Difference Between DDA and Bresenham’s Algorithm (With Table)

The field of computer graphics is vast and constantly evolving. It involves various concepts and ideas that may seem complicated for beginners. In the midst of this, one of the most basic things to do in graphical media is ‘drawing a line’. For this purpose, DDA and Bresenham’s algorithm are two algorithms that can be used to approximate a line segment. 

DDA vs Bresenham’s Algorithm

The difference between DDA and Bresenham’s algorithm is that the DDA algorithm mostly uses multiplication and division in its operations while applying floating purpose values whereas Bresenham’s algorithm mostly used addition and subtraction in its operations while applying spherical off functions. Moreover, it is often argued that the DDA algorithm is not as efficient as the latter.

DDA stands for ‘digital differential analyzer’. It is essentially an algorithm that is used to estimate variables that exist between two points. Most people use it for converting vector lines, triangles, and polygons, into their raster counterparts. It is even possible for them to be extended to non-linear functions using DDA.

Meanwhile, Bresenham’s algorithm is used specifying the starting and ending points between a line must be drawn in computer graphics. Most people use it in bitmap images to create line primitives. The extension of this algorithm can even be used to draw circles. However, despite being one of the oldest algorithms designed, it is very efficient as compared to others.

Comparison Table Between DDA and Bresenham’s Algorithm

Parameters of ComparisonDDABresenham’s Algorithm
MethodIt only uses multiplication and division.It only uses addition and subtraction.
EfficiencyIt is not as efficient as the latter.It is very efficient despite being one of the oldest.
SpeedIt is not as fast as the latter.It is one of the fastest algorithms for line drawing.
PrecisionIt is not very accurate or precise.It is very accurate and precise.
ComplexityIt uses complex calculations in its work.It uses simple calculations in its work.
OptimizationIt does not allow optimization.It allows optimization.
PriceIt is expensive.It is on the cheaper end.

What is DDA?

DDA is an acronym for ‘digital differential analyzer’. It comes in software as well as hardware forms. Essentially, it is a tool that helps estimate variables between two points. Further, a line segment can be drawn through these variables. Such an algorithm is often used to convert vector lines, triangles, and polygons into raster.

A noteworthy use of the DDA algorithm is that once it converts line segments into raster, it can even use them in non-linear functions. This can further be applied to texture mapping, traversing shapes from 3D to 2D, and even in making quadratic curves.

The way DDA works is one of the oldest methods in computer graphics. Firstly, the algorithm estimates values for different points. These points are defined by xi, which is calculated using the equations xi = xi-1 + 1 and yi = yi-1 + m. Further, the slope of the line segment is estimated and further calculated before drawing.

However, a limitation of this algorithm is that it is not as efficient as others. When large data sets are in question, the DDA algorithm can become a little slow and less efficient. Even though it uses complex calculations, it is not always accurate and precise. Moreover, it does not allow any form of optimization. Despite this, it is quite expensive as compared to other algorithms.

What is Bresenham’s Algorithm?

Bresenham’s algorithm is one of the earliest methods devised to approximate line segments in computer graphics. It is used to specify certain points through which a straight line can be drawn with approximation. Most people use it in bitmap images to create simple geometric shapes.

Unlike DDA which used multiplication and division in its calculations, Bresenham’s algorithm uses only addition and subtraction. This means that it uses easy calculations which saves time and proves to be more efficient. Moreover, it is one of the most precise and accurate methods for computing values. It allows optimization and is also on the cheaper end of the spectrum.

The algorithm is extensively used in graphic chips and plotters. Due to this, it is the basis for many software graphic libraries. Many people use its extensions to draw shapes like circles and spheres. As the calculations are very simple, it is even used in firmware for several graphic cards.

Regardless, there have been numerous modifications made to the algorithm since its discovery, which was in 1962. Earlier, it could only be used to draw simple segments and shapes. However, in today’s time, the algorithm can even be used to draw ellipses, Bezier curves, and cubes.

Main Differences Between DDA and Bresenham’s Algorithm

  1. DDA only uses multiplication and division whereas Bresenham’s algorithm only uses addition and subtraction.
  2. DDA is not as efficient as the latter whereas Bresenham’s algorithm is very efficient despite being one of the oldest.
  3. DDA is not as fast as the latter whereas Bresenham’s algorithm is one of the fastest algorithms for line drawing.
  4. DDA is not very accurate or precise whereas Bresenham’s algorithm is very accurate and precise.
  5. DDA uses complex calculations in its working whereas Bresenham’s algorithm uses simple calculations in its working.
  6. DDA does not allow optimization whereas Bresenham’s algorithm allows optimization.
  7. DDA is expensive whereas Bresenham’s algorithm is on the cheaper end.

Conclusion

DDA and Bresenham’s algorithm have a very similar purpose in computer graphics. Each of them is used to draw line segments and much more. However, while DDA uses multiplication and division to do so, Bresenham’s algorithm uses only addition and subtraction. Due to this, DDA is more complex, less efficient, and not very accurate. On the other hand, Bresenham’s algorithm is simple, efficient, and relatively accurate.

Another major difference between the two is that DDA can often become expensive despite its limitations. Therefore, it may not be the optimal solution for larger data sets. Meanwhile, Bresenham’s algorithm can be used for large data sets while being much more affordable.

References

  1. https://ieeexplore.ieee.org/abstract/document/865882/
  2. https://dl.acm.org/doi/abs/10.1145/127719.122734
2D vs 3D x
2D vs 3D