Reduced Second Moment Measure
Multitype K Function (i-to-any)
Recompute Envelopes
Marked K-Function
The Soft Core Point Process Model
Convert to Pixel Image
Multitype K Function (Cross-type)
Test Whether Function Objects Are Compatible
The Strauss / Hard Core Point Process Model
Fit the Neyman-Scott cluster process with Cauchy kernel
Inhomogeneous Cross Type L Function
Saturated Pairwise Interaction model
Take Complement of a Window
The Lennard-Jones Potential
Marked Nearest Neighbour Distance Function
Extract Subset of Function Array
Inhomogeneous Cross K Function
Extract Subset of Image
Morphological Closing
Convert Data To Class psp
Diggle-Gratton model
Diagnostics for random marking
K function of a model
The Fiksel Interaction
Distance Map
Apply Function to Every Neighbourhood in a Point Pattern
Geyer's Saturation Point Process Model
Test Whether Pixel Images Are Compatible
Convert Pixel Image to Matrix
Model Compensator of K Function
Multitype Nearest Neighbour Distance Function (i-to-any)
Marked J Function
Kaplan-Meier Estimator using Histogram Data
Compute Fitted Effect of a Spatial Covariate in a Point Process Model
The Strauss Point Process Model
Multitype J Function (i-to-j)
Coerce Hyperframe to Data Frame
Apply a Function to a Point Pattern Broken Down by Factor
Residual G Function
Test Whether Points Are Inside A Window
Distance to Boundary of Window
Determine A Common Spatial Domain And Pixel Resolution
Beta Ganglion Cells in Cat Retina
Multitype Nearest Neighbour Distance Function (i-to-j)
Inhomogeneous Marked K-Function
Hughes' Amacrine Cell Data
K-function
Intensity Estimate of Point Pattern Using Tessellation
Optimise Irregular Trend Parameters in Point Process Model
Extract Subset of Line Segment Pattern
Empty Space Function of a Three-Dimensional Point Pattern
Convert Data To Class owin
Extract Subset of Point Pattern on Linear Network
Convert Pixel Image from Numeric to Factor
Plot a Pixel Image
Border Region of a Window
Convert a Window to a Polygonal Window
Collapse Several Function Tables into One
Function Arrays for Spatial Patterns
Concatenate x,y Coordinate Vectors
Multitype L-function (cross-type)
Convert Pixel Image to Matrix or Array
Artificial Data Point Pattern
Extract Interaction Structure
Interactively Add Points
Convolution of Pixel Images
Chorley-Ribble Cancer Data
Inhomogeneous Linear Pair Correlation Function
Coerce Line Segment Pattern to a Data Frame
Beta Ganglion Cells in Cat Retina, Old Version
Diameter of an Object
Test Whether An Object Is A Pixel Image
Piecewise Constant Saturated Pairwise Interaction Point Process Model
K-function using FFT
Extract coordinates and marks of multidimensional point pattern
L-function
Influenza Virus Proteins
Test Whether An Object Is A Fitted Point Process Model
Corners of a rectangle
Areas of Morphological Dilations
Window Frame
Create a Linear Network
Smoothing Estimate of Covariate Transformation
Neighbourhood density function
Methods for Fitted Point Process Models on a Linear Network
Scott's Rule for Bandwidth Selection for Kernel Density
Extract Dummy Points Used to Fit a Point Process Model
Parameter influence measure
Pairwise Distances Between Two Different Multi-Dimensional Point Patterns
Coerce Point Pattern to a Data Frame
Clark and Evans Aggregation Index
Centroid of a window
Intersection of Two Tessellations
Exponential Energy Marks
Rectangular grid of points
Inhomogeneous Multitype K Dot Function
Clark and Evans Test
Mosaic Random Field
Generic Pairwise Interaction model
Test Whether Function Arrays Are Compatible
Berman-Huntington points and lines data
Japanese Pines Point Pattern
Coefficients of Fitted Point Process Model
Local pair correlation function
Pairwise distances in Three Dimensions
Convex Hull of Points
Number of Line Segments in a Line Segment Pattern
Integral of a Pixel Image
Interactively join vertices on a plot
Diggle's Heather Data
Intersection, Union or Set Subtraction of Two Windows
Evaluate Logical Expression Involving Pixel Images and Return
Region Where Expression is True
The Hard Core Point Process Model
Third order summary statistic
Diggle-Gates-Stibbard Point Process Model
Convex Hull of Points
Pairwise distances between two different sets of points
Loglikelihood of Spatial Logistic Regression
Three-Dimensional Box
Infinite Straight Lines
Convert Function Value Table to Function
Fit the Matern Cluster Point Process by Minimum Contrast
ANOVA for Fitted Point Process Models
Hybrid Geyer Point Process Model
Test Whether A Point Pattern is Multitype
Classify Points in a Point Pattern
Nearest Neighbour Distance Function G
Evaluate Expression Involving Functions
Log Likelihood and AIC for Point Process Model
Spherical Contact Distribution Function
Lansing Woods Point Pattern
Ord's Interaction model
Geometrical Calculations for Three-Dimensional Box
Plot a Simulation Envelope
Model Compensator of Nearest Neighbour Function
Interactively Define a Polygon
Fit a Log-Gaussian Cox Point Process by Minimum Contrast
Kolmogorov-Smirnov Test for Point Process Model
Combine Hyperframes by Rows or by Columns
Tabulate Marks in Neighbourhood of Every Point in a Point Pattern
Identify Covariates Involved in each Model Term
Function Value Table
Exchange X and Y Coordinates
Test Whether A Point Pattern is Marked
Find Line Segment Nearest to Each Point
Area of Part of Disc
Convert Window to Pixel Image
Apply Gaussian Blur to a Pixel Image
Difference of Disc Areas
Pair Correlation Function
Nearest neighbour distances in three dimensions
Lookup Tables
Humberside Data on Childhood Leukaemia and Lymphoma
Empirical Intensity of Point Pattern
Convert Window to Another Unit of Length
Interaction Distance of a Point Process
Pairwise distances between two different point patterns
Multi-Dimensional Box
Kernel Smoothed Intensity of Point Pattern
Generic Ord Interaction model
Spatial smoothing of observations at irregular points
Test Whether Objects Are Compatible
Nearest Neighbours Between Two Patterns
Pool Data from Several Ratio Objects
The Area Interaction Point Process Model
Kernel Smoothed Intensity of Split Point Pattern
Perspective Plot of Pixel Image
Internal spatstat functions
Evaluate Expression Involving Pixel Images
Multitype pair correlation function (i-to-any)
Create a Pixel Image Object
Apply Affine Transformation To Point Pattern
Plot a Spatial Kolmogorov-Smirnov Test
Extract or Replace Subset of Tessellation
Nearest Neighbour Distance Distribution Function
of a Three-Dimensional Point Pattern
Plot a plotppm Object Created by plot.ppm
Morphological Erosion
Connected components of an image or window
Inhomogeneous Neighbourhood Density Function
Simulation Envelopes of Summary Function
Envelope for Point Patterns on Linear Network
Bounding Box of a Window or Point Pattern
Generate a Default Pattern of Dummy Points
Apply Affine Transformation To Window
Combine Function Value Tables
Calculate four standard summary functions of a point pattern.
Harkness-Isham ants' nests data
Class of Images
Infinite Order Interaction Family
Multitype J Function (i-to-any)
Fry Plot of Point Pattern
Aherne's hamster tumour data
Plot a List of Things
Intersect Infinite Straight Lines with a Window
Gorilla Nesting Sites
Test Whether An Object Is Empty
Extract or Change Coordinates of a Spatial or Spatiotemporal Point Pattern
Convert dataset to another unit of length
Methods for Distance Functions
Histogram of Pixel Values in an Image
Window in Shape of Letter R
Distance Map of Point Pattern
Mark Correlation Integral
Convert Line Segment Pattern to Pixel Image
Fit Point Process Model to Data
Convex Hull
Evaluate Expression Involving Function Arrays
Inhomogeneous Multitype L Dot Function
Cross Validated Bandwidth Selection for Spatial Smoothing
Fit a Log-Gaussian Cox Point Process by Minimum Contrast
Recognise Stationary and Poisson Point Process Models
Influence Measure for Spatial Point Process Model
Fit the Neyman-Scott Cluster Point Process with Variance Gamma kernel
Mosaic Random Set
Intensity of Fitted Point Process Model
Test Whether a Window is Convex
Move Point To Nearest Line
Pairwise shortest-path distances between points on
a linear network
Reflect In Origin
Methods for Spatial Logistic Regression Models
Level Set of a Pixel Image
Simulate systematic random point pattern
Pairwise Distances in Any Dimensions
Create List of Plotting Layers
Pairwise distances
Distance to Boundary of Window
Rotate
Simulate Point Process Models using the Metropolis-Hastings Algorithm.
California Redwoods Point Pattern (Ripley's Subset)
Bootstrap Confidence Bands for Summary Function
Identify Segments in a Line Segment Pattern
Apply Vector Translation To Point Pattern
Distance Between Two Point Patterns
Spatial Logistic Regression
Simulated Point Pattern
Foxall's Distance Functions
Simulate point patterns using the Metropolis-Hastings algorithm.
The Triplet Point Process Model
Intensity of a Dataset or a Model
Summary of a Line Segment Pattern Dataset
Fit Point Process Model to Point Pattern on Linear Network
Hyper Data Frame
Print Brief Details of a Spatial Window
Estimate the I-function
Test Whether Marks Are Present
Exact Maximum Pseudolikelihood Estimate for Stationary Strauss Process
Inhomogeneous Pair Correlation Function
Define Point Process Model for Metropolis-Hastings Simulation.
Set Default Control Parameters for Metropolis-Hastings Algorithm.
Convert Data to Hyperframe
Make Pixel Images Compatible
Convert Polygonal Region into Different Format
Colour Lookup Tables
Extract Subset of Signed or Vector Measure
Morphological Opening
Lambert's W Function
Point and Click Interface for Exploratory Analysis of Point Pattern
Fit the Matern Cluster Point Process by Minimum Contrast Using Pair Correlation
Dummy Function Returns Number of Points
Compute Integral of Function Against Cumulative Distribution
List Triangles in a Graph
Murchison gold deposits
Convert Pixel Image to Data Frame
Convert and Compare Colours in Different Formats
Square Window
Fit the Thomas Point Process by Minimum Contrast
Model Formulae for Gibbs Point Process Models
Nearest neighbour
Fitted Conditional Intensity for Point Process Model
Reset Values in Subset of Image
Methods for Intensity Functions of Two Spatial Covariates
Pairwise Interaction Process Family
Pair Correlation Function of a Three-Dimensional Point Pattern
Linear Pair Correlation Function
Random Perturbation of a Point Pattern
Hutchings' Bramble Canes data
Inhomogeneous Multitype Pair Correlation Function (Type-i-To-Any-Type)
Subdivide a Window or Tessellation using a Set of Lines
Apply Affine Transformation To Pixel Image
Pool Data
Difference of Disc Areas
Analysis of Deviance for Spatial Logistic Regression Models
Summarizing a Pixel Image
Create Point Pattern on Linear Network
Pseudoscore Diagnostic For Fitted Model against General Alternative
Apply Scalar Dilation
Internal Options in Spatstat Package
Determine Duplicated Points in a Spatial Point Pattern
Divide Image Into Sub-images
Pair Correlation Function of Point Pattern
Simulate a Fitted Gibbs Point Process Model
Chi-Squared Test of CSR for Split Point Pattern
Class owin
Compute Areas of Tiles in a Tessellation
Prediction from a Fitted Cluster Point Process Model
Apply Expansion Rule
Nearest Neighbour Distances in Any Dimensions
Convert Spatial Object to Pixel Image
Apply Vector Translation To Window
Plot a tessellation
Plot a Spatial Window
Urkiola Woods Point Pattern
Extract List of Tiles in a Tessellation
Reduced Sample Estimator using Histogram Data
Simulate Neyman-Scott Point Process with Variance Gamma cluster kernel
Plot a Colour Map
Poisson Point Process on a Linear Network
Quadrature Scheme Based on Pixel Grid
Extract Subset of Function Values
Generate Poisson Random Line Process
Estimate the J-function
Convert Data To Tessellation
Fit the Thomas Point Process by Minimum Contrast
Randomly Shift a Line Segment Pattern
Plot Result of Berman Test
Simulate from a Fitted Point Process Model
Summary of a List of Things
Estimate window from points alone
Superimpose Several Geometric Patterns
Evaluate an Expression in a Function Table
Dirichlet Tessellation of Point Pattern
Pool Data from Several Function Arrays
Convert Point Pattern to Pixel Image
Spruces Point Pattern
Perfect Simulation of the Strauss-Hardcore Process
Pseudoscore Diagnostic For Fitted Model against Area-Interaction Alternative
Plot a List of Point Patterns
Place Points Evenly Along Specified Lines
Extract or Replace Subset of a List of Things
Simulation Envelopes of Summary Function for 3D Point Pattern
Beadlet Anemones Data
Class of Point Matchings
Mark Variogram
Distance Map of Window
Simple Example of Linear Network
Leverage Measure for Spatial Point Process Model
Check Whether Point Process Model is Valid
Simulate Matern Cluster Process
Mark Connection Function
Nearest neighbours in three dimensions
Methods for three-dimensional point patterns
Plot Pixel Image on Linear Network
Marks of a Point Pattern
Distance for a Point Pattern Matching
Nearest-Neighbour Correlation Indices of Marked Point Pattern
Generate N Random Multitype Points
Apply Affine Transformation
Test Whether An Object Is A Window
Generate Poisson Point Pattern on Line Segments
Circular Window
Plot a Signed or Vector-Valued Measure
Compute Images of Constructed Covariates
Midpoints of Line Segment Pattern
Endpoints of Line Segment Pattern
Pair Correlation Function obtained from K Function
Pair Correlation Function obtained from array of K functions
Extract Subset of Multidimensional Point Pattern
ANOVA for Fitted Point Process Models on Linear Network
Extract Quadrature Scheme Used to Fit a Point Process Model
Predicted or Fitted Values from Spatial Logistic Regression
plot a Fitted Point Process Model
Diameter of a Window
Kaplan-Meier and Reduced Sample Estimator using Histograms
Plot a List of Things
Update a Fitted Point Process Model
Multidimensional Space-Time Point Pattern
Plot a fitted cluster point process
plot a Spatial Line Segment Pattern
Chi-Squared Dispersion Test for Spatial Point Pattern Based on
Quadrat Counts
Pairwise distances
Summary of a Point Pattern Dataset
Methods for Point Patterns on a Linear Network
Basis for Harmonic Functions
Orientation Angles of Line Segments
Inhomogeneous Multitype Pair Correlation Function (Cross-Type)
Signed or Vector-Valued Measure
Random Thinning
Perfect Simulation of the Hardcore Process
Interpret Fitted Model for Metropolis-Hastings Simulation.
Lengths of Line Segments
Apply Function to Image Broken Down by Factor
Weighted Empirical Cumulative Distribution Function
Plot a linear network
Profile Maximum Pseudolikelihood
Convert Line Segment Pattern to Another Unit of Length
Print News About Latest Version of Package
Generate N Random Points
Plot a three-dimensional point pattern
Poisson Point Process Model
Distance Map of Line Segment Pattern
Inhomogeneous Linear K Function
Tropical rain forest trees
Deprecated spatstat functions
Update a Fitted Cluster Point Process Model
Convert Data to Three-Dimensional Box
Ord Interaction Process Family
Scatterplot Matrix for Pixel Images
Random Re-Labelling of Point Pattern
Simulate Matern Model I
Estimate Variance of Summary Statistic by Subdivision
Generate N Uniform Random Points
Summarise Marks in Every Neighbourhood in a Point Pattern
Subset of Quadrature Scheme
Random Shift
Apply Vector Translation To Line Segment Pattern
Define Point Process Model for Metropolis-Hastings Simulation.
Test Whether An Object Is A Point Pattern
Default Expansion Rule for Simulation of Model
California Redwoods Point Pattern (Entire Dataset)
Poisson Line Tessellation
Methods for Multidimensional Space-Time Point Patterns
Data and Code From JRSS Discussion Paper on Residuals
Simulate Thomas Process
Find Pixel Nearest to a Given Point
Create a Window
Smooth a Signed or Vector-Valued Measure
Method of Minimum Contrast
Q-Q Plot of Residuals from Fitted Point Process Model
Perimeter Length of Window
plot a Spatial Point Pattern
Set Covariance of a Window
Morishita Index Plot
Name for Unit of Length
Plot a Fitted Spatial Logistic Regression
Rotate a Window
Create a Point Matching
Fit Cluster or Cox Point Process Model
Fit the Neyman-Scott Cluster Point Process with Variance Gamma kernel
Triplet Interaction Family
Rotate a Point Pattern
Pseudoscore Diagnostic For Fitted Model against Saturation Alternative
Kernel Smoothing of Line Segment Pattern
Nearest neighbour distances between line segments
Number of Points in a Point Pattern
Pixel Image Approximation of a Window
Resample a Point Pattern by Resampling Quadrats
Methods for Linear Networks
Nearest Neighbours in Any Dimensions
Simulate a Fitted Spatial Logistic Regression Model
Spokes pattern of dummy points
Divide Multidimensional Point Pattern into Sub-patterns
Cut margins from rectangle
Sample Quantiles of Pixel Image
Convert Data To Class ppp
Pairwise distances between line segments
Pairwise distances
Geometrical Calculations for Multi-Dimensional Box
Evaluate an Expression in Each Row of a Hyperframe
Osteocyte Lacunae Data: Replicated Three-Dimensional Point Patterns
Pine saplings in Finland.
Lurking variable plot
Distance Map as a Function
Extract or Replace Subset of Point Pattern
Generate Multitype Poisson Point Pattern
Point Patterns of New Brunswick Forest Fires
Summarizing a Fitted Point Process Model
The Piecewise Constant Pairwise Interaction Point Process Model
Inverse-distance weighted smoothing of observations at irregular points
Apply Affine Transformation To Line Segment Pattern
Cartesian Coordinates for a Pixel Raster
Simulate Stratified Random Point Pattern
Weighted kernel smoother
Test Whether A Point Process Model is Marked
Residual Diagnostics for Multiple Fitted Models
Simulate Poisson Cluster Process
Approximate a Polygon by a Simpler Polygon
Summary of a Split Point Pattern
Sufficient Statistic of Point Process Model
Circumradius and Diameter of a Linear Network
Bronze gradient filter data
Combine Two Line Segment Patterns
Create a Point Pattern
Methods for Intensity Functions of Spatial Covariate
Inhomogeneous K-function
Class of Line Segment Patterns
Count Multiplicity of Duplicate Points
Variance-Covariance Matrix for a Fitted Point Process Model
Compute Quadrature Weights Based on Grid Counts
Plot Leverage Function
plot a Spatial Quadrature Scheme
Saturated Pairwise Interaction Point Process Family
Smoothed Relative Density of Pairs of Covariate Values
Ratio object
Volume of an Object
Class of Quadrature Schemes
Methods for Units
Locally Scaled K-function
Rescale Data to Lie Between Specified Limits
Delta Metric
Generate N Uniform Random Points On Line Segments
Print a Fitted Point Process Model
Apply Vector Translation
Generate N Uniform Random Points in a Disc
Multitype L-function (i-to-any)
Create Pixel Image on Linear Network
Marks of a Line Segment Pattern
Extract or Replace Sub-Patterns
Estimate the empty space function F
Weighted Histogram
Simulate Gauss-Poisson Process
Perfect Simulation of the Diggle-Gratton Process
Quadrat counting for a point pattern
Perfect Simulation of the Diggle-Gates-Stibbard Process
Spatial Covariance of a Pixel Image
Convert Line Segment Pattern to Binary Pixel Mask
Methods for Cluster Point Process Models
Variance-Covariance Matrix for a Fitted Cluster Point Process Model
Simulate Simple Sequential Inhibition
Maximum, Minimum, Mean, Median, Range or Sum
of Pixel Values in an Image
Methods for Multi-Dimensional Box
Build Point Process Model for Metropolis-Hastings Simulation.
Extract the Variables in a Point Process Model
Plot Influence Measure
Predict Point Process Model on Linear Network
Identify Pixelwise Maximum of Several Pixel Images
Pairwise distances between two different line segment patterns
Divide Point Pattern into Sub-patterns
Theoretical Distribution of Nearest Neighbour Distance
Crossing Points in a Line Segment Pattern
Test Expansion Rule
Print Brief Details of an Image
Generate Poisson Point Pattern in Three Dimensions
Divide Region into Quadrats
Prediction from a Fitted Point Process Model
Convert Point Pattern to Another Unit of Length
Ponderosa Pine Tree Point Pattern
Areas of Morphological Erosions
Remove Marks
Plot a Function Array
Coefficients of Fitted Spatial Logistic Regression Model
Galaxies in the Shapley Supercluster
Generate N Uniform Random Points in Three Dimensions
The Spatstat Package
Nonparametric Estimate of Spatially-Varying Relative Risk
Three Dimensional Point Pattern
Print Brief Details of a Point Pattern Dataset
Plot Entries in a Hyperframe
Pixel Values Along a Transect
Spatial Scan Test
Determine Whether One Window is Contained In Another
Point and Click Interface for Displaying a Point Pattern
Rounding of Pixel Values
Convert Data to Numeric Values by Constructing Dummy Variables
Class of Point Patterns
Create a Line Segment Pattern
Linear K Function
Morphological Dilation
Multitype pair correlation function (cross-type)
L-function
Cressie-Loosmore-Ford and Maximum Absolute Deviation Tests
Test whether Object is Multitype
Vertices of a Window
Generate grid of parallel lines with random displacement
Cross Validated Bandwidth Selection for Kernel Density
Summarizing a Quadrature Scheme
Extract Original Data from a Fitted Point Process Model
Set Control Parameters for Metropolis-Hastings Algorithm.
Create a Tessellation
Randomly Shift a List of Point Patterns
Berman's Tests for Point Process Model
Generate N Uniform Random Points in Any Dimensions
Apply Vector Translation To Pixel Image
Fitted Probabilities for Spatial Logistic Regression
Simulate Baddeley-Silverman Cell Process
Residual K Function
Print Brief Details of a Line Segment Pattern Dataset
Nearest neighbour distances
Extract the Interaction from a Fitted Point Process Model
Determine Type of Window
Nearest Neighbour Clutter Removal
Diagnostic Plots for Fitted Point Process Model
Simulate Neyman-Scott Point Process with Cauchy cluster kernel
Create Colour-Valued Pixel Image
Print a Quadrature Scheme
Swedish Pines Point Pattern
Determine Initial State for Metropolis-Hastings Simulation.
Simulate Neyman-Scott Process
Force Point Process Model to be Valid
Mark Correlation Function
Summary of a Spatial Window
Rotate a Line Segment Pattern
Compute Quadratic Forms
Test Whether A Point Process Model is Multitype
Simulate Log-Gaussian Cox Process
Residuals for Fitted Point Process Model
Print Progress Reports
Methods for Three-Dimensional Box
Convert Pixel Image to Another Unit of Length
Generate a Quadrature Scheme from a Point Pattern
The Multitype/Hard Core Strauss Point Process Model
Distance to Boundary of Window
K-function of a Three-Dimensional Point Pattern
Fit the Neyman-Scott cluster process with Cauchy kernel
Compute Quadrature Weights Based on Dirichlet Tessellation
Chicago Street Crime Data
Area of a Window
Pairwise distances between two different three-dimensional point patterns
Interpolate a Pixel Image
Find Largest Circle Inside Window
Identify Points in a Point Pattern
Stoyan's Rule of Thumb for Bandwidth Selection
Pairwise distances
Layered Plot
Plot Function Values
Create a Function Value Table
Perfect Simulation of the Strauss Process
Convert Window Back To Rectangle
Data Sharpening of Point Pattern
Union of Data and Dummy Points
Extract Design Matrix from Point Process Model
Update Control Parameters of Metropolis-Hastings Algorithm
Pool Data from Several Envelopes
The Multitype Hard Core Point Process Model
Safely Convert Point Pattern Window to Binary Mask
Contour plot of pixel image
The Multitype Strauss Point Process Model
Cross Validated Bandwidth Selection for Relative Risk Estimation
Biological Cells Point Pattern
Compute Disc of Given Radius in Linear Network
Crossing Points of Two Line Segment Patterns
Make Periodic Copies of a Spatial Pattern
New Zealand Trees Point Pattern
Longleaf Pines Point Pattern
Generate Poisson Point Pattern
Specify Simulation Window or Expansion Rule
Uniform Random Points on a Linear Network
Read Point Pattern From Data File
Simulate Matern Model II
Apply Smoothing to Function Values
Calculate Summary Statistic for All Types in a Multitype Point Pattern
Randomly Shift a Point Pattern
Simulate a Fitted Cluster Point Process Model
Extract Unique Points from a Spatial Point Pattern
Class of Fitted Point Process Models
Generate Poisson Point Pattern in Any Dimensions
Delaunay Triangulation of Point Pattern