Quad Mesh Generation Algorithm Based On Direction Field And Pattern

Quad meshes are important representations with a large number of applications in geometric modeling,texture mapping,finite element simulation,computer animation,architecture,etc.In contrast to triangle meshes,quad meshes have the property of tensor product in nature,and each patch can be trivially mapped to a rectangular texture.In addition,the edges of quad meshes can capture the geometric features and semantic features in a natural way.Therefore,a lot of attention has received in the last years to generate high quality quad meshes.However,it is a challenge to generate high quality quad meshes.The main reasons are: 1)There may be totally different subjective quality criteria on the output quad meshes in different applications.But,these quality criteria are interrelated,and even conflicted with each other.2)It is quite difficult tocontrolthe placement of singularities for the automatic methods.And the user-assisted methods,able to manually modifying the placement of singularities,require a lot of redundant and complicated user input.So it is often quite challenging even for professional artists to manually generate a perfect quad mesh.To overcome these problems this dissertation proposes the corresponding solutions:1)Propose a new controllable quadrangulation method based on direction field,extending the previous automatic approaches.By introducing the techniques of geodesic and 3D sketching,this method allowsthe user to explicitly control the direction field.Moreover,to correct the conflicts and deviations of the user interaction,this dissertation presents the corresponding solutions and then extends the approach of measuring cross field smoothness.So the user can control the orientation of edges and the placement of singularities.2)Design a set of new more complex topological patterns for the pattern-based manual quadrangulation method.By the face-flow collapse operation,the input patches can be reduced and extracted as new patterns.Then these patterns enlarge the solution space of quadrangulating and provide the user with more options.3)Develop a quad mesh generation system based on the above algorithms.The results demonstrate the effectiveness of this system.