Class3 - Hidden Surfaces and Introduction to Transforms and...

Hidden Surfaces and Introduction
to Transforms and Projections
HW3
Ulrich Neumann
CS580
(Computer Graphics Rendering)

Hidden Surface Removal (HSR)
–
Image-order (pixel) or object-order (poly)
methods
–
Edge (line) or surface visibility methods
•
wireframe lines are hard to deal with
–
simple z-buffer does not work
–
edge-crossing and object sorting methods

Raycasting
For every ray through a pixel,
perform a ray-intersection with every object.
Keep the closest intersection.
Image plane
View point or focal point

Painter's algorithm
•
Just render in order
–
front to back or back to front.
•
View dependent and doesn’t work for
overlapping tris.

Painter’s Algorithm (2)
Failure cases:
- Farthest z extent is insufficient
- Cannot resolve dependency cycles
top
front
View
direction

Warnock algorithm
•
Overcomes problem of view dependent ordering and intersecting
geometry by approach based on divide and conquer.
•
Subdivide screen until single region has simple front/back
relationship
•
Sub areas are completely visible / hidden, or area is too small to
subdivide again
•
Usually use quad tree subdivision
•
Useful for curved surfaces and antialiasing where the subdivision is
done to sub-pixel levels.
•
Efficient and concentrates work where needed --adaptively --
common theme in graphics

Area Subdivision (Warnock)
1. Initialize the area to be the image plane
2. Four cases:
1. No polygons in area: done
2. One polygon in area: draw it
3. Pixel sized area: draw closest
polygon
4. Front polygon covers area: draw it
Otherwise, subdivide and recurse

BSP tree
•
view-independent binary tree structure that
allows view dependent front to back or back to
front traversal.
–
More detail in later class.

BSP Trees
Advantages

view-independent tree

anti-aliasing

transparency
Disadvantages

many, small polygons

over-rendering

hard to balance tree

BSP Trees
Advantages

view-independent tree

anti-aliasing

transparency
Disadvantages

many, small polygons

over-rendering

hard to balance tree

Portals
Separate environment into cells
Preprocess to find potentially visible polygons
from any cell

Portals
Treat environment as a graph
Nodes = cells, Edges = portals
Cell to cell visibility must go along edges

Z buffer
•
Compare each new pixel’s depth to current pixel