Yingcai Xiao

Chapter 5

Basic Data Representation

Characteristics of Data

• DiscreteInterpolation

P1, P2• Regular/Irregular• Data Dimensions 

Data Structure Data Structure Design Criterion

• Compact (save space)

• Efficient (fast retrieval)

• Map-able (easy to convert)

• Minimal Coverage (small foot prints)

• Simple (easy to use)

DatasetDataset

• Data objects in the visualization pipeline are called datasets

• consisting of two pieces: an organizing structure and supplemental data attributes.

 

DatasetDataset

Structure: topology and geometry•Topology: is the set of properties invariant under certain geometric transformations.•Geometry: is the instantiation of the topology; the specification of positions in a 3D space.•VTK Model: the structure consists of cells and points. The cells specify the topology; while the points specify the geometry  

DatasetDataset

Dataset Attribute:•Data to be visualized. •Associated with each point.•Typical attributes: scalars, vectors, normals, texture coordinates, tensors, and user-defined data. 

Cell TypesCell Types

• A data set consists of one or more cells• A cell is defined by a “type” and an ordered list of

point• Type: topology, cell type• Ordered list: geometry, points• Together: organizational structure• Use Set: all the cells using a point:

U(pi) = {Ci: pi Ci} 

• A data set consists of one or more cells• A cell is defined by a “type” and an ordered list of

point• Type: topology, cell type• Ordered list: geometry, points• Together: organizational structure• Use Set: all the cells using a point:

U(pi) = {Ci: pi Ci} 

Cell TypesCell Types

Vertex: zero-dimensional cell, It is defined by a single point. vtkVertexLine: one dimensional cell. It is defined by two points. vtkLinePolyline: is a composite one-dimensional cell consisting of n connected lines. It is defined by an ordered list of n+1 points. vtkPolyLineTriangle: is a primary two-dimensional cell. The triangle is defined by a counter-clockwise ordered list of three points. vtkTrianglePolygon: is a primary two-dimensional cell. The polygon is defined by an ordered list of three or more points lying in a planeTetrahedron: is a primary three-dimensional cell. It is defined by a list of four nonplanar point. VtkTetrahedron 

Vertex: zero-dimensional cell, It is defined by a single point. vtkVertexLine: one dimensional cell. It is defined by two points. vtkLinePolyline: is a composite one-dimensional cell consisting of n connected lines. It is defined by an ordered list of n+1 points. vtkPolyLineTriangle: is a primary two-dimensional cell. The triangle is defined by a counter-clockwise ordered list of three points. vtkTrianglePolygon: is a primary two-dimensional cell. The polygon is defined by an ordered list of three or more points lying in a planeTetrahedron: is a primary three-dimensional cell. It is defined by a list of four nonplanar point. VtkTetrahedron 

Attribute Data

Attribute data is information associated with the structure of the dataset. It is what to be visualized.

Dataset Attribute Model

Scalars Vectors Normals Texture Coordinates Tensors (The rank of a tensor is the dimension of the matrix

containing its values.) User-defined

Type of Datasets

Dependent on topology of the dataset.

Uniform Grid (uniform in each direction, vtkImageData)

Parameters:

Dimension: nx, ny, nz

Origin: x0, y0, z0

Spacing: dx, dy, dz

Type of Datasets: Uniform Grid Uniform Grid

IJK space

x = i*dx + x0

y = j*dy + y0

z = k*dz + z0

Data array (i, j, k), loop i first, then j, k last.

Simple, compact and speedy retrieval.

Not flexible

Represented by vtkImageData in VTK.

Example: Fig. 5-18.

Rectlinear Grid

Dimension: nx, ny, nz

Nonuniform spacing, but straight grid lines.

float x[44]={0.0,1.2,2.8,3.9…….}

float y[33]={1.0,……………}

float z[22]={0.8,……………}

Rectlinear Grid

IJK space.

x = x[I]; y = y[J]; z = z[K]; Data array (i, j, k), i changes first, then j, k last.

Simple

compact (takes O(nx + ny + nz) more space)

speedy retrieval

Little more flexible

 

Rectlinear Grid (Example Code)

vtkFloatArray * xCoords=vtkFloatArray::New();

for(i=0;i<44;i++) xCoords-> InsertNextValue(x[i])

vtkFloatArray * yCoords=vtkFloatArray::New();

for(i=0;i<33;i++) yCoords-> InsertNextValue(y[i])

vtkFloatArray * zCoords=vtkFloatArray::New();

for(i=0;i<22;i++) zCoords-> InsertNextValue(z[i])

 

vtkRectiLinearGrid * rgrid=vtkRectiLinearGrid::New();

rgridsetXCoordinates(xCoords); rgridsetYCoordinates(yCoords);

rgridsetZCoordinates(zCoords);

rgridSetDimensions(44,33,22);

 

Structured Grid

Dimension: nx, ny, nz

Nonuniform spacing

IJK space (no formula)

Coordinates of each grid node need to be given.

x(I,J,K), y(I,J,K), z(I,J,K)

Data Set:

Internal Memory Structurein

Generic Form

Unstructured Grid

• No dimensions parameters: nx, ny, nz

• No IJK space

• Coordinates of each node need to be given

• Most flexible, can represent any structures of data

• Not compact (need space to save xyz values and cell information)

• Slow retrieval

Data SetInternal MemoryStructure

Unstructured Surface

Polygonal Surface (PolyData)

No dimensions parameters: nx, ny, nz

No IJK space

Coordinates of each node need to be given

Data value(s) on each node needs to be given

Structure Representation

P1 of T1 and P2 of T2 are connected at P(1,0,0)

 

Structure RepresentationThe Wrong Way: Making Copies

class Tri { public: point P1, P2, P3; };

 

T2.P2.x=1.0;

T2.P2.y=0.0;

T2.P2.z=0.0;

………

Tri T1, T2;

T1.P1.x=1.0;

T1.P1.y=0.0;

T1.P1.z=0.0;

…….

Structure Representation: Wrong WayEach triangle keeps a copy of the vertex values.

Drawback: if the coordinate of P is changed, all cells having a copy of its value need to be updated.

 

Structure Representation: Correct Way

Save the vertex values in an array (Point List).

Store the indexes of the vertexes for each triangle in the triangle definition  

Structure RepresentationThe Correct Way: Indexing

Point List

P0.x=0.0;

P0.y=0.0;

P0.z=0.0;

P1.x=1.0;

P1.y=0.0;

P1.z=0.0;

P2.x=1.0;

P2.y=1.0;

P2.z=0.0;

P3.x=0.0;

P3.y=1.0;

P3.z=0.0;

Structure RepresentationThe Correct Way: Indexing

class Tri{ public: int ID1, ID2, ID3; };

 

Tri T1, T2;

T1.ID1=0;

T1.ID2=1;

T1.ID3=3;

T2.ID1=1;

T2.ID2=2;

T2.ID3=3;

Structure Representation: The Correct Way: IndexingEach triangle keeps an index list (cell list) of its vertexes.

If the coordinate of P is changed, none of the cells using it needs to be changed. Only the one copy of its value in the point list needs to be updated.

 

DatasetDataset

Structure: topology and geometry•Topology: is the set of properties invariant under certain geometric transformations.•Geometry: is the instantiation of the topology; the specification of positions in a 3D space.•VTK Model: the structure consists of cells and points. The cells specify the topology; while the points specify the geometry  

Data SetInternal MemoryStructure

Summary of VTK Data StructuresSummary of VTK Data Structures