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_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
• PGS_Meshing
  • Mesh generation (excluding triangulation) from shapes
• 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_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_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

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/perimeter
• Width & Height
• Diameter
• 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		Interpolation

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).
Perimeter Extraction	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
Delaunay triangulation of shapes where steiner points generated by poisson disk sampling are inserted.

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).
Centroid Quadrangulation	Edge Collapse Quadrangulation	Split Quadrangulation	Spiral Quadrangulation

Geometric Optimisation

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

Circle Packing

Front Chain		Trinscribed
Maximum Inscribed		Stochastic
Square Lattice		Hex Lattice

Coloring

Construction

Supercircle	Supershape	Star
Random Convex Polygon	Heart	Ring	Linear Spiral
Fermat Spiral	Sierpinski Curve

Point Sets

Random	Gaussian	Square Grid	Hex Grid
Phyllotaxis	Poisson	Hexagon	Ring
Halton LDS	Hammersley LDS	Plastic LDS	Jittered Plastic LDS
N-Rooks LDS	Distance Prune

Tiling & Subdivision

Random Quad Subdivision	Random Rect Subdivision	Random Triangle Subdivision	Islamic Tiling
Doyle Spiral		Hexagon Tiling	Penrose Tiling