Martín, Domingo, et al. “A survey of digital stippling.” Computers & Graphics 67 (2017): 24-44.

• Traditional stippling
• Digital stippling
• Stippling techniques
• Digital stippling and halftoning

Traditional Stippling

The goal of traditional stippling is: to use dots to represent tone, shape, texture, etc.
This process is very time-consuming and typically results in relatively small artworks. The ideal viewing distance is about 35cm–65cm, at which both the color and shape of dots are distinguishable. — Artists uphold the principle that “every dot has its purpose.”

This precise dot-by-dot style contrasts with halftoning, where dots/pixels are ideally not visible, and only their tonal contribution matters.

Stippled artworks are static once created, so dot layout patterns are crucial as they convey local tone. Artists usually aim to avoid visible dot patterns, although some elements may be intentionally emphasized by lines, such as in hedcut styles.

Stippling is often combined with linework: dots represent tone and texture, lines emphasize edges and contours.

Digital Stippling

Dot Placement

Dot placement should meet three criteria:

1. Even placement for a given tone
2. Irregular and random distribution
3. Density should reflect local darkness

Overlapping is generally avoided, but traditional methods sometimes use overlapping to convey darker tones.

Early stippling techniques produced artifacts due to patterns introduced by Voronoi diagrams and Lloyd’s method.

Artifacts are usually undesirable since they imply artificial structure.

Modern artifact avoidance methods include:

• Randomness/noise
• Probability density functions
• Poisson disk distributions
• Non-repeating tiling
• Capacity-constrained relaxation
• Example-based placement: matches characteristics from real drawings to avoid overly mechanical results

Artifacts may also be intentionally introduced to emphasize structural elements, like edges.
Thresholding or increasing contrast in weighted Voronoi diagrams can highlight edges.
The hedcut style deliberately arranges dots along linear features.

Zoomable stippling images require adaptive refinement methods that avoid introducing new artifacts during zoom transitions.

Dot Characteristics

Most methods assume black dots on white backgrounds.
Initially, all dots were idealized as circles. Later improvements allowed arbitrary shapes or pixels to represent dots.

Approaches include:

• Shape replacement (e.g., Hiller, Dalal)
• Short hatches or overlapping strokes
• Pixel-based stippling
• Shape-aware stippling to match hand-drawn styles
• Recent methods also consider grayscale and color texture

Stippling Techniques

Centroidal Voronoi Diagrams

Goal: even distribution of dots with minimum overlap

Lloyd’s method:

1. Generate Voronoi diagram
2. Move each dot to the centroid
3. Repeat

Deussen’s method:
Uses tone image or manual brush input, followed by CVD-based relaxation.

Brush types:

• Edit brush: add/delete dots
• Relaxation brush: improve uniformity
• Jitter brush: introduce randomness
• Shape brush: change size or style

Secord’s method:
Introduced tone-weighted CVD using density function $$\rho(x, y)$$
Centroid calculation:

Precomputed stipple levels enable fast rendering:

for all pixels (x,y) in [0,1]×[0,1]:
    map (x,y) to stipple level l
    copy dots from level l into region around (x,y)

Reduces resolution

Hiller’s method:
Extends WCVD to polygons. Adjusts centroids and orientation by moments of inertia.

Balzer et al.:
Addressed WCVD artifact chains by introducing capacity constraints:

Optimal uniform capacity:

Energy minimization:

Distribution Functions

Secord’s PDF sampling:
Sample from $$p(x)$$:

1. Integrate $$C(x) = \int_0^x p(t)dt$$
2. Invert $$x' = C^{-1}(x)$$
3. Uniform y-axis sampling to get x-values

Kopf’s blue-noise via Wang tiles:
Uses dart-throwing with shrinking radius. Handles tile seams with Voronoi diagrams and Dijkstra paths.

Jones & Dunbar:
Incremental methods with Voronoi or Poisson disk approximations.

Xu:
Used capacity-constrained Delaunay triangulation:

For variable density:

General Sampling

Ebeida:
Unbiased Poisson disk with guaranteed spacing:

1. Grid with cell size $$r/\sqrt{2}$$
2. Phase 1: throw darts
3. Approximate gaps with polygons
4. Phase 2: sample in gaps

Schloemer:
Maximizes distance between points using Delaunay triangulation circumcenters.

Heck et al.:
Proposed new blue-noise types: stepped and unimodal, to reduce aliasing.

Example-Based Methods

Barla:
Extracted layout features from example patterns, synthesized similar stroke clusters.
Used Lloyd’s for seed locations.

Kim:
Mapped tone to GLCM texture features, used rejection sampling to match statistics.
GLCM Example:

Martín:
Considered dots as grayscale/colored textures instead of black dots.

Structure-Aware Methods

Mould:
Graph-based pixel importance: $$\alpha d + \beta g$$
Seed points expand by shortest path. New dots placed at high-gradient frontiers.

Li & Mould:
Priority-based dot placement based on contrast and structural saliency.
Error is distributed to neighbors for iterative refinement.

Hedcut

Kim:
Extracted feature lines, generated distance field, created parallel guides, placed dots via constrained Lloyd’s.
Later added isocontour guidance.

Son et al.:
Extracted feature vector field → structural grid → dot placement at intersections, parameterized by tone and structure.

Evaluation & Benchmarks

Halper:
Studied perception in NPR; explored how different styles affect user cognition.

Isenberg et al.:
Compared hand-drawn vs digital stipples.
Users preferred artistic character of manual drawings, but acknowledged accuracy of digital ones.
Artifacts from WCVD and overuse of dots were noticeable.

Digital Stippling vs. Halftoning

Both aim for continuous tone on binary media.

But stippling is artistic, while halftoning is algorithmic.
Stippling uses visible, meaningful dots, often aligned with image features.
Halftoning aims for invisible, tone-only dots, arranged for perceptual consistency.

Digital stippling still lacks the aesthetic control of traditional techniques. Most approaches still function like halftoning, though with larger dots and sometimes structural awareness.