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2-opt local search Repeatedly reverses sections of a route whenever the swap shortens its total length.
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Adaptive stippling Places marks at variable spacing or size according to local image tone, detail, or an error measure.
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Affine transformation Maps coordinates with combinations of translation, rotation, scaling, and shear while preserving straight lines and parallelism.
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Arc interpolation Evaluates points along a circular or elliptical arc from its geometric parameters.
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Arc-length resampling Redistributes points along a curve so consecutive samples are separated by approximately equal physical distances.
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Arc-to-Bézier conversion Approximates circular or elliptical arcs with one or more cubic Bézier curve segments.
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Archimedean spiral Generates a spiral whose radius increases linearly with angle, producing nearly constant spacing between turns.
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Attractor-field integration Moves particles or curve samples through a vector field formed by attracting and repelling points or shapes.
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B-spline curves Constructs smooth piecewise-polynomial curves controlled by points, knots, and polynomial degree.
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Bayer ordered dithering Compares image values against a repeating threshold matrix to create a regular distribution of binary marks.
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Bentley–Ottmann sweep-line algorithm Finds intersections among line segments by sweeping an ordered event line across the geometry.
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Bézier curves Defines smooth parametric curves from endpoints and control points using Bernstein polynomials.
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Blue-noise sampling Distributes samples with few low-frequency clumps while avoiding the rigid appearance of a grid.
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Bresenham line algorithm Steps through a discrete grid to approximate a straight line using inexpensive incremental error calculations.
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Catmull–Rom splines Interpolates a smooth curve through a sequence of control points using neighboring points to determine tangents.
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Cellular automata Updates cells on a grid from local neighborhood rules to produce evolving spatial patterns.
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Centerline tracing Extracts a single path along the middle of strokes or elongated regions in a raster image.
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Chaikin corner cutting Smooths a polyline by repeatedly replacing each corner with two points placed along its adjacent edges.
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Circle packing Places non-overlapping circles inside a boundary while satisfying size, spacing, or density constraints.
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CMYK color separation Decomposes an image into cyan, magenta, yellow, and black coverage channels.
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Color quantization Reduces a large set of image colors to a smaller representative palette while minimizing visual error.
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Concave hull Builds a boundary around a point set that can bend inward and follow the set more closely than a convex hull.
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Concentric infill Fills a region with successively inset or outset copies of its boundary.
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Contour extraction Finds curves that follow boundaries or equal-valued levels in raster, scalar-field, or elevation data.
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Convex hull Computes the smallest convex polygon containing a set of points.
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Cross-hatching Overlays two or more families of hatch lines at different angles to build tone or texture.
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Curl noise Derives a divergence-free vector field from the curl of a noise field, producing swirling motion without obvious sinks or sources.
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Curve flattening Approximates arcs and parametric curves with polylines while keeping deviation or segment length below a tolerance.
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De Casteljau's algorithm Evaluates or subdivides a Bézier curve through repeated linear interpolation of its control points.
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Delaunay triangulation Connects points into triangles so no input point lies inside any triangle's circumcircle.
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Differential growth Iteratively moves and subdivides a chain under attraction, repulsion, and smoothing forces so it grows without collapsing onto itself.
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Distance transform Assigns each raster cell its distance to the nearest foreground, background, or boundary cell.
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Douglas–Peucker simplification Recursively removes polyline vertices whose removal stays within a specified perpendicular-error tolerance.
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Dubins path planning Finds a short path between oriented points using straight segments and fixed-radius turns.
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Edge detection Locates strong changes in image intensity or color that are likely to correspond to visual boundaries.
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Edge tangent flow Builds a smooth orientation field that follows nearby image edges while reducing local directional noise.
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Error-diffusion dithering Quantizes each image sample and distributes its quantization error to neighboring samples that have not yet been processed.
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Fast marching method Propagates a front through a weighted domain by solving an Eikonal equation in order of increasing arrival time.
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Fermat spiral fill Fills a region with a Fermat (parabolic) spiral whose in-and-out arms interleave, so a single continuous path enters and exits at the boundary with near-uniform spacing.
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Flood fill Visits connected cells or regions starting from a seed while respecting a boundary or value condition.
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Floyd–Steinberg dithering An error-diffusion method that passes quantization error to four nearby pixels using fixed weights.
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Fourier series drawing Approximates a periodic shape as a sum of rotating sinusoidal components or epicycles.
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Fractal noise Combines multiple scaled octaves of coherent noise to produce detail at several spatial frequencies.
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G-code toolpath generation Translates drawing geometry into ordered machine moves, coordinate commands, feed settings, and pen-control actions.
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Genetic path optimization Evolves candidate route orderings through selection, crossover, and mutation according to a travel-cost score.
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Greedy nearest-neighbor path ordering Repeatedly selects the unvisited path endpoint nearest to the current pen position, optionally reversing paths.
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Halftoning Represents continuous tone with discrete marks whose size, spacing, shape, or density varies.
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Harmonograph curves Combines damped sinusoidal oscillations to model the paths produced by a mechanical harmonograph.
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Hatching Fills a region with parallel or locally oriented lines clipped to the region boundary.
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Hexagonal grid generation Tiles the plane with regularly spaced hexagonal cells using axial, cube, or offset coordinate systems.
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Hidden-line removal Determines which portions of projected 3D edges are occluded by surfaces and removes or splits those portions.
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Hilbert curve Recursively constructs a continuous space-filling curve that visits every cell of a square grid.
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Homography Maps points between two planes with a projective transformation defined by a 3-by-3 matrix.
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Image-guided flow fields Converts image gradients, edges, brightness, or structure tensors into a vector field that guides curves.
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Inverse kinematics Computes actuator positions or joint angles needed to place a tool at a requested Cartesian coordinate.
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Island detection Identifies disconnected components, enclosed loops, or path groups that are isolated from the rest of the geometry.
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Isoline extraction Traces curves through positions where a sampled scalar field equals selected values.
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k-d tree nearest-neighbor search Partitions points recursively by coordinate axis to accelerate spatial range and nearest-neighbor queries.
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K-means color clustering Alternates between assigning samples to the nearest color center and updating each center to its cluster mean.
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L-systems Repeatedly rewrites symbols with grammar rules and interprets the result as drawing commands.
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Lawnmower infill Covers a region with parallel back-and-forth passes connected in alternating directions.
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Liang–Barsky line clipping Clips a line segment against an axis-aligned rectangle by updating the valid interval of its parametric equation.
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Line joining and merging Connects nearby compatible segment endpoints, reversing direction where necessary, to form longer continuous polylines.
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Line-segment intersection Tests whether two finite segments cross and, when they do, computes their intersection point and parameters.
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Linear interpolation Computes intermediate values along a straight interval between two known values or points.
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Lissajous curves Plots two perpendicular sinusoidal motions with independently chosen frequencies, phases, and amplitudes.
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Low-pass path smoothing Suppresses high-frequency changes in sampled coordinates or motion commands while retaining slower shape changes.
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Marching squares Extracts isoline segments from a two-dimensional sampled field by classifying the corners of each grid cell.
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Martinez polygon clipping Uses a sweep-line process to compute boolean operations on simple or self-intersecting polygons.
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Maze generation Builds a connected network of passages with methods such as depth-first backtracking, randomized Prim, or Kruskal growth.
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Medial axis transform Finds the centers and radii of maximal disks contained inside a shape, forming a skeletal representation.
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Minimum spanning tree Connects all vertices of a weighted graph with minimum total edge weight and no cycles.
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Morphological erosion Shrinks foreground regions by removing pixels or cells that do not contain a chosen structuring element.
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Motion planning Chooses a feasible sequence of movements that respects geometry, machine limits, obstacles, and tool state.
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NURBS curves Represents smooth rational spline curves with weighted control points, a knot vector, and polynomial basis functions.
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OpenSimplex noise Generates coherent gradient noise on a simplex-like lattice with fewer directional artifacts than classic grid noise.
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Orthographic projection Projects 3D points onto a plane along parallel rays without perspective size reduction.
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Penrose tiling Covers the plane aperiodically with a small set of tiles constrained by matching or substitution rules.
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Perlin noise Interpolates pseudo-random gradients on a lattice to create smooth, spatially coherent noise.
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Perspective projection Projects 3D points onto a plane so apparent size decreases with distance from the viewer.
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Physarum simulation Models agents that deposit and follow a diffusing trail field, producing adaptive transport-like networks.
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Point-in-polygon test Determines whether a point lies inside, outside, or on the boundary of a polygon using crossing or winding rules.
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Poisson-disc sampling Generates samples with a guaranteed minimum separation while retaining an irregular, natural distribution.
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Polygon Boolean operations Computes union, intersection, difference, or exclusive-or between polygonal regions.
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Polygon offsetting Constructs parallel boundaries at a specified distance from polygon edges while resolving joins and self-intersections.
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Polygon packing Places polygonal shapes within a boundary while avoiding overlap and optimizing space, density, or another objective.
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Potrace Transforms a thresholded bitmap into smooth vector outlines through path decomposition, polygon fitting, and curve optimization.
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Quadtree spatial indexing Recursively divides a two-dimensional region into four cells so spatial queries can ignore empty or distant areas.
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Random walk Builds a path through successive random or probability-weighted steps from the current position.
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Raster-to-vector tracing Converts raster regions, edges, or strokes into geometric paths such as polylines and Bézier curves.
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Ray casting Projects rays from a viewpoint or query point and finds their first intersections with scene geometry.
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Ray hatching Casts rays or probes across projected surfaces and converts visible intervals into hatch strokes.
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Ray marching Advances a ray through a field in steps, often using signed distance values to choose safe step lengths.
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Ray tracing Traces rays through a scene to evaluate intersections, visibility, lighting, and reflections.
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Reaction–diffusion Simulates interacting substances that spread and react locally, producing spots, stripes, and labyrinthine structures.
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Rectangular packing Arranges rectangles within a bounded area to minimize unused space or satisfy layout constraints.
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Scanbeam processing Sweeps through ordered vertex events while maintaining active edges for the current horizontal or vertical band.
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Scanline polygon filling Intersects regularly spaced scanlines with polygon edges and fills the alternating interior intervals according to a fill rule.
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Signed distance fields Represent a shape with a scalar value giving distance to its boundary and a sign indicating inside or outside.
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Simplex noise Generates coherent gradient noise on simplex cells, scaling efficiently to multiple dimensions.
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Single-line font rendering Represents glyphs as centerline strokes rather than closed filled outlines, as in Hershey-style fonts.
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Skeletonization Iteratively thins a binary shape to a one-pixel-wide topology-preserving skeleton.
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Space-colonization growth Grows a branching network toward nearby attraction points while removing points reached by existing branches.
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Spiral infill Covers a region with a continuous inward or outward spiral derived from repeated offsets or a spiral field.
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Spirograph curves Generates hypotrochoid or epitrochoid paths from a circle rolling inside or outside another circle.
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Stippling Represents tone or form with discrete dots whose density, size, or distribution varies spatially.
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Streamline integration Numerically traces curves that remain tangent to a vector field from selected seed points.
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String-art line selection Iteratively chooses chords between fixed anchor points to reduce the difference from a target image.
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Superformula Generalizes the superellipse to a single polar equation whose few parameters sweep from circles and polygons to petals, stars, and organic blobs.
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Thresholding Classifies image samples by comparing intensity, color, or another measure with one or more thresholds.
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Tone- and feature-aware circular scribbling Builds a continuous path from circular scribbles whose placement, loop size, and motion respond to image tone and features.
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Traveling Salesman Problem optimization Searches for a short route that visits every required point or path once before returning or stopping.
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Truchet tiling Builds patterns by rotating or selecting tiles that contain compatible arcs or line fragments.
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Turtle graphics Generates paths by moving an oriented cursor with relative commands such as forward, turn, and branch.
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Vatti polygon clipping Computes boolean operations on general polygons using scanbeams, local minima, and an active edge structure.
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Voronoi diagram Partitions a plane into cells containing the locations closest to each generating site.
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Wave Function Collapse Assigns compatible tiles or states to cells by repeatedly propagating local constraints and resolving uncertainty.
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Weave path ordering Splits and orders intersecting paths so alternating segments appear to pass over and under one another.
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Weighted Voronoi stippling Iteratively relocates Voronoi sites toward density-weighted cell centroids derived from a target image.
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Worley noise Measures distance to nearby random feature points to produce cellular bands, ridges, and regions.
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Z-buffer visibility Stores the nearest depth reached at each sampled image location and rejects geometry farther from the viewer.
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Zingl–Bresenham curve algorithm Incrementally approximates Bézier curves and conic sections on a discrete grid using error terms.