this terms course last term we both worked on learning 2 things –processing –the concepts of...

This terms course

• Last term we both worked on learning 2 things– Processing – The concepts of graphics etc.

• This term will focus more on the basic concepts– Graphics, 2D and 3D– Sound

• The course will go more into the maths and theory

Aims

• Understand Vectors– Position/displacement, direction, length

• Use Vectors in Processing programs– in 2D and 3D

• Understand Transforms

• Use Translations and Scales

• Use pushMatrix and popMatrix

Vectors

• x and y are the coordinates of points

• In maths we can group them together as a single object (x,y)

• This is called a vector

Vectors

• A vector can represent 2 things

Vectors


• A position on the screen

• (A position vector)

(x,y)

Vectors


• A displacement between two points

• (A displacement vector)

(x,y)

Vectors

• A position vector is really a displacement from the origin (0,0)

(x,y)

Vectors

• Position Vectors– drawing shapes– positions of object

• Displacement Vectors– Velocities, movements

Maths on Vectors

• You can do maths on vectors• Normally you do each operation on each

element separately• It normally help to think about vectors as

displacement vectors

Vector addition

• add vectors

• (x1, y1) + (x2, y2) = (x1+x2, y1+y2)

• do one displacement after another

(x1,y1)

(x2,y2)

(x1+x2,y1+y2)

Vector subtract

• subtract vector

• (x1, y1) - (x2, y2) = (x1-x2, y1-y2)

• The displacement of one position relative to another

• Very useful

(x1,y1)

(x2,y2)(x2+x1,y2+y1)

Length of a vector

• you can calculate the length (magnitude) of a vector using Pythagoras' theorem

• l2 = x2 + y2

• l = sqrt(x2 + y2)

x

yl

Length and direction

• You can think of a vector as having a length and a direction

• The direction is a vector that is in the same direction but of length 1

• Calculate it by dividing each component of a vector by the length– (x/sqrt(x2 + y2), y/sqrt(x2 + y2))

• Called normalising

Length and direction

• Very useful to be able to think about both• Length

– know the distance between two objects– know how fast an something is moving (e.g. for

setting a max speed)

• Direction– Move at a constant speed in a direction given

by two points– Turn an object to face the direction its moving

in

Vectors in 3D

• We can also do the same things in 3D• An extra item, z, represents depth• pass in an extra parameter OPENGL or

P3D to size• The maths works the same

– length is sqrt(x2 + y2 + z2)

Vectors in Processing

• dist() gives the distance between two points– length of the displacement between them

Vectors in Processing

• dist() gives the distance between two points– length of the displacement between them

• PVector is a class for representing vectors• Its new to the latest version of Processing

Exercises

• Rewrite my last example to use PVector• make it work in 3D

Aims

• Understand Vectors– Position/displacement, direction, length

• Use Vectors in Processing programs– in 2D and 3D

• Understand Transforms

• Use Translations and Scales

• Use pushMatrix and popMatrix

Transformations

• Translate

• Rotate

• Scale

Transformations

• Transformations act on the whole processing screen

Transformations

• Translate moves the whole coordinate system by a x and y direction

Transformations

• Anything before the translate call is draw normally

Transformations

• Anything before the translate call is draw normally

• Anything after the call is drawn relative to the new transformed coordinate system

Transformations

• Scale will change the size of the coordinates relatives to the origin (0, 0)

Transformations

• The order of transforms is very important

• Changing the order changes the result

Transformations

• A transform applies to all the code that happens after it

Transformations


• That means it also applies to other transforms

Transformations


• Translate()

• Translate()

• Translates everything twice

Transformations


• A translate followed by a rotate means “apply the translate to the result of rotate”

Transformations


• Translate()

• Rotate()

• Means translate the result of rotating

Transformations


• Rotate()

• Translate()

• Means rotate the result of translating

Transformations

• This is the opposite order you would expect

• Translate()

• Rotate()

• Is a bit like rotating then translating

Order of transforms

The normal best order is

Translate

Rotate

Scale

This means that an object is scaled the same why no matter how it is rotated

It is translated the same way no matter how it is rotated

Order of transforms

• Rotate

• Translate

Order of transforms

• Rotate

• Translate

• Doesn’t end up at the end point of translating

Order of transforms

• Translate

• Rotate

Order of transforms

• Translate

• Rotate

• Rotates about its centre– if you use

rectMode(CENTER)

• Translates to the correct position

Order of transforms

• Similarly if you scale an object differently along x and y and as well as rotating the order matters

• If you do – Scale()– Rotate()

• The result is no longer a rectangle (skewed)

• (see program)

Multiple transforms

• But what if we want to draw more than one thing?

Multiple transforms

• But what if we want to draw more than one thing?

• If we transform the first one then the second, the first transform will apply to the second as well

Transform Matrices

• A transform is represented internally as a matrix

• A 3D array of number

• The details of how doesn’t matter at the moment

Transform Matrices

• Up to now we have only had 1 matrix

• All transforms are combined together into this matrix

• To draw more than one object we need more than one matrix

Transform Matrices

• Up to now we have only had 1 matrix

• All transforms are combined together into this matrix

• To draw more than one object we need more than one matrix

• Multiple matrices are stored in a “Stack”

Stacks

• A Stack is like a stack of paper

1

2

3

4

Stacks


• You can put things on it– “Push” it on a stack

1

2

3

4

5

Stacks


• You can put things on it

• And take things off– “Pop” it off the stack

1

2

3

4

Stacks


• You can put things on it

• And take things off– “Pop” it off the stack

1

2

3

Stacks

• The last thing to be put on is the first to be taken off

• Last in, first out

1

2

3

Matrix Stacks

• Storing matrices as a stack means that the most recent transforms are the ones you remove first

• Generally what you want

• Global transforms that affect the whole picture are at the bottom

• Transforms that only affect a single object at the top

Pushing and Popping Matrices

• PushMatrix() creates a new matrix and puts it on the top of the stack

• You can then do any transforms you like

• PopMatrix() will then remove the matrix from the stack

• i.e. it will remove all the transforms you have done

Multiple Objects

• For multiple objects:– PushMatrix() before drawing each object– Do all the transforms for that object– PopMatrix() to get rid of the transforms before

moving on to the next matrix

Transforms in 3D

• Translation works exactly the same in 3D• need an x,y and z for the translation vector• rotation is more complex: next lecture

Exercises

• Draw a rectangle, rotating, translating and scaling it

• Draw multiple rectangles in multiple positions using PushMatrix and PopMatrix

• Do the same with boxes in 3D

this terms course last term we both worked on learning 2 things –processing –the concepts of...

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