Processing Geometry Suite

Processing Geometry Suite is a software project that provides easy access to 2D geometric algorithms in the form of a Processing library. Over time it has grown to include an incredibly comprehensive range of algorithms.

The focus of the library is on visualisation rather than providing underlying data structures. To this end all methods in the library are static and most of them take in and return PShapes or PVectors.

Docs are hosted via GitHub Pages here.

Overview

Library functionality is split over the following classes:

• PGS_CirclePacking
  • Circle packings of shapes, subject to varying constraints and patterns of tangencies
• PGS_Coloring
  • Minimal colorings of meshes (or mesh-like shapes)
• PGS_Construction
  • Construct uncommon/interesting 2D primitives
• PGS_Contour
  • Methods that produce various contours from shapes: medial axes, straight skeletons, offset curves, etc.
• PGS_Conversion
  • Conversion between Processing PShapes and JTS Geometries (amongst other formats)
• PGS_Hull
  • Convex and concave hulls of polygons and point sets
• PGS_Meshing
  • Mesh generation (excluding triangulation) and processing
• PGS_Morphology
  • Methods that affect the geometry or topology of shapes (buffering, simplification, smoothing, etc.)
• PGS_Optimisation
  • Solve geometric optimisation problems, such as finding the maximum inscribed circle, or the closest vertex to a coordinate
• PGS_PointSet
  • Generates sets of 2D points having a variety of different distributions and constraints
• PGS_Processing
  • Methods that process a shape in some way: compute hulls, partition, slice, etc.
• PGS_SegmentSet
  • Generates sets of random non-intersecting line segments
• PGS_ShapeBoolean
  • Boolean set-operations for 2D shapes
• PGS_ShapePredicates
  • Various shape metrics (area, circularity, etc.) and predicates ("do these shapes intersect?")
• PGS_Tiling
  • Tiling, tessellation and subdivision of the plane using periodic or non-periodic geometric shapes.
• PGS_Transformation
  • Various geometric and affine transformations that affect vertex coordinates
• PGS_Triangulation
  • Delaunay triangulation (constrained and refined) and earcut triangulation of shapes and point sets
• PGS_Voronoi
  • Voronoi Diagrams of shapes and point sets

Installation

Examples

A number of example Processing sketches are provided in examples.

Illustrations

Much of the functionality (but by no means all) is demonstrated below:

2D Boolean Operations

Union	Intersection	Subtraction	Symmetric Difference
Complement	Mesh Union	Mesh Intersection	Mesh Subtraction

Transformation

Rotate Around		Translate To	Touch Scale
Rotate a shape around its centroid or an arbitrary point.		Translate a shape such that its centroid matches some position.	Scale one shape such that it touches another.
Resize	Homothetic Transformation	Shear	Align
	Projection-transform a shape with respect to a fixed point.		Maximum-overlap alignment.

Geometric Predicates & Metrics

Intersects	Contains Shape	Contains Point	Containing Cell
Do shapes intersect with each other?	Does one shape fully contain another?	For individual points and point sets.	Which cell contains the query point?

Metrics

• Length/perimeter
• Width & Height
• Diameter
• Circularity
• Similarity
• Sphericity
• Elongation
• Density
• Holes
• Maximum interior angle
• Is simple?
• Is convex?
• Equal? (structural and topological equivalence)
• Distance
• Area
• Centroid
• Median

Contour

Isolines		Offset Curves
Isolines from intra-shape euclidean distance, or point sets.		Inner and exterior offset curves; based on miter, bevel or round offset styles.
Straight Skeleton	Medial Axis		Chordal Axis
	Medial axis transform with feature pruning via distance, area or axial angle.		Chordal Axis Transform
Distance Field	Center Line
A contour map based on a distance field of a shape

Morphology

Buffer	Erosion-Dilation	Minkowski Addition
	A negative followed by a positive buffer (in a single operation).	Minkowski sum and difference (a.k.a buffer one shape using another shape; the examples add a rotating & growing triangle).
Smoothing	Gaussian Smoothing	Rounding
Radial Warp	Sine Warp	Field Warp
Simplification	Chaikin Cutting		Interpolation
Variable Buffer	Precision Reduction	Hobby Curve Simplification	Elliptic Fourier Smoothing

Hull

Concave Hull			Convex Hull of Polygons
Concave hull of point sets via breadth-first or depth-first approaches.
Convex Hull	Snap Hull
	A variable-convexity hull.

Geometry Processing

Points on Perimeter		Point on Perimeter	Perimeter Extraction
Find N points (evenly distributed) along the perimeter of a shape, or points every D distance (with optional perpendicular offset).		Find a point some fraction along the perimeter of a shape (with perpendicular offset).
Splitting	Convex Partitioning	Equal Partitioning	Trapezoid Partitioning
Subdivide (recursively) a shape into quadrants.	Partition a shape into convex polygons.	Partition a shape into N equal area polygons.
Slicing	Constrained Random Point Set	Segment Set Intersection
Slice a shape in two along a given line.	Generate constrained random point sets where all points lie within a shape.	Find all points of intersection between a collection of line segments.
Shape Intersection	Polygonize Lines		Hidden Line Removal
Find all points of intersection between two shapes.	Find the polygonal faces formed by a set of intersecting line segments.		Remove linework occulted by shapes (for pen plotting)
Densification	Tangent Angle	Eliminate Slivers	Clean Coverage
Extract Holes	Nest

Triangulation

Delaunay Triangulation		Earcut Triangulation
Poisson Delaunay Triangulation
Delaunay triangulation of shapes where steiner points generated by poisson disk sampling are inserted.

Voronoi Diagrams

Voronoi Diagram (inner)		Voronoi Diagram (compound)
Centroidal Relaxation

Meshing

Urquhart Faces		Gabriel Faces	Triangulation Dual
Polygon faces of an Urquhart Graph (derived from a triangulation).		Polygon faces of a Gabriel Graph (derived from a triangulation).
Relative Neighbour Faces	Spanner Faces	Centroid Quadrangulation	Edge Collapse Quadrangulation
Split Quadrangulation	Spiral Quadrangulation	Mesh Smoothing	Mesh Subdivision
Mesh Simplification	Stochastic Merge	Area Merge	Extract Inner Edges

Geometric Optimisation

Maximum Inscribed Circle	Minimum Bounding Rectangle	Maximum Inscribed Rectangle	Maximum Perimeter Square
Minimum Bounding Circle		Minimum Bounding Ellipse
Minimum Bounding Triangle	Envelope	Problem of Apollonius
Largest Empty Circle	Largest Empty Circles	Closest Point Pair	Farthest Point Pair
Closest Vertex	Circle Covering	Visibility Polygon / Isovist
Bin Pack		Rectangle Bin Pack
Hilbert Sort Faces

Circle Packing

Front Chain		Trinscribed
Maximum Inscribed		Stochastic
Repulsion		Square Lattice
Hex Lattice		Tangency Pack
Obstacle

Coloring

Construction

Supercircle	Supershape	Star
Random Convex Polygon	Heart	Ring	Arc
Linear Spiral	Fermat Spiral	Rectangular Spiral	Hilbert Curve
Sierpinski Carpet	Sierpinski Curve	Sierpinski Tri-Curve (TRI)	Sierpinski Tri-Curve (TETRA)
Koch Snowflake	Blobbie	RSFC	Taijitu
Arbelos	Teardrop	Sponge
Gear	Super Random Polygon	Random Bezier Polygon

Point Sets

Random	Gaussian	Square Grid	Hex Grid
Phyllotaxis	Poisson	Hexagon	Ring
Halton LDS	Hammersley LDS	Plastic LDS	Jittered Plastic LDS
Sobol LDS	N-Rooks LDS	Distance Prune	Hilbert Sort
EMST	Cluster	Weighted Median

Segment Sets

Graph-matched		Stochastic	Noded
Parallel	Polygon Interior Segments

Tiling & Subdivision

Random Quad Subdivision	Random Rect Subdivision	Random Triangle Subdivision	Hatch Subdivision
Islamic Tiling	Doyle Spiral		Hexagon Tiling
Penrose Tiling	Square-Triangle Tiling