# ParaView/Users Guide/VTK Data Model

## Contents

## Introduction

To use ParaView effectively, you need to understand the ParaView data model. Here, we will introduce the the VTK data model used by ParaView briefly. For more details, you can refer to one of the VTK books.

The most fundamental data structure in VTK is a data object. Data objects can either be scientific datasets such rectilinear grids or finite elements meshes (see below) or more abstract data structures such as graphs or trees. Since ParaView is geared toward scientific visualization, we will focus on the former and touch briefly on the latter when necessary.

Datasets are formed of smaller building blocks: mesh (topology and geometry) and attributes.

## Mesh

Even though the actual data structure used to store the mesh in memory depends on the type of the dataset, some abstractions are common to all types. We describe these here and we briefly describe the data structures below for each dataset. In general, a mesh consists of vertices (points) and cells (elements, zones). Cells are used to discretize a region and can have various types such a tetrahedra, hexahedra etc. Each cell contains a set of vertices. The mapping from cells to vertices is called the connectivity. Note that even though it is possible to define data elements such as faces and edges, VTK does not represent these explicitly. Rather, they are implied by a cell's type and its connectivity. One exception to this rule is the arbitrary polyhedron which explicitly stores its faces. Here is an example mesh that consists of 2 cells. The first cell is defined by vertices (0, 1, 3, 4) and the second cell is defined by vertices (1, 2, 4, 5). These cells are neighbors because they share the edge defined by the points (1, 4).

So far, we talked about the topology only. A mesh is fully defined by its topology and the spatial coordinates of its vertices. In VTK, the point coordinates may be implicit or explicitly defined by a data array of dimensions (number_of_points, 3).

## Attributes (fields, arrays)

An attribute (aka data array or field) defines the discrete values of a field over the mesh. Examples of attributes include Pressure, Temperature, Velocity and Stress Tensor. Note that VTK does not specifically define different types of attributes. All attributes are stored as data arrays which can have an arbitrary number of components. ParaView makes some assumptions in regards to the number of components. For example, a 3 component array is assumed to be an array of vectors. Attributes can be associated with points or cells. It is also possible to have attributes that are not associated with either. The following example demonstrates the use of a point-centered attribute. Note that the attribute is only defined on the vertices. Interpolation is used to obtain the values everywhere else. The interpolation functions used depends on the cell type. See VTK documentation for details.

The figure below demonstrates the use of a cell-centered attribute. Note that cell-centered attributes are assumed to be constant over each cell. Due to this property, many filters in VTK cannot be directly applied to cell-centered attributes. It is normally required to apply a Cell Data to Point Data filter. In ParaView, this filter is applied automatically when necessary.

## Uniform Rectilinear Grid (Image Data)

A uniform rectilinear grid (aka image data) defines its topology and point coordinates implicitly. To fully define the mesh for an image data, VTK uses the following:

- Extents - these define the minimum and maximum indices in each direction. For example, an image data of extents (0, 9), (0, 19), (0, 29) has 10 points in the x-direction, 20 points in the y-direction and 30 points in the x-direction. The total number of points is 10*20*30.
- Origin - this is the position of a point defined with indices (0, 0, 0)
- Spacing - this is the distance between each point. Spacing for each direction can defined independently

The coordinate of each point is defined as follows: *coordinate = origin + index*spacing* where coordinate, origin, index and spacing are vectors of length 3.

Note that the generic VTK interface for all datasets uses a flat index. The (i,j,k) index can be converted to this flat index as follows: idx_flat = k*(npts_x*npts_y) + j*nptr_x + i.

A uniform rectilinear grid consists of cells of the same type. This type is determined by the dimensionality of the dataset (based on the extents) and can either be vertex (0D), line (1D), pixel (2D) or voxel (3D).

Due to its regular nature, an image data requires less storage than other datasets. Furthermore, many algorithms in VTK have been optimized to take advantage of this property and are more efficient for image data.

## Rectilinear Grid

A rectilinear grid defines its topology implicitly and point coordinates semi-implicitly. To fully define the mesh for a rectilinear grid, VTK uses the following:

- Extents - these define the minimum and maximum indices in each direction. For example, a rectilinear grid of extents (0, 9), (0, 19), (0, 29) has 10 points in the x-direction, 20 points in the y-direction and 30 points in the x-direction. The total number of points is 10*20*30.
- 3 arrays defining coordinates in the x-, y- and z-directions. These arrays are of length npts_x, npts_y and npts_z. This is a significant savings in memory as total memory used by these arrays is npts_x+npts_y+npts_z rather than npts_x*npts_y*npts_z.

The coordinate of each point is defined as follows: *coordinate = (coordinate_array_x(i), coordinate_array_y(j), coordinate_array_z(k))".*

Note that the generic VTK interface for all datasets uses a flat index. The (i,j,k) index can be converted to this flat index as follows: idx_flat = k*(npts_x*npts_y) + j*nptr_x + i.

A rectilinear grid consists of cells of the same type. This type is determined by the dimensionality of the dataset (based on the extents) and can either be vertex (0D), line (1D), pixel (2D) or voxel (3D).

## Curvilinear Grid (Structured Grid)

A curvilinear grid defines its topology implicitly and point coordinates explicitely. To fully define the mesh for a curvilinear grid, VTK uses the following:

- Extents - these define the minimum and maximum indices in each direction. For example, a rectilinear grid of extents (0, 9), (0, 19), (0, 29) has 10 points in the x-direction, 20 points in the y-direction and 30 points in the x-direction. The total number of points is 10*20*30.
- An array of point coordinates. This arrays stores the position of each vertex explicitly.

The coordinate of each point is defined as follows: *coordinate = coordinate_array(idx_flat)". The (i,j,k) index can be converted to this flat index as follows: idx_flat = k*(npts_x*npts_y) + j*nptr_x + i.*

A curvilinear grid consists of cells of the same type. This type is determined by the dimensionality of the dataset (based on the extents) and can either be vertex (0D), line (1D), quad (2D) or hexahedron (3D).