Rasterisation 1

Learn about the basics of rasterisation!

object based 1

loop over all objects and vertices to transform them to pixels

object-based 2

works well with pipelined architectures but needs large amounts of memory

object-based 3

struggles to model interactions between objects like reflections, these need to be approximated or fudged

image based 1

loop over all pixels to determine what objects affect their value

image based 2

common for global illumination models

result of each fragment belonging to one primitive

there can be many fragments per pixel. some of them will occlude others so we need to decide which determines the pixel colour (z buffer)

dda

digital differential analyser

when do we use the modified dda algorithm?

where |m| > 1

what do we do in the modified dda algorithm?

swap x and y - advance vertically one pixel at a time, calculate the change in x and round to the nearest pixel

motivation for Bresenham’s algorithm

dda is efficient but requires floating point addition, bresenham uses only integer operations

what two assumptions do we make with bresenham’s

pixel centers are halfway between integers, 0 <= m <= 1

given 0 <= m <= 1, what pixels do we need to consider

exactly to the right of the current pixel, and the pixel above that

removing bresenham floating point arithmetic step 1

change our increment to delta y

removing bresenham floating point arithmetic step 2

multiply by 2 to avoid comparing to 0.5

removing bresenham floating point arithmetic step 3

compare to 0 instead of 1

removing bresenham floating point arithmetic step 4

update d and y when d >= 0

odd even test

counts number of crossings of polygon edges - points with an even number are inside

when is odd even test not ideal?

self-intersecting polygons

winding number test

how many times a point is encircled, or, if following the edges from point p, how many full turns are needed. increase for anti-clockwise, decrease for clockwise. a point is considered inside if the winding number is non zero