since the distance between the two control points generally corresponds to the arc length.
+lcc0612 I'm sorry for the delay in response! I read your comment a few days ago, but I didn't want to reply immediately before I had a go at implementing a solution. I didn't even realize the interpolated points along a bezier weren't equidistant, so even if I was to generate a pixel at every point along the arclegnth, it wouldn't guarantee continuity. I decided to adopt your idea of just using a high-res approximation. For computing the equidistant points (something I needed for my purposes), I used that high-res approximation and used a binary search for each equal-length point to find the closest interpolated bezier point. So, all points are (more or less) equidistant. I uploaded a video of what I did with this :) I made an editor similar to yours, and used the equidistant plotting to overlay textures that point along the normal of each generated line. Thanks again for continuing to make inspiring videos! Love them!
+Mr.Kian Hello again! That sounds great, congrats on the progress you've made =) I've seen your video and I think I understand what you've been trying to do now. Sounds fun! Really happy to know my work has been an inspiration. It's an honor =)
Great video, helped me understand a lot, although at the end when you said the 2 control points have to move in relation to eachother for the curve to appear smooth, wouldn't it also work to use the control point before the last one of your 1ste curv as the start of the 2nd curve, and the last point of the 1ste curve as the 2nd point of the 2nd curve?
Hello and thank you for your comment! In fact, that's how it's usually done! Rather than putting two points at the same position, we just use the one point for both curves.
@@NERDfirst Maybe you can elaborate on the parametric and geometric continuity, how it affects the smoothness of the curves etc etc Yeah would love to hear how you would explain it! :))
If you have the curve drawn, know the start and end points (and any points in between), is there any way to get the corresponding control points from that?
+Thomas Johnsen Ulland (Butz) Hello and thank you for your comment! While intuitively, it seems possible by "reverse engineering" the math, it seems rather involved when I actually tried to work it out. We know the start and end points of the curve, which allows us to figure out the first and last control point for each segment. Substituting these known values into the Bezier curve equation of appropriate degree eliminates two variables, so the remaining unknowns are t, and the in-between control points. (eg. For the cubic curve, you are left with t, P1 and P2). If we know what value of t corresponds to what position on the curve, then it's easy - It's just simultaneous equations, which we can create as many as we need to solve for all the in-between control points. If the ts are unknown though, that would be harder, and I gotta confess I haven't quite figured it out. It's not simultaneous equations anymore, since each equation you introduce, you also introduce one extra variable (another unknown t).
Hello and thank you for your comment! That version of the equation happens to be listed on Wikipedia under the "Explicit Representation" section: en.wikipedia.org/wiki/Bézier_curve#Explicit_definition
Hello and thank you for your comment! I'm sorry I don't speak Arabic, but Google Translate has given me a pretty good idea of your question. I can only respond in English I'm afraid! There are two ways to get a curve with 5 points. You can either use a more complex equation (to the 5th order), or connect multiple curves of a lower order. The equation for the 5th order can be seen here. You will also find the explicit definition that allows you to generate a curve of any order: en.wikipedia.org/wiki/B%C3%A9zier_curve#Explicit_definition
Hello and thank you for your comment! The "whiteboard" sections are done in Windows Journal and captured with CamStudio. The parts in which I click around on an interactive Bezier curve comes from a homemade Java program.
Kavya Kishan Unfortunately I don't think I really know enough on the topic to do that... I'll do some further research (after my exams are over) and we'll see!
![[MV] A leap of faith...ความเชื่อใจครั้งสุดท้าย (From "Petrichor the series")](http://i.ytimg.com/vi/U1piZH2CNXA/mqdefault.jpg)
The best bezier curve explanation so far. Thanks!
Dzintars Klušs You're welcome! Very happy to be of help =)
Wonderful visualisation of how bezier curves are generated! It was the first result when searching for "bezier curve" and it did not disappoint!
Hello and thank you very much for your comment! Glad you found the video useful :)
Thank you so much! After 4 years of engineering I actually understood what Bezier curve is!!
You're welcome! Very happy to be of help =)
Thanks for the simple explanation. I appreciate the basic explanation without too much jargon. The math equations (and color coding) helped.
+Vee Cel You're welcome! Happy to be of help =)
Great explanation, thank you. I really appreciated the pictorial representation of the formula changing as the value of t changes - gave me a really helpful insight.
Hello and thank you very much for your comment! Glad you found the video useful :)
The best explanation of Bezier curve ever. You are awesome man. than you a lot
You're welcome! Very happy to be of help!
That was a hell of an explanation. Thanks. It will help me with my exam.
So helpful! I was doing a deep dive to figure out the Bézier curves in a drawing program (and why the control points/curves don't do what I want/expect them to do). This helped immensely!
Hello and thank you very much for your comment! Very happy to be of help =)
Excellent presentation of the Bezier curve. Definitelly better than my university professor
Thank you very much! Glad to be of help :)
Just finished the video.
Hey, that was great. Not too fast like some other amateur lecturers, and your animations were clear and powerful.
+onlyAerik Thank you very much! Glad you liked the presentation style =)
Very well explained, Thank you very much !!
damn you explained it very nicely and brief too. mostly youtubers just jump in the math without explain the main concept. thanks buddy
Hello and thank you very much for your comment! That's exactly what I aimed to do, and I'm so very happy to hear I've achieved it =) Very happy to have been of help!
this is really insightful. I enjoyed every bit of the lecture!
0612 tv.
Hello and thank you very much for your comment! Glad you liked the video =)
please keep making such videos.......!!!! dont stop.....it will benefit a lot of people...!!!!
Thank you very much, I certainly will =)
Great explanation for programmers who might be into graphics more than maths.
+stuaxo Thank you very much! Glad you found the video useful =)
+lcc0612 Can you tell me what can i do with multiple points.
+Simon Lam Hmmm... I'm gonna need a bit more information about what exactly you're trying to achieve!
For a bezier curve of degree n, groups of (n+1) points come together to form the "outer shell" of one curve, as demonstrated in the video. If you want to have a spline (ie. Multiple bezier curves stuck together), the last point and first point of two adjacent curves should coincide.
I think i have the idea but not sure is it correct. Please correct me thanks.. The last point of one curve and the first point of the second curve is the mid point from the adjacent point.
+Simon Lam Hmmm... I'm not really sure what you're saying I'm afraid. Sorry.
Here, have a diagram: www.dropbox.com/s/5bnpp6s8gt7yz8v/bezier%20midpoint.jpg?dl=0
The last control point of the red curve segment and the first control point of the green curve segment must share the same location. Since a bezier curve goes through its first and last point, that shared point should appear on the curve. However, it does not have to be the midpoint of anything, as each individual curve can be of arbitrary length.
I think I'd like the the cubic bezier best honestly. Its the easiest for my brain to wrap around when editing.... but then you showed me that thing at the end so Ill stick with what premiere pro gives me! Thanks!
Hello and thank you for your comment! Yeah for sure, this is more of just an insight into a commonly available tool.
Loved it, Made to much sense & easy to digest. I am immensely grateful. Thank you!
You're welcome! Very happy to be of help =)
This is the best explaination out of the other 4 videos that I just watched. Thanks
You're welcome! Very happy to be of help =)
That was great. I didn't even know what a bezier curve was. I was just trying to understand my Pages settings. Thanks.
You're welcome! Very happy to be of help =)
Excellent explanation! Thanks for the incite.
+GurnBograt1986 You're welcome! Happy to be of help =)
Thanks! Was hoping you'd get into the math a bit more though.
Hello and thank you very much for your comment! I'm sorry the math was lacking! Are there any points you'd like me to clarify here?
lcc0612 No, thank you though! :)
Great explanation, bro. Thanks for sharing.
+Awab elmahe You're welcome! Very happy to be of help :)
Hi, Your video and explanation was very clear, even explaining the Bezier curve equation. That was fun how your explanation was on par with animated graphics. Thank you very much!
Hello and thank you very much for your comment! Glad you liked the video =)
Thanks for explaining this in a way a non-math person can understand!!!
You're welcome! That's exactly what I was aiming for :) Glad to be of help!
Crystal clear explanation. Thanks.
You're welcome! Very happy to be of help :)
the equation for quadratic are basically in the form (a+b)^2=a^2+2ab+b^2 and the one for cubic is (a+b)^3=a^3+3a^2b+3ab^2+b^3...easy to remember
Thank you for sharing =) Personally I advocate looking it up wherever possible, no need to unnecessarily memorize.
Nice formatting! Educational, too!
Unclewich Thank you very much! Glad you liked the video =)
Thank you! Absolutely the best explanation I've ever seen.
You're welcome! Very happy to be of help :)
great video! simple, clear and very complete. keep it up!
Thank you very much! Glad you liked the video =)
Very clear. Excellent animation.
Thank you! Glad you found the video useful =)
i really got the beasic concept so easily before my graphics bezier presentation... thank u so much it will helpme alot.. :)
+Komal Kotak You're welcome! Very happy to be of help, and all the best for your presentation!
thank you so much it really cleared my concepts i would look forward for more videos on splines and bezier-spline curves .....
+Anisha Roy You're welcome! Glad you liked the video =) Unfortunately it's not very likely for me to explore other curve types due to my own lack of familiarity with them. But I'll look them over and see what I can do.
Thanks for your explanation. I am enlightened.
You're welcome! Very happy to be of help =)
It was very helpful.I understood how bezier curve works. Thank you.
+Andrew Johny You're welcome =) Happy to be of help!
Best Bezier curve explanation video I have ever seen. Thank u very much for the video, Pls give me the link of more videos u made.
You're welcome! Very happy to be of help!
My channel is at th-cam.com/users/lcc0612, I have over 700 videos now, I'm sure you can find other things that interest you!
we just started doing motion of bars/cams that are moving with endpoints attached to collars on control rods. When we got to discussing the instantaneous center method for calculating the velocity vectors of the collars and the angular velocities/accelerations of the cams, I got curious if anything described the path of the collars in a more interesting way.
damned if that's not a bezier curve IRL!
+onlyAerik Thanks for sharing! I can't say I've heard of that, but that sounds interesting! It would be cool to be able to model a real life problem with Bezier curves!
Also I hear that bezier curves were invented just for car design.
Imagine some of those "incorrectly" sharp points and abruptly straight edges were actually placed carefully in the design of a car. Like where the trunk lid closes. Or the engine hood.
Seams like bezier curves are useful for placing flush seams, and as few seams as possible in sheet metal construction.
+onlyAerik Very interesting, I have to look deeper into this in the future when I have more time.
And, while I'm not sure if Bezier curves were specifically invented _for_ car design, its use _in_ car design is a classic application. C1 and higher level continuities are used to ensure "smooth surfaces" for good aerodynamics.
best explanation so far, thanks
You're welcome! Very happy to be of help =)
thanks for simple explanation of bezier curve..
You're welcome! Glad you found the video useful =)
It was really helpful for me. Thanks
You're welcome! Very happy to be of help =)
REALLY APPRECIATE THE EXPLANATION ITS WAS EXCELLENT !!
Thank you very much! Glad you found the video useful :)
Thanks - really helpful. Liked the writing animation style too.
You're welcome! Very happy to be of help =)
Awesome explanation, thanks so much
droodftw123 You're welcome! Very happy to be of help =)
Fantastic explanation, thank you!
You're welcome! Very happy to be of help =)
your explanation is great!!
Thankyou very much :)
You're welcome! Very happy to be of help =)
Nicely explained. Kudos!!
Akshay Karwal Cheers! Very happy to be of help =)
Great explination, many thanks!
You're welcome! Very happy to be of help :)
The first e in Bézier is prononunced like the first e in Wednesday. Good clear tutorial, thankyou.
Hello and thank you very much for your comment! Thanks for the tip, and glad you liked my work!
Great explanation:) Why do people downvote this video???
Hello and thank you very much for your comment! I wouldn't worry too much about the dislikes, at the end of the day what's the most important is I'm doing what I love and people are benefiting =)
Excellent, thank you!
You're welcome! Glad you liked the video :)
thank you. i’m in graphic design class and came here out of boredom
Thank you so much...clear and to the point
+Nivida Kadam You're welcome! Very happy to be of help =)
Really well explained. Thanks!
husticik You're welcome! Very happy to be of help!
Cool and instructive !
Thank you very much! Glad you found the video helpful =)
Thanks, i'm not going to fail my exams, it's so clear now
You're welcome! Very happy to be of help, and all the best for your exams =)
This is so concise and helpful! Thank you so much
You're welcome! Very happy to be of help =)
Thank you for the video!, can you explain the difference between C1 or C2 continuity?
Hello and thank you for your comment! Unfortunately, the definition is quite technical so I'll point you to an external source: www-isl.ece.arizona.edu/ACIS-docs/HTM/DATA/ACIS/FCG/03MATH/0003.HTM
This is pretty informative video. Thanks dude!
You're welcome! Glad to be of help =)
Thank you very much! It was very enlightening!
***** You're welcome! Very happy to be of help =)
Great explanation . Thank you ^_^
You're welcome! Happy to be of help =)
Wow, really cool, thank you so might for your time !!!
You're welcome! Very happy to be of help =)
Yes, this is what i needed, thanks!
You're welcome! Glad to be of help =)
That was really helpful. Thanks.
You're welcome! Happy to be of help =)
wonderful explanation...
+cinu skaria Hello and thank you very much for your comment! Happy to be of help =)
Great explanation!
Thank you very much! Happy to be of help =)
very nicely explained.
+Tapasya Kala Hello and thank you very much for your comment! Very happy to be of help =)
awesome explanation great video thanks
Hello and thank you for your comment! Glad to be of help =)
Awesome, thank you!
You're welcome! Glad to be of help =)
Great video for fundemental understanding. I have one question. Why do some implementations of Bezier curve alghorithm use combination (nCk) in the formula before (1-t)?
Hello and thank you for your comment! You should be seeing derivatives of the bezier curve function, the coefficients are sometimes expressed as combinations.
@@NERDfirst Hell yeah. I just haven't noticed that 2 is made from the combination. So in fact, there is 2C2, 2C1 and 2C0 before these multiplications in the equation, right? Thanks a lot.
Great explanation
Hello and thank you very much for your comment! Very happy to be of help =)
Thanks a lot mate! awesome explanation
+Abhinav Aggarwal You're welcome! Very happy to be of help =)
You use the word "basically" a lot, but the explanation was really good.
MisterMumkin Sorry about that! From time to time I fall into a rut of continuously reusing one particular word. I've even changed the words on several occasions =P Glad you found the video useful anyway!
It is a so nice video that helps me a lot
Hope you make more and more video like this
+sdu200 xbw Thank you very much for your comment and subscription! Hope you enjoy your stay =)
Best Explanation....!!!
Hello and thank you very much for your comment! Glad to be of help =)
Very nice! What software/tech did you use to create the equation part of your video?
Hello and thank you for your comment! The handwriting was done in Windows Journal and screencaptured with CamStudio. I used a Wacom graphics tablet for the handwriting.
You're welcome =)
Brilliant!
+Dilip Raj Baral Thank you very much! Glad you liked the video =)
Love the demonstration :)
I have one question if you wouldn't mind helping me.
How do I calculate the 'n of segments for a given bezier to draw in order for it to appear smooth when rasterized? I was thinking the number of segments would be equal to the arc-length? If so, is there a standard formula to calculate this for cubic bezier curves?
Thank-you!
+Mr.Kian Hello and thank you very much for your comment! That is a very interesting problem - I searched around and as far as I can see, there doesn't seem to be any cut-and-dried solution to compute an "ideal" number of segments.
You are very likely right in approaching this from the point of view of arc length. I have found some pretty scary looking math here for that: math.stackexchange.com/questions/12186/arc-length-of-b%C3%A9zier-curves
However, I wonder if you really need to calculate things this precisely to achieve what you want. I believe a high-resolution approximation would suffice, and there probably isn't a need to compute one segment for every pixel onscreen.
Here's a suggestion - Perhaps try using the euclidean distance between two control points to decide how much resolution you want that segment of the curve to have. I think that would be a pretty decent heuristic, since the distance between the two control points generally corresponds to the arc length.
+lcc0612 I'm sorry for the delay in response! I read your comment a few days ago, but I didn't want to reply immediately before I had a go at implementing a solution.
I didn't even realize the interpolated points along a bezier weren't equidistant, so even if I was to generate a pixel at every point along the arclegnth, it wouldn't guarantee continuity.
I decided to adopt your idea of just using a high-res approximation. For computing the equidistant points (something I needed for my purposes), I used that high-res approximation and used a binary search for each equal-length point to find the closest interpolated bezier point. So, all points are (more or less) equidistant.
I uploaded a video of what I did with this :) I made an editor similar to yours, and used the equidistant plotting to overlay textures that point along the normal of each generated line.
Thanks again for continuing to make inspiring videos! Love them!
+Mr.Kian Hello again! That sounds great, congrats on the progress you've made =) I've seen your video and I think I understand what you've been trying to do now. Sounds fun!
Really happy to know my work has been an inspiration. It's an honor =)
You made my day.
Thank you! Glad to be of help :)
Great video, helped me understand a lot, although at the end when you said the 2 control points have to move in relation to eachother for the curve to appear smooth, wouldn't it also work to use the control point before the last one of your 1ste curv as the start of the 2nd curve, and the last point of the 1ste curve as the 2nd point of the 2nd curve?
Hello and thank you for your comment! In fact, that's how it's usually done! Rather than putting two points at the same position, we just use the one point for both curves.
Can you explain more on the curvature of bezier curve??
Hello and thank you for your comment! Can you elaborate more on what you mean? What are the specific objectives of learning this?
@@NERDfirst Maybe you can elaborate on the parametric and geometric continuity, how it affects the smoothness of the curves etc etc Yeah would love to hear how you would explain it! :))
so awesome love it thanks
You're welcome! Glad to be of help :)
best explanation
Thank you very much! Very happy to be of help =)
very helpful
Vishal Kaushal Thank you for your comment! Glad you liked the video =)
Great help man
TechRetards Hello and thank you very much for your comment! Glad to be of help!
If you have the curve drawn, know the start and end points (and any points in between), is there any way to get the corresponding control points from that?
+Thomas Johnsen Ulland (Butz) Hello and thank you for your comment! While intuitively, it seems possible by "reverse engineering" the math, it seems rather involved when I actually tried to work it out.
We know the start and end points of the curve, which allows us to figure out the first and last control point for each segment. Substituting these known values into the Bezier curve equation of appropriate degree eliminates two variables, so the remaining unknowns are t, and the in-between control points. (eg. For the cubic curve, you are left with t, P1 and P2).
If we know what value of t corresponds to what position on the curve, then it's easy - It's just simultaneous equations, which we can create as many as we need to solve for all the in-between control points.
If the ts are unknown though, that would be harder, and I gotta confess I haven't quite figured it out. It's not simultaneous equations anymore, since each equation you introduce, you also introduce one extra variable (another unknown t).
i am glad you make this video thanks a lots..Dude
You're welcome! Very happy to be of help =)
nice work!
Thank you! Glad you liked the video =)
thank yoou for sharing:)
Sachin Sharma You're welcome! Glad you found the video useful =)
it was..indeed :)
You are so good!!!
Hello and thank you very much for your comment! Very happy to be of help =)
thanks bro !!!
You're welcome! Very happy to be of help =)
Great Video
Thank you very much! Glad you liked the video =)
excellent!
Thank you! Glad you liked the video =)
nice brother...have xam 2morrow....might be able to write something now about it :-D
+Harry Littrell Hello and thank you for your comment! Good luck for your exam =)
Thanks man !!
Mahefa Reb You're welcome! Glad you liked the video =)
Any commercial software is available to change the shape of any curve by using Bezier Curves technique?
Hello and thank you for your comment! Not really sure what you're asking, but many programs out there support bezier curves.
Nice explanation, how would this equation look for 5 points? :D
Hello and thank you for your comment! That version of the equation happens to be listed on Wikipedia under the "Explicit Representation" section: en.wikipedia.org/wiki/Bézier_curve#Explicit_definition
Oh thank you! I haven't looked it up on Wikipedia because when I'm looking for math stuff on it, mostly it's too complicated Imo ;D
You're welcome! Yeah it's true, technical wikipedia articles get _hella_ technical, so it might not be a good learning resource.
Thanks man!
You're welcome! Happy to be of help =)
شكرا جزيلا شرح ممتاز , لكن اذا كان المنحني متكون من خمس نقاط كيف ستكون المعادله ؟
Hello and thank you for your comment! I'm sorry I don't speak Arabic, but Google Translate has given me a pretty good idea of your question. I can only respond in English I'm afraid!
There are two ways to get a curve with 5 points. You can either use a more complex equation (to the 5th order), or connect multiple curves of a lower order.
The equation for the 5th order can be seen here. You will also find the explicit definition that allows you to generate a curve of any order: en.wikipedia.org/wiki/B%C3%A9zier_curve#Explicit_definition
not problem I'm understand now until 100 points after I'm focus on your video very well I'm can't how I'm thank you very very very much
Brilliant
Thank you very much! Glad you liked the video =)
Hey,
Just wondering what program you used for your demonstrations?
Hello and thank you for your comment! The "whiteboard" sections are done in Windows Journal and captured with CamStudio. The parts in which I click around on an interactive Bezier curve comes from a homemade Java program.
thank youuuu so much!
Kavya Kishan You're welcome! Happy to be of help =)
Please make a video on B spline curves too.
Kavya Kishan Unfortunately I don't think I really know enough on the topic to do that... I'll do some further research (after my exams are over) and we'll see!