CS 184: COMPUTER GRAPHICS

NOTE: Tonight: discussion sections 7-9pm in 320 Soda hall

Lecture #12 -- Th: 10/7, 2004.

Putting together a Simple 3D Rendering Pipeline

Scene Hierarchy --> Rendering Hierarchy
Put the Camera node "above" the World node.
Use inverse transformations whenever you need to move "upwards" in the scene tree.

Finding the proper sequence ...
We need to think about the exact order in which we want to do all the necessary operations:
-- culling, backface elimination, clipping, shading, rasterizing ...
General principles:
-- Do least expensive, most work-saving steps first.
-- Don't throw away information you may need later.

One possible practical 3D Rendering Pipeline

• Read in the scene description (build appropriate internal data structures).
• Process the master geometry at the leaf nodes (calculate face and/or vertex normals).
• Define a camera type (for now using a parallel projection).
• Place this camera in the World (probably using the "look_at" transformation).
• Find how the World lies in the VRCS coordinate system (use inverse camera transformation).
• Fit the view volume into the canonical half-cube (non-uniform scaling).
• Do hierarchical bounding-box culling in 3D (using 6-bit outcodes on the 8 Bbox corners).
• Eliminate the backwards facing polygons (check z-components of transformed face normal).
• Clip the polygons at the leaves of the scene hierarchy that straddle the canonical half-cube (against 6 planes).
• Later:
• Compute the color/shading on the remaining polygon fragments (assume diffuse ambient lighting only).
• Raster-fill the polygons (turn on the pixels that represent the visible area of the polygon).
• Resolve overlapping polygons (use z-buffer to render front-most pixel).

ASG#5:  "3D Parallel Projections and the Crystal Ball Interface"

First, make some simple 3D scene (consisting of convex objects).
You may use some imported SLIDE objects from a library of polyhedra.
For instance the "triacontrahedron" which is the "dual of the icosidodecahedron".
Make large visible time/mouse dependent chages,
so that we can see that your algorithms can handle dynamic scenes.

Then get the basic rendering process to work.
First just use a default parallel projection down the z-axis as you have been using in the past assignments.
Once you can see something on the screen, debugging becomes much easier (and more fun).

Then add the other modules:
Bounding box culling, back-face elimination, polygon clipping.
Just modify suitably your 2D code for these modules.
You can use the flat-shaded rendering mode, and let the z-buffer take care of eliminating features hidden by occlusion
(you will implement that module in a later assignment).

Finally, add a "Crystal Ball" interface to manipulate the 3D object/scene.
This provides a convenient way to twiddle an object around for interactive inspection.
The conceptual idea is that your screen is some large crystal ball that contains the scene that you are seeing.
With appropriate mouse motions on its surface, you can rotate that ball and its content.

Interactive Viewing Control:  "Crystal Ball" Interface

We will do better: We will turn the object in the screen coordinate system,
so that it always responds properly to the mouse cursor movements as initiated by the viewer.

3D Rotations around an arbitrary axis

2.)  Another way to achieve the above effect is to use the "change of basis" matrix .
Define a local coordinate system with its z-axis aligned with the rotation axis.
Do a coordinate transform that expresses the world coordinates in this new coordinate system,
in which the desired rotation can be done easily (around the z-axis).
Then do a change of basis back to the old coordinate system.

3.)  A third way is to use vector algebra to decompose the vector from the origin to the point to be transformed
into two components: one parallel to the rotation axis, and the other perpendicular to it.
Only that second component needs to be rotated, and this can be done in a plane perpendicular to the rotation axis.
The overall transformation matrix then results from a composition of these vector components (see lab notes).

The general SLIDE rotation statement does all this work for you !  

Where should this extra transformation go ?

Should that subtree include the lights ?
Discuss the pros and cons ...
... and the SLIDE solution.

Camera Parameters for Parallel Projection

Rendering in SLIDE

NOTE: Between 10/12 and 10/14 you will have to do: Take-Home Quiz #2

Bring your level of understanding up-to-date and reserve about a 2-hr time slot.

Reading Assignment:

Current Homework Assignment: