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Making Papercraft Toys from Meshes using Strip-based Approximate Unfolding

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## Making Papercraft Toys from Meshes using Strip-based Approximate Unfolding

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**Making Papercraft Toys from Meshesusing Strip-based**Approximate Unfolding Jun Mitani* Hiromasa Suzuki† University of Tokyo Siggraph2004**Outline**• Introduction • Triangle strip • Detailed Method • Results • Conclusion and Future Work**Introduction**• Motivation • Related work • Elber 1995; Pottmann&Farin 1995; Hoschek 1998 • These methods approximate parametric surfaces such as B-spline surfaces or rational Bézier surfaces by sets of ruled surfaces such as parts of cones or cylinders. • Chen et al. 1999 They are hard to handle free form models of triangulated meshes Elber 1995 Hoschek 1998**Introduction**• Sorkine et al.2002;Lévy et al. 2002;Sheffer 2002 • Mesh parameterization • Generate the pattern by placing triangular faces on a plane Sheffer 2002 Lévy et al. 2002 Sorkine et al. 2002**Triangle strip**• Unfolding a polyhedron requires cuts, butwe can easily unfold a triangle strip without cuts. • Triangle strips canbe connected by branching triangles to form a triangle tree. • Ourstripsaregenerated by changing the geometry and topology of the originalmeshes**Detailed Method**• Feature Line Extraction and Partitioning • Generation of Zonal Regions • Addition of Internal Cut-Lines • Smoothing of Cutting Lines • Simplification to Generate Strips • Unfolding and Packing**Detailed Method**• Feature Line Extraction and Partitioning • Generation of Zonal Regions • Addition of Internal Cut-Lines • Smoothing of Cutting Lines • Simplification to Generate Strips • Unfolding and Packing**Feature Line Extraction and Partitioning**• Garland et al. 2001; Katz and Tal 2003; Lévy et al. 2002 • Extracts feature lines • Lines withsharp edges and which are longer than some predefined length.**Feature Line Extraction and Partitioning**• Merge small charts algorithm 1. Select the chart C with the smallest number of triangles. If Chas more than predefined number of triangles (e.g. 3% of alltriangles), finish. 2. For each chart H other than C, count the number of edgeslying on the border between H and C (excluding theextracted feature lines). 3. Merge C with the chart for which the count is maximal, andrepeat from step 1.**Detailed Method**• Feature Line Extraction and Partitioning • Generation of Zonal Regions • Addition of Internal Cut-Lines • Smoothing of Cutting Lines • Simplification to Generate Strips • Unfolding and Packing**Generation of Zonal Regions**• Assign a value toeach triangle • Thevalue is the topological distance from the nearest partborder or feature line to thetriangle. • Zonal region borders are added along edges that connect triangles with assigned values nw and nw+1 (for n=1,2,3,…, and w is a positive integer)**Generation of Zonal Regions**• Segment the part by placing region borders onedges • Mergenarrowinternal areas • The borders of zonal areas：border cut-lines**Detailed Method**• Feature Line Extraction and Partitioning • Generation of Zonal Regions • Addition of Internal Cut-Lines • Smoothing of Cutting Lines • Simplification to Generate Strips • Unfolding and Packing**Addition of Internal Cut-Lines**feature cut-line**Addition of Internal Cut-Lines**• Algorithm to extract core lines (有時間在探討) 1. Add all triangles in the region to a list T, and make an outerloop L of the region that is a list of edges incounterclockwise order. 2. Update L by removing a triangle from T. (1) (2) (3) (4) (5) (6)**Addition of Internal Cut-Lines**3. Repeat step 2 until Tis empty. • These lines are too complicated to craft , so we simplify each core line. (1) (2)**Addition of Internal Cut-Lines**• Algorithm to simplify core lines 1.Create an edge-vertex tree of the core lines. (a) Make a list L of the vertices that are leaves ofthe edge-vertextree. (b) Repeatedly remove one vertex in L . When the number of vertices is reduced to a predefined ratio (e.g. 15%), go tostep 2. If L becomes empty, update the edge-vertex treeand repeat from (a).**Addition of Internal Cut-Lines**2. If there are any vertices nearer than a predefined distance(e.g. 0.3w) to the outer loop, remove the edges that connectthese vertices from core line. • The resulting core lines have been simplified. • We call these corelines center cut-lines. (2) (3)**Detailed Method**• Feature Line Extraction and Partitioning • Generation of Zonal Regions • Addition of Internal Cut-Lines • Smoothing of Cutting Lines • Simplification to Generate Strips • Unfolding and Packing**Smoothing of Cutting Lines**• Connectivity smoothing • Geometrical smoothing**Detailed Method**• Feature Line Extraction and Partitioning • Generation of Zonal Regions • Addition of Internal Cut-Lines • Smoothing of Cutting Lines • Simplification to Generate Strips • Unfolding and Packing**Simplification to Generate Strips**• Cohen [1999]**Detailed Method**• Feature Line Extraction and Partitioning • Generation of Zonal Regions • Addition of Internal Cut-Lines • Smoothing of Cutting Lines • Simplification to Generate Strips • Unfolding and Packing**Unfolding and Packing**• Place one of triangles in thestrip on plane • Recursively add those triangles connected totriangles already in the plane • When they intersect, wedivide the unfolded strip into two. • The problem of packing pieces has been studied elsewhere (see [Milenkovic 1999])**Results**(1) (2) (3) (4) (5) (9) (6) (7) (8)**Conclusion and Future Work**• Effectiveness of the keep the smoothness of original meshes. • Cannot specify the approximation tolerance to the input mesh model**補充-Detect Feature**• Compute a sharpness criterion on the edges. • Choose a threshold so that a certain proportion of the edges is filtered out. • Grow a feature curve.**補充-Chart圖示**紅線：feature line 黑線：輪廓圖的邊 橘線：要計算的邊數