Bresenham's Line Algorithm on DE1-SoC VGA: Complete Lab Tutorial

Introduction: Why Line Drawing Matters in Embedded Display Design

In modern embedded systems, displaying graphics on a screen is a fundamental skill. Whether you're building a retro game console, a medical monitor, or an AI-powered dashboard, the ability to draw lines, shapes, and images efficiently is crucial. This tutorial walks you through implementing Bresenham’s line algorithm on the DE1-SoC FPGA to draw lines on a VGA display, as part of the Ee371 lab 5-display interface. By the end, you'll understand pixel buffer addressing, coordinate systems, and integer-only line drawing—skills that translate directly to real-time graphics in gaming, simulation, and GUI applications.

Understanding the VGA Display and Pixel Buffer

The DE1-SoC Computer includes a VGA controller that outputs a 640×480 resolution image. The image data comes from a pixel buffer—a block of memory where each pixel's color is stored as a 16-bit halfword: 5 bits for red, 6 for green, and 5 for blue. The base address of the pixel buffer is typically 0x00000000 (FPGA on-chip memory). To access a pixel at coordinates (x, y), you compute the offset as y * 640 + x, then multiply by 2 (since each pixel uses 2 bytes). The VGA controller continuously reads this buffer in raster order and sends it to the monitor.

Writing to the pixel buffer is straightforward: you calculate the address and store the 16-bit color value. However, to draw a line between two points, you need to decide which pixels to color. That’s where Bresenham’s algorithm comes in.

The Math Behind Bresenham’s Line Algorithm

Bresenham’s algorithm is an efficient method for drawing lines using only integer arithmetic. It avoids floating-point calculations and works for all slopes. The key idea is to step along the major axis (the axis with the larger distance) and decide whether to increment the minor axis based on an error term.

Let’s consider a line from (x0, y0) to (x1, y1). The algorithm first checks if the line is steep (|dy| > |dx|). If steep, it swaps x and y to ensure the line is drawn along the x-axis for simplicity. Then it ensures x0 < x1. It calculates deltax = x1 - x0, deltay = abs(y1 - y0), error = -deltax/2, and y_step = 1 if y0 < y1 else -1. For each x from x0 to x1, it plots the pixel (x, y) (or swapped if steep), adds deltay to error, and if error >= 0, increments y by y_step and subtracts deltax from error.

This algorithm is widely used in computer graphics, from drawing lines in vintage video games to rendering vector graphics in modern AI-generated art tools.

SystemVerilog Implementation on DE1-SoC

In the lab, you are provided with a skeleton line_drawer.sv file. Your task is to implement the draw_line function using the pseudocode from Figure 4. The module interfaces with a VGA driver that provides a 38,400-byte framebuffer. You'll need to write color values (black/white only in this lab) to the appropriate pixel addresses.

Here’s a simplified outline of the SystemVerilog code:

module line_drawer ( input logic clk, input logic reset, input logic start, input logic [9:0] x0, y0, x1, y1, output logic done, output logic [17:0] addr, output logic [15:0] color, output logic write_en ); 
 // State machine and registers 
 // Implement Bresenham's algorithm 
 // Write pixel at each step 
endmodule

You'll need to handle signed arithmetic carefully. Use signed types for error and y_step. The color is 16-bit: for white, use 16'hFFFF; for black, 16'h0000. The address is computed as base_addr + (y * 640 + x) * 2.

Testing Your Implementation

After compiling the Quartus project and uploading to the FPGA via LabsLand (choose VGA interface), you should see a rainbow gradient initially, then a black screen. Your line-drawing code will be called from the top module to draw lines. For example, drawing a line from (0,0) to (100,100) should produce a diagonal line. Test with various slopes, including steep and shallow lines, and ensure the algorithm works for all cases.

Real-world analogy: Think of this like a self-driving car's path planning. The car needs to move from point A to B in discrete steps, adjusting its steering (y increment) based on an error term (distance from ideal path). Bresenham's algorithm does exactly that for pixels.

Common Pitfalls and Debugging Tips

Data types: Use signed for error and y_step. Unsigned types cause incorrect behavior for negative slopes.
Address calculation: Ensure you multiply (y*640 + x) by 2. Forgetting the factor of 2 will write to wrong pixels.
Color format: The 16-bit halfword uses 5-6-5 bits. For white, set all bits to 1. For black, all 0.
Steep line handling: When is_steep is true, plot (y, x) instead of (x, y). Swap the coordinates in the draw_pixel call.
Timing: The VGA controller reads the buffer continuously. Your writes are interleaved, but ensure you don't write during blanking intervals if required by the driver.

Extending the Lab: From Lines to Shapes and Games

Once you have line drawing working, you can extend it to draw rectangles, triangles, or even wireframe 3D objects. This is the foundation for retro gaming on FPGAs. For instance, you could create a Pong game where the paddle and ball are drawn using lines and rectangles. Or, combine with an AI algorithm to generate procedural landscapes.

Trend connection: In the world of AI art generators like DALL·E or Midjourney, the underlying graphics pipeline often uses Bresenham-like algorithms for rendering vector primitives. Understanding this low-level graphics gives you insight into how AI tools create images from text prompts.

Conclusion

Implementing Bresenham’s line algorithm on the DE1-SoC is a classic embedded systems exercise that combines hardware interfacing, memory addressing, and algorithm design. By completing this lab, you gain practical skills in FPGA-based VGA graphics—skills that are directly applicable to careers in embedded systems, game development, and hardware acceleration for AI. Remember to test thoroughly and enjoy the satisfaction of seeing your lines appear on the monitor!