Lecture 2

Basic Data Representation

(includes text and images from the 3rd edition of the VTK User's Guide)

Four views of the Earth

Discrete nature of data (Chap 5 vtk)

Interpolation

• (nearest neighbour)
• linear
• quadratic
• cubic
• spline

A familiar example is a weather map showing the current temperature across the state or country, but the data is only sampled at certain scattered stations which is then interpolated.
 http://www.sws.uiuc.edu/warm/icnstationmap.asp

Here is another nice example of interpolating winds from the San Francisco Bay area

http://sfports.wr.usgs.gov/wind

Structured or Unstructured Data

• Regular (Structured)
  • stored more compactly, faster computation
  • single mathematical relationship within composing points (geometry) and cells (topology)
• Irregular (Unstructured)
  • more adaptive

Dimension (number of independent variables)

Abstract Dataset

• Structure
  • Topology - set of properties invariant under rotation, translation, non-uniform scaling
  • Geometry - instantiation of topology, the specification of positions in 3-space
  • Consists of one or more Cells (topology) and Points (geometry)
• Data Attributes - supplemental info associated with topology or geometry eg scalars, vectors, normals, texture coords, tensors

Cells specify topology while points specify geometry

Types of Datasets (each of these has their own class in vtk)

• image data - points and cells on a regular rectangular lattice
  • if points and cells are arranged on a plane -> pixmap / bitmap / image
  • if arranged as stacked planes -> volume
  • regular (structured) geometry and topology
• rectilinear grid - points and cells on a regular lattice
  • rows, columns, planes are parallel to x-y-z coordinate system
  • regular topology, geometry only partially regular (spacing between points may vary)
• structured grid
  • regular topology, irregular geometry
  • warped into any configuration w/o overlap or intersection
  • topology stored implicitely
  • geometry explicitely represented by array of point coordinates
  • cells are quadrilaterals (2D) or hexahedron (3D)
  • useful for finite difference computions - fluid flow, heat transfer, combustion
• unstructured points - points irregularly located in space
  • no topology, completely unstructured geometry
  • typically converted to a more structured form for visualization
• polygonal data
  • unstructured topology and geometry
  • collection of graphics primitives (vertices, lines, polygons, triangle strips, etc)
• unstructured grid
  • most general
  • completely unstructured topology and geometry
  • requires most memory and processing
  • used in structural design, vibration, dynamics, heat transfer

Cell

• type plus connectivity list (ordered list of points)

Linear Cells - linear or constant interpolation functions

• vertex - 0D cell
  • single point
• polyvertex - composite 0-dimensional cell
  • arbitrary ordered list of points

• line- 1D cell
  • 2 points - direction is from first to second
• polyline - composite 1-dimensional cell
  • one or more connected lines, from point i to i+1

• triangle - 2D cell
  • counter-clockwise ordering of 3 points
• triangle strip - composite 2-dimensional cell
  • one or more triangles, (i, i+1, i+2) defines a triangle
  • points need not lie in a plane
• quadrilateral - 2D cell
  • ordered list of 4 points in a plane,
  • counter-clockwise ordering, convex, edges do not intersect
• pixel* - 2D cell
  • special case of quadrilateral
  • ordered list of 4 points in a plane
  • each edge is parallel to one of the 3 axis
  • each edge perpendicular to its adjacent ones
  • points ordered in direction of increasing axis coordinate
  • 4 'traditional' pixels form the corners of this kind of pixel
• polygon - 2D cell
  • ordered list of 3+ points lying in a plane
  • counter-clockwise ordering
  • may be concave, but not intersecting

• tetrahedron - 3D cell
  • 6 edges and 4 triangular faces defined by 4 non-planar points
• hexahedron - 3D cell
  • 12 edges and 6 quadrilateral faces defined by 8 vertices, convex
• voxel* - 3D cell
  • special case of hexahedron
  • 12 edges and 6 quadrilateral faces defined by 8 vertices, convex
  • each face is perpendicular to one of the axis
  • point list ordered in direction of increasing coordinate value
  • 8 'traditional' voxels form the corners of this kind of voxel
• wedge - 3D cell
  • 3 quadrilateral faces and 2 triangular and 9 edges defined by 6 vertices
  • must be convex, faces and edges must not intersect
  • ordered list of 6 vertices
• pyramid - 3D cell
  • 1 quadrilateral face and 4 triangular faces and 8 edges defined by 5 vertices
  • 4 points defining base must be convex, apex not coplanar w/ base

Nonlinear Cells

more accurate rate interpolation functions
model curved geometry better

linear easily converted to linear graphics primitives. nonlinear (except maybe for NURBS) must first be converted (tesselated) into linear form

• quadratic edge - 3 points - 2 points at endpoints, 1 in middle of edge
• quadratic triangle - 6 points - 3 at endpoints, 3 in middle of edges
• quadratic quadrilateral - 8 points - 4 at vertices, 4 in middle of edges
• quadratic tetrahedron - 10 points - 4 at vertices, 6 in middle of edges
• quadratic hexahedron - 20 points - 8 at vertices, 12 in middle of edges

Attribute Data

• scalar - single value at each location in dataset
• vector - magnitude and direction
• normal - direction vector (magnitude = 1)
• texture coordinate (2D, 3D)
• tensor (generalization of vector and matrix)
  • rank 0 - scalar
  • rank 1 - vector
  • rank 2 - matrix
  • rank 3 - 3D rectangular array

Some More examples with ParaView

gcanyon.raw (which can be found at ftp.evl.uic.edu in pub/INcoming/andy) contains a height map of the grand canyon as a 625x376 greyscale image. ParaView can load this image by setting the data type to 'unsigned char', the File Dimensionality to 2, and then setting the extents as 0-624, 0-375. This will bring up a greyscale image. then you can use the Contour filter to define a series of contours. As the scalar values in the file range from 103 to 224 you could set up contours at 125, 150, 175 and 200 for example. These contours would initially all be in the same plane, but you can also translate them in Z. You may also need to edit the colour map and reset the range (it should be 103 to 224)

Using paraview 2.X you can also take the data and extract a surface from it. Once you have the surface you can warp it onto 3D. With paraview 3 beta you need to tetrahedralize the data and then apply the warp scalar.

A dataset that comes with the vtk cdrom in VTKData/Data is ironProt.vtk. Since it is a .vtk file the header of this file contains the information that vtk needs to properly load the data in. Like the visible woman dataset we can use the contour tool to generate contours. In the image below there is a contour at 50 shown as wireframe, another contour at 200 shown as a surface, and then a cutting plane.

Some nice examples:

Nasa hurricane season animation

airplane flight patterns across the US - http://youtube.com/watch?v=dPv8psZsvIU

Coming Next Time

Fundamental Algorithms (1 of 2)