What’s New in Geometry

Charles Pooh, Wolfram Research

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Overview

Multi-Paradigm Modeling

Graphics & Visualization

Computational Geometry

Import Geometry

Increase workflow efficiency by importing data directly from a wide range of 3D geometric and modeling formats, including STL, OBJ and DAE.

Import["ExampleData/747.3ds.gz"]

Geometry from Curated Data

Direct access to a large volume of curated 3D geometric models such as polyhedra, knots, anatomical structures, and geometric features.

AnatomyData[,"MeshRegion"]

Geometry in Wolfram Data Repository

Easy access to a collection of standard geometric models.

ResourceData["Stanford Dragon"]

Multi-Paradigm Modeling

Model geometric regions using meshes, implicit representation, primitive instancing and more. Combine and transform regions to create new ones.

Primitive Instancing

Ball[]//Region

Implicit Representation

ImplicitRegion[x^2+y^2==1,{x,y}]//Region

Meshes

MeshRegion[{{0,0,0},{1,0,0},{0,1,0},{0,0,1}},Tetrahedron[{1,2,3,4}]]

Constructive Solid Geometry

({{, , , , }})

CSGRegion["Difference",]

CSGRegion["Difference",]

And More …

Bridge domains and analyze geometry using graphs, reconstruct geometry from images or compute on maps.

From Image

Import["ExampleData/CTengine.tiff","Image3D"]

ImageMesh[%]

From Graphics

Graphics[{Disk[{0,0}],Circle[{1,0}]}]

DiscretizeGraphics[%]

From Geography

(Entity["France", Entity["Country","France"], "Entity[\"Country\", \"France\"]", "country"])["Polygon"]

DiscretizeRegion[%]

High-Quality Graphics & Region Visualization

Render geometric regions with insightful structure or realistic appearance. Gain immediate insight by visualizing your data and functions over geometric regions.

Region[Ball[]]

VertexColors & VertexNormals

MeshRegion and BoundaryMeshRegion now support VertexColors and VertexNormals for smooth colors objects.

mr=;

MeshRegionQ[mr]

MeshRegion[mr,VertexColors->{}]

Computation Geometry

({{, , , (Spacer1), , , , (Spacer1), , , }, {"points", , "mesh", , "points", , "mesh", , "points", , "mesh"}, {"1D", , , , "2D", , , , "3D", , }})

({{, , }, {"1D", "2D", "3D"}})

New: ReconstructionMesh

({{, , , (Spacer1), , , , (Spacer1), , , }, {"points", , "mesh", , "points", , "mesh", , "points", , "mesh"}, {"1D", , , , "2D", , , , "3D", , }})

pts=RandomPoint[ResourceData["Stanford Bunny"],10000];

Graphics3D[Point[pts]]

ReconstructionMesh[pts]

Voronoi in 3D

({{, , }, {"1D", "2D", "3D"}})

pts=RandomReal[1,{25,3}];

Graphics3D[Point[pts]]

VoronoiMesh[pts,]

Progress in Graphs & Networks      
Thursday 3:35 PM CDT

Region Reconstruction
Thursday 4:20 PM CDT

Office Hour — Geometry
Friday 8:30 PM CDT

Office Hours — Graphs & Networks
Friday 2:00 PM CDT

Wolfram R&D Live
Every Wednesday 11:00 PM CDT
(wolf.ram/RDLive)

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