1 Softwareprojekt über Anwendungen effizienter Algorithmen, WS 2012/2013 Prof. Dr. Günter Rote Kurvenapproximation SWP Anwendungen von AlgorithmenTeam 3 Team 3: Stefan Behrendt, Ralf Öchsner, Ying Wei

2 SWP Anwendungen von AlgorithmenTeam 3 Our task Technique Technologies Flow of process Preparations for Greedy approach Greedy approach Analysis Demo …. Outline

3 SWP Anwendungen von AlgorithmenTeam 3 Our task Approximation of point sequences by spline Input : The points with an order A predefined tolerance error Output : A Curve, which goes through the selected points from original given points and can sufficiently good approximate the original point sequence

4 Technologies : C++, Lua, IPE QT Cubic Hermite spline, Cubic Bezier spline, Interpolation Greedy Algorithm SWP Anwendungen von AlgorithmenTeam 3 Technique

5 SWP Anwendungen von AlgorithmenTeam 3 Flow of process Calculate all Tangents of original given Points 1) Convert Selected Hermite Points & Tangents to Bezier control points 2) Then draw curve again by Bezier cubic spline 1) Convert given points and computed Tangents to Bezier control points in order to prepare with Greedy 2) Select points & Tangents using Greedy 1) Convert given points and computed Tangents to Bezier control points in order to prepare with Greedy 2) Select points & Tangents using Greedy Add spline into IPE for display

6 SWP Anwendungen von AlgorithmenTeam 3 Tangents Calculation

7 SWP Anwendungen von AlgorithmenTeam 3 Preparations for Greedy Approach

8 SWP Anwendungen von AlgorithmenTeam 3 Greedy Approach

9 SWP Anwendungen von AlgorithmenTeam 3 Greedy Approach

) else if at the end, and the error >maxError (i==(size of points-1) && (errorUntil(i)>Error)) then insert points[i-1] into hermite[end-1]; insert tangent[i-1] into tangents[end-1]; 2.3.3) else (when the error > maxError), insert points[i-1] into hermitePoints[end-1]; insert tangent[i-1] into tangents[end-1]; 3) Convert the selected hermitePoints to cPoints again. Method is the same with 2.2) T(n)=n 4) add bezier spline to IPE Greedy Approach SWP Anwendungen von AlgorithmenTeam 3

11 SWP Anwendungen von AlgorithmenTeam 3 Analysis

12 SWP Anwendungen von AlgorithmenTeam 3 Demo DEMO…

13 Thanks For Attention! Questions and Suggestions for improvement? SWP Anwendungen von AlgorithmenTeam 3