CS453/553 Scientific Visualization Project 2 Due 11:59pm October 20, 2021 The purpose of the this project is to help you (1) understand scalar field topology. (2) be able to generate contour-based visualization. (3) acquire skills in extracting scalar field topology. Detailed tasks are listed below. Please submit everything necessary to compile and run your program, and a project report that contains results and discussions. Feel free to explore and have fun! 1. (20 points) Given function (,) = 3 62 + 32 3 3 + 3 a. Locate the critical points of (,) by first computing its gradient vector and finding where the gradient vector is a zero vector. b. Classify the critical points into local max, local min, and saddles by computing the Hessian of (, ) and checking the number of positive eigenvalues. 2. (40 points) For each provided dataset under the scalar_data folder, visualize the following scalar fields () = using contours: a. Evenly divide the interval [min, max] into N sub-intevals (you will experiment what N is optimal for each given dataset) and then extract the contour for each of the sub-values. Color the contours with the same color. How does this technique compare with existing techniques based on colors and height fields b. Now color the contours using different colors with the color scheme from project 1 but render the underlying surface with a solid color. What do you think about this visualization c. Combine contours with height fields. What do you find d. Combine colors/height/contours. e. Discuss the strengths and weaknesses of each of the schemes you have implemented (both projects 1 and 2). Be sure to include both text and images to support your argument. 3. (40 points) This part is about scalar field topology: a. For each given data set, extract and visualize its critical points. b. (553 students only) Extract and visualize all contours containing at least one critical point. Compare this method with the visualization in 2(a).
