Slide 1Content1. IntroductionPictureGraph: Height-PlotGraph: 3-D Height-PlotSlide 7Visualization - CognitionWhat is Scientific VisualizationGoal of Scientific VisualizationExample: Scalar DataExample: Vector DataExample: Unstructured DataExample: Volume VisualizationExample: Information Visu.Slide 162. Computer Visualization PipelineGaussian Function in 1-DSlide 19Slide 20Gaussian Function in 2-DPipeline Step 1: Data AcquisitionPipeline Step 2: Data MappingSlide 24Pipeline Step 3: RenderingShadingSlide 27Visualization PipelineVisualization Pipeline: Summary3. 2-D data Visualization- (Nov. 1, 2010)Visualization with Matlab2-D Data VisualizationHeight-Plot MethodHeight PlotGaussian FunctionSlide 36Slide 37sine FunctionHeight-Plot of 2-D Gaussian2-D ArraySlide 41Slide 42Slide 43(continued) (Nov. 4, 2010)Slide 45Slide 46Slide 47Nested FOR loopsSlide 492-D height plotSlide 51Slide 52Slide 53Slide 54Image method and Colormap (Nov. 4, 2010)ColorSlide 57ColormapComputer ColorSlide 60(continued) (Nov. 9, 2010)RGB CubeRGB SystemColormap in MatlabExample: Re-usable functionColormap in MatalbcolormapSlide 68Colormap: re-scaleSlide 70“image” method in MatlabSlide 72Slide 73Slide 74The EndCDS 130 - 003Fall, 2010Computing for ScientistsVisualization(Oct . 28, 2010 – Nov. 09, 2010)Jie ZhangCopyright ©Content1. Introduction2. Computer Visualization Pipeline3. 2-D Data Visualization–Height-plot method–Color map methodReferences:(1) “Data Visualization: Principles and Practice”, by Alexandru C. Telea, A. K. Peters Ltd, ISBN-13: 978-1-56881-306-6, 2008(2) CDS 301 “Scientific Information and Data Visualization”, Fall 2009 at http://solar.gmu.edu/teaching/2009_CDS301/index.html1. IntroductionWhat is visualization? Why visualization?PictureA Picture Is Worth a Thousand WordsCave Painting: the dawn of civilizationGraph: Height-PlotHeight plot of thePredator-Prey ModelNumeric output of thePredator-Prey ModelA graph is worth one thousand numbersYearPopulationGraph: 3-D Height-PlotNumeric output: a 2-Dimension data array,which is the same as ……Graph: 3-D Height-PlotHeight plotA graph is worth one million numbersVisualization is a cognitive process performed by humans in forming a mental image of a domain spaceVisualization - CognitionHuman Cognition•Most effective way human takes in information, digest information, making decision, and being creative.•The most important among the five sensesScientific visualization is an interdisciplinary branch of science primarily concerned with the visualization of three dimensional phenomena (meteorological, medical, biological etc) where the emphasis is on realistic rendering of volumes, surfaces, illumination sources with a dynamic (time) component.Friendly (2008), alsohttp://en.wikipedia.org/wiki/Scientific_visualizationWhat is Scientific Visualization At Information AgeGoal of Scientific Visualization•Provide scientific insights•Effective communicationExample: Scalar Data•Height plot of a 2-D data, and the contour lines•In topology, the data are of 2-D: a curved surface •The data are mapped into 3-D geometric space in computer memory•The data are then rendered onto a 2-D visual plane on a screenExample: Vector DataStream tubes: show how water flows through a box with an inlet at the top-right and an outlet at the lower-left of the box; the data are (1) 3-D volume, (2) vectorExample: Unstructured DataScattered Point Cloud and Surface Reconstruction.The data are a set of sampled data points in 3-D space, and the distribution of data is unstructured; need to reconstruct the surface from the scattered pointsSampled data Rendered dataExample: Volume Visualization3-D data of human head. Instead of showing a subset (e.g, a slice as in CT images), the whole 3-D data are shown at once using the technique of Opacity Transfer FunctionExample: Information Visu.•The file system of FFmpeg, a popular software package for encoding audio and video data into digital format•Information, such as name and address, can not be interpolated; the visualization focuses on the relations.An attempt at visualizing the Fourth Dimension: Take a point, stretch it into a line, curl it into a circle, twist it into a sphere, and punch through the sphere.--Albert Einstein--2. Computer Visualization PipelineHow to do it by a computer? We illustrate the process using the well known 2-D Gaussian function: )(22),f(yxeyxGaussian Function in 1-DIt is straightforward to visualize the 1-D Gaussian function)(2)f(xex(1) Choose a data domain, e.g., x in [-3.0, 3.0](2) Choose a set of regular points in x, e.g., step size 0.5: x1=-3.0, x2=-2.5, x3=-2.0, x4=-2.5……….X13=3.0(3) Calculate the corresponding functional value f(xi)(4) Draw the 13 data points (xi, f(xi)) for i=1:13(5) Connecting these points to form a curve, which shows the Gaussian functionGaussian Function in 1-D)(2)f(xexx=-3.0:0.1:3.0; %declare the domain space and define the grid % x: one dimensional data arrayy=exp(-power(x,2)); %calculate the discrete functional value % y: also one dimensional data arrayplot(x,y,'*')hold onplot(x,y)xlabel('x')ylabel('y')title('Gaussian 1D')print -dpng 'Gaussian_1d.png'X: 1-D data array interval or domain: from -3.0 to 3.0 sub-interval: 0.1 value=[-3.0, -2.9, -2.8,………2.9, 3.0] number of elements: N=61Gaussian Function in 1-D)(2)f(xexGaussian Function in 2-DWe know the result. In a height-plot format, It should look like something below. But how to do it through the computer?)(22),f(yxeyxA 3-D height plot showingthe Gaussian SurfaceThe Grid on the domainCreated by PARAVIEW, a power visualization packagePipeline Step 1: Data AcquisitionStep 1: data acquisition. For any input data (experiment, simulation etc) , convert the data into a discrete dataset over a regular gridGaussian Example: •Choose a uniform grid in the domain space•Nx=30 (i=1:30)•Ny=30 (j=1:30)•Calculate the functional value at these grid points•This creates a set of 30 X 30, or 900 in total discrete 3D data points [x,y,z]Pipeline Step 2: Data MappingStep 2: Mapping the discrete dataset onto a 3-D scene. Neighboring discrete data points are grouped to form graphic primitive shapes that a computer can handle efficiently, e.g., point, line, triangle, quadrilateral, and tetrahedronComputer graphics only handles a 3-D sceneGaussian Example:•Form a set of four-vertex polygons or quadrilateral in 3-D space•For each