This is a course on the theoretical underpinnings of 3D Graphics in computing, suitable for students with a suitable grounding in technical computing.

1. RENDERING PART
TWO
THIS TIME, IT’S PERSONAL
Michael heron

2. INTRODUCTION
 In the previous lecture we talked about the
nature of light reflection in rendering.
 Complex and governed by physics
 Approximations only
 In this lecture we are going to talk about some of
the other things that are involved in the
rendering process.
 Rasterisation
 Hidden surface removal

3. RASTERISATION
 Rasterisation is the process of turning a rendered
3D model into a two dimensional pixelized image.
 Most usual technique for creating real-time 3D
images.
 Directly competes with other techniques such as ray
tracing
 Rasterisation is comparatively fast.
 But limited by the number of polygons to be drawn.

4. RASTERISATION
 Three processes for rasterisation:
 Determine which squares of the 2D display are
occupied by the polygon.
 Determine the depth of each square.
 More on this later
 Determine the colour of squares.
 Process can introduce complications.
 Adjacent polygons should fit together without gaps.
 Can be complicated by nature of resolution.

5. RASTERISATION
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Graphical representation of
3D scene held ‘off screen’ in
the frame buffer before
being drawn.
It contains the colour and
intensity of each pixel to be
drawn on the screen.
When all polygons
rasterised, the buffer is
drawn to the screen.

6. HIDDEN SURFACE REMOVAL
 Because processing cost is dependent on
the number of polygons to be rendered,
useful to restrict the number of polygons
to draw.
Polygons are sometimes partially or
completely hidden by other polygons.
 Occluded
 Determined by rasterisation.
 A process by which we can reduce the
number of polygons we draw is important.
Handled in two separate ways

7. HIDDEN SURFACE REMOVAL
Object model
What the viewer would see
Entire polygons
hidden from view point
Some polygons closer
to viewer (overlapping)

8. HIDDEN SURFACE REMOVAL
 Surfaces that are completely occluded are simply
culled.
 They never get drawn.
 Partially occluded polygons get dealt with using a
Hidden Surface Removal algorithm.
 Most well known of these is the z-buffer algorithm.

9. HIDDEN SURFACE REMOVAL
1. 2.
Stage one deals
with culling
backface
polygons
Stage two deals
with partial
occlusion.

10. CULLING
 Culling done relative to viewing angle.
 If difference between the viewing angle and the
surface normal is greater than 90 degrees, the
surface is invisible.
 Also known as back-face culling
 Remove those triangles not facing the camera from
the rendering queue.
 Deals with complete occluded polugons.

11. CULLING
If the difference is greater than 90 degrees,
then we remove the polygon from the list
Of objects to be rendered.

12. AFTER CULLING
 Having removed the hidden polygons, we need to
decide upon overlapping polygons.
 All polygons drawn as separate entities. No
knowledge of relationship in the scene.
 Need an algorithm to decide on how partially
occluded polygons are to be drawn.
 Such as the z-buffer algorithm.

13. THE PAINTER’S ALGORITHM
 Deals with hidden visibility by drawing things
farthest to nearest.
 Like a painter on a canvas.
 Requires some pixels to be redrawn several
times.
 And has some problems with overlapping shapes.
 Compensation for this complicated and expensive.
 Splitting polygons.

14. THE PAINTER’S ALGORITHM

15. Z-BUFFERING
 For each pixel, we could sort each polygon
by depth.
Draw only the one nearest.
Sorting a costly process
 And done for each pixel to be rendered.
 Z-Buffering achieves the same effect
without sorting.
Dramatic performance improvement in terms
of CPU.
Quite costly in terms of memory
representation.
Many hardware architectures have dedicated
z-buffer chips.

16. Z-BUFFER
 The Z-Buffer is a 2D array that maps onto
the same dimensions as the image.
As we encounter polygons, we make a note of
their depth (z) value.
 We assume our viewport is on the positive
z-axis
And we are looking down that z-axis towards
the scene.
 Done during rasterisation.
We keep a track of the depth of each image we
are to draw.
We store the colour and the intensity as we do
this.

17. Z-BUFFER
 While doing the rasterisation, we can
compare the z value against our current
‘nearest’ shape.
If it’s farther away, we don’t render it.
 Skip it, move on to the next
If it’s closer than our previous closest, it
becomes the new closest match.
 It replaces the colour and intensity as it does so.
 The end result is that the frame buffer
contains only the information relating to
the nearest polygon for any pixel.

18. Z-BUFFER

19. PROCESS
 3D Scene leads to definition of
relationship of objects.
Scene gets broken down into polygons to
represent 3D shapes.
 Back-face culling used to eliminate
polygons that are invisible.
 Rasterisation goes over each non-culled
polygon to determine where it falls on the
viewing screen.
Colour and intensity of each pixel determined
Z-buffering used to ensure proper handling of
partial occlusion.

20. Z-BUFFERING AND TRANSPARENCY
 The Z-Buffer algorithm doesn’t work for
transparent polygons.
Alas!
 The z-buffer occludes things behind other
things.
With transparency, we should be able to see
the things we are in front of.
 A quick fix:
Draw opaque polygons first
Then draw translucent polygons
 Can be combined with alpha blending.

21. OTHER KINDS OF HSR
 Contribution culling
If objects are too small to contribute to a scene,
then we simply discard them.
 Viewport culling
If objects are outside our viewing projection,
we don’t process them.
 Other visibility algorithms exists
Binary tree partitioning
Warnock algorithm
Ray Casting

22. IMPORTANCE OF HSR
 Despite huge improvements in GPU
hardware, efficiency still important.
Hardware has gotten more powerful
Models have gotten more complex.
 A certain frame-rate is required in order
for ‘realistic’ motion to be experienced.
Trade-off between polygon count and frame-
rate.
 Easiest way to reduce polygon count
without compromising graphical quality.

23. SUMMARY
 Important to be able to cull hidden polygons and
pixels.
 Reduces rendering cost.
 Two related processes.
 Culling
 Visibility
 Z-Buffering one of the most common processes in
use today.