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.
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
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).
A number of example Processing sketches are provided in examples.
Much of the functionality (but by no means all) is demonstrated below:
| Union | Intersection | Subtraction | Symmetric Difference |
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| Complement | Mesh Union | Mesh Intersection | Mesh Subtraction |
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| Rotate Around | Translate To | Touch Scale | |
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| 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 |
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| Projection-transform a shape with respect to a fixed point. | Maximum-overlap alignment. | ||
| 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? |
- 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
| Isolines | Offset Curves | ||
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| 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 | |
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| Medial axis transform with feature pruning via distance, area or axial angle. | Chordal Axis Transform | ||
| Distance Field | Center Line | ||
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| A contour map based on a distance field of a shape | |||
| Buffer | Erosion-Dilation | Minkowski Addition | ||
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| 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 | ||
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| Radial Warp | Sine Warp | Field Warp | ||
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| Simplification | Chaikin Cutting | Interpolation | ||
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| Variable Buffer | Precision Reduction | Hobby Curve Simplification | Elliptic Fourier Smoothing | |
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| Concave Hull | Convex Hull of Polygons | ||
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| Concave hull of point sets via breadth-first or depth-first approaches. | |||
| Convex Hull | Snap Hull | ||
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| A variable-convexity hull. | |||
| Points on Perimeter | Point on Perimeter | Perimeter Extraction | |
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| 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 |
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| 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 | |
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| 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 | |
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| 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 |
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| Extract Holes | Nest | ||
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| Delaunay Triangulation | Earcut Triangulation | ||
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| Poisson Delaunay Triangulation | |||
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| Delaunay triangulation of shapes where steiner points generated by poisson disk sampling are inserted. | |||
| Voronoi Diagram (inner) | Voronoi Diagram (compound) | ||
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| Centroidal Relaxation | |||
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| Urquhart Faces | Gabriel Faces | Triangulation Dual | |
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| 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 |
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| Split Quadrangulation | Spiral Quadrangulation | Mesh Smoothing | Mesh Subdivision |
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| Mesh Simplification | Stochastic Merge | Area Merge | Extract Inner Edges |
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| Maximum Inscribed Circle | Minimum Bounding Rectangle | Maximum Inscribed Rectangle | Maximum Perimeter Square |
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| Minimum Bounding Circle | Minimum Bounding Ellipse | ||
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| Minimum Bounding Triangle | Envelope | Problem of Apollonius | |
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| Largest Empty Circle | Largest Empty Circles | Closest Point Pair | Farthest Point Pair |
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| Closest Vertex | Circle Covering | Visibility Polygon / Isovist | |
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| Bin Pack | Rectangle Bin Pack | ||
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| Hilbert Sort Faces | |||
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| Front Chain | Trinscribed | ||
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| Maximum Inscribed | Stochastic | ||
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| Repulsion | Square Lattice | ||
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| Hex Lattice | Tangency Pack | ||
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| Obstacle | |||
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| Supercircle | Supershape | Star | |
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| Random Convex Polygon | Heart | Ring | Arc |
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| Linear Spiral | Fermat Spiral | Rectangular Spiral | Hilbert Curve |
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| Sierpinski Carpet | Sierpinski Curve | Sierpinski Tri-Curve (TRI) | Sierpinski Tri-Curve (TETRA) |
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| Koch Snowflake | Blobbie | RSFC | Taijitu |
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| Arbelos | Teardrop | Sponge | |
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| Gear | Super Random Polygon | Random Bezier Polygon | |
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| Random | Gaussian | Square Grid | Hex Grid |
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| Phyllotaxis | Poisson | Hexagon | Ring |
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| Halton LDS | Hammersley LDS | Plastic LDS | Jittered Plastic LDS |
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| Sobol LDS | N-Rooks LDS | Distance Prune | Hilbert Sort |
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| EMST | Cluster | Weighted Median | |
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| Graph-matched | Stochastic | Noded | |
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| Parallel | Polygon Interior Segments | ||
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| Random Quad Subdivision | Random Rect Subdivision | Random Triangle Subdivision | Hatch Subdivision |
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| Islamic Tiling | Doyle Spiral | Hexagon Tiling | |
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| Penrose Tiling | Square-Triangle Tiling | ||
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