I finished 3D modelling, covered clipping, and started 3D viewing.

My slides (ODF) Slides in PDF

Vrml examples

Chapter 3 of the OpenGL programmer’s guide on Modeling and Viewing.

BSP Tree Applet

My slides (ODF) Slides in PDF

To run the programs at CSE, do the following:

% 3421
% cd ~cs3421/public_html/labs/nate

If you want to run things at home, then you can go to Nate Robin’s page for the tutors, which is here. This has source and executables for Windows and MacOS. If you are a linux user, then you may find the following makefile useful for getting it to compile. (Note: You might to adjust the paths probably to tell it where your implementation of OpenGL is).

Shapes

To get the shapes demo up and running type

% ./shapes

This will start the first little demo we are going to have a look at. Shapes shows you all the different types of primitives that can go between glBegin() and glEnd() statements. Note that while in class we have been using Java, and here it is C, the differences are mostly cosmetic.

In the left window you have the output from OpenGL, and in the right window you have the code that generated that output. Note that to have a look at options, you can right click the mouse in either window (each has different options). For example, if you right click in the screen-space view, you can choose to toggle colours at vertices.

Have a play with the applet. Get a grip of the various types of things you can do with OpenGL. Also, try to break things. Try to get polygons that don’t behave as they should etc.

Here are some questions to guide your experimenting.

• If you toggle vertices, what happens to the colour of the polygon?
• Why does OpenGL have this interpolation of colour features? Why does a polygon engine allow you to set corner colours individually and then interpolate between them?
• What type of shapes would you use quadrilateral strips, triangle fans and triangle strips?
• Surely, you don’t need polygons AND quads AND triangle strips AND quad strips. Isn’t just polygons enough? What about line loops and line strips … surely we could implement just lines and polygons? Why does OpenGL support these strange and exotic data structures?

Transformations

To get started with the transformation demo, at the prompt type:

% ./transformation

This allows you to manipulate a variety of different models (right-click in the screen space view). Again, experiment with various settings and objects. The goal is to discover how various changes affect and interact. You may wish to use the following questions to direct your interaction.

• In the initial order of operation, in what order are the three operations done?
• What is the order of parameters to glRotatef()?
• Is this order of operations the “natural” order to do these transformations in? Why do you think that the designers chose this particular order of transformations?
• Try swapping the order of the rotations and the translations. First try to work out the effect of first rotating by 90 degrees and then translating by 3 units, and then compare this with the opposite order?
• What is the relationship between the “world-space view” and the “screen space view”? Why is it, that, for example, translating by negative values in the x direction actually leave the model where it is and moves the camera back? Is moving the camera along positive z the same as moving the objects in the scene by negative z?

Question 1

Consider the following x-y pairs.

Assuming x and y were two axes in a right handed coordinate system, would the z axis for each of these point into the page or out of the page?

Question 2

You have two vectors v1=(-1, -1, 0) and v2=(4, 2, 0).

(a) What is the dot product of the two vectors?
(b) Normalise the two vectors.
(c) what is the cosine of the angle between the two vectors?
(d) What is the cross product of the two vectors?

Question 3

(a) The old CSE logo is made from 35 small 3D cubes. Each of these cubes has a side length of 0.7 units. Find the transformation that transforms a basic cube with centre (0,0,0) and a side length of 2 (such that corners are (1,1,1) and (-1,-1,-1)) to the small cube with centre (0,4,2) (one of the cubes in the logo).
(b) Consider a local to world transformation, with the basis (0.35,0,0), (0,0.35, 0) and (0,0,0.35) for u,v and n respectively, and with offset (0, 4, 2). Is this an orthogonal basis? Orthornormal? What is the matrix for the local to world transformation in this case?

Question 4

Consider the following sequence of matrix operations in OpenGL. Show what happens to the modelview matrix stack after each operation, and calculate where the points A, B, C and D get transformed to in world space (NOTE: For convenience, the usual jogl “gl.” has been removed). In other words, where do A, B, C and D end up?

glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glScalef(3,3,3);
glBegin(GL_POINTS); <-- A
glVertex3f(1,2,1); 
glEnd(); 
glRotatef(90, 0, 1, 0);
glBegin(GL_POINTS);
glVertex3f(2,1,3); <-- B
glEnd();
glPushMatrix();
glTranslatef(1,0,0);
glMultMatrix(1,0,0,0,0,2,0,0,0,0,1,0,0,0,0,1);
glPopMatrix();
glBegin(GL_POINTS);
glVertex3f(0,2,0); <-- C
glEnd(); 
glTranslatef(0,1,0);
glBegin(GL_POINTS); 
glVertex3f(1,0,0); <-- D
glEnd();

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polyLineDraw: OpenGL and mouse input.

polyTess: OpenGL polygon tesselation.

Toy1: Simplest 3D program - draw the teapot.

Toy2: Calls Starwars to make an X wing fighter.

Toy3: Rotating about x, y and z axes

ToyFinal: Big demo of all the objects list below

StarWars: Use matrix stack to make a Xwing

Function2D: A surface defined by the sinc function.

BezierPatch: One Bezier patch defined by 16 control points.

FractalTree: A simple fractal tree

CSELogo: The Old CSE logo

trackball: Uses quaternions to create a virtual trackball. The code is converted from C code in GLUT, so it’s ugly.

Vector3D: 3D vector functions like cross product.

My slides (ODF) Slides in PDF

Vrml examples

Chapter 3 of the OpenGL programmer’s guide on Modeling and Viewing.