DaVinci Resolve Fusion: Lissajous Figures Tutorial

hi this is Simon Amstell and welcome to another tutorial for black magic fusion and today we're going to be taking a look at an interesting technique that uses expressions and other tricks to create lissajous figures so lissajous figures are fascinating phenomenon and they were first described in 1815 by the american mathematician Nathaniel Bowditch but they were named after the French physicist Jalan Tuan Lisa Zhu so what it is is when a particle is influenced simultaneously by two simple harmonic motion patterns at right angles to each other the resultant motion of a particle traces a curve and that curve is called a Lisa who figure if you look online you'll see some great practical experiments to demonstrate this using things like a bucket of sand on the end of a piece of string but we're going to be looking at doing it digitally in fusion so let's get started so I'm going to start with a background node let's make this gray and let's make it a thousand pixels square look at that so then let's make another background node and this one that I'm going to make five hundred pixels square and let's just change its color anything will do something like this so I'm going to add a circular mask to that let's just merge it over our background look at that so I'm going to make the lips 0.9 5.9 turn off solid no not point eight turn off solid and let's have a border width of point zero one then with our merge I'm going to position this down in the bottom left hand corner so that's 0.25 on X and 0.25 on Y then we're going to take that and merge it over itself and in our second merge we're going to move this up to the top right hand corner so it's 0.75 on X and point seven five on Y and that now looks like that so then I'm going to copy this ellipse and background come on see c'mon fee and let's merge it over our result here let's change this background color go for white let's change this ellipse size two point zero five and let it set it to solid with no border width so now I want to animate this little white dot to follow each of these two circles so I'm going to look at this circle here first of all so after that background and before the merge I'm going to add a transform tool and then we're going to come to the transform Center and we're going to modify with the expression and we'll come over to the modifiers panel so we're going to add an expression to point one and what we're going to do here is after that first point five we're going to type plus n1 and after the second point five we're going to type plus in two so let's now set an expression for number one creating expression here so this is going to be sign as I n open brackets time divided by open brackets n 4 x + 9 closed brackets closed brackets x + 3 and then we're going to copy that and we're going to set an expression for n 2 paste that in there and then we can just swap the sign for coz and then I'm just going to come over to the point expression and enter P 1 X and P 1 Y 2 come back to our numbers here I'm going to enter a value of 4 for number for number in 4 and a value of 4 for number 9 then before I do anything else I'm going to come to the merge here and I'm just going to move it into position into this bottom left hand corner so again 0.25 0.25 for both X and why so let's come back to our transform modifiers and we just need to adjust this n3 number so I'm going to go for 0.45 and you'll see that's put it on the edge of the circle so now we get the dotter rotating around the circle so what we're doing here is something very simple and useful using sine on one of the position values and cosine on the other and using time to drive them create this circular orbiting effect for more on this I had urge you to watch my expressions tutorial which I'll link to in the comments and so what we're doing with these other values number three as you saw was just was just positioning the dot on the edge of the circle number four is the speed of the rotation and number nine is just going to be a multiplier for the speed of the rotation on I'll explain why we're using that later on need to make sure that number nine is set to one or something there we go so then I'm going to hit f2 to rename this transform as ball a and then what I'm going to do is I'm going to copy it and paste it and let's rename it as ball B then I can take my dot shape pipe it into ball B and pipe the output of ball B over that merge let's look at the result so we've got another ball here and we need to just make some adjustments to it so first of all I'm going to adjust its merge position so it's in the top right so let's go for point seven five and point seven five and now you'll see that they're both following their respective circles obviously at the same speed now the whole principle of this is to see what happens when these move at different speeds and that's what creates the Allah says you affect so what we're going to need to do is to be able to control the ratio of the two movements so what I'm going to do is I'm going to come to ball a and I'm going to use number five here and what I'm going to do is I'm going to publish it so that'll allow me to come to ball B and instead of using number four there I'm going to connect that to ball a Center number in five so then I need to come back to ball a and here number five I need to just change that value so I'm going to go for five for that and let's look at the result so now you can see that we've got those two moving at different paces but what we're also going to need to be able to do is to have our multiplier here our number nine multiplier as something that can be accessed by our ball be transformed as well so let's publish that number nine value come over to ball B and here it's number nine we're going to connect to ball A's number nine and now I can control everything from this panel here so number five is the speed of this ball here and this is the multiplier that will apply to both both balls so I can set that to four and you play you'll see they're moving nice and slow so that's their multi the higher use value for the multiplier they slur the overall effect okay next thing I want to do is I want to create some lines that are connected to these balls that are going to help us to identify the Alyssa's u pattern so what I'm gonna do is I'm going to make a bit of space here and again I'm going to make a new background this time I'm going to make it thousand pixels wide by five pixels high and let's make it red and then here I'm going to add a merge after my background and I'm going to add that over the top and you'll see I've now got that red line there now what we want to do is we want to get this red line to follow this bottom left-hand ball so to do that we're going to come to the merge and we're going to add an expression to that center value and we're just going to modify this expression so we're happy with the with 0.5 for the x value we just need to adapt the Y value so I'm going to type ball a which is the name of our ball that we want to reference dot center dot Y over 2 now it's really important when you're entering references to other parameters that you get the formatting exactly right ball a here is the name of my source transform node and you'll notice that it has no space and the capital A and the capital B must be entered correctly notice also that Center uses the American spelling and the position parameter that we're referencing in this case Y has got to be uppercase of course you could always do it the lazy way and use pick whip but it's a good idea to train yourself how to do it this way because often it's a lot less fiddly and hey it makes you look much more professional doesn't it so let's have a look at what we've now got so now that line is following the vertical position of that ball and we can do the same thing with the other one but we need to make a variant of this background so I'm going to copy that background and paste it and then I'm going to just change its width and height so 5 pixels wide by a thousand pixels high because we want this to be vertical let's make a little bit more space here and pipe that over the top of that so we've got a new merge and let's actually look at the final result we can do the same thing with this merge here so we're going to add an expression to the center and we're going to adapt not the Y value this time but the x value so I want to leave that 0.5 there and I'm going to do point five plus ball B dot dot x over two and then let's look what happens so now our vertical line is following feed dot in our top right circle so now we can finally look at creating military effect and so what we want to do is we want to have a dot that follows the intersection of these two lines and they won't be using a trails to get it to draw a line so I think I'm going to copy this ellipse here the white ellipse so the background and its mask copy and paste let's just change that background color to something different and then we're going to pipe that over the top of our final merge there so to animate this I'm going to add a transform before the merge so how to transform there and then I'm going to select the center and I'm going to modify with expression so let's come over to the modifiers here point one I'm going to connect to ball a center point result come back to the transform center point - I'm going to connect to the ball B center point result come back to the transform Center so then what we're going to do is we're going to come to the position here and for the X expression I'm going to type P to X and for the Y expression I'm going to type p1 Y and finally I need to come to my merge and I need to position it in the right place so the x value is going to be 0.75 and the Y value is going to be 0.25 because that's this our bottom right-hand corner of the frame so now you'll see that our dot is nicely following that intersection I'm just going to increase this timeline to a thousand frames long and so for our final step after that transform I'm going to add a trails and then we come to the beginning just going to restart the trails let's see what happens so we've got our nice release as you drawing and we can have hours of fun with this so the thing to remember here is that ball a is the thing that's driving everything so this expression here and it's these two values here numbers four and five so what we could actually do is we could come over here to the number controls and we could rename those so number four is the divisor and number five is the dividend so we can come back and you'll see if those names have changed it makes it a little bit easy to understand so currently we're looking at five over four so let's instead look at three over two and we need to just reset our trails and then have a look at it and you can see it's a much simpler pattern like that now you'll notice that obviously our trails is not creating of a full line and we've got these separate dots and that's the reason I've added the multiplier here I'm going to just restart that we come to the ball a modifiers when we are number nine was this factor that we could multiply our basic divisor and dividend by so I'm just going to increase that number let's go full say six and then restart it and you'll see it's much smoother and slower so really we just need to set that speeds to be something that's that's that makes it smooth enough actually let's go for ten even there and again restart the trails have not look at it you can see it's starting to be much more joined up like that so depending on the complexity of the the shape you'll want to adjust the speed so I urge you to have fun with different values for the divisor and dividend the classic ratios tend to be whole numbers separated by one so for example one over two three over two five over four and that kind of thing but you can experiment with anything you like obviously if the values are the same so let's enter a ten by ten restart the trails what we get is a perfect circle so a circle is in fact the simplest instance of a Lisa jus curve very interesting so I hope you enjoyed that thanks very much indeed for watching and stay safe and well

Channel: Simon Ubsdell

Views: 2,801

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Id: Sju4oFDa_d0

Length: 16min 5sec (965 seconds)

Published: Thu Jun 04 2020