Skip to content

linewidth_analysis.md

Latest commit

 

History

History
116 lines (96 loc) · 4.42 KB

linewidth_analysis.md

File metadata and controls

116 lines (96 loc) · 4.42 KB

Line Width Analysis and Recommendations

This document details the impact of line_width settings on the rasterization of vessel tracks using Datashader.

Overview

When rasterizing vector lines into a pixel grid, the line_width parameter controls how the line is drawn. This choice involves a trade-off between visual quality (smoothness) and analytical interpretability (counts vs. density).

1. Aliased Rendering (line_width = 0)

Uses Bresenham's algorithm to select exactly one pixel per step along the major axis.

  • Pros: Produces Integer Counts. If a pixel has a value of 5, exactly 5 vessel tracks passed through it (or near its center). This is the "fairest" way to count events (vessel transits).
  • Cons: Visually jagged. Diagonal lines may appear thinner or disconnected at high zooms compared to anti-aliased lines.
  • Note: While line_width=0 counts transits, it does not strictly conserve distance (a diagonal track of length $\sqrt{2}$ contributes 1 count, whereas an anti-aliased line might distribute $\approx 1.41$ mass). However, for statistical analysis of "how many ships passed here", line_width=0 is the standard.

Example: Steep Diagonal (-1, -1) to (0, 1)

+---+---+---+
| 0 | 1 | 0 |
+---+---+---+
| 0 | 1 | 0 |
+---+---+---+
| 1 | 0 | 0 |
+---+---+---+

2. Anti-Aliased Rendering (line_width = 1)

Produces smooth, anti-aliased lines that represent the spatial coverage of the vessel track.

  • Pros: High visual quality, no "jaggies".
  • Cons: Introduces fractional values (e.g., 0.29) and may saturate (clip) at 1.0 for diagonal lines, potentially over-representing density in terms of pure "pixel mass".

Example: Diagonal (-1, -1) to (1, 1)

+------+------+------+
| 0.00 | 0.29 | 1.00 |
+------+------+------+
| 0.29 | 1.00 | 0.29 |
+------+------+------+
| 1.00 | 0.29 | 0.00 |
+------+------+------+

Explanation of Values:

  • 1.00 (Center): The diagonal line segment length inside the pixel is $\sqrt{2} \approx 1.41$. Multiplied by the line width ($1$), the total "mass" is $1.41$, which exceeds the pixel area ($1.0$), resulting in a saturated value of 1.00.
  • 0.29 (Neighbors): This value ($1 - 1/\sqrt{2} \approx 0.293$) represents the partial coverage of the adjacent pixels by the 1-unit wide line.

Example: Steep Diagonal (-1, -1) to (0, 1)

+------+------+------+
| 0.33 | 0.78 | 0.00 |
+------+------+------+
| 0.78 | 0.33 | 0.00 |
+------+------+------+
| 0.78 | 0.00 | 0.00 |
+------+------+------+

Example: Horizontal Top Edge (-1, 1) to (0, 1)

+------+------+------+
| 0.50 | 0.50 | 0.00 |
+------+------+------+
| 0.00 | 0.00 | 0.00 |
+------+------+------+
| 0.00 | 0.00 | 0.00 |
+------+------+------+

(The line runs along the top edge y=1, so only half its width is inside the pixel grid, resulting in 0.50 coverage.)

3. Advanced: Mass Conservation (line_width ≈ 0.71)

To achieve a density where the accumulated value is strictly proportional to the vessel's travel distance without saturation bias, one can use a fractional line width.

  • Use line_width ≈ 0.71 ($1/\sqrt{2}$).
  • Why? At line_width=1, a diagonal track deposits $\approx 1.41$ mass per pixel, which is clipped to $1.0$, under-representing diagonal movement relative to horizontal movement.
  • Result: With line_width=0.71, the maximum coverage (diagonal) is $1.0$, preventing clipping.
    • Horizontal: 1 pixel transit $\rightarrow$ Value 0.71. Total Mass/Length = 0.71.
    • Diagonal: $\approx 0.71$ pixel transits per unit length $\rightarrow$ Value 1.0 per pixel. Total Mass/Length = $1.0 \times 0.71 = 0.71$.
    • Conclusion: Mass is strictly proportional to length (scaled by 0.71).

Examples with line_width ≈ 0.71

Straight (Horizontal):

+--------+--------+--------+
| 0.0000 | 0.0000 | 0.0000 |
+--------+--------+--------+
| 0.7071 | 0.7071 | 0.7071 |
+--------+--------+--------+
| 0.0000 | 0.0000 | 0.0000 |
+--------+--------+--------+

Steep Diagonal:

+--------+--------+--------+
| 0.2328 | 0.5490 | 0.0000 |
+--------+--------+--------+
| 0.5490 | 0.2328 | 0.0000 |
+--------+--------+--------+
| 0.5490 | 0.0000 | 0.0000 |
+--------+--------+--------+

Diagonal:

+--------+--------+--------+
| 0.0000 | 0.2071 | 0.7071 |
+--------+--------+--------+
| 0.2071 | 0.7071 | 0.2071 |
+--------+--------+--------+
| 0.7071 | 0.2071 | 0.0000 |
+--------+--------+--------+