Representing 3D on 2D

One of the thing I felt most important to CG is the fact that we are trying to represent 3-dimesional objects on 2 dimensions, our computer screen.

Therefore, besides the X and Y axis, the Z axis is utilised for perspective control (orthogonal and modelview, will come back to this in a moment); ex: Z_near, Z_far.

Initially on my GL assignment I made the mistake of drawing my ground plane on X & Y axis, causing all my models to seem like they're stuck on their side to the wall. Wrong! Should draw the ground plane on the X and Z axis!

When drawing & loading model vertices, always remember... counterclockwise to look at the front side. Right hand rule.

CG works by: modelling --> animating --> rendering.

Texture mapping= rendering the surface without requiring additional polygons to represent minute details.

Coordinate system

This I gotta find out more: model space, world space, eye space, normalised projection space, normalised device space, image space.

2D TRANSFORMATION

translation
rotation
scaling
homogeneous coordinates
composite transformation


Rigid Motion (Euclidean Transformation) preserves the distance and angle : Identity, Translation, Rotation. ∴ Shape and orientation does not change!


Linear Transformation: Identity, Rotation, Scaling, Shearing, Reflection.

Affine Transformation: add translation to linear transformations ∴ giving us affine transformation.


3D TRANSFORMATION

homogeneous coordinate
translation, scaling
rotation
composite transformation
change the orthonormal basis

3D Affine Transformation Matrix... absolutely beautiful. Draw it tomorrow.


3D Viewing and Projection

World to Eye Coordinate Transformation
Eye Coordinate System
(related to orthonormal basis)

Grr... Projection Transformation.

2 types of projection: perspective & parallel. The key factor here is COP (Center Of Projection). If projection plane is finite == perspective. Infinite projection plane == parallel.


*****Will come back and finish this. Now I need to sleep. And have mathematical nightmares.
















Oooh... I need to come back to these:
http://www.faqs.org/faqs/graphics/algorithms-faq/
http://kesen.huang.googlepages.com/