3.2 Trigonometry

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En provenance du cours de University of London

Creative Programming for Digital Media & Mobile Apps

37 notes

University of London

Creative Programming for Digital Media & Mobile Apps

37 notes

This course is for anyone who would like to apply their technical skills to creative work ranging from video games to art installations to interactive music, and also for artists who would like to use programming in their artistic practice. This course will teach you how to develop and apply programming skills to creative work. This is an important skill within the development of creative mobile applications, digital music and video games. It will teach the technical skills needed to write software that make use of images, audio and graphics, and will concentrate on the application of these skills to creative projects. Additional resources will be provided for students with no programming background. At the end of this course, you will be able to: * Write creative, audiovisual programs in the Processing environment that run on desktop and mobile * Programatically manipulate sound in creative ways * Display images and image sequences * Generate interactive, algorithmic graphics * Work with a 2D physics engine to create a basic game

À partir de la leçon

Audio Visualiser

This week is all about creating an Audiovisualiser. This is a really popular and interesting topic that has lots of applications, from music players, to game engines, to more complex things such as DSP. We'll be learning about algorithmic graphics, audio analysis, and also about using the accelerometer features of your phone. Remember that many desktops don't have accelerometers, no matter how much you shake them!

3 Introduction 1:54

3.1 Transforms (part 1) 8:29

3.1 Transforms (part 2) 5:36

3.2 Trigonometry 5:26

3.3 Accessing Accelerometer Data 12:31

3.4 Audio Analysis 16:19

3.5 Building Audio Visualisers25:54

Rencontrer les enseignants

Dr Marco Gillies
Senior Lecturer
Computing Department, Goldsmiths, University of London
Dr Matthew Yee-King
Lecturer
Computing Department, Goldsmiths, University of London
Dr Mick Grierson
Reader
Computing Department, Goldsmiths, University of London

The last thing I want to talk about today is another powerful mathematical function

that we can use a lot enjoying, and, the, these functions are, trigonometry which

he, probably studied in high school or the equivalent.

and they are three functions that relate to triangles.

relate angles and triangles. So, if we look at the slide here, we've

got a right angled triangle. We've got an angle A in that triangle,

and then we can label the sides. The adjacent side, which means the side

that's next to the angle. The opposite side, ones opposite it.

And the hypotenuse, which is the long the long angle, the long side of the

triangle. And this trigonometric functions are

defined in terms of these three sides. The sine of an angle is the opposite side

to that angle divided by this hypotenuse, the length of the opposite side divided

by the hypotenuse. In the case of the tangent, it's also

defined the same way. Now, we're not actually going to use

these to work with angles or triangles, and I'm going to show you something

different. I'm actually just interested in working

with sine as a function, because it's a really instant function.

And it's really powerful for doing graphics animation, and I'm going to show

you what it does. So, if we're drawing the circle, you can

that the vertical line in the circle is the opposite of the angle in the middle

of the circle as we rotate around. So, we can see we're drawing a circle,

and I'm tracing out the path of the actual sine function at the same time as

drawing the circle. And you can see, is that when the angle

is. When it starts again, it's near zero, the

sine function zero. It gets increasingly more negative, then

increasingly more positive. And then it goes back down to zero again,

and it starts the way around a circle. So, it repeated itself exactly, going

negative, going positive again. And what's powerful about is that it's

repetitive oscillating function. So, it goes up and down, up and down, up

and down all the time. It looks a little bit like a wave.

In fact, it's a very important mechanism for modeling sound wave.

Sound waves act a lot like sou, sine waves.

In fact, we can build up any sound wave out of a whole load of si, of si, of sine

functions of different sizes and frequencies.

So, what do we, what can we do with this? Well, before we come to that, I'll talk a

little bit more about the function. So, this is More detail about the sine,

sine function, this is how we would write it out.

we're using the function sine, which is the calculates the sine of an angle, but

we're putting some other numbers in. Firstly t, we can think of this as time,

if you're working with animation with sounds, the sine function is changing

over time. Then we've got, we multiply the result by

A. That's called the amplitude, that's how

high it gets and also how low it gets. That's how big the sine wave is.

In audio, that is closely related to the volume of audio.

If you take, if you're listening to sound.

Then we have the frequency, that's how many of the ups and downs you get in a

second, say, if you're dealing with time. and that what I'm showing you in the

diagram here is that the distance from one point to next identical point is one

divided by the frequency of wave. And finally you got the phase, and that,

we can really just think of that wave's as a starting point to the sine wave, say

how off, far off the zero point your actual function is starting.

And you can combine together at different sine waves at slightly different phases,

and you get an interesting effect. Say, you're starting one at point, and

you're starting another one a little bit later, and you combine them together, and

that'll [INAUDIBLE] an interesting visual [INAUDIBLE] effect.

And there's a lot you can with sine waves.

So, a sine wave can be used nicely in graphics.

It has a nice shape. it starts to look a bit like a water

wave. You can [INAUDIBLE], you could model

water with sine waves. And certainly, if you add a bunch of sine

waves together, you can get quite a nice model of it, or even landscapes.

And importantly you can use in animation. And that's really powerful because the

great thing about sine wave is that it oscillates.

It goes up and down repeatedly. And that's a really useful thing for

animating moving objects. And we'll see make work, work a lot with

sine wave [INAUDIBLE]. The other great thing for sine wave is,

as I said, it's a fantastic tool for modeling audio functions, and I think

Matthew will talk about that in a later [MUSIC] [MUSIC]

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