Advanced Graphics Study Guide

Advanced Graphics, Dr Neil Dodgson, University of Cambridge Computer Laboratory
Part II course, 2000


Part 4: Other 3D modelling mechanisms
A: Generative models
B: Converting swept objects to polygons
C: Constructive Solid Geometry
D: Implicit surfaces, voxels and marching cubes
E: Subdivision surfaces
...back to part 3 | on to part 5...

4A) Generative models

Sweeps

These are three dimensional objects generated by sweeping a two dimensional shape along a path in 3D. Two special cases of the sweep are surfaces of revolution, where the path is a circle; and extrusions, where the path is a straight line.

Surfaces of revolution are covered in R&A section 6-2. Sweeps are covered in R&A section 6-3 and FvDFH section 12.4.

Extrusion

<Image:
an example extrusion.> <Image:
the same extrusion, rendered tranparently.>
On the left (above) is an example extrusion. On the right is its generating polygon (the red star), with the generated 3D object shown in semi-transparent cyan.

Surface of revolution

<Image:
an example surface of revolution.> <Image:
the same surface of revolution, rendered tranparently.>
<Image:
the same surface of revolution, rendered tranparently.> On the left (above) is an example surface of revolution. On the right (above) is its generating quadrilateral (the red polygon), with the generated 3D object shown in semi-transparent cyan. Below that is another view of the same surface of revolution.

Revolution or extrusion?

<Image:
a 3D object.> <Image:
the same object generated as a surface of revolution (rendered tranparently).>
<Image:
the same object generated as an extrusion (rendered tranparently).> Some objects can be generated in more than one way. The hollow cylinder shown above (left) could be generated as either a surface of revolution (above right) or as an extrusion (immediately right).

General sweeps

If we push the idea of a sweep to its limit we can think of many things which could be modified to produce a three dimensional swept shape: <Image: a swept object: but is it art?> At right is a swept object with a circular cross-section, semi-circular path, and varying scale.

You may be able to think of parameters, other than those in the list above, which could be modify.

Exercises
  1. [1998/7/12] Show how the following object can be represented as a swept object.
    <Image: the object from the 1998 exam question> <Image: the object from the 1998 exam question>

  2. Use the following different methods of specifying a geometrical model for this picture (assuming it's a three dimensional model and not a line drawing). Come as close as you can to the original for any of the methods, and describe the difficulties in using a particular method for this model.
    1. Extrusions
    2. Surfaces of revolution
    3. General sweeps
  3. For each of the following categories list five real-world objects which could be represented by the primitives in the category.
    1. The ray-tracing primitives in Part 2A
    2. Extrusions
    3. Surfaces of revolution
    4. General sweeps
  4. A flume (water tunnel) at a swimming complex is modeled as a circle swept along a particular path. The designers also want to model the volume swept out by a person traveling down the flume. (We can approximate the cross-section of a person with something roughly elliptical and we'll assume the `virtual' person doesn't move legs or arms while hurtling along.) Explain which parameters in the list would be need to be modified to specify the shape of the flume and which would need to be modified to model the volume swept out by a person traveling down the flume (alternatively, specify which parameters would be held constant, in each case, for the entire length of the sweep).


Part 4: Other 3D modelling mechanisms
A: Generative models
B: Converting swept objects to polygons
C: Constructive Solid Geometry
D: Implicit surfaces, voxels and marching cubes
E: Subdivision surfaces
...back to part 3 | on to part 5...


Neil Dodgson | Advanced Graphics | Computer Laboratory

Source file: p4a.html
Page last updated on Thu Sep 14 16:58:06 BST 2000
by Neil Dodgson (nad@cl.cam.ac.uk)