WEBVTT 00:00.450 --> 00:03.950 Welcome to mathematics and images. 00:03.950 --> 00:10.770 So in this lecture we're going to learn how maths works in images and it can be difficult to comprehend 00:10.770 --> 00:13.620 at first if maths is not your strong point. 00:13.620 --> 00:21.080 Do not worry we are going to be doing some very basic maths nothing too arduous now. 00:21.090 --> 00:27.330 If you think about how a computer is showing you an image it is a series of values. 00:27.360 --> 00:31.500 Each pixel of an image will have as searson red green and blue. 00:31.500 --> 00:33.030 Value. 00:33.030 --> 00:40.590 Initially we're going to focus on monochrome or grey scale and that is where the red green and blue 00:40.590 --> 00:41.550 channels. 00:41.580 --> 00:46.520 So colour is generated from those three channels have the same value. 00:46.530 --> 00:50.260 Now if they all have a value of zero then you get a black image. 00:50.310 --> 00:57.430 They all have a value of one or 100 percent or if the slider goes up to 255. 00:57.630 --> 01:02.850 Then you will have a white image and anything in-between where all the values of the same for red green 01:02.850 --> 01:05.970 and blue you'll end up with some shade of grey. 01:06.030 --> 01:10.690 Now each pixel on an image will have its own values. 01:10.740 --> 01:17.180 However to keep things simple we will have one value for all the pixels of our image. 01:18.160 --> 01:20.740 Now basic mathematics is just that. 01:20.740 --> 01:25.880 We're not going to do a deep dive into all the mathematical functions that are available to us. 01:26.110 --> 01:30.920 We're literally going to be adding subtracting dividing and multiplying. 01:30.970 --> 01:35.550 These are all just as you would expect them to be when you combine them together. 01:35.590 --> 01:38.220 So one plus one is two. 01:38.240 --> 01:40.000 It is as simple as that. 01:40.000 --> 01:47.110 Now you can build things up to make them more complicated or not necessarily more complicated but more 01:47.110 --> 01:48.180 functional. 01:48.400 --> 01:51.990 But they are just simple steppingstones. 01:52.300 --> 02:00.550 Now it is important that we understand that values of less than zero or greater than one are still passed 02:00.550 --> 02:04.840 through the system unless we use a clamping feature. 02:04.900 --> 02:10.460 We will also see that the colour mix and convert are maths nodes function almost the same. 02:10.480 --> 02:13.120 However there are different options. 02:13.120 --> 02:20.020 They both got add subtract divide and if you use them you're going to get exactly the same result if 02:20.020 --> 02:22.930 you leave everything a standard will have a quick look at that. 02:23.020 --> 02:28.000 But when you're dealing with images it's probably best to use just the mix node. 02:28.800 --> 02:34.330 So let's go play with some basic mathematics now and hop on over in a blender. 02:34.800 --> 02:40.670 Right so over in the default blend file and this is all we need to do our compositing test. 02:40.680 --> 02:46.170 There is one thing I want to do and demonstrate for you and which will be one of the differences between 02:46.170 --> 02:51.660 a mixed node and a maths node and we need to have a bit of colour in our image because if we render 02:51.660 --> 02:58.590 out that cube it is just grey some going to go and change the diffuse colour of my cube to red or yellow 02:58.590 --> 03:00.180 or pick a colour you like. 03:00.390 --> 03:00.810 Excellent. 03:00.810 --> 03:06.420 And I'm going to render that out now that's rendered out we can go straight into the compositing set 03:06.420 --> 03:14.990 up so we can see a 3D view are image which isn't quite going yet and our node editor and because we're 03:15.000 --> 03:20.950 in the compositing view our node editor has also been switched over to the compositing mode. 03:21.030 --> 03:22.950 I'm going to put a ticking use notes. 03:23.070 --> 03:27.030 I'm going to put a tick in backdrop which won't do anything at the moment because we don't have the 03:27.120 --> 03:33.180 appropriate output node and I'm was going to turn on auto render and auto render will do is if we change 03:33.180 --> 03:36.450 anything in our scene it will automatically re render it. 03:36.480 --> 03:41.270 Now I don't want it taking what however long it's going to take 5 seconds. 03:41.280 --> 03:42.730 Every single time. 03:42.930 --> 03:50.850 So I'm going to turn down my samples to one when I hit render And now if I move that cube it updates 03:51.000 --> 03:52.280 nice and quickly. 03:52.320 --> 03:56.190 Of course it's not going to be very high def or anything along those lines. 03:56.190 --> 04:00.810 I'm also going to be a bit pernickity here and turn my lamp to a sunlamp. 04:00.810 --> 04:04.930 This is one of these things that I've lost with the setting of maybe two. 04:05.250 --> 04:10.920 Now nothing's changed nothing's changed in that render and it won't automatically update unless something 04:10.950 --> 04:12.480 else in our scene has changed. 04:12.480 --> 04:15.890 I could move the lamp rotate if I can't do it from this view however. 04:16.080 --> 04:17.820 So if I go ahead and move the lamp. 04:17.940 --> 04:22.090 Now when I go back to our compositing view it should all be updated he says. 04:22.110 --> 04:23.270 Is it not. 04:23.700 --> 04:24.330 There we go. 04:24.370 --> 04:25.110 We have to move. 04:25.110 --> 04:31.290 In this case that's all sorted we can by the way instead of moving it like that and actually potentially 04:31.290 --> 04:37.720 destroying your set up you can move it by zero and it will also update worthwhile knowing. 04:37.950 --> 04:41.970 So the final thing here is we can't see what's going on we need another output. 04:42.050 --> 04:45.740 Known So all going to add in an output that's a viewer. 04:45.980 --> 04:50.940 Then when we plug the image into vats as well we can see it in the background so we can see an update 04:50.940 --> 04:52.110 in two different places. 04:52.110 --> 04:57.630 Now this is a great way of trying out changes or in this case just sampling areas. 04:57.660 --> 05:01.710 I'm going to turn off for the moment so our backgrounds are nice and clear and I'm also going to get 05:01.710 --> 05:05.130 rid of The View and know just to keep things simple. 05:05.460 --> 05:06.600 So let's have a look. 05:06.600 --> 05:08.900 I'm going to unplug that for the moment so this will go black. 05:08.910 --> 05:10.830 Because nothing is being rendered. 05:11.160 --> 05:22.090 And we've got a colour mix so you can get add colour mix or add converter maths. 05:22.110 --> 05:24.490 Let's look at these side by side. 05:24.540 --> 05:29.640 They're very similar in what they do but they have different inputs and different outputs so they both 05:29.640 --> 05:31.360 have a series of options. 05:31.410 --> 05:34.010 I.e. the function it's going to perform. 05:34.870 --> 05:38.990 And these are more maths orientated and these are more image orientated. 05:39.920 --> 05:45.200 Now the inputs we've both got a clamp here the inputs I'm going to skip the factor for the moment the 05:45.200 --> 05:47.690 inputs themselves are taking in three values. 05:47.690 --> 05:49.560 That's why they are coloured in yellow. 05:50.000 --> 05:52.850 And the output is going to output three values. 05:52.880 --> 05:57.510 Now the inputs here are just taking in one value and outputting one value. 05:57.560 --> 06:04.250 So if we link all of these together in this order and make sure these are set to multiply and the reason 06:04.250 --> 06:09.470 I'm going to set them to multiply as an asset to a value of one and the bottom one here is white so 06:09.470 --> 06:10.950 that's also one. 06:11.000 --> 06:15.280 So when we multiply by 1 we get the same output. 06:15.590 --> 06:23.420 I'm going to plotly image in to hear the top note there and I'll get a plug the value this image output 06:23.420 --> 06:28.370 of a multiply into here and then finally the view across as well. 06:28.370 --> 06:34.430 And what we should get is a black and white image because it's taking the average of the three outputs 06:34.430 --> 06:37.090 here and then outputting only one. 06:37.090 --> 06:39.990 So that's essentially made this grey scale for us. 06:40.010 --> 06:46.280 If we wanted so now for the rest of this particular tutorial I am not going to use the maths node just 06:46.280 --> 06:50.420 to demonstrate it does exist and if you're just processing a single value. 06:50.570 --> 06:54.820 In fact it would work very well with just greyscale images you can use the maths node. 06:54.860 --> 06:59.750 Otherwise I'd recommend using the mixed node because it's all about mixing images. 06:59.750 --> 07:05.390 Let's plug that back in and make sure everything's working perfect case so we knew there was something 07:05.390 --> 07:11.630 just a little simpler just so we can get the hang of things only get rid of the renda layer inputs and 07:11.720 --> 07:19.500 add in another type of input which is a value and I'm going to duplicate that so I have two of them. 07:20.840 --> 07:28.610 So now if we have our multiply here if we multiply point five and point five together we get a value 07:28.610 --> 07:31.180 that should be the same and we can test it. 07:31.170 --> 07:36.950 If you keep your eyes down here I'm going to create another value node and set it as point to 5 and 07:36.950 --> 07:42.430 plug that straight in to our image and it should look no different. 07:42.440 --> 07:43.000 Excellent. 07:43.010 --> 07:44.250 So that's working well. 07:44.250 --> 07:47.400 I'll get rid of the extra value input. 07:48.170 --> 07:54.080 Now let's have a look at what happens if we add one and one together or that's one in 11 minutes had 07:54.080 --> 08:01.040 one and one together and add we get a white image but because we haven't clamped the values coming out 08:01.040 --> 08:03.570 of here are two. 08:04.590 --> 08:11.900 On both the RG and B channels and we can test that by duplicating our mix note. 08:12.210 --> 08:16.950 And this time let's make this nump number larger let's make it nine. 08:16.950 --> 08:19.960 So you've got a total of 10 coming out. 08:20.190 --> 08:23.570 So if we divide 1. 08:24.850 --> 08:26.100 By 10. 08:26.910 --> 08:28.430 We should get. 08:28.470 --> 08:29.870 I'm surprised that came out white. 08:29.880 --> 08:32.240 Oh we're still having divide. 08:32.250 --> 08:34.790 There we go we get a dark dark grey. 08:35.130 --> 08:41.640 If we clamps that it doesn't matter what these values coming in will be because it will clamp the value 08:41.850 --> 08:49.240 at a maximum of one or two hundred fifty five on each of the RG B channels and clamping. 08:49.260 --> 08:50.950 There we go it's gone white. 08:51.090 --> 08:51.790 Excellent. 08:51.810 --> 08:57.780 So we got a good grasp here of our node setups and how the mix node can be used. 08:57.930 --> 09:02.460 There are lots of other options we won't be dealing with them quite at this moment in time. 09:02.700 --> 09:06.930 But you've got your multipliers and as I've already stated if you multiply something by one you get 09:06.930 --> 09:14.140 the same thing coming out as worthwhile knowing if you're mixing masks together and we've got the fact 09:14.140 --> 09:21.630 a slider here very important if you want to have 100 percent influence of well let's say we can do this 09:21.660 --> 09:26.700 let's go ahead and add in that render layer again so inputs render layer. 09:26.740 --> 09:29.230 No it's getting a bit small there size zoom back in. 09:29.340 --> 09:31.290 So we have an image here. 09:32.400 --> 09:35.240 That we can use as a factor. 09:35.550 --> 09:40.410 And at the moment we're adding these two different images together one of nine and one to one which 09:40.410 --> 09:47.880 will both be white if we have let's say we add in point 1 and point five and see if that's made any 09:47.880 --> 09:52.110 difference as it comes through I'm going to get rid of this divide as well so we are just dealing with 09:52.110 --> 09:58.620 the one and now we go we can actually see the cube it's not that strong probably because of the colours 09:58.650 --> 09:59.910 I've picked. 09:59.910 --> 10:03.950 Let's play with these values here so they're being added together. 10:03.990 --> 10:08.460 There we go we can see the image a little better now so we can see that we're using this image here 10:08.460 --> 10:13.450 not the best image as a mask for these two colours coming through. 10:14.630 --> 10:18.240 If we pick one of the other options we get different results. 10:18.260 --> 10:24.080 In fact you can go through and play with these and see what results you get in how it effects an image. 10:24.080 --> 10:29.630 Now obviously at the moment with these two values coming through the output will always be grey until 10:29.630 --> 10:33.800 we get colour coming through and then you would get a different effect. 10:33.800 --> 10:40.940 Now one of the things to just be aware of is if we have a value of one and a value of nauts let's just 10:40.940 --> 10:43.350 delete the rendle air to make things simple again. 10:43.490 --> 10:49.820 And we set this to mix mixing is the one that's not really explained very well because it's not saying 10:49.880 --> 10:50.940 average. 10:51.950 --> 10:55.230 But the facts are down here can be very confusing. 10:55.280 --> 11:02.900 So a factor of 1 means that it's weighted towards this bottom one completely a factor of Zero means 11:02.900 --> 11:04.920 it's weighted towards the top one. 11:05.030 --> 11:10.490 So this can be very confusing if you want a pure average between the two you're going to have to put 11:10.490 --> 11:11.830 in point five. 11:11.990 --> 11:18.800 And then the average of 1 and 0 when you add them together and divide them by the total number you have. 11:18.950 --> 11:21.880 So you will end up with point five. 11:21.920 --> 11:27.440 Now I'm going to test my theory here by making another valley you know putting in point five and just 11:27.440 --> 11:30.310 linking it across and seeing if there's any change in the image. 11:30.440 --> 11:36.950 There's not so that just confirms that a factor of point five when your mixing will average the two 11:37.010 --> 11:38.180 inputs. 11:38.180 --> 11:38.900 Excellent. 11:39.080 --> 11:43.410 Now we've got a handle on using image a maths together. 11:43.430 --> 11:48.510 It's time for a challenge and our challenge is what is the output value. 11:48.530 --> 11:52.470 Now this is going to be quite straightforward mathematics. 11:52.820 --> 11:56.690 If your experience with mathematics you may even find this a real doddle. 11:56.690 --> 12:03.140 But what I'd also like you to do as well as giving the answer is what the Shade of Grey will be. 12:03.640 --> 12:10.240 Or whether it'll be black or white and do compare that over in blender as well and make sure what you 12:10.240 --> 12:14.210 think the answer results in is what happens. 12:14.620 --> 12:18.200 So what happens if you add point five and point five together. 12:18.490 --> 12:21.940 What happens if you subtract one from point five. 12:22.720 --> 12:23.250 Clamped. 12:23.260 --> 12:26.180 What does adding point five and one result in. 12:27.050 --> 12:30.520 What happens if you multiply point five and point five. 12:31.630 --> 12:34.590 What happens if you multiply 0 by 1. 12:35.630 --> 12:39.010 What happens if you divide point 5 by 1. 12:39.730 --> 12:42.830 And what happens if you divide point five by point five. 12:43.700 --> 12:46.150 Pause a video now go through those. 12:46.150 --> 12:49.340 Answer them and do check over in blender. 12:49.400 --> 12:53.530 If the colour output that you thought would happen is what happens. 12:55.220 --> 13:01.090 Okay Welcome back let's go have a look at the answers so giving an answer and what the Shade of Grey 13:01.090 --> 13:01.840 will be. 13:01.930 --> 13:03.930 Or of course if it's black or white. 13:04.270 --> 13:10.650 So what happens when you add point five and point five when you get one which will turn out to be white. 13:11.360 --> 13:19.310 What happens when you subtract one from point five you get minus point five which is black because we've 13:19.310 --> 13:22.340 gone to zero and we can't really go beyond it. 13:23.050 --> 13:23.930 If clamped. 13:23.930 --> 13:31.130 What does adding point five and one equal or that equals one because it's clamped so it can't go any 13:31.130 --> 13:31.820 higher than one. 13:31.820 --> 13:37.410 If you added a million and one together you would still get the answer one. 13:37.700 --> 13:40.010 And that would also be white. 13:40.010 --> 13:46.730 Now what does a multiplying point five point five together you'll get a point twenty five together which 13:46.730 --> 13:50.570 will be a darker grey than you had initially. 13:50.600 --> 13:58.000 What does multiplying zero by 1 while multiplying anything by zero is always zero. 13:58.010 --> 14:02.810 They do have to be cautious about this because if you got something in your scene that is zero and you're 14:02.810 --> 14:09.780 not using it as a mask it will cancel out colours especially when multiplying and will result in black. 14:09.830 --> 14:15.950 And of course as we've experienced in the past nothing in the real world except maybe a black hole is 14:15.980 --> 14:17.300 truly black. 14:17.300 --> 14:24.440 So do be very cautious if you ever end up multiplying something by zero unless it's a mask. 14:24.440 --> 14:31.330 Now dividing north point five by one well you get point five which is a mid level grey. 14:31.390 --> 14:34.700 And then finally point five by point five. 14:34.700 --> 14:38.780 If you divide them you get a value of one which is white. 14:38.810 --> 14:39.980 How did you guys get on. 14:39.980 --> 14:41.450 Did you find this straightforward. 14:41.450 --> 14:46.820 It is pretty basic maths but when you think about how it relates to colours sometimes that can be a 14:46.820 --> 14:48.210 little confusing. 14:48.290 --> 14:53.780 Remember to play with the sliders see if you can get a bit of an intuition for it. 14:53.780 --> 14:59.690 Share your work in discussions in anything you've discovered over on the forum and I will see you guys 14:59.900 --> 15:01.270 in the next lecture.