SCIENTIFICVISUALIZATION

Lecture 9Lecture 9part 1part 1

Scientific Visualization GroupVisual Information Technology and ApplicationsLinköping University

CONTENTS

• More Scalar Algorithms• Vector Algorithms• Modelling Algorithms

– Decimation– Triangulation– Mesh smoothing

• Unstructured points

DIVIDING CUBES

• Similar to Marching Cubes• Rendering points faster than

rendering polygons• Generate points at display

resolution• Zooming creates holes!• Can be deployed iteratively

DIVIDING CUBES

DIVIDING CUBES iterations

DIVIDING CUBES

• Nice example with Iron Protein EX: 9:1

CUTTING• Cutting surface defined by

an implicit function– For each cell point evaluate

F(x,y,z)– Find contour of F(x,y,z)=0– Interpolate attribute data

along cut edges– Does it sound familiar? (MC

algorithm with F(x,y,z))

• Implemented in VTK usingvtkCutter

CLIPPING• Clipping defined by an

implicit function– For each cell point evaluate

F(x,y,z)– Find contour of F(x,y,z)=0– Interpolate attribute data

along cut edges– Insert new points along

edges

• Implemented in VTK usingvtkClipPolyData

• Streamribbons: Start two streamlines closeand draw a surface connecting them (createsa ribbon)

• Streamsurfaces: Start a number ofstreamlines on a curve, then draw as asurface

• Streampolygons:transport polygonaccording to vectorfield derivatives

VECTOR FIELDS

STREAM POLYGON• Map strain, shear and

rotation to n-sidedpolygon

• Align polygon normalwith the local vector

• Connect edges ofpolygons to form“tubes”

• Radius of tube could beproportional to vectormagnitude Example 9:2

CRITICAL POINTS• Critical points are

found in cells where allvector componentspass through 0

• Iterative proceduresused to find criticalpoints

• Use the eigenvalues ofthe Jacobian

CRITICAL POPINTS IN 2D

MODELLING ALGORITHMS

• Visualizing geometry• Data extraction• Probing• Triangle strip generation• Connectivity• Polygon normal

generation• Mesh decimation and

compression

•Mesh smoothing•Swept volumes andsurfaces•Visualizing unstructuredpoints•Multidimensionalvisualization•Texture algorithms

The Zoo

DATA EXTRACTION

• Geometry extraction– Range of cell Ids– Spatial extraction– Subsampling

• Select every nth datapoint

– Masking• Select every nth cell

•Thresh holding–selection based onvalue of attribute date–Use clipping if cells areon the boundary

PROBING• Sample one data set

with another data set• Constitutes a

generalization of cuttingusing general data sets– Can be user as means for

data extraction byprobing of a subregion

– Probing along specialdata sets can give subsetslike plans for contours ...

TRIANGLE STRIP GENERATION• To achieve better

performance• Gather polygons into

triangle strips• Start with unmarked

triangle• “Grow” a strip in

direction of first foundunmarked neighbor

• Memory savings canbe large

CONNECTIVITY

• Important to find structures that aretopologically connected

• Contours, isosurfaces, etc.• Use neighbor operator to find cells that share

boundary features• Recursively visit all cells and give them a

connectivity ID• Can be used to reduce “noise” in datasets

NORMAL GENERATION• Point normals not always

supported in file formats• compute polygon

normals around a point• average normals to point

– Need to check forconsistency in ordering ofpoints in polygon

– Traverse all neighboursand mark as consistent tofind surface

•Check for largedifferences in normals–Define “feature angle”–If angle larger duplicatepoints, i.e. split surface andintroduce an edge

•Example 9:3

DECIMATION• Point classification

– simple• surrounded by complete cycle of

triangles, each edge used byexactly two triangles

– complex• if point used by triangle not in

cycle or each edge not used byexactly two triangles

– boundary• Point on the boundary of the

mesh– interior edge

• when angle between triangles incycle exceeds the feature angle

– corner• more than one feature edge

•Decimation Criterion–Complex and corner points are notdeleted–Approximate area around point with plane(least square or area average)–Delete point if distance to plane is smallerthan specified parameter d

•Triangulation–use 3D divide and conquer technique tofill hole–split the the loop into two halves–checks aspect ratio of resulting triangle–continue to split until each loop has threeedges

Example 9:4

UNSTRUCTURED POINTS• Splatting

– sample points withstructured points data set

– Use Gaussian function to“splat” the point on thegrid

– Use standard techniquesfor structured points tovisualize

•Interpolation–Build an interpolationfunction that represents eachof the points in the data set–Sample the new functionover the a structured pointsdata set–use standard techniques forstructured points to visualize

DELAUNAY TRIANGULATION

• Build a triangular mesh (2D) or tetrahedralmesh (3D) from unstructured points

Bounding triangle Create new triangulationInsert point