Fundamentals of Data Representation: Vectors

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UNIT 1 - ⇑ Fundamentals of Data Representation ⇑

← Bitmaps Vectors Comparison between vector and bitmaps →


Vector Graphics - images defined using mathematics and geometry such as points, lines, curves, and shapes or polygon(s). Allowing for scalability. Objects and properties stored mathematically.


Drawing list - a set of commands used to define a vector image


Vector graphics are made up of objects and their properties. An object is a mathematical or geometrically defined construct such as a rectangle, line or circle.

<rect ... />
<line ... />
<circle ... />

Each of these objects has properties to tell you the size, colour, position etc. Take a look at the next example to see how drawing lists are built from objects and properties.

Rectangle Circle Combination
Image Svg example1.svg Svg example4.svg ExempleSimple.svg
Drawing
List
<rect x="14" y="23"
 width="250" height="50"
 fill="green"
 stroke="black" stroke-width="1" />
<circle cx="100" cy="100" r="50"
 fill="red"
 stroke="black" stroke-width="5" />
  <rect
     width="100" height="80"
     x="0" y="70"
     fill="green" />
  <line
     x1="5" y1="5"
     x2="250" y2="95"
     stroke="red" />
  <circle
     cx="90" cy="80"
     r="50"
     fill="blue" />
   <text x="180" y="60">
     Un texte
   </text>
Notes x and y give the top left start location Note that the centre co-ordinate is defined through cx and cy
r gives the radius
Note that the circle is on top, this is because it was drawn last.
To leave out an edge stroke don't put the stroke command in.
The line has start x1,y1 and end x2,y2 coordinates.
Extension:SVG

There are several vector graphic formats out there, but an easy one to get started with is Scalable Vector Graphics (SVGs). SVGs are very easy to create and are supported by all modern major web browsers. To create an SVG, you need to add the tags <svg xmlns="http://www.w3.org/2000/svg"> at the beginning and </svg> at the end. Copy the following into a text file and save it as image.svg

<svg xmlns="http://www.w3.org/2000/svg">
  <rect
     width="100" height="80"
     x="0" y="70"
     fill="green" />
  <line
     x1="5" y1="5"
     x2="250" y2="95"
     stroke="red" />
  <circle
     cx="90" cy="80"
     r="50"
     fill="blue" />
   <text x="180" y="60">
     Un texte
   </text>
</svg>

Once you have saved this, drag it into a browser window and you should see some shapes. SVGs are very powerful and you can attach code to their structure, making them interactive. If you want to learn more about how make SVGs take a look at w3schools

Exercise: Vector Graphics

What is a drawing list

Answer :

a set of commands used to define a vector image

Give some objects that can be used in vector graphics:

Answer :

  • Line
  • Text
  • Rectangle
  • Circle

Give the properties needed to display a rectangle:

Answer :

  • x,y
  • width, height
  • fill
  • stroke (colour), stroke-width

Give the properties needed to display a line:

Answer :

  • x1,y1 - start coordinates
  • x2,y2 - end coordinates
  • width
  • fill
  • stroke (colour)

Give the definition of a vector image:

Answer :

images defined using mathematics and geometry such as points, lines, curves, and shapes or polygon(s). Allowing for scalability

Write a drawing list to create the following image:

CPT-Graphics-VectorList1.svg

Answer :

<rect
     width="1" height="1"
     x="2" y="1"
     fill="white" <!--optional you can leave this out-->
     stroke="black"
     stroke-width=1 /> <!--another small value will do-->
<rect
     width="1" height="1"
     x="11" y="0"
     fill="white" <!--optional you can leave this out-->
     stroke="black"
     stroke-width=1 />
<rect
     width="10" height="4"
     x="2" y="6"
     fill="black"
     stroke="red"
     stroke-width=5 /> <!--another small value will do-->
<circle
     cx="7" cy="5"
     r="2"
     fill="blue" />
What would the following drawing list produce:
<line
     x1="0" y1="0"
     x2="6" y2="6"
     stroke="red" />
<rect
     width="4" height="4"
     x="1" y="1"
     fill="yellow"
     stroke="green"
     stroke-width=1 />
<line
     x1="6" y1="0"
     x2="0" y2="6"
     stroke="black" />

Answer :

CPT-Graphics-VectorList2.svg

In the above code, name the objects involved

Answer :

rect and line

In the above code, list 4 different properties

Answer :

  • Fill
  • Stroke
  • Stroke-width
  • Width
  • Height
  • X,Y