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Generate Isomers from Chemical Formulas
Symmetry data and utilities related to crystallography and X-ray scattering
Compute polygons for hyperbolic tilings
Represent a hyperbolic polygon embedded in the Poincaré disk
Represent a hyperbolic line segment or polyline embedded in the Poincaré disk
Give the distance between two points in hyperbolic space
Create a graph of a regular hyperbolic tiling
WWW Graph of Computational Geometry for Link Analysis Ranking Experiments
WWW Graph of Computational Geometry for Link Analysis Ranking Experiments
WWW Graph of Computational Geometry for Link Analysis Ranking Experiments
A Wolfram Language implementation of the area method for geometry
Invert the geometry of selected atoms in a molecule
Compute polygons, circles, compositions and transformation functions for the tessellation of the upper half-plane by the modular group
Solve a system of trigonometric or hyperbolic equations
Use the curvature flow image filter to smooth the boundary of a snowflake
Approximate the generalized Voronoi mesh for non-overlapping geometries
Classify and plot any polynomial of degree two or less in three or fewer variables
Solve for a given quantity in a geometric scene
Find a quadric surface that passes through nine given 3D points
Textual information of definitions, common notions, postulates, and theorems from Euclid’s Elements
Convert a list of points into a list of substitution rules
Compute the principal curvatures of a surface
Create a list of all triangles with side lengths a and b and angle β opposite the side with length b
Determine whether a set of points lie on a line
Determine whether a set of points lies in a plane
A collection of lesser-known circular and hyperbolic trig functions and their inverses
Generate a mesh geometry from points without including exterior concave perimeter areas or holes
Create quadrilateral polygon with two parallel sides
Represent a spherical polygon
Show the spherical Voronoi diagram of a set of points on a sphere
Get the flow of an iterated function at a fixed point
Generate points on a geodesic grid
Create an interface for constructing a GeometricScene
Get a GraphicsComplex for ConvexHullMesh
Compute expressions for Dupin cyclide surfaces
Turn an image into a jigsaw puzzle
Compute the aberrancy of a plane curve
Graphics primitive for the arc of a polygon vertex
Construct special triangles of a triangle
Move back and forth from the squared space or square root space of an algebraic number field
Produce random spatial graphs by sprinkling points into a flat (Euclidean) Riemannian manifold
Produce random spatial graphs by sprinkling points into a Riemannian manifold with a specified intrinsic algebraic curvature function
Produce random spatial graphs by sprinkling points into a Riemannian manifold with an arbitrary extrinsic curvature
Generate the graph associated with a parametric description of a manifold
This paclet is for recreational mathematics and math puzzles
Compute the radius of aberrancy of a plane curve
Construct a specified Kimberling center of a triangle
Construct a specified tetrahedron center
Construct special tetrahedra of a tetrahedron
Generate the canonical form of a convex polyhedron
Get the osculating parabola of a plane curve
Get the osculating conic of a plane curve
Generate Koay's uniformly distributed points on a sphere
Determine whether a list of side lengths can form a right triangle
Determine whether a triple of integers constitutes a Pythagorean triple
Alfred Gray’s associated surfaces taken from his original notebooks of his book "Modern Differential Geometry of Curves and Surfaces with Mathematica"
Generate the circumcircle of a 3D triangle
Return an origin-centered simplex where the square of all edge lengths is 2
Generate the incircle of a 3D triangle
Compute the projection matrix for a given vector space
Provide a STensor object for abstract indices tensor computation
Produce causal graphs by dynamically triangulating a specified region of a (potentially curved) spacetime
Produce causal graphs by dynamically triangulating a flat (Minkowski) spacetime
Compute the turning number of a curve
Extract the underlying graphical primitives from plots and graphics
Compute the curve of aberrancy of a plane curve
Compute the Laplace–Beltrami operator of a mesh region
Get curves defined over a sphere
Compute the evolute of a curve
Compute a Groebner basis and a conversion matrix from the input polynomials to the basis
Generate the power triangulation of a set of circles
Computational tools for Geometric Algebras
Given a metric, convert between covariant and contravariant components of a tensor
Compute the Gaussian curvature for a metric
Compute projections of the Wolfram–Ricci curvature tensor of a graph and many associated properties
Compute the Wolfram–Ricci scalar curvature of a graph and its associated properties
Create 3D shapes from 2D polygons via extrusion along the z axis, or create 3D extrusions of 3D polygons along a 3D vector
Compute the natural equations of a curve
Interactively change bond lengths, bond angles and torsion angles
Calculate characteristic properties for a generalized mapping between two coordinate systems
Software monad for Geometric Nearest Neighbors workflows
Convert graphics primitives to well-known text (WKT)
Calculate the convex layers of a set of 2D points
Compute and visualize the roots of fractional (noninteger) derivatives of polynomials
Plots of Alfred Gray’s Surfaces collection
Compute the mean curvature of a surface
Generate the power diagram of a set of circles
Represent a metric tensor (field) for a Riemannian or pseudo-Riemannian manifold
Compute the Wolfram–Hausdorff dimension of a graph and its associated properties
Compute the Dixon resultant with respect to a set of polynomials and variables
Represent the Einstein curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold
Represent the Ricci curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold
3D model of the Stanford Armadillo
3D model of the Stanford Dragon
3D model of a fan disk component
3D model of the Stanford Happy Buddha
3D model of a chimpanzee head
3D model of the Stanford Bunny
3D test model of a space shuttle
3D test model of a Viking lunar lander
Molecular modeling of dynamic gearing and gear-slippage in bis(9-triptycyl)methane
Convert a 3D region into a 3D image, deform and transform it back to the mesh region
Ermer-Lifson CFF for alkanes, alkenes, and alkylbenzenes
Represent the Riemann curvature tensor (field) for a Riemannian or pseudo-Riemannian manifold
Pack smaller rectangles into a larger rectangle
A collection of Graphics and Graphics3D tools
Computes convex polytopes in n-dimensions
Represent a canonical decomposition of the metric for a Riemannian or pseudo-Riemannian manifold via the ADM formalism
Determine whether a given Riemannian or pseudo-Riemannian manifold is a solution to the vacuum Einstein field equations
Represent a stress-energy tensor (field) over a Riemannian or pseudo-Riemannian manifold
Represent the Christoffel symbols for (the Levi-Civita connection over) a Riemannian or pseudo-Riemannian manifold
Get the orientation of a simplex
Collection of parameterized solid models for CAD applications
Decompose a Riemannian or pseudo-Riemannian manifold into a union of discrete hypersurfaces
Determine whether a given stress-energy tensor (field) is a solution to the Einstein field equations
Get the coordinates of the points on a hexagonal spiral
Calculate the radical hyperplane of two hyperspheres
Determine whether a given ADM decomposition is a solution to the vacuum ADM equations
A version of VectorAngle for 2D vectors that can return negative angles
Get the coordinates of the points on a square spiral with sides parallel to the axes
Generate a mesh region representing the tetrahelix
Get the coordinates of the points on a triangular spiral
Lattice points in a square in zigzag order from the bottom-left to the top-right corner
Get a tetartoid given three values
Find the tangency points on a circle emanating from a point
Return the orthocenter of a triangle
Find the barycentric coordinates of a point
Get the standard simplex for a specified dimension
Fill holes in MeshRegion objects
Represent a polygon with notched corners
Modify a BSplineCurve object to have explicit settings for certain options
Perform Lloyd's algorithm to find evenly spaced points in a region
Represent a polyline with rounded corners
Generate a geodesic dome from a polyhedral base
Make a hole in the middle of a polygon
Given a 3D triangle, return an equivalent 2D triangle along with a transformation function
Generate three cyclic harmonic quadrangles from a reference triangle
Plot the Frenet–Serret frame of a curve
The canonical forms of polyhedra with 4 to 9 faces
Compute a translation surface parametrization
Find the minimum-volume enclosing ellipsoid of a set of points
Create a smooth parametrized function from a list of points with flexible control over smoothing
Compute the normal vector to a 3D polygon
Get the shortest displacement between two points in a box with periodic boundary conditions
Compute the angle between two planes in R^3
Reflect a set of points over a line, plane or hyperplane defined by points
Get the Nagel point of a triangle
Generate three congruent Johnson circles given a reference triangle
Build a regular polygon on a given line segment
Construct the Malfatti circles of a triangle
Compute the intersection point of a plane and line
Compute the area of a planar 2D polygon using 3D points
Generate a random chord of a circle
Compute the Voronoi entropy of a mesh region
Smooth curve interpolation based on local procedures for a multiple-valued curve
Generate the minimal mesh region with integer vertices that contains all points
Given a simplex and point, find the cevians
Get the distance and normal line between a point and line
Compute the coefficients of the first fundamental form of a surface
Compute the area element for a surface
Compute the Cesàro equation for a planar curve
Get the measure of a simplex or simplicial complex
Represent a polygon with rounded corners
Generate a tessellation of the plane with specified cell shapes
Create a graphic of nested circles and polygons inside an initial regular polygon
Compute the geometric supplement to a given angle using degrees
Compute the geometric complement to a given angle using degrees
Compute the reference angle to a given input angle
Compute the reference angle to a given input angle using degrees
Represent a cylinder with rounded edges
Compute the geometric complement to a given angle
Outline polygons by beam-like representation
Chamfer a given polyhedron
Create a BSplineSurface primitive representing a disk
A curved line between two points
Compute the geometric supplement to a given angle
Plot a list of vectors in space
Generate the Steiner circumellipse of a 2D triangle
Get the four main points of the Euler line of a triangle
Compute shortest tours visiting all lattice points within each Voronoi cell in a region
Find the shortest paths between two points in 2D regions
Represent the extrinsic curvature tensor field for a Riemannian submanifold
Compute the pedal of a curve
Compute the negative pedal curve
Compute the catacaustic of a curve
Compute the parametrization of a curve projected onto the unit sphere
Compute the unit normal of a surface
Given edge lengths of a tetrahedron, return the dihedral angles opposite those edges
Graphics3D primitives for a torus
Return the Gergonne point of a triangle
Given edge lengths of a triangle, return the angles opposite those edges
Find the intersection of two circles
Convert an ordinary Graphics3D object to a sketch-styled raster image
Return the Monge point and six midplanes of a tetrahedron
Return the lines passing through three or more points, given a set of points
Evaluate the Cayley-Menger matrix of a simplex
Determine the geolocation of a photograph
Generate a surface twisting a curve
Compute the coefficients of the second fundamental form
Get trigonometric datasets including closed-form values
Convert a point reflected in a spherical mirror to its spherical anamorphosis map in a plane parallel to the xy-plane
Generate a Morton (z-order) curve
Evaluate the shortest distance between two points in a box with periodic boundary conditions
Compute the moving orthonormal frame of a surface
Compute the components of the Ricci curvature for a metric
Divide an image into a list of colored polygons centered around the origin
Compute a strophoid curve
Display specific unit cells in a 3D lattice
Project 3D graphics onto a plane
Generate a random surface with B-splines
Display the set of polygons obtained by extending polyhedron edges perpendicularly inward by a given distance
Compute the inversion of an object with respect to a reference circle in the Euclidean plane
Compute the inversion of a curve
Compute the parallel surface of a surface
Compute the contrapedal curve
Compute parallel (offset) curves
Translate a boundary element mesh
Make a random scribble graphic
A cellular automata method for creating cartograms
Find the ellipsoidal loci of the quartiles of matrix
Get the three Lucas circles of a given triangle
Interpolate over values given at the vertices of a polygon
Find the cumulative probability within the specified elliptic domain
Compute the polar radius of a regular polygon
Evaluate the piecewise spherical linear interpolant of given data
Reflect a polyhedron over a given face
Find ellipsoidal location statistics
Make 2D and 3D graphics with specified polygons and corresponding textures
Compute the perpendicular surface of a curve
Compute the Darboux vector field of a curve
Compute the Gaussian curvature of a surface
Compute the tangent developable surface of a curve
Find an instance of n-dimensional vectors that produce a specified distance matrix
Represent a cuboid with rounded edges
Display Voronoi cells for specific lattice points in a 3D lattice
Compute the Voronoi cell for a 3D lattice
Generate the circumcircle of a spherical triangle
Put a circle around an expression
Find the exspheres of a triangle or tetrahedron
Decompose a graphics 3D primitive into polygons when possible
Plot a list of points as numbered labels
Draw an arc through three points
Create a polygon from a list of midpoints
Generate a biarc through two points
Create Graphics primitives of a closed curve that encloses a set of points
Get the three mixtilinear incircles of a triangle
Generate the Brocard inellipse of a 2D triangle
Represent a 3D annulus with rounded edges
Display an interactive plot with all relevant information for a given conic section
Generate a BSplineCurve primitive representing a circle
Generate the Lemoine inellipse of a 2D triangle
Generate a graphical representation of a protractor
Represent a spherical cap in 3D graphics
Create a dynamically rotating Graphics3D object
Plot a set of inequalities distinguishing between different regions
Divide an image into an array of colored squares
Represent a Reuleaux polygon
Give all the polyominoes of a specified rank
Compute the signed area of a polygon
Plot a quadric surface, automatically determining the regions of interest, view direction and scaling
Generate a cubic B-spline curve that passes through given points
Compute the orthotomic of a curve
Compute the catacaustic of a curve at infinity
Compute the control points of a Bézier curve that interpolates a given set of points
Compute the parametrization of a tube of variable section
Convert a 3D curve into a parametrized tube
Compute the curvature of a curve
Compute the tangential angle of a curve
Compute the torsion of a curve
Compute the tangent plane of a parametric surface
Plot cubic lattice crystallographic planes with h, k, l Miller indices
Remove duplicated graphical elements from a polyhedron
Find the partition of a triangle into cevian triangles with congruent incircles
Compute the involute of a curve
Compute the total signed curvature of a curve
Plot a curve defined by its curvature and torsion
Compute the inverse cotangent of a number and return a result in degrees
Compute properties of the tangent line to a curve at a given point
Get an Association of the properties of a given circle
Compute the integral describing the area between two plane curves
Compute properties of the tangent and normal lines to a curve at a given point
Compute the defining properties of the osculating circle for a curve at a point
Get an association of the properties of a conic section
Get an Association of the properties of a given ellipse
Get the Lucas cubic curve of a triangle
Compute the cotangent of an angle given in degrees
Successive pairwise rhumbline distances between a list of geodetic positions
Compute the cosine of an angle given in degrees
Compute the inverse cosine of a number and return a result in degrees
Find a cubic plane curve that passes through nine given 2D points
Compute the area, volume or content of a simplex
Produce a rhombus for use in graphics
Find the intersection of two lines
Find the number of intersections of the diagonals of a regular polygon
Compute the inverse sine of a number and return a result in degrees
Generate the general inellipse of a 2D triangle with specified contact points
Find a conic equation that passes through five given points
Get the isogonal conjugate of a point with respect to a triangle or tetrahedron
Get an Association of the properties of a given hyperbola
Compute the points that form a generalized Koch curve
Computes the secant of an angle given in degrees
Find the number of diagonals of a regular polygon
Find the number of regions partitioned by the diagonals of a regular polygon
Compute the distance of a position on Earth's surface from the center of Earth
Compute the mean of a collection of angles
Get uniformly distributed points on a disk
Get a list of spatial distances between consecutive pairs of locations
Generate random vectors in any dimension of unit length
Compute properties of the secant line to a curve between two points
Evaluate the multidimensional corner angle
Crop an image to contain only pixels included in a predefined region
Compute the Whewell equation for a plane curve
Find the distance between two geographical locations along a rhumb line
Find the best-fit sphere for a set of points
Find the parameterization of a curve that linearly connects a list of points
Get an association of the properties of the given parabola
Compute properties of the normal line to a curve at a given point
Compute the evolutoid of a curve
Compute the inverse tangent of a number and get a result in degrees
Determine if two line segments intersect
Get the rotations and reflections of an array
Filter regions based on their overlap
Get all signed permutations of a list
Find the equation for an ellipse given two foci and a point
Compute the inverse secant of a number and return a result in degrees
Given a 2D triangle and a point, get the specified data
Compute properties of the line parallel to a given line and passing through a given point
Multidimensional polar angle of a corner
Merge multiple regions into a single boundary mesh
Find the equation for a hyperbola given two foci and a point
Generate a geometric transformation function for inversion about a point
Compute the tangent of an angle given in degrees
Compute the inverse cosecant of a number and return a result in degrees
Compute the cosecant of an angle given in degrees
Compute properties of the line normal (perpendicular) to a given line and passing through a given point
Remove phase jumps from phase angle data
Get the Hessian normal form of a plane passing through three given points in space
Get the shortest segment between skew lines
Get the parabolas that go through four points
Get the isotomic conjugate of a point with respect to a triangle or tetrahedron
Compute the area of a triangle from the edge lengths
Compute the apparent visual shape of an object or region traveling with constant velocity
Find the Hausdorff distance between two sets of elements
Test if three given lengths make a triangle
Create a graph corresponding to a Goldberg polyhedron
Get data about various black hole models
Represent a cylinder-like 3D object with protrusions
Generate the hexagonal tiling pattern of the spectre and its supertile
Create an unfolding net for a given polyhedron
Generate random Rorschach tests
Represent an array as polyomino regions
Compute the point group symmetry symbol of a molecule or a polyhedron
Get lattice points in a variety of arrangements
Determine the configuration of stereoisomers
Create a graph of an order-n geodesic sphere
Plot polygons after iteratively applying a translation, scaling and rotation
Compute the Betti numbers for a simplicial complex
Generate the Lévy C curve
Identify the main object in an image
Identify the main object in an image
Compute the stereographic projection from the unit sphere to a plane
Compute the rectifying plane of a space curve
Compute the normal plane of a space curve
Get an approximation to a parametric curve
Compute the osculating plane of a space curve
Compute the radial curve of a given curve
Compute the normal vector of a curve
Compute the binormal vector of a curve
Compute the generalized helicoid of a curve
Compute the geodesics for a parametrized surface
Compute the focal set of a surface
Get the parametrization of a seashell surface
Compute the Poincaré polynomial for a simplicial complex
Generate a graph corresponding to a hexagonal grid
Compute the tangent vector of a curve
Compute the angle between the hands of a clock
Generate an interactive graphical quiz on the plotting of linear functions
Visualize the directional derivative in a 3D plot
User interface for drawing 2D mesh regions
Generate the Minkowski sausage curve
Show the trajectory of a ball bouncing in a regular n-sided polygon
Generate an interactive graphical quiz on the plotting of cubic functions
Approximate a parametric surface with different graphics primitives
Decompose a pair of polygons into disjoint fragments
Get the osculating circle of a curve
Finds the position of a primitive Pythagorean triple in Barning-Hall tree
Generate a quiz to assess understanding of slope fields
Generate primitive Pythagorean triples in a tree form using Fibonacci matrices
Generate a quiz to assess understanding of linear functions
Generate a quiz to assess understanding of linear transformations
Generate a quiz to assess understanding of geometric translations
Generate a quiz to assess understanding of geometric transformations
Generate a quiz to assess understanding of geometrical transformations of cubics
Generate a quiz to assess understanding of geometrical transformations of quadratics
Find the tangent plane of a function at a point
Generate an interactive graphical quiz on the plotting of quadratic functions
Generate the hexagonal tiling pattern of the hat and its supertiles
Generate a hexagonal tiling pattern from a set of hexagonal Wang tiles
Find the topological boundary of a simplex or simplicial complex
Generate random Mondrian patterns
Generate a random Koch curve
Get the faces corresponding to a polyhedral graph
Compute the Hexagrammum Mysticum for six points on a conic section
Compute the sine of an angle given in degrees
Display the Ferrers diagram of a partition with dots
Closed form of cos(2π/p) where p is a Fermat prime (3, 5, 17, 257, 65537) a la Gauss
Create a noncontiguous cartogram
Get the hyperplane that best fits a set of points
Compute the asymptotic curves of a parameterized surface
Get the roots of a derivative for applying the Lucas–Gauss theorem on a set of points
Generate Schmidt arrangements of circles
Create a mesh region from a molecule
Create a triangular grid graph with customizable width and height, represented as a parallelogram composed of triangular grids
Get a physicist's constructive proof of Fuchs's theorem on hyperelliptic curves
Multidimensional scaling algorithm for embedding pairwise distances into a Cartesian space
Generate a quiz to assess understanding of geometric rotations
Fit a line to data points in n-dimensional space
Convert a rotation matrix to an equivalent unit quaternion
Generate a quiz to assess understanding of geometric reflections
Find the ordinary differential equation constraining periods of certain symmetrical curves
Compute the angle between two subspaces
Generate interpolating nodes from points on a curve
Find the area between two plane curves
Compute the loxodrome distance between two points on a unit sphere
Find the position relative to the mean spherical Earth (MSE) for a point in the Earth-centered inertial (ECI) coordinate system
Identify which polar curves are associated with the given equations
Get the Hessian normal form of a line passing through two given points on the Cartesian plane
Create a non-overlapping cartogram type with visual equalization, partial topology preservation and no shape preservation
Classifies and plots any polynomial of degree two or less in two or fewer variables
Compute Moran's I spatial autocorrelation coefficient
Return uniformly distributed random rotations in quaternion form
Calculate the ray transfer matrix of a Gaussian optical system
Compute the directional derivative of a function
An improved sigmoidal interpolation function
Print a human-readable form of a hypothesis in an abstract 2D geometric scene
Calculate integer 2D point locations along a line using Bresenham's method
Convert Bouwkamp format into a diagram
Plot intrinsic curves in 3D
Create a kaleidoscope version of an image
Return a substitution tiling
Perform persistent homology on a point cloud dataset
Install or update the finite element FEMAddOns paclet
Plot the composition of cycles having different radii, frequencies and phases
Create a triangular set decomposition for a given list of polynomials and variables
Compute the properties of a specified rose curve
Generate a tiling pattern from a set of Wang tiles
An interactive plot for the areas inside the rose curve
Generate a tiling pattern from a set of local template constraints
Get the Euclidean distance between two real vectors without using absolute value
Compute the inversion surface
Compute the normal surface of a curve
Compute the binormal surface to a curve
Plot the catacaustic of a curve
Compute the Enneper-Weierstrass parametrization
Compute the parametrization of a canal surface
Compute the Björling formula
Simulate hard spheres moving in an n-dimensional box
Make plots of Penrose tiles
Find the best-fit circle for a set of points
Plot a curve defined by its curvature
Compute the implicit curvature of a curve
Return the Christoffel symbol for a given metric
Generate circle packings covering a picture
Iteratively construct graphs up to a termination condition
Explore graph traversals while deleting visited components
Find minimal sets of templates for constructing tiling patterns
Show the Gershgorin disks of a square matrix
Compute the shape operator on a surface
Display a 3D model using a continuous line
Convert a unit quaternion to an equivalent rotation matrix
Generate the hat tiling using combinatorial hexagons
Obtain topological information of polymers or biopolymers and other simple or complex structures
Convert TensorContract expressions into an equivalent form using Dot and Tr
Given tensors and their indices, sum over repeated indices
Generate the axis-angle representation of a three-dimensional rotation matrix
Evaluate the Theodorus function
Evaluate the solution of the standard Kepler equation
Generate trees describing the essential combinatorial structure of the aperiodic hat tiling
Get a skew graph on a torus with a given number of hexagonal cells
Transform components of tensors with arbitrary rank with regard to their transformation behavior under any given mapping
Visualize the distribution of molecule shapes in a 2D scatter plot
Locations of spruce trees annotated with diameter marks
Quickly cluster a point cloud by recursive separation
Classification of Steiner Surfaces
Compute the Weingarten matrix of a surface
Compute the normal curvature of a curve on a surface
Plot a predator-prey pursuit curve
Compute the Ricci scalar for a metric