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.

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_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 PShapes and JTS Geometries
• PGS_Morphology
  • Methods that affect the geometry or topology of shapes (buffering, simplification, smoothing, etc.)
• PGS_Optimsation
  • Solve geometric optimisation problems, such as finding the maximum inscribed circle, or the closest vertex to a coordinate
• PGS_Processing
  • Methods that process a shape in some way: compute hulls, partition, slice, etc.
• PGS_ShapeBoolean
  • Boolean set-operations for 2D shapes
• PGS_ShapePredicates
  • Various shape metrics (area, circularity, etc.) and predicates ("do these shapes intersect?")
• 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

Processing IDE — Quick

Download the latest PGS.jar from releases and simply drag-and-drop it onto the Processing IDE.

Processing IDE — Permanently

Download the latest PGS.jar from releases and save it to Documents\Processing\libraries\PGS\library.

Result: Documents\Processing\libraries\PGS\library\PGS.jar.

(Note the .jar and the folder must be called PGS — rename the .jar if this is not the case).

Maven/Gradle

PGS is hosted as an artifact for use in Maven or Gradle projects via Jitpack — follow the instructions there (very easy).

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

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
	Projection-transform a shape with respect to a fixed point.

Geometric Predicates & Metrics

Intersects	Contains Shape	Contains Point
Do shapes intersect with each other?	Does one shape fully contain another?	For individual points and point sets.

Metrics

• Length
• Circularity
• Similarity
• Holes
• Is simple?
• Is convex?
• Distance
• Area
• Centroid

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.
Voronoi Diagram		Circle-site Voronoi Diagram
Straight Skeleton	Medial Axis
	Medial axis transform with feature pruning via distance, area or axial angle.

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		Field Warp
Simplification	Chaikin Cutting

Geometry Processing

Points on Perimeter		Point on Perimeter	Densification
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).
Partitioning		Splitting	Slicing
Partition a shape into simple (convex) polygons.		Subdivide (recursively) a shape into quadrants.	Slice a shape in two along a given line.
Constrained Random Point Set		Segment Set Intersection
Generate constrained random point sets where all points lie within a shape. Points can be distributed entirely randomly or according to grid with configurable tightness.		Find all points of intersection between a collection of line segments.
Concave Hull			Convex Hull
Concave hull of point sets via breadth-first or depth-first approaches.
Snap Hull	Shape Intersection	Polygonize Lines
A convex hull with some level of shape-feature snapping.	Find all points of intersection between two shapes.	Find the polygonal faces formed by a set of intersecting line segments.

Triangulation

Delaunay Triangulation		Earcut Triangulation
Poisson Delaunay Triangulation	Urquhart Faces		Gabriel Faces
Delaunay triangulation of shapes where steiner points generated by poisson disk sampling are inserted.	Polygon faces of an Urquhart Graph (derived from a triangulation).		Polygon faces of a Gabriel Graph (derived from a triangulation).

Geometric Optimisation

Maximum Inscribed Circle	Minimum Bounding Rectangle	Maximum Inscribed Rectangle
Minimum Bounding Circle		Minimum Bounding Ellipse
Envelope	Closest Vertex	Problem of Apollonius
Closest Point Pair	Farthest Point Pair

Circle Packing

Front Chain		Trinscribed
Maximum Inscribed		Stochastic
Square Lattice		Hex Lattice

Construction

Supercircle	Supershape	Star
Random Convex Polygon	Heart