- Prerequisites for this lecture are: 6-1, 6-2 and 6-3.

- consider the problem of making a
barrels appear to roll across a plank
- this is complicated by the issue of the ramp gradient

- fortunately Bresenham discovered an
algorithm which given two points
- determines the elements of a 2-dimensional grid that should be selected to best approximate the line

- Bresenham’s line algorithm also uses integer arithmetic which adds to its complexity

- returning to the problem of making a
barrel roll down a plank
- we know the x position, but we need to compute the y value

- we know the start and end points of the ramp
- in the previous slide the start position is (1, 2) and the end position is (5, 4)
- the dx value is 5-1 = 4
- the dy value is 4-2 = 2
- therefore our gradient is
- we need to calculate
- we know the point (1, 2) exists on the line
- using
- we could use this formula to calculate the value given an value
- notice how we need floating point values to compute
it
- also notice how we calculated the gradient

- Bresenham’s algorithm hunts for the correct gradient by using integer arithmetic and by manipulating the numerator and denominator of the fractional value of

2. Moving along a line

3. Bresenham’s line algorithm

4. y = mx + c

Index

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