Image Analysis | 3D Modeling | Combined Solutions

About sphere-polyhedra model

Sphere-polyhedron is a combination of spheres and a special class of polyhedra, called zonohedra. Sphere-polyhedron can be made from polyhedron by rounding its edges and vertices with spheres of a certain radius r. Examples:

The simplest case of sphere-polyhedron is a sphere; sphere-polyhedron is a usual polyhedron when r=0. Sphere-polyhedron is always central-symmetric, and all its facets are central-symmetric polygons. You can know more about mathematical basis of sphere-polyhedron concept, and also try to build your own sphere-polyhedra at the following page: What is the sphere-polyhedron?
 

Instructions

Follow these easy steps to start developing your model:

• Enter parameters for the model. Click on the name of a parameter to get the description.
• Click "Execute" button to build your model. Note: if you attempt to pack more then 100 particles you will have to enter your registration code.
• Once the building of the model is complete you will be able to see its detailed report. You will also be able to create and view cross-sections planes, rotate the model, save your data (by building and saving detailed report) and perform other actions.
• If you found interesting solution, please save scenario of your pack as a text file or as a link in "Favorites" browser list.
   

Parameters: Number of objects you want to pack: Packing kind: Best (slow) Normal Touching  Pack in bunker:   x  x  (X x Y x Z) Number of checked positions L: Random rotating: Compactness parameter (%): Preferred start X:  ΔX: Preferred start Y:  ΔY: Method for making random sizes R: Uniformly Gaussian Lognormal Mean R: DR: ... for random sizes r: Uniformly Gaussian Lognormal mean r: dr: ... for random radius increments RI: Uniformly Gaussian Lognormal mean RI: DRI: Sphere-polyhedra kinds: Fractions of kinds: Volume fractions mode: Used colors: Invisible colors: Bunker colors: Preferred directions: 1.0,0.0,0.0 0.0,1.0,0.0 0.0,0.0,1.0 1.0,1.0,1.0   Δφ:  20.0 20.0 20.0 20.0 Used directions:   Flags: Reproducible results Repaint while packing  Recalculate while packing Warn if cannot pack (in status)    Actions: Dilated objects: Added radius r:   Packing restrictions: New object must touch the packed object #  New object may touch any objects New object must touch 1 object with same color New object must touch 2 objects with same color New object must touch 3 objects with same color  ? New object may touch invisible objects New object can touch maximum 2 invisible objects New object can touch maximum 1 invisible object New object cannot touch invisible objects  ? The restrictions above act only for >  objects Restricted max. d: Memory/performance parameters: Maximal number of sphere-polyhedra: ( Mb) Maximal average count of generatrix segments: ( Mb) Grid dimension N: ( Mb) Grid step D: Check all possible positions Sleep time percent: % Packing timeout: sec Saving/restoring scenario: help

Results:         [Java-applet for building the pack should run here]    Left Mouse Button rotates the pack Shift + Left Mouse Button shifts the pack Right Mouse Button changes the scale Ctrl + Left Mouse Button cuts the pack Scale: Cut at depth: % Show dissected Rotating: → ← ↓ ↑ ↻ ↺             objects packed Report: D - radius of containing sphere:  Containing parallelepiped:       ≤x≤ , ≤y≤ , ≤z≤      * * = Summary volume of all objects:  Some info for all used colors:     color: number of packed objects; mean volume; summary volume      Mean density in sphere with center (0,0,0) and radius R=...:     R= :      R= :      R= :      R= :      R= :  Number of touching neighbours (base color , touching color ): minimal  maximal  average  ±    Also     ( calculation) for visible objects only, in the following parallelepiped:       ≤x≤ ,      ≤y≤ ,      ≤z≤ ,     with step dXY = Parallelepiped sizes: x * y * z = * * , V = Number of visible objects in the parallelepiped: n = ,     including objects that are partially outside the parallelepiped: ,     only objects that are fully inside the parallelepiped: Occupied volume w = , w /n = ,     ρ = (¾w /πn)1/3 = , w /V (density) = , Free surface = , /(xy) = , /(yz) = , /(xz) = ,      /n = , /V = , /w = ,     (free surface/4πn)3/2 / ρ3 =   Also     ( calculation) for visible spheres only, between two following objects:      # and #     by algorithm: Gauss-Seidel Quickest Descent Conjugate Gradients     with maximal allowed discrepancy:     by applying voltage (0.0V and 1.0V) current (1.0A) to the selected objects      Try to estimate good start approximation (only when applying voltage)      Recalculate all network (can be cleared if the model didn't change)     All visible objects must be spheres or, as an exception, bunker walls. Number of nodes (visible objects): Number of resistors (contacts): Number of connected visible components: Voltage between selected objects V = Current between selected objects I = Conduction between selected objects I/V = Detailed report: Title:   Picture  Text

Comments

Any changes in the "Maximal number of sphere-polyhedra", "Maximal average count of generatrix segments" and "Grid dimension N" parameters will take effect after pressing the "Execute" button; at which point the rebuilding of the packing will occur.

Changes to the "Number of objects you want to pack" value will be committed when the "Apply" button is pressed.

All other parameters can be changed dynamically even during the building process. The changes will take effect immediately. The number and text parameter changes will take effect as cursor leaves the value box.

Current version is 2.2.05

Please click here to see the history of changes since the previous versions.

Coming soon:

• Redesing of this page for more convenient customizing parameters and viewing results.

Smart Imaging Technologies
AlgART Laboratory
Project director Daniel Alievsky