Scien&fic Data Model Han-Wei Shen The Ohio State University - - PowerPoint PPT Presentation

Scien&fic Data Model

Han-Wei Shen The Ohio State University

What is a Data Model?

How do you describe the data represented by this image?

Data Model

• Describe the objects represented by the data

Data Model

• Describe the objects represented by the data

– Structures of the objects

u v

Data Model

• Describe the objects represented by the data

– Structures of the objects – Proper&es of the objects

u v Temperature Pressure Cloud density … (u,v)

Data Model

• Describe the objects represented by the data

– Structures of the objects – Proper&es of the objects – Rela&onships between the objects

u v Temperature Pressure Cloud density … (u,v)

Scien&fic Data Model

Temperature Pressure Cloud density …

• Data set – a single or

mul&ple valued func&on

Data Model

m dependent variables xi (i=1..m) n independent variable vj (j = 1..n) Each dependent variable yi can have a tensor rank k

– k = 0 : scalar; k = 1: vector; k = 2; 2D matrix, etc.

y1 = f1(x1, x2, x3, ..., xn) y2 = f2(x1, x2, x3, ..., xn) ym = fm(x1, x2, x3, ..., xn)

…

Scien&fic Data Model

• Independent variables

(dimensions) – Spa&al coordinates (longitude, la&tude, height) – Time – Zone ID – …

• Dimensionality - number of

independent variables

u v

• Data set – a single or

mul&ple valued func&on

Temperature Pressure Cloud density … (u,v)

• Dependent variables

– The func&on values of independent variables – The number of values associated with each dependent variable can be described by its tensor rank – 0: scalar – 1: vector – 2: n x n matrix …

Domain Discre&za&on

u v u v Con&nuous Domain u v compute values

Scien&fic Data Set

Scien&fic Data Set = u v Domain Structure

• Topology: property invariant

under transforma&on

• Geometry: instan&a&on of

topology with specific posi&ons

• Consists of Points and Cells,

which define the Mesh u v A[ributes One or mul&ple values (scalars, vectors, tensors) defined at points or cells Domain Structure + A[ributes

Domain Structure - Cell

u v u v

• Cells are the fundamental building blocks of

scien&fic data sets

• Cells define how points are connected

together to form the basis for interpola&on

• Cells can be of different dimensionality

– 0 D: Ver&ces – 1 D: Line; Polylines; – 2 D: Triangle; Quadrilateral; Polygon – 3 D: Tetrahedron; Hexahedron; Voxel;

Cell Types

Ver&ces Line Polyline

1D

Triangle Quad Polygon

2D

Tetrahedron Cube Hexahedron Pyramid

3D

A[ributes

• Scalars (e.g. density), Vectors (e.g.

momentum), , Tensors (e.g. stress tensor)

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structures)

• Structured Grid
• Unstructured Grid

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structures)

– Structured Grid – Consis&ng of a collec&on of points and cells arranged on a regular

labce

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structures)

– Structured Grid – Consis&ng of a collec&on of points and cells arranged on a regular

labce – Every point in the structured grid can be indexed by (i,j) in 2D, (i,j,k) in 3D, etc.

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structures)

– Structured Grid – Consis&ng of a collec&on of points and cells arranged on a regular

labce – Every point in the structured grid can be indexed by (i,j) in 2D, (i,j,k) in 3D, etc. – The posi&on of the points, and hence the geometry of the cells, can be either implicitly defined (Cartesian gird), or explicitly specified (rec&linear or curvilinear grid)

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structures)

Cartesian Grid

– Structured Grid

• Cartesian mesh

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structures)

Cartesian Grid Rec&linear Grid

– Structured Grid

• Cartesian mesh
• Rec&linear mesh

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structures)

Cartesian Grid Rec&linear Grid Curvilinear Grid

– Structured Grid

• Cartesian mesh
• Rec&linear mesh
• Curvilinear mesh

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structure)

– Unstructured Grid

• Also called irregular grid data

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structure)

– Unstructured Grid

• Also called irregular grid data
• Unstructured grid points are irregularly

distributed in space

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structure)

– Unstructured Grid

• Also called irregular grid data
• Unstructured grid points are irregular

located in space

• It is ocen a result of space tessella&on

with simple shapes

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structure)

– Unstructured Grid

• Also called irregular grid data
• Unstructured grid points are irregular

located in space

• It is ocen a result of space tessella&on

with simple shapes

• Explicit connec&vity informa&on to form cells is

necessary

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structure)

– Unstructured Grid

• Polygonal mesh

Polygonal mesh

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structure)

– Unstructured Grid

• Polygonal mesh
• Tetrahedral mesh

Polygonal mesh Tetrahedral mesh

Scien&fic Dataset Types

• Data sets are categorized into different types

based on their underlying grid (domain structure)

– Unstructured Grid

• Polygonal mesh
• Tetrahedral mesh
• Hybrid Mesh

Polygonal mesh Tetrahedral mesh Hybrid mesh