Midpoint Line Algorithm and Bresenham's Algorithm

In computer graphics, scan conversion of lines and arcs represents fundamental and crucial tasks, with the core objective of converting continuous geometric shapes into discrete pixels. The Midpoint Line Algorithm and Bresenham's Algorithm are two classical, high-efficiency implementation methods particularly suitable for resource-constrained environments.

The Midpoint Line Algorithm determines the selection of the next pixel by calculating the positional relationship between the midpoint of the line segment and the ideal line. Its core concept utilizes a discriminant function to avoid floating-point operations, requiring only integer additions, subtractions, and bit manipulations. For line drawing, the algorithm processes different cases based on slope values, ensuring efficient generation of continuous pixels in any direction.

Bresenham's Algorithm represents another optimized approach based on incremental calculations, especially proficient in handling scan conversion for lines and arcs. This algorithm determines pixel progression through recursive error term updates, completely eliminating multiplication and division operations while requiring only integer additions and comparisons. For arc drawing, the algorithm reduces computational load through symmetry properties, calculating only one-eighth of the arc before generating the complete shape via mirroring.

In practical applications, both algorithms can be efficiently implemented in MATLAB. For instance, line drawing can be achieved through loop iterations and conditional statements to fill pixels, while arc drawing requires combining parametric equations with symmetry optimization. These algorithms remain particularly common in embedded systems or early graphics hardware, and continue to serve as classic case studies in graphics education.

Understanding these two algorithms facilitates deep mastery of rasterization fundamentals and establishes a foundation for subsequent learning of more complex techniques like graphic filling or anti-aliasing.