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