This document provides an overview of polygonal modelling techniques used in 3D computer graphics. It discusses how polygon meshes are constructed using vertices, edges, and faces. Common operations for constructing meshes like box modelling and extrusion modelling are described. Refining models by manipulating individual vertices is also covered. The document emphasizes the importance of using reference materials when building 3D models.

1. 2672QCA 3D MODELLING
FOR VISUALISATION

2. POLYGONAL MODELLING
Using Mesh-Based Polygonal Modelling to
virtualise any object as a digital asset.

3. POLYGON MESHES
POLYGONAL OPERATIONS
A detailed consideration of
common operations.
OVERVIEW
An overview of polygonal
modelling theory.
How do meshes form geometric
shape?
LECTURE CONTENTS
01
02
03
04 REFERENCE MATERIALS
Appropriate processes for
creating new models.

4. OVERVIEW
01
An overview of polygonal
modelling theory.

5. INTRODUCTION
In 3D computer graphics, Polygonal modelling is an approach for modelling objects by
representing or approximating their surfaces using polygon meshes.
The basic object used in mesh modelling is a vertex, a point in three-dimensional space.
Two vertices connected by a straight line become an edge. Three vertices, connected to
each other by three edges, define a triangle, which is the simplest polygon in Euclidean
space.

6. GEOMETRIC
THEORY
In Euclidean geometry, any three non-collinear points determine a plane. For this reason,
triangles always inhabit a single plane. This is not necessarily true of more complex
polygons.
The flat nature of triangles makes it simple to determine their surface normal, a three-
dimensional vector perpendicular to the triangle's surface.

7. GEOMETRIC
THEORY
Every triangle has two face normals, which point to opposite directions from each other.
In many systems only one of these normals is considered valid – the other side of the
polygon is referred to as a backface, and can be made visible or invisible depending on the
desires of the designer.

8. POLYGONS AND THEIR NORMALS

9. POLYGONAL MESHES
How do meshes form geometric
shape?
02

10. A polygon mesh is a collection of vertices, edges and faces that defines the shape of a
polyhedral object.
The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple
convex polygons (n-gons).
As polygonal meshes are extensively used in computer graphics, algorithms also exist for ray
tracing, collision detection, and rigid-body dynamics with polygon meshes.
If lines are drawn for each edge, instead of rendering the faces, then the model becomes a
wireframe model.
POLYGON MESH

11. ELEMENTS OF POLYGONAL MESH

12. Objects created with polygon meshes must store different types of elements. These include
vertices, edges, faces, polygons and surfaces.
In many applications, only vertices, edges and either faces or polygons are stored.
A renderer may support only 3-sided faces, so polygons must be constructed of many of these,
as shown on the previous slide.
However, many renderers either support quads and higher-sided polygons, or are able to
convert polygons to triangles on the fly, making it unnecessary to store a mesh in a
triangulated form.
ELEMENTS OF A POLYGONAL MESH

13. POLYGONAL OPERATIONS
03
A detailed consideration of
common operations.

14. Although it is possible to construct a mesh by manually specifying vertices and faces, it is
much more common to build meshes using a variety of tools.
One of the more popular methods of constructing meshes is box modelling, which uses two
simple tools:
The subdivide tool: splits faces and edges into smaller pieces by adding new vertices. For
example, a square would be subdivided by adding one vertex in the centre and one on each
edge, creating four smaller squares.
The extrude tool: is applied to a face or a group of faces. It creates a new face of the same size
and shape which is connected to each of the existing edges by a face. Therefore, performing the
extrude operation on a square face would create a cube connected to the surface at the location
of the face.
POLYGON MODELLING CONSTRUCTION

15. BOX MODELLING

16. A second common modelling method is sometimes referred to as extrusion modelling.
In this method, the user creates a 2D shape which traces the outline of an object from a
photograph or a drawing.
The user then uses a second image of the subject from a different angle and extrudes the 2D
shape into 3D, again following the shape’s outline.
This method is especially common for creating faces and heads. In general, the artist will
model half of the head and then duplicate the vertices, invert their location relative to some
plane, and connect the two pieces together. This ensures that the model will be symmetrical.
EXTRUSION MODELLING

17. EXTRUSION MODELLING

18. There are other specialized methods of constructing high or low detail meshes exist.
Sketch based modelling is a user-friendly interface for constructing low-detail models quickly,
while 3D scanners can be used to create high detail meshes based on existing real-world
objects in almost automatic way.
These devices are very expensive, and are generally only used by researchers and industry
professionals but can generate high accuracy sub-millimetric digital representations.
ADVANCED MODELLING TECHNIQUES

19. ADVANCED MODELLING TECHNIQUES

20. Also referred to as "pushing and pulling vertices," most models require some level of manual
refinement.
When refining a model, the artist moves individual vertices along the x,y, or ​z-axis to finetune
the contours of the surface.
A sufficient analogy for refinement might be seen in the work of a traditional sculptor:
When a sculptor works, they first block out the large forms of the sculpture, focusing on the
overall shape of his piece. Then they revisit each region of the sculpture with a "rake brush" to
finetune the surface and carve out the necessary details.
Refining a 3D model is very similar. Every extrusion, bevel, edge-loop, or subdivision, is
typically accompanied by at least a little bit of vertex-by-vertex refinement.
REFINING AND SHAPING

21. REFERENCE MATERIALS
Appropriate processes for
creating new models.
04

22. Reference material is vital when building 3D models for production.
If you're recreating something from real life, you want the actual object in your hands so you
can examine it, measure it and see it from every angle.
When it's not possible to get the actual object, photographs are a great help in making sure your
modelled geometry matches as closely as possible.
REFERENCE MATERIAL

23. If the object to be created does not yet exist, the same still holds true.
You want as much reference as possible, but this reference will likely come in the form of
drawings and sketches.
Sometimes concepts are created in 3D, but many times they exist as 2D drawings.
These drawings can be created quickly and many iterations vetted without even touching the
computer.
REFERENCE MATERIAL CONTD

24. REFERENCE MATERIAL CONTD

25. THANKS!
Does anyone have any questions?