1 Particle Advection Particle Advection 4/28/2003 R. Crawfis, - PDF document

Data Types Vector Field Visualization � Computational Science generates data with many different properties: � Spatial dimensions (2D, 3D, 1D helical, …) � Time properties Roger Crawfis � scalar fields, vector fields, tensor fields Ohio State University � Data sample point locations or mesh structure. 4/28/2003 R. Crawfis, Ohio State Univ. 2 Categorization of Techniques Advection Techniques � Requires accurate numerical integration and � Advection-Based Techniques interpolation. � Global Texturing Techniques � Examples: � Automatic Classification Techniques � Individual particles � Streamlines � Streaklines � Pathlines � Timelines � 2D properties of separation 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 3 4 Particle Advection Particle Advection � Obeys a simple first-order differential equation. � Solve using: � Euler’s Method � 4 th Order Runga-Kutta Method � Adaptive Runga-Kutta � Other higher-order techniques Particle 4/28/2003 R. Crawfis, Ohio State Univ. 5 4/28/2003 R. Crawfis, Ohio State Univ. 6 1

Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 7 8 Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 9 10 Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 11 4/28/2003 R. Crawfis, Ohio State Univ. 12 2

Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 13 14 Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 15 16 Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 17 4/28/2003 R. Crawfis, Ohio State Univ. 18 3

Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 19 20 Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 21 22 Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 23 4/28/2003 R. Crawfis, Ohio State Univ. 24 4

Particle Advection Particle Advection 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 25 26 Particle Advection Particle Advection � Connect the dots? 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 27 28 Streamlines Streamlines Many streamlines can give a good overall feeling for the � A more continuous representation is the vector field. These are color-coded according to a different streamline. data value. � Lose any hint of the velocity magnitude. Streamline 4/28/2003 R. Crawfis, Ohio State Univ. 29 4/28/2003 R. Crawfis, Ohio State Univ. 30 5

Illuminated Streamlines Illuminated Streamlines � Adding cylindrical lighting greatly aids in the perception of 3D space. Class Project from Sweden Short Course Stalling, IEEE Visualization ‘96 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 31 32 Stalling, IEEE Visualization ‘96 Illuminated Streamlines Flow Separation � Electro-magnetic � In 2D, the streamline has the nice current through property that 2 curves will not cross. the torso. � In other word, a particle release to the top of the streamline will stay to that side. Chris Johnson, Univ. of Utah 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 33 34 Time-varying fields Streaklines � What if your vector fields are time � Treat the current curve as a weightless varying? piece of string blown by the wind. � Streamlines � Character of curve can change � Streaklines � Pathlines � Timelines 4/28/2003 R. Crawfis, Ohio State Univ. 35 4/28/2003 R. Crawfis, Ohio State Univ. 36 6

Streaklines Streaklines � Each point on the previous curve is � It is possible to gets curves that cross advected. themselves. Lost the nice property of separation. � The curve is extended for the current time by connecting it back to the beginning. 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 37 38 Pathlines Pathlines � Keep a running history of where a particle has been. � All current points stay fixed, and the current flow is used to extend the string in the direction of the flow. 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 39 40 Ribbons and Tubes Timelines � Ribbons can be � A rack of particles is placed in the flow. used to show the � Treat it as a string and let it advect. curl or vorticity of the flow. Time = t 2 Chris Johnson, Univ. of Utah Time = t 1 4/28/2003 R. Crawfis, Ohio State Univ. 41 4/28/2003 R. Crawfis, Ohio State Univ. 42 7

Problems with Advection Algorithms Stream Surfaces � The flow can quickly converge, making it � Stream Surfaces can be generated difficult to get a representation of the flow explicitly as outlined by Hulquist: in downstream areas. � Start with segmented curve Class Project from Sweden Short Course � Advect each vertex forward � If adjacent vertices diverge, add new vertices � The flow may diverge too greatly. � If adjacent vertices converge, Class Project from Sweden Short Course merge the vertices � If too much divergence, let the � The user is required to be in the process. surface split and form a tear. 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 43 44 Stream Surfaces Stream Surfaces - Implicit � Stream Surfaces can also be generated implicitly as outline by van Wijk: � Place a continuous function on the inlet’s of a Split flow simulation. Merge � For each sample point, trace backwards to inlet � The value at the inlet intersected with the streamline is used to generate a function f(x,y,z) � Take iso-contour of the function f(x,y,z) to get a stream surface. Initial seed http://www.zib.de/Visual/projects/vector/ 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 45 46 Flow Volumes Flow Volumes � Build a bounding volume of the flow and represent the � This results in a 3D unstructured grid that needs interior of this volume: to be volume rendered. � Seed polygon (square) is used as smoke generator. � Constrained such that center is perpendicular to flow. � Square can be subdivided into a finer mesh. � Like explicit stream surfaces, the volume is adaptively subdivided in areas of high divergence. 4/28/2003 R. Crawfis, Ohio State Univ. 47 4/28/2003 R. Crawfis, Ohio State Univ. 48 8

Flow Volumes Flow Volumes � This virtual dye injector can simulate steady � Color can be added to show magnitude or state from a snapshot of time and mimic other properties of the data. compressible or incompressible materials (regardless of the underlying simulation) 4/28/2003 R. Crawfis, Ohio State Univ. 4/28/2003 R. Crawfis, Ohio State Univ. 49 50 9