This is a course on the theoretical underpinnings of 3D Graphics in computing, suitable for students with a suitable grounding in technical computing.

1. INTRODUCTION TO 3D
Michael Heron

2. INTRODUCTION
 For the next three weeks we will be talking about
3D graphics.
 Specifically, 3D graphics using the open source blender
package.
 Module will concentrate on technical content.
 I have absolutely no artistic skill in the slightest.
 Seriously.
 Content time broken up into:
 Two lectures
 One tutorial
 One lab prep
 Four hour lab slot

3. GRAPHICS
 Graphical images on a computer monitor are made
up of 2D arrays of pixels.
 The number of pixels in that array is dependant on the
system’s resolution.
 Pixels represent a single element of an image.
 Represented by a colour code.
 Pixels have a depth.
 Represents the expressive palette of colours.
 8 bit depth represents 256 colours
 24 bit represents 16.8 million colours

4. COLOUR REPRESENTATION
 Colours are usually represented by an RGB value.
 An array of three digits corresponding to the blend of
colours.
 An RGB value of {0,0,0} represents white.
 An RGB value of {255,255,255} represents black.
 Other colours made up of points in-between.

5. 4-BIT COLOUR

6. 8-BIT COLOUR PALETTE
© Lucasarts, 1990

7. 24-BIT COLOUR PALETTE
© Lucasarts, 2009

8. DISPLAYING GRAPHICAL INFORMATION
 Graphics are displayed on a computer monitor
using rasters.
 Lines of pixels.
 CRT monitors make use of electron guns to display
images on the screen.
 Three guns (red, green, blue)
 Guns fire beams at the phosphor coating on the inside
of the monitor.
 This occurs many times per second.
 Governed by the monitor’s refresh rate.

9. DISPLAYING GRAPHICAL INFORMATION
 An LCD works somewhat differently.
 A backlight is used to create light
 This light passes through two substrates of polarised
glass.
 While this is happening, an electrical current causes the
crystals within the substrates to align.
 The combination of these substrates allows for the desired
colours to appear at the appropriate point.
 There are other ways too
 Not important at this time.

10. REPRESENTING GRAPHICS (2D)
 Two main way of representing graphics in a
computer.
 Rasters, comprised of arrays of pixels.
 Vectors, comprised of collections of objects expressed
as mathematical formulae.
 Rasters used to represent photographs and other
such bitmaps.
 Vectors used to represent more asbtract models.

11. REPRESENTING GRAPHICS (3D)
 In three dimensions, vectors are used almost
exclusively for representing shapes.
 Images built up of collections of vertices, points, and
polygons.

12. DIFFERENCES IN REPRESENTATION
 2D Images
 Raster
 Permits great amounts of detail but no representation of
relationship between objects.
 Substantial file size
 Vector
 Permits relationship of objects.
 Minimal details permitted
 Difficult to represent details using basic shapes
 Several trade offs
 Processing Power
 Realism
 Modifiability
 Expressive Potential.

13. 3D GRAPHICS
 Complex 3D scenes can be created as 2D images.
 Often done using ray-tracing or other technologies.
 Not real-time
 Goal of 3D graphics is to permit photorealistic
representations of complex spatial topographies.
 Difficult task
 Requires much investment in building environments and
objects within them
 Many applications require real-time rendering.
 Games

14. PHOTOREALISM
 3D Graphics seeks to achieve photrealism by:
 Vector representation of 3D Objects
 Texturing of 3D objects in materials
 Interaction of light on objects
 Shadows
 Reflections
 Colour
 Glare
 Photorealism is important for many contexts.
 Simulation, entertainment, research, medical teaching

15. 3D ON A COMPUTER
 Not possible to show 3D images on a computer.
 Monitor is an inherently 2D device.
 Techniques are used to simulate the appearance
of three dimensions.
 Use of perspective, layering, projection of a plane onto
a fixed view.
 Many different interacting parts.

16. 3D MODELLING
 3D Modelling is a multi-stage process.
 Representation
 Build a model of 3D Objects
 Shapes
 Surface textures
 Sometimes using bitmaps.
 Rendering
 Geometric translations
 Projection to 2D
 Light representation

17. THE CARTESIAN PLANE

18. SIMPLE 3D OBJECT
(x1,y1,z1) (x2,y2,z2)
(x3,y3,z3)
(x4,y4,z4)
(x5,y5,z5) (x6,y6,z6)
(x7,y7,z7)(x8,y8,z8)
© Glenn Rowe

19. MORE COMPLEX REPRESENTATIONS
http://www.fallingpixel.com/3d-models/13227

20. 3D REPRESENTATIONS
 Complex shapes represented by polygons
 Triangles and Rectangles mostly
 Number of polygons defines the accuracy of the
representation
http://www.nvnews.net/reviews/evolva_preview.shtml

21. TRANSFORMATIONS
 Transformations used in 3D to manipulate images.
 Three main transformations used in Blender.
 Grab (translate)
 Used to move shapes around fixed axis
 Rotate
 Used to rotate shapes around a fixed axis
 Scale
 Used to scale shapes up or down
 Underlying representation done using matrix
manipulation.

22. PROJECTION
 Projection is the process that transforms 3D objects
onto a 2D plane.
 Three co-ordinate models.
 Local, defines the shape’s vertexes
 World space, defines the shape in relation to other shapes.
 Viewing space, defines the location and size of the shape
when displayed on the monitor.
 Process turns {x,y,z} into just {x,y}

23. PROJECTION STYLES
 Parallel Projection
 Shows relationship between objects
 Not realistic
View plane
3D object

24. PROJECTION STYLES
 Perspective Projection
 Represents objects more realistically by converging
vertexes at a point.
 Foreshortening permits perspective.
View plane
3D object
Centre of projection

25. PROJECTION
 Both assume a camera location.
 The camera defines our view on the world.
 To change the view of an object, we can:
 Move the camera
 Move the object.
 Must get our heads around a viewport that has no
fixed representation in the world space.

26. SUMMARY
 Next three weeks about 3D graphics.
 Using Blender.
 3D Graphics consist of
 Representation of objects
 Representation of a world
 Representation of a view port
 Rendering
 Complex transforms applied to turn 3D
representation into 2D view.