 Interaction System代写

## August 31, 2018

Interaction-System代写 The very first step is to encode the surface or algebraic curve into the computer program, and visualize it as a sanity check.

### Problem Statement

Finding the intersections of two or more surfaces, or algebraic curves, is one of the fun- damental and important problems in computational geometry. Visualizing the intersections will give an intuitive and pictorial understanding of these intersections, complementing the rigorous mathematical analysis to them. Therefore we propose to implement a surface vi- sualization and interaction system, in which the intersections of surfaces are computed by computational geometry algorithms and visualized via computer graphics technologies. By ”interaction” it means that the user is able to manipulate the visualization of the surface or the intersections of multiple surfaces. For example, the user can zoom in, zoom out, rotate, and translate the surface. Empowering a system with the ability of interaction improves the user experience by a huge amount.

### Solution Approach  Interaction-System代写

The solution for this project can be divided into four steps, described as follows.

Surface Modeling and Visualization. The very first step is to encode the surface or algebraic curve into the computer program, and visualize it as a sanity check. To this end, we assume that the algebraic curve is a polynomial of 3 variables (i.e., it lives in 3D). Under this assumption, the intersections of the surface and 3D coordinate grids are computed, and then triangle meshes are formed using the intersections as vertices.

Intersection Computation. Surfaces are approximated by triangle meshes in the pro- gram, hence if two or more surfaces intersect at a point, there should be triangles, one from each surface, that have an intersection. In other words,  by  finding intersections of triangles we can find the intersections of the surfaces, which is where computational geometry algorithms come into play.  Interaction-System代写

Intersection Visualization. Once the intersections of surfaces are correctly computed, the visualization is merely the first step. More exactly, we can obtain a triangle mesh from the intersections, and then visualize the mesh by computer graphics technology (e.g., OpenGL library).

User Interaction. The functionality of zooming in, zooming out, rotation, and translation can be implemented through GLFW or GLUT library.   One problem we may  meet   is that some intersections of surfaces can are hidden from the view in any starting viewpoint as the surface can be wavy. Hence, the program need to know which inter- sections are hidden from the given viewpoint, and then suggest the user to change the viewpoint to check the hidden intersections.

### Expected Project Results  Interaction-System代写

The final result of this project will be a workable prototype of the proposed software sys- tem, where the functions mentioned above are basically implemented in a bug-free manner.

### Technical Supervising Faculty   Interaction-System代写

The faculty who will be guiding you in the project.

if applicable.