ACGV 2008, Lecture 1 Tuesday January 22, 2008

Transcription

1 Advanced Computer Graphics and Visualization Spring 2008 Ch 1: Introduction Ch 4: The Visualization Pipeline Ch 5: Basic Data Representation Organization, Spring 2008 Stefan Seipel Filip Malmberg Mats Lind Gustav Taxén Martin Ericsson IT-institutionen, TDB Scientific Visualization with 12 Lectures 4 Computer exercises --- laborationer 4 Assignments Written exam Dictionary Interpreting data in visual terms vi su al ize To form a mental image of; envisage: try to visualize the scene as it is described To make visible Visualization offers a way to see the unseen When data is complex: Collected/Computed When numerous data Visualization is not a substitute to, but in addition to, statistical analysis and other quantitative methods Visualization takes advantage of human sensory abilities Pattern recognition, Trend discovery, etc. 1

2 Graphs are one type of visualization Some more sophisticated examples Scientific 3500 Computing Number of Processors Mflop/sec Unknowns IBM SP2 EstP2A/TrueP P2A P2A Estimation of a Disk (Definition 5) SubsFact 1 SubsFact 4 SubsFact 8 SubsFact 16 Nuclear, Quantum, and Molecular Modeling Structures, Fluids, and Fields Radius Advanced Imaging and Data Management Computer Graphics Computer Graphics Creating images with a computer 3D Components Model: geometry, surface properties, Lighting: number, positions, properties Viewpoint Projection Pixar Animation Studios, All Rights Reserved. Visualization is more than computer graphics! Scientific Visualization Visualization serves many purposes Scientific visualization is the process of exploring, transforming, and viewing data as images The dimensionality of the data is generally larger than or equal to 3 Visualization is often interactive We are not trying to create realistic images, but to visualize data in an informative way Dependent on the task given Pretty pictures For further analysis Debugging... 2

3 Visualization can be used in General development of every step of most processes visualization Problem formulation Mathematical modelling Software/Hardware Simulation Result Interpretation Rather new discipline still developing into sub-areas Tool users vs tool developers Collaboration among computer scientists and computational scientists Faster computers, high-speed networks, new user-interfaces Ch 4: The Visualization Pipeline Visualization pipeline, cont d Visualization addresses the issues transformation and representation Transformation: converting data from its original form into graphics primitives and into computer images The pipeline consists of objects to represent data objects to operate on data indicated direction of data flow (arrow connections between objects) Representation: the internal data structures and the graphics primitives Visualization transforms a computational form into a graphical form Data objects Process objects Represent information Provide methods to create, access, and delete data Operate on input data to generate output data New data or new form To modify data is not really allowed; reserved for process objects Source objects initiate (read, generate) visualization data flow Filter objects maintain visualization data flow Mapper objects terminate (write, graph) visualization data flow 3

4 A visualization pipeline Pipeline topology Data Object Computational methods, Measured data Source Process Object Filter Display Mapper Procedural, Reader Transforms the data Creates geometric primitives How to connect data objects and process objects Pipeline connections type concerns the form of data that process objects take as input or generate as output multiplicity deals with # of input and # of output allowed Feedback loops view intermediate results Executing the pipeline Memory and Computation Trade-off Causing each process object to operate Most often repeated executions due to user interaction change parameters of process object change input to process object For efficiency reasons, see to that only execute the process objects whose input has changed Synchronization between process objects required prior to execution Visualization is resource demanding in computer memory due to input size computational times due to algorithm complexity Static memory model intermediate data saved to reduce overall computation Dynamic memory model intermediate data discarded, but may have to be re-computed Combination of static and dynamic models Ch 5: Basic Data Representation Criteria on data representation First, visualization data is discrete by nature digital computers are used to acquire, analyze, and represent the data information is measured or sampled at a finite number of points Hence, all information should be represented in discrete form Interpolation functions generate data values in between known points Compact Efficient σ(n) Mappable from external formats, to graphics primitives Minimal set of data representations covering maximum # of data types Simple designs easier to understand easier to optimize 4

5 Definition of a dataset Collection of Cells and Points Cells specify Topology Shape such as triangle, tetrahedron Points specify Geometry Point coordinates assigned to a topology Data attributes Data associated with topology or geometry Points located where data is known Cells allow interpolation between them Cells specify Topology Vertex Polygon Poly-vertex Line Poly-line Triangle Triangle strip Quadrilateral Pixel Tetrahedron Hexahedron Voxel Wedge Pyramid Cells Meshes consist of Cells A Cell is defined by an ordered list of points Counter clockwise ordering of points specify the direction of the surface normal (using the right-hand rule) Cells can have different shapes and sizes 2D: Triangles, Quadrilaterals, etc. 3D: Tetrahedra, Hexahedra, Pyramids, etc. Meshes can consist of one or more types of Cells Tetrahedron 0 Hexahedron Tetrahedron Triangle Quadrilateral Hexahedron Pyramid Mesh Dataset types Unstructured Grid Organizing structure plus data attributes Uniform Grid Regular topology Regular geometry Rectilinear Grid Regular topology Partially regular geometry Structured Grid Regular topology Irregular geometry The most general form of a dataset A collection of vertices, edges, faces, any cell type Connectivity information must be explicitly stored 5

6 How are unstructured meshes How are unstructured meshes different than regular grids? different than regular grids? Regular Grids mesh info accessed implicitly using grid point indices Unstructured Meshes mesh connectivity information must be stored efficient in both computation and storage handles complex geometries and grid adaptivity typically use finite difference (FD) discretization Cartesian grids or logically rectangular grids typically use finite volume or finite element (FE) discretization mesh quality becomes a concern Data attributes assigned to points or cells Visualization of attributes Scalar Vector magnitude and direction Normal a vector of magnitude 1 used by the graphics system to control shading Texture coordinate mapping data points into a texture space Tensor mathematical generalizations of vectors and matrices Scalar Color Mapping Contouring 3D isosurface Contour value of 5 Visualization of attributes Multi-dimensional images Vector Oriented Line Oriented Glyph Streamline A multi-dimensional image can be considered as a function f(x,y,z,t,b), where z: third spatial direction t: time sequence t: time sequence b: spectral bands Different combinations, for example f(x,y,z,t) is a 4D image representing a time sequence of volume images 6

7 Next: Ch 6: Fundamental Algorithms Iso-surface reconstruction, etc. 7